Improving Adaptive Optics Image Quality in High Powered Eyes

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1 Improving Adaptive Optics Image Quality in High Powered Eyes Xiaolin Zhou orcid.org/ Submitted in total fulfillment of the requirements of the degree of Doctor of Philosophy Dec 2016 Department of Optometry and Vision Sciences The University of Melbourne Victoria, Australia Produced on archival quality paper

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3 Abstract Adaptive optics (AO) retinal imaging has been widely used for high resolution in vivo imaging studies in the human eye over the last two decades. More recently, this technology has been applied to image the retina of small animals such as rodents. Small animal eyes offer many advantages for the scientific study of retinal diseases, and theoretically have potential for superior image quality compared to human eyes. Unfortunately, to date AO image quality in practice is inferior to state-of-the-art image quality obtained from the human eye, and the cause of these limitations has not been fully understood. This work aimed to investigate and address the limitations to AO image quality in rodent eyes, and explore novel techniques in adaptive optics correction and image processing to overcome these limitations. The first experiment used optical modelling to test several commonly made assumptions in human AO imaging. These assumptions were found to be inappropriate for extrapolation to rodent eyes, due to their very high power and dioptric thickness of the retina. Specifically, results showed that AO image quality for the human eye is robust against positioning errors of the AO corrector and to differences in imaging depth and wavelength compared to the wavefront beacon. On the other hand, image quality for the rat eye declined sharply with each of these manipulations. The second experiment used a purpose-built flood-illumination AO ophthalmoscope designed for rat eyes to validate the modelling results from the first experiment, using physical model eyes of varying optical power. It was found that in general, AO image quality from the lower powered (60 D) model eye was much less susceptible to manipulations similar to those described in the first experiment, compared to the higher powered (220 D) model eye, thus confirming the optical modelling results. The same optical system was then used to account for these limitations as much as possible, while imaging adult pigmented Long-Evans rats. However the images obtained showed only modest improvement compared to the pilot experiment. It is argued that this occurred primarily due to intra-ocular scatter and the challenging wavefront sensing step in the rat eye which are exacerbated in our flood illumination setup. i

4 The third and fourth experiments explored two novel techniques, HiLo imaging and non-sensing AO, to address problems with intra-ocular scatter and wavefront sensing respectively. Both experiments resulted in noticeable improvements in AO image quality from the rat eye. In conclusion, with almost twice the numerical aperture, retinal image resolution for rodent eyes is potentially far better than the human eye, provided aberrations can be corrected with AO. This thesis explored the limitations to AO image quality in rodent eyes, as well as practical methods to improve image quality by addressing these limitations. Although the final flood-illumination AO image quality from the rat eye was still inferior compared to scanning AO modalities, the findings from this thesis could be used to improve the AO image quality for all imaging modalities for both human and rat eyes. ii

5 Declaration This is to certify that: i. The thesis comprises only my original work towards the PhD, ii. iii. Due acknowledgement has been made in the text to all other material used, The thesis is less than 100,000 words in length, exclusive of tables, maps, bibliographies and appendices. Xiaolin Zhou iii

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7 Preface Three journal papers of which I am the primary author are included in this work in their published format, with permission from OSA publishing. Paper 1, shown in Chapter 3: Zhou, X., Bedggood, P., et al. (2012). "Limitations to adaptive optics image quality in rodent eyes." Biomed. Opt. Express 3(8): Paper 2, shown in Chapter 6: Zhou, X., Bedggood, P., et al. (2014). "Improving high resolution retinal image quality using speckle illumination HiLo imaging." Biomed Opt Express 5(8): Paper 3, shown in Chapter 7: Zhou, X., Bedggood, P., et al. (2015). "Contrast-based sensorless adaptive optics for retinal imaging." Biomed. Opt. Express 6(9): For Paper 1, I was responsible for all data collection and analysis. A conference abstract also arose from this paper, which was presented as a poster at the annual ARVO meeting in May 2012: Zhou, X., Bedggood, P., and Metha, A. Limitations to adaptive optics imaging quality in highly powered eyes (abstract). In ARVO 2012; 6-10 May, Fort Lauderdale. For Papers 2 and 3, I was responsible for most data collection and all data analysis, but was assissted in animal handling by past and present members of the Ocular Physiology Laboratory at my department. In addition, the general adaptive optics algorithm used to obtain retinal images in this work was developed by Dr Phillip Bedggood for his PhD thesis. All other work referred to in the results in this thesis is my own, obtained under the guidance of my supervisors, Associate Professor Andrew Metha and Dr Phillip Bedggood. v

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9 Acknowledgements First and foremost, I would like to thank my supervisors, Associate Professor Andrew Metha and Dr Phillip Beddggood, whose wisdom, expertise in the field of adaptive optics, passion for knowledge, constant guidance and patience led me through the course of my candidature. I would also like to thank my advisory committee members, Professor Allison McKendrick and in particular, Associate Professor Bang Bui, for his writing tips and the kind support of his Ocular Physiology Laboratory. In addition, I would also like to thank other past and present members of the Ocular Physiology Laboratory at the Department of Optometry and Vision Sciences, in particular Dr Vicky Wong, Dr Christine Nguyen and Dr Zheng He, for their expertise and time during the rat imaging experiments. To God, thank you for reaching out to me, your love, abundant blessings and your guidance. To my dear wife Fiona, thank you for your love, encouragement and support throughout the years. Thank you for believing in me. To my parents, thank you for your patience and support to see me through this endeavour. Finally, I would like to acknowledge the Australian Postgraduate Award and a postgraduate travel grant from Optometry Australia in 2012 as financial support during my candidature. vii

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11 Table of Contents Abstract... i Declaration... iii Preface...v Acknowledgements... vii Table of Contents...ix List of Figures xiii List of Tables xvii Chapter 1 Literature review Introduction Diffraction Aberrations Chromatic aberrations Monochromatic aberrations Seidel aberrations Exact aberrations Mathematical models of exact aberrations Ocular aberrations Source of ocular aberrations Temporal properties of ocular aberrations Normative aberration data of human eyes Normative aberration data of rodent eyes Effect of higher-order ocular aberrations on retinal image quality Principle of adaptive optics retinal imaging Principle of the Shack-Hartmann wavefront sensor Conceptual layout of a flood-illumination AO ophthalmoscope Non-common path aberrations Other AO imaging modalities Optical properties of rodent eyes Optical parameters of the rodent eyes Spatial vision of rodent eyes Imaging resolution of rodent eyes In vivo imaging of rodent eyes Benefits of in vivo imaging in rodents Rodent eye imaging without AO ix

12 1.8.3 Rodent eye imaging with AO Challenges of in vivo AO imaging in rodent eyes Challenges of wavefront sensing in rodent eyes Challenges and advantages of flood AO imaging in rodent eyes Methods for improving flood AO image quality in rodent eyes Increasing image quality with HiLo imaging Non-wavefront sensing AO imaging Chapter 2 Pilot experiment: in vivo flood AO imaging in a rat Introduction Methods Animals used Animal handling Flood AO ophthalmoscope Results and discussions Conclusion and outline of the following chapters Chapter 3 Identifying limitations to adaptive optics image quality in rodent eyes using optical modelling Introduction Paper 1: Limitations to adaptive optics image quality in rodent eyes Supplementary results for Paper Results from off-axis points for Fig. 8 in Paper Reversal of component curves in Fig. 8 in Paper Testing the validity and robustness of the rat schematic eye results Impact of modelling different values of refractive error Impact of modelling different values of anterior corneal curvature Impact of modelling different values of anterior corneal asphericity Conclusion Chapter 4 Flood illumination adaptive optics ophthalmoscope Introduction ZEMAX modelling General aspects Modelling optical surfaces Optimisation of angles of incidence Complete AO ophthalmoscope layout Flood illumination adaptive optics ophthalmoscope Flood AO ophthalmoscope layout Illumination arm x

13 Wide-field imaging and pupil monitor arm AO arm Alignment of components Positioning of components at pupil conjugates Minimizing corneal reflection Adaptive optics imaging procedure Alignment of the eye AO imaging Conclusion Chapter 5 Validation of optical modelling results Introduction Methods Construction of the physical model eyes The physical manipulations Shifting imaging plane Shifting sensing wavelength Shifting the axial position of the model eyes The challenge of wavefront sensing on acetate sheet A suitable image quality metric Results and discussions Correlating MI to residual RMS using standard images Results and discussions of physical manipulations Manipulation 1: Shifting imaging plane Manipulation 2: Shifting sensing wavelength Manipulation 3: Shifting axial position of the model eye Summary of results and general discussion Comparison between virtual and physical manipulations Explanation of discrepancies of results for high-powered eyes In vivo AO imaging of rat eyes Methods Results and discussions Typical SHWS spots from the rat Retinal image quality from the rat Summary of results and general discussion Chapter 6 Improving adaptive optics image quality using HiLo imaging Introduction xi

14 6.2 Paper 2: Improving high resolution retinal image quality using speckle illumination HiLo imaging Chapter 7 Improving adaptive optics image quality using non-sensing AO Introduction Paper 3: Contrast-based sensorless adaptive optics for retinal imaging Chapter 8 General discussion and conclusions Summary of experiments Achievements in this work Summary of limitations of experiments Conclusion References xii

15 List of Figures Figure 1.1. Simulated representation of a typical diffraction pattern and Airy disk... 2 Figure 1.2. Two-dimensional representation of the PSF... 2 Figure 1.3. Aberration-free image formation... 5 Figure 1.4. Aberration leading to a distorted wavefront... 6 Figure 1.5. Simulated Zernike wavefront maps Figure 1.6. Wave aberration maps of the cornea, the internal optics and the complete eye Figure 1.7. Corneal and internal aberrations in Zernike terms in a number of young subjects Figure 1.8. Corneal, internal and overall (eye) wave aberrations of two human subjects Figure 1.9. Normal aberration data from a population of 109 healthy human subjects 17 Figure Averaged normative aberration data from 20 eyes of the C57BL/6J mouse Figure Effect of AO correction on the amplitude of measured Zernike terms in the eyes of 8 mice Figure In vivo retinal images from a rat eye Figure Simulated effect of aberration on retinal imaging in the mouse eye Figure A photo of the square lenslet array used in the SHWS in our laboratory.. 27 Figure Principle of a Shack-Hartmann wavefront sensor Figure Examples of Shack-Hartmann spots Figure Conceptual layout of a flood-illumination AO ophthalmoscope Figure Diagrammatic comparison of human and rat schematic eyes Figure Numerical aperture calculation of a thin lens Figure Some example images of in vivo fluorescence retinal imaging in mouse eyes without AO Figure Some example AO images from the mouse eye Figure 2.1. Small animal platform for the rat used in the pilot experiment Figure 2.2. Primate flood-illumination AO ophthalmoscope adapted for imaging the rat in the pilot experiment Figure 2.3. AO images of human cone mosaic and capillaries Figure 2.4. Representative best AO image of a large blood vessel in the rat eye in the pilot experiment Figure 3.1. Rat schematic eye: Effect of error in corrector position both on- and 10 off-axis Figure 3.2. Rat schematic eye: Effect of reversing sensing/imaging plane on residual SA at various AO corrector positions xiii

16 Figure 3.3. Rat schematic eye: Effect of reversing sensing/imaging wavelength on residual SA at various AO corrector positions Figure 3.4. Rat schematic eye: Effect of corrector position in the presence of separation between imaging and sensing planes Figure 3.5. Rat schematic eye: Effect of separation between imaging and sensing planes after optimizing for defocus, with various corneal curvature values 85 Figure 3.6. Rat schematic eye: Effect of separation between imaging and sensing planes after optimizing for defocus, with aspheric and spherical corneas at various eccentricities Figure 4.1. Scaled bird s-eye view of the rat AO ophthalmoscope using a nonplanar design Figure 4.2. Front view of the AO ophthalmoscope as seen by the eye being imaged.. 97 Figure 4.3. Scaled (1:1) layout of the non-planar design flood-illumination AO ophthalmoscope Figure 5.1. Photos of the model eye constructed in a cage-mounting system Figure 5.2. Diagrammatic representation of the dioptrically thick model retina Figure 5.3. Manipulation 1: shifting imaging plane Figure 5.4. Manipulation 2: shifting sensing wavelength Figure 5.5. Manipulation 3: shifting the axial position of the model eye Figure 5.6. Example SHWS image showing the bimodal appearance of the spots in a 220 D model eye with an artificial retina Figure 5.7. Standard images with corresponding MI and RMS values Figure 5.8. Normalised MI values plotted against residual RMS, from the simulated ROIs in Figure Figure 5.9. Reference and resultant ROIs obtained from manipulation 1 in a 60 D model eye Figure Effect of shifting imaging plane in a 60 D model eye after optimising for defocus Figure Reference and resultant ROIs obtained from manipulation 1 in a 220 D model eye Figure Effect of shifting imaging plane in a 220 D model eye after optimising for defocus Figure Reference and resultant ROIs obtained from manipulation 2 in a 60 D model eye Figure Effect of shifting wavefront sensing wavelength in a 60 D model eye after optimising for defocus Figure Reference and resultant ROIs obtained from manipulation 2 in a 220 D model eye Figure Effect of shifting wavefront sensing wavelength in a 220 D model eye after optimising for defocus Figure Reference and resultant ROIs from manipulation 3 in a 60 D model eye 145 xiv

17 Figure Effect of the relative axial position displacement in a 60 D model eye under manipulation 3, after optimising for defocus Figure Reference and resultant ROIs used for manipulation 3 in a 220 D model eye Figure Effect of the relative axial position displacement in a 220 D model eye under manipulation 3, after optimising for defocus Figure Photos of the custom-made, stereotaxic small animal platform for the rat Figure Typical SHWS spots from the rat eye with the use of a rigid contact lens Figure Comparison of best corrected AO images from the rat AO ophthalmoscope and pilot data from the primate AO ophthalmoscope Figure Retinal cone image from a healthy human eye obtained using the rat AO ophthalmoscope xv

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19 List of Tables Table 1.1. Zernike polynomial up to the 14 th term (4th order) Table 1.2. List of studies examining the refractive error of rodent eyes Table 1.3. Parameters of the rat eye Table 1.4. Parameters of the human eye Table 1.5. Comparison of NA and lateral resolution between human and rodent eyes 39 Table 4.1. Focal length and angles of incidence onto the optical elements in the imaging path of the AO ophthalmoscope xvii

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21 Chapter 1 Literature review Chapter 1 Literature review 1.1 Introduction This literature review first introduces the general concepts of diffraction and aberration, which fundamentally affect the quality of all optical images, followed by a description of the particular ocular aberrations in both human and rodent eyes. The review then moves on to describe the principle of the flood illumination adaptive optics (AO) imaging technique used in this thesis, before concentrating on the literature concerning AO imaging of rodent eyes using various AO modalities. Compared to scanning-based AO imaging modalities, flood AO has the advantage of obtaining images at much higher frame rates, which is advantageous in the study of the in vivo dynamics of microscopic structures. In addition, the challenges of wavefront sensing in rodent eyes will be also described, as well as the cause of the typically inferior image quality using a flood AO ophthalmoscope. Lastly, methods that show potential to improve flood AO image quality in rodent eyes will be discussed. The ultimate goal of this thesis was to improve flood AO image quality in rodent eyes. 1.2 Diffraction The aim of an imaging system is to focus light emitting from each point in the object plane to a single point in the image. The propagation of light through space can be treated as the propagation of a wave, which is limited by the wave phenomenon of diffraction. Diffraction arises when a wave with certain wavelength λ travels through an aperture of finite diameter d, and results in characteristic deflections of the light energy around the edge of the aperture. When a monochromatic point source with plane wavefront is shone onto a circular aperture (in the case of image formation by a lens, the diameter of the lens is the aperture size), the resultant image some distance from the aperture (the "far-field", or equivalently at the focal point of an imaging system) is a circular pattern that appears bright at the centre, with concentric rings of alternating bright and dark bands. This is a typical diffraction pattern, the centre of which is known 1

22 Chapter 1 Literature review as the Airy disk, which is the intense circle of light containing most of the light energy of the diffraction pattern, bounded by the first minima, as shown in Figure 1.1. Figure 1.1. Simulated representation of a typical diffraction pattern and Airy disk, formed when a monochromatic point source of light is shone through a circular aperture. If the intensity of the Airy disk is plotted against position on the image plane, a threedimensional point-spread-function (PSF) can be obtained. The PSF therefore describes the response of an imaging system to a point source. The two-dimensional side profile of the PSF is often used to indicate its extent, and hence image quality of the optical instrument. This is represented in Figure 1.2. Figure 1.2. Two-dimensional representation of the PSF. The vertical axis represents the intensity, while horizontal axis represents position. The angular radius θ of the Airy disk (defined as the angular distance between the maxima and the first minima of the PSF), is given by the following formula (Hecht and Zajac 1974): 1.22λ θ = d Equation 1.1 2

23 Chapter 1 Literature review where λ and d are the wavelength of light and aperture diameter, respectively. This quantity is useful for describing image degradation due to diffraction, with smaller θ representing a more compact PSF, and hence better image resolution, which is defined as the minimum distance between which two adjacent points are discernible as separate in an image. As the equation suggests, diffraction can be reduced by decreasing the wavelength λ, or increasing the aperture diameter d, but can never be removed completely. In retinal imaging (and indeed for any imaging instrument), image quality is ultimately limited by diffraction when aberrations of the system are minimised or reduced to zero. Since the effects of diffraction are more pronounced with smaller pupil size, pupil dilation with eye drops is often employed to obtain optimal and stable pupil diameters during AO imaging. Another measurement of image quality is the Strehl ratio, which describes the ratio between the observed peak intensity of a real PSF (where both aberration and diffraction are present) and the ideal PSF (where only diffraction is present) of a point source object in an optical system. A system with a Strehl ratio of 0.8 or above is considered to be diffraction-limited, which means most of the aberrations are corrected and the image quality of the system is close to that where diffraction is the only limiting factor (Born and Wolf 1999). An equivalent metric for image quality is the Maréchal criterion, which states that a system is considered to be diffraction-limited when its root-mean-square (RMS) wavefront error is less than λ/14, where λ is the imaging wavelength (Born and Wolf 1999). The RMS wavefront error will be explained in section 1.4. It is worth to note that in practical terms, the definition of a diffractionlimited system is arbitrary, since aberrations, which is described below, can be minimised but not completely removed. 1.3 Aberrations Apart from diffraction, real imaging systems also suffer from aberrations. Aberrations occur when a light beam passing through an optical system deviates from its course predicted by Gaussian optics, which utilises cardinal points to analyse the paraxial properties of rays and assumes ideal image formation (Smith and Atchison 1997). Aberrations can be divided into two broad categories: chromatic aberrations, which 3

24 Chapter 1 Literature review describe the effects on polychromatic light of non-uniform refractive index for different constituent wavelengths; and monochromatic aberrations, which describe deviations from Gaussian propagation for light of a single wavelength. This section will give an overview of these two categories of aberration and their significance to ocular imaging Chromatic aberrations When light travels from one medium to another, the velocity of its propagation changes depending on how strongly it interacts with the charged particles in the medium (Smith and Atchison 1997). The ratio between the speed of light travelling in vacuum and a given medium is termed the refractive index of that medium. Since the speed of light in vacuum is always greater than in other media, the refractive index of any medium is always greater than one. In addition, the direction of the light rays travelling at an angle to the surface normal also change as they travel between media with different refractive indices. The process of light rays which travel at an angle to the surface normal crossing a boundary between two media of different refractive indices is called refraction (Smith and Atchison 1997), which involves the change of both the speed and direction of the light. The refractive index of optical media generally varies with wavelength, a phenomenon known as dispersion. In general, the refractive index increases with shorter wavelengths, and so the power of any given lens is typically greater for shorter wavelengths. This dependency of power on wavelength is termed longitudinal chromatic aberration (LCA). On the other hand, transverse chromatic aberration (TCA) describes the dependency of image location (within the image plane) or size on wavelength. LCA occurs for objects on- or off-axis, whereas TCA occurs only for objects off-axis. To obtain the highest image quality possible, it is therefore beneficial to perform imaging using light sources with as small a bandwidth (monochromatic light) as practically possible. (One of the exceptions to this is the optical coherence tomography (OCT), which requires a broadband light source for retinal imaging.) However, monochromatic light also suffers from aberrations which affect image quality. 4

25 Chapter 1 Literature review Monochromatic aberrations Monochromatic aberrations occur when light of a single wavelength deviates from the path predicted by Gaussian propagation. It is more important and technically challenging to correct for monochromatic aberrations in an optical system, especially when high-resolution retinal imaging is the goal. Therefore unless specified, the term aberration will be used to refer to monochromatic aberrations in the remainder of this thesis. In rotationally symmetrical optical systems with a small aperture and a small field, Seidel aberrations give an accurate estimate of aberration levels (Smith and Atchison 1997). On the other hand, in rotationally asymmetrical systems, or systems where aberrations are irregular and hence cannot be predicted by Seidel aberrations (such as ocular aberrations), finite or exact aberrations must be found by tracing real rays (Smith and Atchison 1997). Both Seidel and exact aberrations will be described in more detail below Seidel aberrations In order to understand Seidel aberrations, the concept of wave aberrations will be introduced first. Consider an ideal lens without any aberration each ray emitting from a single object point will be perfectly focussed onto one image point, as shown in Figure 1.3. Figure 1.3. Aberration-free image formation. Note the wavefront in image space is a perfect replication of that in object space. 5

26 Chapter 1 Literature review The wavefront of the beam can be represented by a curve (or curved surface in threedimensions) normal to the path of the individual rays in the beam arising from a single object point, and can be considered as a collection of points across the beam that are perfectly in phase with each other. In the ideal case, the wavefront of light from a single object point is spherical after being refracted by the lens, with the centre of curvature centred on the paraxial image point, as represented in Figure 1.3 in two-dimensions. Hence the ideal lens perfectly reconstructs the wavefront, and point-to-point image formation occurs. In reality, there may be imperfection in the shape or refractive index distribution of the lens which will cause the refracted rays to intersect the optical axis at different points in image space. The refracted wavefront is no longer spherical but distorted, or aberrated, as shown in Figure 1.4. The image is no longer a perfect point but rather a blurry spot, the size of which depends on the type and amount of aberrations present. Figure 1.4. Aberration leading to a distorted wavefront. Note the distorted wavefront is more curved peripherally than the original. The wave aberration of a ray is therefore defined as the difference in optical path length from object to image space, between that of any ray and that of the pupil ray the ray that passes from the object point through the centre of the aperture stop and lands on the image point, which in a coaxial system suffers no aberration (Smith and Atchison 1997). The optical path length is defined as the product of the refractive index and physical distance of optical media traversed by a ray (Smith and Atchison 1997). Seidel aberrations are an approximation of the exact aberrations (section ) of a system (Smith and Atchison 1997). In monochromatic light, there are five types of Seidel aberrations. These are spherical aberration, coma, astigmatism, field curvature 6

27 Chapter 1 Literature review and distortion, each of which can be represented by an equation that takes into account the constructional parameters of an optical system, such as the position of the aperture stop, location of object and image conjugates, refractive indices, surface curvatures, surface asphericities and surface separations (Smith and Atchison 1997). In addition, these aberrations can be calculated independently and then summed to give the complete aberration profile, and are therefore useful in minimising the amount of low order aberrations when designing optical instruments (Smith and Atchison 1997). Seidel aberrations are also called third order or primary aberrations, since they are derived using the Taylor series approximation of the sine function in Snell s law: 3 α sin( α) α 3! Equation 1.2 where the highest order α 3 is shown and α is the angle that a ray makes with the optical axis (Atchison, Scott et al. 2000). If higher order terms are included in the expansion, as shown in Equation 1.3, a more complete representation of the exact aberrations in the system can be obtained α α α sin( α) = α + + 3! 5! 7! Equation 1.3 Seidel aberrations are limited, however, due to restriction to rotationally symmetric systems, which means they cannot be used to accurately predict the aberration level in the eye, which has a slightly decentred pupil (around 0.5mm nasally) and hence is not rotationally symmetric (Westheimer 1970). In addition, the eye contains irregular aberrations beyond those described by Seidel aberrations, reducing visual performance and retinal image resolution when the pupil is large (Liang and Williams 1997a). For these reasons, exact aberrations in the eye must be mapped out in order to perform high resolution AO imaging Exact aberrations As shown in Equation 1.3, exact aberrations will be obtained when the full sine expansion is employed. However, unlike Seidel aberrations which can be readily represented by equations, exact aberrations must be found by real ray tracing through an optical system due to the complexity of the expansion (Smith and Atchison 1997). In theory, the resulting actual wavefront can then be compared to an ideal wavefront at 7

28 Chapter 1 Literature review each point at some reference surface in the system, and the amount of exact aberrations can be obtained. This is called the 'wavefront error', and can be calculated for each beam of light emanating from each object point. In practice, however, it is impossible to trace every single ray in a beam. For this reason, a limited number of sampling points can be used to approximate the actual wavefront in a system. Naturally, the more sampling points used, the more accurate this approximation will be. Once the actual wavefront is estimated, the amount of aberrations can be modelled by fitting a series of polynomials to the data (see section 1.4). The reference plane chosen for wavefront error determination is usually the pupil plane (such as the entrance pupil of the eye) of an optical system. This is because in the pupil plane, aberrations manifest as pure phase changes, whereas in planes other than the pupil, part of the information manifests as changes in intensity, which cannot be measured readily by phase detecting devices such as the Shack-Hartmann wavefront sensor (SHWS), the lenslet array within which is made conjugate to (i.e., at the image plane of) the entrance pupil of the eye (Roorda, Miller et al. 2006). Similarly, the correction of aberrations also occur at the pupil plane (therefore the wavefront corrector, usually a deformable mirror (DM), is also made conjugate to the entrance pupil of the eye), so that only phase changes are imparted to the beam. 1.4 Mathematical models of exact aberrations As mentioned above, the wavefront error arising from calculations of exact aberrations, although complex in form, can be represented by mathematical models for easy analysis and visualisation. One model that has gained considerable popularity since the advent of AO ocular imaging is the Zernike series, which represents a set of two-dimensional functions defined over a unit circle. It is widely used in computer algorithms which provide real-time measurement and correction of the ocular aberrations in both human and animal subjects (Liang, Grimm et al. 1994; Liang and Williams 1997a; Hofer, Artal et al. 2001; Roorda, Romero-Borja et al. 2002; Thibos, Hong et al. 2002; Cheng, Barnett et al. 2004; Hermann, Fernandez et al. 2004; de la Cera, Rodriguez et al. 2006; Fernandez, Vabre et al. 2006). 8

29 Chapter 1 Literature review Another model is the Taylor series, which utilises a series of polynomials to represent the total wave aberrations in the pupil plane, as a function of coordinates x and y within the pupil (Howland and Howland 1977; Atchison, Scott et al. 2000). However, due to the many advantages of the Zernike series over Taylor series as discussed below, it is not commonly used to model ocular aberrations. An overview of the Taylor series representation is available elsewhere and it will not be covered in detail here (Atchison, Scott et al. 2000). The primary reason for the popularity of Zernike series is that the two-dimensional Zernike functions are orthogonal to one another in the sense that the integral of the point-wise product of any pair of functions over the whole pupil is zero (Atchison, Scott et al. 2000). This means each Zernike term represents a distinct mode of aberration, which serves as a basis function or building block for the total aberrations. Furthermore, due to its orthogonal nature, inclusion of higher-order Zernike terms in the description of a particular wavefront aberration profile will not require changes of the low order terms, whereas adding higher terms with Taylor series will require low order terms to change (Atchison, Scott et al. 2000). Finally, individual low-order Zernike terms correspond well with individual Seidel aberrations. For example, there are terms for spherical aberration, coma and astigmatism (Thibos, Hong et al. 2002). On the other hand, the representation of individual Seidel aberrations with the Taylor series is only achieved by combining multiple terms, making the Taylor series representation less direct for the diagnosis of problems in the system. As a measurement of the impact of aberrations on the wavefront, one can calculate the root-mean-square (RMS) of the error of the actual wavefront compared to the ideal wavefront, over many points. This is equivalent to taking the square root of the sum of the square of all the Zernike coefficients in the series fitted to the wavefront, after applying an appropriate normalisation coefficient to each term (Atchison, Scott et al. 2000). Similarly, the impact of each Zernike order on the whole wavefront can also be evaluated by taking the RMS wavefront error of that particular order. This is an advantage since the RMS wavefront error of ocular aberration can be calculated very quickly from the Zernike coefficients. The mathematical form of Zernike aberrations can be expressed as follows (Atchison, Scott et al. 2000): 9

30 Chapter 1 Literature review k ( ρθ, ) = nn ( 2) W C R n n= 0j= m 2 m n cos( mθ ) sin( mθ ) Equation 1.4 where W(ρ, θ) is the total wave aberration at points with diameter ρ from the pupil centre and angle θ from the positive X-axis, as appropriate in polar coordinates; Cn(n+2)+m 2 is the coefficient for the n(n+2)+m th 2 Zernike term; m Rn is a polynomial as a function of ρ; k is the maximum order of the Zernike polynomial; n is the current order being considered; m is the meridional frequency, which indicates the number of times the aberration repeats itself around the circular pupil, given by m = 2j n, where j is an integer from 0 to n (for example, the possible values of m are -2, 0 and 2 when n = 2); cos is used when m 0 and sin is used when m < 0. A simplified form of the Zernike series can be written as (Atchison, Scott et al. 2000) W, CZ i i i= 0 ( ρθ) where C i is the Zernike coefficient of the ip = Equation 1.5 th Zernike term Z i. This notation is convenient because it simplifies the relationship between the coefficient and the Zernike term. To help visualise Zernike aberrations, Table 1.1 shows the first 14 Zernike terms (15 if the constant term is included) in polar and monomial expressions, as well as their equivalents in Seidel aberrations where appropriate (Liang, Grimm et al. 1994). The corresponding wavefront contour maps of each of these 14 terms, except for the Z 0 (x, y) term, are shown in Figure 1.5. Note that in Figure 1.5, Radial order corresponds to the value n in Equation 1.4, whilst Meridional frequency corresponds to the value m in Equation 1.4. To better represent the order and frequency of each Zernike term, sometimes it can be represented with a double-index numbering scheme m Z n (Thibos, Applegate et al. 2002). For example, instead of writing Z 12, spherical aberration can be written as Z 0 4, indicating that it belongs to the 4 th order Zernike terms, with meridional frequency of zero. 10

31 direction axis Chapter 1 Literature review Table 1.1. Zernike polynomial up to the 14 th term (4th order), the corresponding monomial representation in Cartesian form and the equivalent Seidel aberration. Adapted from Liang et al. (1994). Term Zernike Polynomial Cartesian form Equivalent Seidel aberration Z 0 (x, y) 1 1 Constant term Z 1 (x, y) ρ sin(θ) x Tilt in xp Z 2 (x, y) ρ cos(θ) y Tilt in y direction Z 3 (x, y) ρ 2 sin(2θ) 2xy Astigmatism at 45 or 135 Z 4 (x, y) 2ρ y 2 + 2x 2 Defocus Z 5 (x, y) ρ 2 cos(2θ) y 2 x 2 Astigmatism at 0 or 90 Z 6 (x, y) ρ 3 sin(3θ) 3xy 2 x 3 Z 7 (x, y) (3ρ 3 2ρ) sin(θ) 2x + 3xy 2 + 3x 3 Coma along x axis Z 8 (x, y) (3ρ 3 2ρ) cos(θ) 2y + 3y 3 + 3x 2 y Coma along yp Z 9 (x, y) ρ 3 cos(3θ) y 3 3x 2 y Z 10 (x, y) ρ 4 sin(4θ) 4y 3 x 4x 3 y Z 11 (x, y) (4ρ 4 3ρ 2 ) sin(2θ) 6xy + 8y 3 x + 8x 3 y Z 12 (x, y) 6ρ 4 6ρ y 2 6x 2 + 6y x 2 y 2 Spherical aberration + 6x 4 Z 13 (x, y) (4ρ 4 3ρ 2 ) cos(2θ) 3y 2 + 3x 2 + 4y 4 4x 2 y 2 4x 4 Z 14 (x, y) ρ 4 cos(4θ) y 4 6x 2 y 2 + x 4 Figure 1.5. Simulated Zernike wavefront maps representing individual Zernike term up to the 14 th term (Thibos, Hong et al. 2002). The first term is not shown since it does not affect the shape of the wavefront. The corresponding mathematical representation of the Zernike term is shown in Table 1.1. Reproduced with permission from OSA publishing (copyright holder). A few points are worth remembering when dealing with Zernike aberrations. First, the terms Z 0, Z 1 and Z 2, also known as piston, tip and tilt respectively, are often ignored in wavefront calculations because they do not affect the image quality per se although tilt does affect the overall image position (Liang, Grimm et al. 1994). Second, the terms Z 4, 11

32 Chapter 1 Literature review Z 3 and Z 5, also known as defocus and astigmatism, respectively, represent low order aberrations, and can be corrected with conventional optical spectacles (Liang, Grimm et al. 1994). Finally, those terms from the 3 rd order onwards, i.e. those beyond Z 5, are considered higher order aberrations, since they cannot be corrected by conventional spectacles (Liang, Grimm et al. 1994). Some examples of higher order aberrations are: coma (Z 7, Z 8 ), trefoil (Z 6, Z 9 ), and spherical aberration (Z 12 ). 1.5 Ocular aberrations Ocular aberration profiles are often complicated, but they can be conveniently represented by Zernike polynomials. It is well known that monochromatic aberrations in the human eye are asymmetric and vary with time (fast, temporal fluctuation and slow, age-related change, see section 1.5.2) (Liang, Grimm et al. 1994; Calver, Cox et al. 1999; Hofer, Artal et al. 2001; McLellan, Marcos et al. 2001). For this reason, this section will provide an overview of the source and temporal properties of ocular aberrations, as well as normative aberration data using past studies on the human eye. Since this thesis focuses on improving the image quality in rodent eyes, normative aberration data on rodent eyes will also be presented where available, although the literature concerning human eyes is far more abundant. The effect of ocular aberrations on retinal imaging will also be shown with examples from rodent eyes. Details on the optical parameters of rodent eyes will be presented in section Source of ocular aberrations To explore the origin of the ocular aberrations amongst the possible contributing surfaces within the eye, Artal et al. conducted a study in which they directly measured the total and corneal aberrations in eyes of young subjects using a SHWS (Artal, Guirao et al. 2001). They inferred the internal ocular aberrations based on the difference between total and corneal aberrations. They showed that when measured alone, the anterior cornea or the internal optics (for which the crystalline lens is the main component) exhibit higher aberration levels than the complete eye, indicating an important role of the lens in partially negating the corneal aberrations (Artal, Guirao et al. 2001). This is shown in Figure 1.6, where wave aberration maps of the cornea, internal optics and the complete eye from one subject, along with their corresponding point-spread functions are displayed (Artal, Guirao et al. 2001). 12

33 Chapter 1 Literature review Figure 1.6. Wave aberration maps of the cornea, the internal optics and the complete eye over a 5.9 mm pupil (Artal, Guirao et al. 2001). (a): cornea alone; (b): internal optics alone; (c): complete eye. Corresponding PSFs (each image subtending 20 minutes of arc of visual field) are shown below each aberration map. It is clear that the complete eye exhibits significantly less aberrations than either the cornea or the internal optics alone. Reproduced with permission from ARVO journals (copyright holder). To understand their mutual mitigation effect, corneal and internal aberrations can be quantified with Zernike polynomials. This can be seen in Figure 1.7, which shows the Zernike terms (horizontal axis) and their magnitude in microns (vertical axis) of the corneal and internal aberrations of eyes of several young subjects (Artal, Guirao et al ). It is clear that many of these terms, particularly C 2 and C 4 have similar magnitudes but opposite signs, resulting in the partial neutralisation of aberrations in the complete eye. 13

34 Chapter 1 Literature review Figure 1.7. Corneal and internal aberrations in Zernike terms in a number of young subjects (Artal, Guirao et al. 2001). Solid symbols: corneal aberrations. Open symbols: internal aberrations. Reproduced with permission from ARVO journals (copyright holder) Temporal properties of ocular aberrations An important property of ocular aberrations is their dynamic nature. On a smaller time scale, aberrations are found to change rapidly with accommodation, fluctuating with amplitudes of 0.03 to 0.5D at temporal frequencies up to 5Hz (Charman and Heron 1988). In a relevant study, Hofer et al. (2001) used a modified SHWS to examine the temporal fluctuations of the eye s aberrations before and after accommodation was paralysed with a cycloplegic agent. They found that the main source of the fluctuations came from defocus, which has its origin in the microfluctuations of accommodation. However, fluctuations in higher order aberrations cannot be accounted for by microfluctuations of accommodation since their magnitude was not reduced by paralysing accommodation (Hofer, Artal et al. 2001). The results suggested that in order to obtain diffractionlimited images in real-time, a correction bandwidth between 1 to 2 Hz with wavefront sensing speed at 10 to 40 Hz are needed for AO systems (Hofer, Artal et al. 2001). Most modern AO imaging devices can achieve these speeds (Fernandez, Iglesias et al. 2001; Rha, Jonnal et al. 2006; Zawadzki, Choi et al. 2007; Geng, Greenberg et al. 2009). On a larger time scale, ocular aberrations also change with age. Several studies have shown that overall ocular aberrations increase in eyes of older human subjects (Calver, 14

35 Chapter 1 Literature review Cox et al. 1999; McLellan, Marcos et al. 2001; Artal, Berrio et al. 2002; Guirao, Redondo et al. 2002). This is thought to be due primarily to the change in the gradient index distribution in the lens (Smith, Bedggood et al. 2008). As a consequence, there is a reduction or even loss of the mutually compensatory effect of the corneal and internal aberrations with age, leading to an overall increase in ocular aberrations and reduction in retinal image quality (Artal, Berrio et al. 2002). This is shown in Figure 1.8, where maps of corneal, internal and total wave aberrations are shown. In the young eye, total aberrations are lower than either corneal or internal aberrations, whereas in the older eye, the opposite is true (Artal, Berrio et al. 2002). Figure 1.8. Corneal, internal and overall (eye) wave aberrations of two human subjects (Artal, Berrio et al. 2002). The row on top is from a young subject and at the bottom from an older subject. Note how the overall aberrations are higher in the older subject. Reproduced with permission from OSA publishing (copyright holder) Normative aberration data of human eyes An understanding of the statistical properties of the eye s aberrations is important for the development of wavefront compensation devices or optical appliances. Several studies have been performed in the past to investigate the monochromatic aberrations in the human eye in small populations. Smirnov looked at the inter-subject variability in these aberrations in twelve eyes (Smirnov 1961). Howland and Howland studied aberrations in 33 subjects using a subjective aberroscopic technique and found large variations from subject to subject (Howland and Howland 1977). An objective 15

36 Chapter 1 Literature review measurement of the wave aberrations in two eyes using a SHWS was performed by Liang et al, which found the measurements were precise, fast and highly repeatable (Liang, Grimm et al. 1994). More recently, data from large population studies using the SHWS method showed that most aberrations can be accounted for by the first four orders of a Zernike expansion, with the most significant contribution originating from defocus and astigmatism (Porter, Guirao et al. 2001; Castejon-Mochon, Lopez-Gil et al. 2002; Thibos, Hong et al. 2002; Cheng, Barnett et al. 2004). This is not surprising since these are the refractive errors in the population that are usually corrected with conventional ophthalmic spectacles. Amongst the higher order aberrations, there are significant amounts of third-order (coma and trefoil) and fourth-order (spherical) aberrations in the population, while the other higher order terms contribute much less to the overall aberration (Porter, Guirao et al. 2001; Castejon-Mochon, Lopez-Gil et al. 2002; Thibos, Hong et al. 2002; Cheng, Barnett et al. 2004). An example of the distribution of Zernike terms is shown in Figure 1.9(a), which is obtained from a population of 109 subjects between 21 and 65 years of age (mean age is 41 years), with an average pupil size of 5.7mm (Porter, Guirao et al. 2001). Accommodation was not paralysed in this experiment. It can be seen that defocus (Z 0 2 ) and astigmatism (Z 2 2, Z 2 2 ) accounted for almost 93% of the total amount of aberration, while coma (Z 1 3, Z 1 3 ), trefoil (Z 3 3, Z 3 3 ) and spherical (Z 0 4 ) aberrations (see insert) dominated the higher order terms. 16

37 Chapter 1 Literature review Figure 1.9. Normal aberration data from a population of 109 healthy human subjects, with an average pupil size of 5.7mm (Porter, Guirao et al. 2001). (a): Mean absolute RMS wavefront error of second to fifth order Zernike terms, with their relative amount in percentage. The insert shows a vertically magnified version of the graph without defocus. (b): Mean values of all Zernike terms in microns. The error bars represent one standard deviation from the mean. The insert shows a vertically magnified version of the graph without the second order terms. Reproduced with permission from OSA publishing (copyright holder). Furthermore, as Figure 1.9(b) shows, the average value of most Zernike terms tends to be zero across the population, with the obvious exception of spherical aberration. This 17

38 Chapter 1 Literature review implies that even though the amount of a particular type of aberration can be predicted from the RMS wavefront error statistics in a population, the sign (positive or negative) of it is not. In addition, when aberrations of the left and right eyes of an individual are analysed, a high correlation in the amount and direction of the aberrations can be found, suggesting a high degree of mirror symmetry between the two eyes (Porter, Guirao et al. 2001; Castejon-Mochon, Lopez-Gil et al. 2002; Thibos, Hong et al. 2002). In addition to monochromatic aberrations, chromatic aberrations are also present in the human eye. The magnitude of LCA is around 2.1 D in the human eye from 400 nm to 700 nm (the visible range of the spectrum), resulting in poor focusing of polychromatic light onto the retinal plane (Ware 1982; Cooper and Pease 1988; Howarth, Zhang et al. 1988). On the other hand, differences in image magnification due to TCA has been shown to be less than 1% for wavelengths between 400 nm to 700 nm in the human eye (Zhang, Thibos et al. 1991; Zhang, Bradley et al. 1993) Normative aberration data of rodent eyes (A more comprehensive review of the rodent eye will be presented in section 1.7. This section only provides a review of the aberration data of rodent eyes.) Since rodents (rat and mouse) are used extensively for the study of the visual system, their refractive errors (mainly defocus) have been the subject of many studies over the years. Various methods have been used to measure the refractive error of rodent eyes, including scleral image (Lashley 1932; Lashley 1937), retinoscopy (Brown and Rojas 1965; Montero, Brugge et al. 1968; Block 1969; Glickstein and Millodot 1970; Massof and Chang 1972; Hughes 1977; Mutti, Zadnik et al. 1992; Mutti, Ver Hoeve et al. 1997; Tejedor and de la Villa 2003; Irving, Kisilak et al. 2005), ophthalmoscopy (Brown and Rojas 1965; Massof and Chang 1972; Hughes 1977), electrophysiology (Brown and Rojas 1965; Partridge and Brown 1970; Hughes 1977; Meyer and Salinsky 1977; Mutti, Ver Hoeve et al. 1997), infrared photoretinoscopy (Schmucker and Schaeffel 2004a; Zhou, Shen et al. 2008) and Shack-Hartmann wavefront sensing (de la Cera, Rodriguez et al. 2006; Geng, Schery et al. 2011). A list of these studies, including the strains of the rodent, method, number of animals and resultant refractive errors is shown in Table 1.2. Studies that used similar methods 18

39 Chapter 1 Literature review are grouped together, separated by horizontal black rows. From Table 1.2, it can be seen that the refractive state of the rodent eyes was controversial. However, the likely refractive state of the rodent eye is emmetropic or myopic, as explained below. Most studies measured refractive error of the rodent eye in vivo, with the exception of two studies by Lashley (1932; 1937), who found large amount of myopia by viewing scleral images from excised rat eyes. However, this method could be prone to error in small eyes (Block 1969) since excised eyes may change shape quickly. Most of the early in vivo studies used retinoscopy to measure the refractive state of the rodent eye, and almost all of them found large amounts of hyperopia. However, it is now understood that this finding is due to the so-called small eye artifact (Glickstein and Millodot 1970), which arises because the retinoscopic reflection originates from the vitreo-retinal interface. Since image formation in the eye occurs at the photoreceptor layer where light is captured, the axial location of the reflection plane has a much larger bearing on retinoscopy results in the rodent eye than in the human eye, overestimating hyperopia readings. Therefore the true refractive state of the rodent eye could be close to emmetropic or even myopic when the small eye artifact is taken into account (Glickstein and Millodot 1970; Hughes 1977). This theory was reinforced by electrophysiological studies that aimed at minimising the unit receptive field size or maximising pattern visual evoked potentials (VEP) while refracting the eye with trial lenses (Brown and Rojas 1965; Partridge and Brown 1970; Hughes 1977; Meyer and Salinsky 1977). All except one study (Mutti, Ver Hoeve et al. 1997) found myopic correction of the rat eye yielded the smallest receptive fields and thus highest acuity. The myopic state of the rodent eye was confirmed by Shack-Hartmann wavefront sensor measurement of the mouse eye using an AO scanning laser ophthalmoscope that was capable of accurate focus control of the WFS beacon on a particular retinal layer (Geng, Schery et al. 2011). These authors showed that, when using a high numerical aperture WFS beacon, the mouse eye was highly hyperopic when the beacon was tightly focused at the anterior retina, but myopic when focused at the posterior retina, as shown in Table 1.2. With a dioptric retinal thickness (dioptric power required to shift focus from the vitreo-retinal interface and the photoreceptor layer) estimated to be ~11 D in the rat 19

40 Chapter 1 Literature review (Hughes 1979a; Geng, Greenberg et al. 2009) and ~30 D in the mouse (Schmucker and Schaeffel 2004a; Geng, Schery et al. 2011), it is therefore conceivable that the large variation in early, retinoscopy-based refractive error measurements of rodent eyes is indeed attributable to the small eye artifact. It is worthwhile to note that unlike the human eye, rodent eyes cannot accommodate since they lack the ciliary muscle responsible for ocular accommodation (Woolf 1956). In addition, it was found that the refractive errors of the rodent eye did not change significantly before and after the application of atropine eye drops (Artal, Herreros de Tejada et al. 1998). Therefore rapid temporal fluctuations in aberrations due to accommodation is unlikely in rodent eyes. Only two recent studies presented aberration data on rodent eyes, both of which were on the mouse. de la Cera et al. (2006) measured the aberrations up to and including fourth order Zernike terms (14 terms in total) in twelve eyes of pigmented mice of the C57BL/6 strain. The measurements were performed on awake animals without cycloplegia, to simulate natural viewing conditions. The authors found large amount of hyperopic defocus (~ ±1.41 D) and astigmatism (3.64±3.70 D) using a WFS beacon with wavelength of 676 nm. Amongst the higher order aberrations (~0.32 µm in total) measured with a 1.5 mm pupil, spherical aberration (~0.15 µm) and coma (~0.10 µm) accounted for the majority of the aberrations. Although the results were repeatable within an animal, the SHWS spots were quite distorted in their study, and no focus control was implemented to ensure the WFS beacon was reflected from a particular retinal layer. Therefore it was not clear whether the refractive state and higher order aberrations were affected by the small eye artifact. 20

41 Chapter 1 Literature review Table 1.2. List of studies examining the refractive error of rodent eyes Study Rodents Method Number of eyes Montero et al., 1968* Block et al., 1969* Rat (Holtzman, Sprague-Dawley) A Rat (Strain unsure) P,A Average refractive error Retinoscopy 3-3 D Retinoscopy D Glickstein & Millodot, 1970* Rat and Mouse P Retinoscopy Rat: 2 Mouse: 2 Rat: +9 D Mouse: +14 D Massof & Chang, 1972* Rat (hooded) P Retinoscopy, Ophthalmoscopy to +17 D Mutti et al., 1992 Tejedor & de la Villa 2003 Irving et al., 2005 Lashley, 1932* Lashley, 1937* Brown et al. 1965* Partridge et al., 1970* Hughes 1977 Meyer et al., 1977 Mutti et al., 1997 Rat (3 strains) P, A Mouse (C57BL/6) P Rat (3 strains) A Rat (3 strains) P, A Rat (albino) A Rat (Long-Evans and an albino) P, A Rat (Long-Evans) P Rat (Dark Agouti) P Rat (Long-Evans) P Rat (Sprague- Dawley) P, A Retinoscopy to D Retinoscopy D Retinoscopy 19 ~+5.3 to ~+15.3 D Scleral image? -12 to -13 D Scleral image 2-3 D Retinoscopy, Ophthalmoscopy, Unit field size 25-2 to -2.8 D Unit field size D Retinoscopy, Ophthalmoscopy Unit field size 20 Anterior retina: +8 to +9.4 D Posterior retina: -2 D VEP 4 Emmetropic to -1.4 D Retinoscopy, VEP to D Schmucker & Schaeffel, 2004 Zhou et al., 2008 Mouse (C57BL/6), ageing study P Mouse (C57BL/6), ageing study P Infrared photoretinoscopy Infrared photoretinoscopy to +9 D, hyperopia increased with age before stabilising at ~ +7 D to +9.4 D, hyperopia increased with age before stabilising at ~ +5 D de la Cera et al., 2006 Geng et al., 2011 Mouse (C57BL/6) P Mouse (C57BL/6J) P Shack-Hartmann wavefront sensing Shack-Hartmann wavefront sensing D 20 Anterior retina: to D Posterior retina -7.4 to D *cited in Hughes 1977; VEP: visual evoked potentials; P: pigmented animal; A: albino animal 21

42 Chapter 1 Literature review More recently, Geng et al. (2011) showed that the retinal layers with the highest reflectance were the vitreo-retinal interface and the outer retina, using B-scan images from OCT (Geng, Schery et al. 2011). By deliberately focusing the WFS beacon on the outer retina, close to the photoreceptor layer, they were able to obtain good quality SHWS spots within a dilated, 2 mm pupil in anaesthetised mice. Aberrations up to and including tenth order Zernike terms were measured in 20 pigmented mouse eyes, shown in Figure It can be seen that defocus (4th term) was the dominant aberration, followed by spherical aberration (12th term). The total amount of higher order aberrations was ~0.38 µm over a 2 mm pupil, which converted to ~0.23 µm over a 1.5 mm pupil, less than that found by de la Cera et al. (2006). In addition, the mouse eye was found to be D hyperopic when the beacon was focused on the anterior retina, and -7.4 D myopic when focused on the posterior retina, using a WFS beacon of 789 nm. This finding confirmed the plausibility of the small eye artifact as an explanation for the spuriously high hyperopic refractive errors in retinoscopic studies shown in Table 1.2. Figure Averaged normative aberration data from 20 eyes of the C57BL/6J mouse, over a 2.0 mm pupil (Geng, Schery et al. 2011). (a): Average Zernike coefficients from 10 left eyes; (b): Average Zernike coefficients from 10 right eyes. Zernike terms from 2nd to 5th order are shown. Error bars represent ±2 times SEM. Lower and higher order aberrations are shown in different scales. Reproduced with permission from OSA publishing (copyright holder). 22

43 Chapter 1 Literature review Although no normative aberration data beyond defocus were available for the rat eye, it is conceivable that it has similar amount of monochromatic aberrations as the mouse eye with a dilated pupil. This is because the rat eye is anatomically similar to the mouse eye except the former is ~2 x larger size (Hughes 1979a; Remtulla and Hallett 1985). The total dioptric power of the rat eye is about half that of the ~560 D in the mouse. As for chromatic aberrations, schematic rodent eyes showed that the LCA over a wavelength difference of approximately 170 nm ( nm) was ~5.6 D for the rat (Chaudhuri, Hallett et al. 1983) and ~8.8 D for the mouse (Hughes 1979b). Experimental results of LCA were similar to the above findings, with ~5.3 D for the rat (Millodot and Sivak 1978; Hughes 1979c), and ~7.7 D for the mouse (Geng, Schery et al. 2011), over similar wavelength range differences. Due to the amount of LCA in the rodent eyes, comparison of their refractive errors need to take into account the wavelength under which measurement was made (Geng, Schery et al. 2011). For this reason, the ~-7.4 D refractive error measured at 789 nm for the mouse eye becomes ~- 15 D at 514 nm (Geng, Schery et al. 2011), which is closer to the wavelength of the scotopic peak sensitivity of ~500 nm in the rod-dominated rodent retina (Jeon, Strettoi et al. 1998). From a functional point of view, being myopic helps rodents focus on their immediate surroundings since their eyes do not accommodate (Woolf 1956) Effect of higher-order ocular aberrations on retinal image quality Conventional retinal imaging in the living eye generally requires correction of low order aberrations, i.e. defocus and astigmatism. However, high-resolution in vivo retinal imaging at the cellular level requires the correction of higher order ocular aberrations with AO, the principle of which will be described in section 1.6. This section will demonstrate the effect of higher-order aberrations on retinal images in the rodent eye, so that the importance of AO correction can be shown. Figure 1.11 shows an example of the measured Zernike terms in 8 mouse eyes before and after AO correction (Jian, Zawadzki et al. 2013). A total of 20 terms, or up to the 5th order, is shown. A plano-concave lens was used to neutralise the corneal power of the mouse in this example, which can be thought of as a component of the adaptive optics correction. It can be seen that the amplitude of both low and higher order aberrations decreased dramatically with AO. Total RMS wavefront error decreased 23

44 Chapter 1 Literature review from an average of ~0.32 µm to ~0.05 µm (Jian, Zawadzki et al. 2013), indicating diffraction-limited imaging (at 860 nm) according to the Maréchal criterion (Born and Wolf 1999). Figure Effect of AO correction on the amplitude of measured Zernike terms in the eyes of 8 mice, adapted from Jian, Zawadzki et al. (2013). Zernike terms up to the 5th order are represented. Red column: mean Zernike terms before AO correction. Blue column: mean Zernike terms after AO correction. Error bars represent 1 standard deviation of the mean. Reproduced with permission from SPIE (copyright holder). The effect of correction of higher order aberrations on retinal images can be seen in Figures 1.12 and 1.13, which show actual AO images and simulated AO images in the rat and mouse eye, respectively. Figure 1.12 shows the retina of a rat obtained using an AO scanning laser ophthalmoscope (AOSLO), averaged over 200 frames (Geng, Greenberg et al. 2009). AO allowed capillaries to be resolved faintly in the rat. The capillaries were better delineated with standard deviation images that used blood flow to increase the contrast of vessels. Figure In vivo retinal images from a rat eye (Geng, Greenberg et al. 2009). (a): Before AO correction. (b): After AO correction. (c): Standard deviation image from a video of 200 frames after AO correction. Scale bar: 20 µm. Reproduced with permission from ARVO journals (copyright holder). 24

45 Chapter 1 Literature review Figure Simulated effect of aberration on retinal imaging in the mouse eye (Geng, Schery et al. 2011). (a): Flat-mounted fluorescence ganglion cell image in the rat retina obtained using a confocal microscope; (b): Simulated ganglion cell image over a 0.8 mm pupil with uncorrected higher order aberrations from the mouse eye in Figure 1.10; (c): Simulated ganglion cell image with all aberrations corrected over a 2 mm pupil; (d): Simulated ideal rod image in the mouse; (e): Simulated rod image with uncorrected higher order aberrations over a 0.8 mm pupil from the mouse eye in Figure 1.10; (f): Simulated rod image with all aberrations corrected over a 2 mm pupil. Scale bar: 20 µm. Reproduced with permission from OSA publishing (copyright holder). Figure 1.13 shows simulated retinal images (Geng, Schery et al. 2011) using the aberration data on the mouse eye in Figure Both mouse ganglion cell images from flat-mounted fluorescence confocal microscope and simulated rod images in the mouse eye were used as the ideal, or original images. It can be seen that when only defocus and astigmatism were corrected, ganglion cell axons were still resolvable, although blurry, due to their low density in the image. However, higher order aberrations had a significant impact on the resolution of individual rods in the complex rod mosaic, presumably due to the overlapping of the blurred PSF of individual rods. As expected, simulated AO correction of higher order aberrations (assuming zero noise, and only diffraction was the limiting factor) improved image quality of both ganglion cell axons and the simulated rod mosaic significantly. 25

46 Chapter 1 Literature review 1.6 Principle of adaptive optics retinal imaging AO retinal imaging relies on the re-construction and correction of ocular aberrations. Conventional wavefront-based AO systems (as opposed to image-based AO systems, which do not require the use of an SHWS. See section ) use a Shack-Hartmann wavefront sensor (SHWS) to measure ocular aberrations, which are then corrected by the deformable mirror (DM). This section provides a description of the working principle of the SHWS, followed by the conceptual layout of a wavefront-based floodillumination AO ophthalmoscope. Other AO imaging modalities will also be briefly described Principle of the Shack-Hartmann wavefront sensor The SHWS was first developed in order to compensate for atmospheric aberrations for ground based telescopes (Shack and Platt 1971). A concise history of its development is available elsewhere (Platt and Shack 2001). Its application in the eye was first described by Liang et al. (1994; 1997a; 1997b) which led to the emergence of AO ocular imaging. Briefly, the SHWS consists of a lenslet array and a charge-coupled device (CCD; areal image sensor) placed at the back focal points of the lenslets. An example of the lenslet array (Adaptive Optics Associates, Inc.) used for the work in this thesis is shown in Figure This square array consists of 65 X 65 lenslets, each is spaced 400 µm apart (pitch) with a focal length of 24 mm, closely packed to ensure adequate sampling of the tested wavefront. 26

47 Chapter 1 Literature review Figure A photo of the square lenslet array used in the SHWS in our laboratory. Each small dot on the glass blank is a single lenslet with a pitch of 400 µm and focal length of 24 mm. When a nominally collimated test wavefront (e.g. light emerging from a small patch of the retina in an ideal eye) strikes the array, it is divided into a number of subapertures by the lenslets. Each lenslet then focuses the light to a spot on the CCD. As shown in Figure 1.15(A), when an ideal or plane wavefront is tested, the resulting array of focused spots is regularly positioned on the optical axis of each lenslet, forming a reference pattern. If an aberrated wavefront is then measured, the resulting pattern becomes an irregular array of spots, as shown in Figure 1.15(B). Since the amount of displacement of each spot with respect to the reference is proportional to the amount of local tilt of the wavefront sampled by the respective lenslet, the magnitude of ocular aberration within the tested pupil area can be calculated by combining the data across the array (Liang, Grimm et al. 1994). 27

48 Chapter 1 Literature review Figure Principle of a Shack-Hartmann wavefront sensor (Liang, Grimm et al. 1994). (A): Individual lenslet bringing light from an ideal wavefront (solid line) and a tilted wavefront (dotted line) to focus; (B): Lens array sampling a larger wavefront. The displacement of each spot from the ideal point of focus is proportional to the local tilt of the wavefront. Reproduced with permission from OSA publishing (copyright holder). Figure 1.16(a) shows an example of the SHWS spot pattern at the back focal points of the lenslet array (i.e. the CCD) for an ideal wavefront. Each square represents the position of the lenslet and each dot represents the ideal focal point, within the centre of each square. With a large amount of defocus, as shown in Figure 1.16(b), most of the spots are displaced from their ideal position. Using standard spot finding algorithms, the relative displacement of each spot from the ideal position in both the horizontal and vertical directions can be calculated. 28

49 Chapter 1 Literature review Figure Examples of Shack-Hartmann spots obtained for (a): an ideal wavefront, and (b): when a large amount of defocus is introduced. The SHWS has been shown to be accurate and repeatable. When spherical and cylindrical lenses were inserted, the measured power agreed well with the nominal power of the lenses (Liang and Williams 1997a). The authors concluded that this should be true for higher order aberrations as well. Furthermore, the average standard deviation of the aberration measurements at different parts of the pupil was found to be around λ/14 in a real eye and λ/487 in an artificial eye (λ = 633 nm), suggesting highly repeatable results (Liang and Williams 1997a). Another advantage of the SHWS is that fixational eye movements have a negligible effect on the wavefront measurements (Liang and Williams 1997a), making it a suitable device for real-time aberration measurement for an AO ophthalmoscope as described below Conceptual layout of a flood-illumination AO ophthalmoscope Flood-illumination AO (flood AO) ophthalmoscopy uses the conventional imaging technique of simultaneously capturing light from all points within a patch of the retina with an optically conjugated 2-D detector, such as a CCD or CMOS (Complementary metal-oxide semiconductor) array. Flood AO ophthalmoscopy was first described by Liang et al (Liang, Williams et al. 1997b). Since then, much improvement had been made and AO technology has been incorporated into other imaging modalities, including AO scanning laser ophthalmoscopy (AOSLO) and AO optical coherence tomography (AO-OCT). 29

50 Chapter 1 Literature review Figure 1.17 shows a conceptual layout of a simplified flood AO ophthalmoscope. A detailed layout of the flood AO ophthalmoscope used in this thesis will be described in Chapter 4. Briefly, a light source, typically an infrared super-luminescent diode (SLD) is introduced into the eye to illuminate a small patch of the retina during wavefront sensing (WFS). Longer wavelength WFS light is often used in human eye imaging for comfort of viewing and to minimise pupil constriction during wavefront sensing. The nominally collimated light reflected from the retina then travels through a series of afocal lens pairs (relay optics) to the DM, which is made optically conjugate to the pupil of the eye. Due to the presence of ocular aberrations, the outgoing wavefront is distorted before it reaches the DM, which is flat at this stage. After being reflected by the DM, the WFS light is captured by the CCD at the back of the SHWS. Figure Conceptual layout of a flood-illumination AO ophthalmoscope. A point source of WFS light is reflected from the retina, shown as solid lines in blue. The intermediate optics are ignored for simplicity. The arrows indicate the direction of travel of the light. The black dashed lines show the communication between the SHWS and the DM in a closed AO loop. BS: beam splitter; DM: deformable mirror; CCD: charge-coupled device; SHWS: Shack-Hartmann wavefront sensor, which consists of a lenslet array and a CCD. The SHWS then relays the information of the aberrated wavefront to a computer, which calculates and sends information regarding the necessary amount of deformation 30

51 Chapter 1 Literature review required for the DM to compensate for the aberration. This process is repeated a number of times until the wavefront is fully corrected. The SHWS, the computer and the DM thus work in a closed loop, where the SHWS measures the resultant aberrations of the eye minus those introduced by the DM, ensuring real-time update and correction of ocular aberrations (Liang, Williams et al. 1997b). Once the aberration correction is at an optimum (when the RMS wavefront errors of the Zernike terms reach a minimum), a second light source used for imaging, typically a superluminescent diode (SLD) or laser diode (LD), is switched on to illuminate an area of the retina at the same location about 1 to 2 in diameter at the same location. The aberrated wavefront from the eye is corrected by the DM, and a high resolution retinal image is captured by the imaging device, such as a CCD. The WFS and imaging lights are typically of different wavelengths so that a dichroic beam splitter can be used to efficiently separate them into the appropriate channels. It is worth noting that unlike the AOSLO, the WFS and imaging lights in a floodillumination AO ophthalmoscope are not typically corrected by AO as it enters the eye (Roorda 2010). However, since light reflected from the retina can be considered to be perfectly diffuse (Campbell and Gubisch 1966), the phase information of the incoming light is effectively scrambled as it reflects off the retina, meaning ocular aberrations are being measured and corrected only as light leaves the eye (Liang, Grimm et al. 1994). In addition, although the shape of the WFS light on the retina may be affected by its first pass into the eye due to ocular aberrations, this will be the same for each lenslet of the SHWS. The resultant aberration measurement and correction is therefore unaffected since the SHWS measures relative displacement of the spots form by each lenslet (Liang, Grimm et al. 1994) Non-common path aberrations It is worth to note that a potential source of error in the measured aberration of the eye could arise due to the non-common optical path between the WFS and imaging light (Sauvage, Fusco et al. 2007; Hofer, Sredar et al. 2011; Sulai and Dubra 2014). This gives rise to non-common path aberrations, or NCPAs, between the WFS and imaging arms. As shown in Figure 1.17, a portion of the optical paths after the last beam splitter is inevitably different between the SHWS and the imaging CCD. The SHWS is 31

52 Chapter 1 Literature review therefore blind to the aberrations of the optical element(s) between the beam splitter and the imaging CCD. By placing a good-quality, well-centred achromatic lens immediately in front of the imaging camera, the NCPAs could be minimised. NCPAs can be calculated by comparing aberrations measured in the imaging arm using image-based AO without a wavefront sensor (section ) and that measured in the WFS arm (Sulai and Dubra 2014). The calculated NCPAs can then be introduced into the DM as a bias during actual experiments to improve image quality. Another cause of NCPAs is the chromatic difference between the WFS and imaging lights. As will be discussed later in a publication presented in Chapter 3 (Zhou, Bedggood et al. 2012), the NCPAs caused by such chromatic difference can be compensated by correcting defocus alone in the human eye. However, chromatic difference between WFS and imaging light can lead to spurious residual aberrations in the rodent eye even with defocus compensation Other AO imaging modalities Apart from flood AO ophthalmoscopy, the other most commonly used modalities for in vivo AO retinal imaging include the AOSLO and AO-OCT. The principles of these modalities have been described in detail elsewhere (Roorda, Romero-Borja et al. 2002; Hermann, Fernandez et al. 2004). This section will give a very brief overview of AOSLO and AO-OCT since almost all studies to date have used these two modalities for rodent eye imaging (Biss, Sumorok et al. 2007; Geng, Greenberg et al. 2009; Alt, Biss et al. 2010; Geng, Dubra et al. 2012; Jian, Zawadzki et al. 2013; Schallek, Geng et al. 2013; Jian, Xu et al. 2014; Zawadzki, Zhang et al. 2015). There are two major differences between flood AO and AOSLO/AO-OCT. First, the latter two use raster scanning of a focused spot on a small patch of the retina to realise the goal of wavefront sensing and imaging. Two scanners are typically used: a resonant scanner which operates at high speed in the order of tens of khz, and a galvanic scanner which has a lower scanning speed of tens of Hz. The reflected light from the retina is then de-scanned by the same scanners, rendering the laser spot stationary at the WFS camera. As a result of the scanning nature of these imaging modalities, the SHWS spots represent an average over the entire scanning field of view (Roorda, Romero-Borja et al. 2002). For the AOSLO, the same light source could be used for wavefront sensing and 32

53 Chapter 1 Literature review imaging due to its scanning nature (Roorda, Romero-Borja et al. 2002), although a separate WFS light source could also be used. For the AO-OCT, the imaging light typically has a much larger bandwidth than the WFS light (Hermann, Fernandez et al. 2004). Second, retinal image formation in the AOSLO typically involve using a confocal pinhole placed immediately in front of a photomultiplier tube to selectively reject outof-focus light (Roorda, Romero-Borja et al. 2002). This allows AOSLO to selectively focus on the retinal plane of interest (axial sectioning ability), reducing the collection of light scattered from other retinal planes and leading to increased lateral and axial resolution compared to flood AO. On the other hand, the AO-OCT is an imaging technique based on low coherence interferometry (Youngquist, Carr et al. 1987) and is optimised for axial resolution. It is therefore typically used to obtain tomographic (sectional) images of the retina, although en-face images can also be obtained, using a spectrometer as the light detector. 1.7 Optical properties of rodent eyes As shown in section 1.5, rodent eyes have similar amount of higher order aberrations as do human eyes. However, there are also some significant differences in optical properties between them. Since the experiments of this thesis were performed on rat eyes in particular, this section will use the rat eye as the main example to give a review of the optical properties of rodent eyes Optical parameters of the rodent eyes The axial length of the rat eye from the anterior cornea to the outer retina is around 6.15 mm (Hughes 1979a), which is about a quarter of the ~24 mm in the human eye (Liou and Brennan 1997). Due to the small size of the eye, a higher refractive power is required to focus images on the retina of the rat. In fact, the total optical power of the rat eye is slightly more than 300 D (Hughes 1979a), a factor of ~5x more than the human eye s 60 D. Such a high optical power is primarily achieved by the crystalline lens, which accounts for ~80% of the refractive power of the rat eye (Hughes 1979a), compared to ~30% in the human eye (Liou and Brennan 1997). In comparison, the mouse eye has a refractive power of ~560 D (Remtulla and Hallett 1985). 33

54 Chapter 1 Literature review As a visual comparison, Figure 1.18 shows diagrams of human (Liou and Brennan 1997) and rat (Hughes 1979a) schematic eyes (the mouse schematic eye is shown elsewhere (Remtulla and Hallett 1985; Schmucker and Schaeffel 2004a) and will not be discussed in detail here), which are represented on the same scale for direct comparison of their relative sizes. Note that the crystalline lens in the rat eye can be seen to occupy a much larger proportion of the eye volume, since it accounts for ~80% of the refractive power of the rat eye. Figure Diagrammatic comparison of human and rat schematic eyes. (a): Human schematic eye (Liou and Brennan 1997); (b): Rat (Hughes 1979a) schematic eye. Both are represented on the same scale. Note the thickness of the retina was not represented in the human schematic eye. Total axial length of the human eye is about 4x the rat eye. Scale bar: 1 mm. Reproduced with permission from the following copyright holders: (a): OSA publishing; (b): Elsevier. As a more detailed comparison, the radius of curvature of each of the refracting and retinal surfaces and the distance between them are also shown in Tables 1.3 and 1.4 for the rat and human schematic eyes, respectively. The radii of curvature of both the anterior and posterior cornea in the rat is about half that of the human eye. However, the 34

55 Chapter 1 Literature review anterior and posterior surfaces of the rat crystalline lens are much more curved, about 1/5 and 1/3 the radius of curvature of that of the human eye. Both the rat and human crystalline lenses have a gradient-index profile that increases towards the centre of the lens (Philipson 1969; Campbell 1984; Jones, Atchison et al. 2005). The distance between the refracting surfaces differ in magnitude between the two eyes. For example, the corneal thickness in the rat eye is about half that of the human eye, whereas the anterior chamber depth is ~1/5 that of the human eye. However, the thickness of the crystalline lens is similar between the two eyes. Similarity of thickness is also seen in the retina of the two eyes, measured as the distance from the inner limiting membrane (ILM) to the outer limiting membrane (OLM). Whereas the rat retina is 170 µm thick, the human retina has a comparable thickness of 250 µm. In fact, it has been found that the thickness of the retina is relatively constant in the eyes of mammals regardless of the physical size of the eye (Glickstein and Millodot 1970). The comparable physical thickness of the retina of rat and human eyes and their difference in total refractive power therefore lead to very different dioptric thickness of their retinas. It has been estimated that a change of optical power at the plane of the eye's entrance pupil of ~11 D is required to change the focus from the anterior to posterior retina when imaging the rat eye, whereas only ~0.7 D is required in the human eye (Geng, Greenberg et al. 2009). In comparison, that number in the mouse retina has been estimated to be ~29 to 39 D (Schmucker and Schaeffel 2004a; Geng, Schery et al. 2011). As mentioned in section 1.5.4, a result of the large dioptric thickness in the highly powered eye is the small eye artifact in retinoscopy measurement of refractive errors. In fact, as described in section 1.9, a large dioptric retinal thickness can also cause problems for wavefront sensing in AO imaging (Geng, Schery et al. 2011). 35

56 Chapter 1 Literature review Table 1.3. Parameters of the rat eye, modified from Campbell and Hughes (1981). Surface Radius of curvature (mm) Anterior cornea Posterior cornea Anterior lens Posterior lens 2.34 ILM of retina * OLM of retina * Distance between surfaces (mm) * Chaudhuri, Hallett et al. (1983) ILM: inner limiting membrane OLM: outer limiting membrane Table 1.4. Parameters of the human eye, modified from Liou and Brennan (1997) Surface Radius of curvature (mm) Anterior cornea Posterior cornea -6.4 Anterior lens Distance between surfaces (mm) Posterior lens ILM of retina 12.0 * 0.25 OLM of retina 12.0 * * Smith et al. (2008) ILM: inner limiting membrane OLM: outer limiting membrane 36

57 Chapter 1 Literature review Spatial vision of rodent eyes Rodent eyes have very poor spatial resolution (Birch and Jacobs 1979; Artal, Herreros de Tejada et al. 1998; Prusky, West et al. 2000). Spatial resolution, or visual acuity, of the eye is normally measured in cycles per degree (cyc/deg), which is the number of high-contrast sinusoidal periods distinguishable over a 1 visual field. In the adult human eye, it is well known that normal visual acuity is around 30 cyc/deg or more (Schwartz 2004). On the other hand, visual acuity is ~1 cyc/deg for pigmented rats and ~0.5 cyc/deg for albino rats (Birch and Jacobs 1979; Prusky, West et al. 2000). As explained below, the cause of the lower visual acuity in rodent eyes is likely limited by neural factors rather than poor optical quality. For example, the rodent retina, which lacks a fovea, is dominated by rods (La Vail 1976; Jeon, Strettoi et al. 1998), which tend to pool signals together at bipolar and ganglion cell levels. Cones accounting for ~1% of the total number of photoreceptors in the rodent eye (La Vail 1976). On the other hand, cones account for ~5% of the total number of photoreceptors in the human retina and concentrate at the fovea (Mustafi, Engel et al. 2009). Due to their roddominated retina, electrophysiological measurement of the size of receptive fields of retinal ganglion cells in rodents showed that they are at least an order of magnitude larger than the human eye (Brown and Rojas 1965; Green, Tong et al. 1977; Balkema and Pinto 1982; Stone and Pinto 1993; cited in Artal, Herreros de Tejada et al. 1998). In addition, maximum retinal ganglion cell density is ~6300 cells/mm 2 in the rat retina, whereas up to cells/mm 2 had been found in the central retina of the human eye (Curcio and Allen 1990), indicating that the rat retina is much coarser in terms of its ability of spatial sampling. In terms of optical quality, section above showed that optical aberrations in the rodent eye are similar to the human eye in magnitude, and that the rodent eye is approximately emmetropic at the photoreceptor plane. The above evidence must conclude that the poor visual acuity of the rodent eye is indeed limited by neurological rather than optical factors. 37

58 Chapter 1 Literature review Imaging resolution of rodent eyes AO retinal imaging has the same principle as microscopy, except that the objective lens in AO retinal imaging is the optics of the eye, and the sample is the retina (Roorda and Duncan 2015). Although the visual acuity of rodent eyes is worse than that of human eyes, the opposite should ideally be true in terms of theoretical resolution when imaging the cellular structures on the retina using AO (Geng, Greenberg et al. 2009; Geng, Schery et al. 2011), since the overall power of the optics of the rodent eye (i.e. the objective lens ) is much higher. In order to readily compare the imaging resolution between rodent and human eyes the concept of numerical aperture (NA) (Roorda and Duncan 2015) will be introduced here. Figure Numerical aperture calculation of a thin lens. F: focal point of the thin lens, or object plane. θ: half angle of the cone of light emitting from the object. f: focal length of the thin lens. d: diameter of the thin lens or pupil. Consider the refracting surfaces of the eye as a simplified thin lens as shown in Figure 1.19 with focal length f. The NA of this thin lens is defined in terms of the half angle θ of the cone of light emitted from its back focal point F: NA = nsi n( θ ) Equation 1.6 where n is the refractive index of the medium that the thin lens is immersed in. Therefore NA is a dimensionless number specifying the range of angle that the lens can accept or emit light. For small angles of θ, NA can also be written as the following approximation: 38

59 Chapter 1 Literature review d NA n 2 f Equation 1.7 where d is the total diameter of the thin lens or pupil, f is its focal length of the thin lens. Suppose the thin lens has zero aberrations and can be considered diffraction-limited, recall that Equation 1.1 gave a definition of the angular resolution of a diffractionlimited system (Hecht and Zajac 1974). In linear form, Equation 1.1 can also be expressed as: l 1.22 f Equation 1.8 = λ d where Δl is the length of the smallest feature that can be resolved using the thin lens and λ is the wavelength of the imaging light. If f and d have the same unit, then Δl is in the same unit as λ. From Equation 1.7 and Equation 1.8, it can be seen that when the values of n and λ are fixed, Δl is inversely proportional to NA: 1 Equation 1.9 l NA Equation 1.9 shows that as the value of NA increases, Δl decreases in value, i.e., smaller features can be resolved with the increase in NA. Table 1.5. Comparison of NA and lateral resolution between human and rodent eyes, modified from Geng et al. (2009). Average axial length (mm) Total power (D) Numerical aperture (NA) Theoretical max lateral resolution at λ = 550 (nm) Human (6.8 mm pupil) 1.68 Rat (3 mm pupil) 0.78 Mouse (2 mm pupil) 0.68 Table 1.5 shows the theoretical maximum lateral resolution in human and rodent eyes, modified from a study by Geng et al. (2009). It can be seen that rodent eyes have more than double the NA values as the human eye when pupils are dilated. This is consistent with the nocturnal habit of rodents, since a larger NA means an increase in the eye s ability to gather light. From Equation 1.7, it can be seen that larger NA value can be realised with a larger pupil diameter or a shorter focal length. In rodent eyes, the ratio between pupil size and 39

60 Chapter 1 Literature review focal length is larger than that in the human eye when the pupils are dilated. As a result, the theoretical maximum lateral resolution (when diffraction is the only limiting factor) in rodent eyes is about twice as the human eye at the same imaging wavelength (Geng, Greenberg et al. 2009). In vivo AO imaging of rodent eyes should therefore produce superior image quality of microscopic retinal structures since better resolution than the human eye is theoretically possible. 1.8 In vivo imaging of rodent eyes In this section, a review of the benefits of in vivo imaging in rodent eyes is described first, from the perspective of advancing biological science. Then, the relevant studies that have used various imaging modalities without and with AO in in vivo imaging of rodent eyes are described Benefits of in vivo imaging in rodents Rodents are widely used in the study of the pathogenesis and treatment of diseases due to their low cost, ease of maintenance and handling, and rapid growth compared to primates (Abbott 2004; Chang, Hawes et al. 2005). In addition, targeted gene manipulation techniques have been well-established in mice (Mansour, Thomas et al. 1988; Capecchi 1989), and have recently become possible in rats (Abbott 2004; Geurts, Cost et al. 2009). Since rodents bear many similarities to humans in terms of genetics and physiology, they are instrumental in the study of disease mechanisms and treatment paradigms in humans. Rodents are also used widely in the study of eye diseases, with several established eye disease models such as glaucoma, diabetic retinopathy and macular degeneration (Bui, Edmunds et al. 2005; He, Bui et al. 2008; Kohzaki, Vingrys et al. 2008; Marc, Jones et al. 2008; Bui, Loeliger et al. 2009). Most studies rely on retinal histopathology by sacrificing multiple animals to perform statistical analysis, in order to follow disease progression or treatment effectiveness over time. Although histopathology yields highresolution images of retinal cells (La Vail 1976), longitudinal studies in the same animal are not possible. Compared to histopathology, in vivo imaging of the rodent retina can also achieve resolution at the cellular level, due to the large NA of rodent eyes. Some studies have 40

61 Chapter 1 Literature review used commercially available confocal scanning laser ophthalmoscopes (cslo) and retinal fundus cameras to obtain images of ganglion cells and capillaries in mice (Paques, Simonutti et al. 2006; Murata, Aihara et al. 2008; Walsh and Quigley 2008; Leung, Weinreb et al. 2011; Zhang, Zam et al. 2014). More recently, resolution in rodent eyes was further improved with the aid of AO (Biss, Sumorok et al. 2007; Geng, Greenberg et al. 2009; Geng, Dubra et al. 2012; Jian, Zawadzki et al. 2013; Schallek, Geng et al. 2013; Zawadzki, Zhang et al. 2015). A major advantage of in vivo rodent retinal imaging is that it is non-invasive, allowing the same animal to be imaged across multiple sessions in longitudinal studies, reducing the effects of inter-animal variation and potentially yielding more accurate data. By the same token, the number of animals being sacrificed for statistical analysis can be substantially reduced. Combined with genetic manipulation in rodents, the contrast of retinal cells can be boosted by labelling them with fluorophores (Biss, Sumorok et al. 2007; Geng, Dubra et al. 2012; Schallek, Geng et al. 2013), making it possible to observe cells such as the retinal ganglion cells, pericytes and macrophages that would otherwise be transparent, with the aid of AO (Geng, Dubra et al. 2012; Schallek, Geng et al. 2013; Zawadzki, Zhang et al. 2015). More details of studies without and with AO imaging in rodent eyes are presented below Rodent eye imaging without AO Due to the large NA of the rodent eyes and the use of transgenic animal strains, in vivo fluorescence retinal imaging of microscopic structures in rodents has been possible even without AO, albeit with reduced lateral and axial resolution compared to AO images. Recall that rodent eyes have similar magnitude of higher order aberrations as do human eyes when pupils are dilated (Porter, Guirao et al. 2001; Geng, Greenberg et al. 2009; Geng, Schery et al. 2011). As a comparison, the dilated human eye has a an averaged pupil size of ~6 mm (Porter, Guirao et al. 2001), compared to ~3 mm and ~2 mm in the rat and mouse eyes, respectively (Geng, Greenberg et al. 2009). In addition, the focal lengths of the human eye is ~17 mm (1/60 D), compared to ~3.30 mm (1/300 D) and ~1.80 mm (1/560 D) in the rat and mouse eyes, respectively. Recall from Equation 1.8 that the linear size of the diffraction-limited PSF of an optical system is related to the ratio of f/d, where f is the focal length of the eye, and d is its diameter. From the 41

62 Chapter 1 Literature review above numbers, the ratio of f/d is ~2.83 for the human eye, ~1.10 for the rat eye and ~0.9 for the mouse eye. Therefore the linear scale of the diffraction-limited PSF in the dilated rat eye is ~2x smaller, and in the mouse eye ~3x smaller than that of the human eye under the same wavelength. From an imaging point of view, the much smaller linear PSF size in rodent eyes means that same amount of higher order aberrations have a proportionally smaller impact on the image quality in rodent eyes compared to the human eye, given low order aberrations are corrected. Rodent retinal imaging without AO has been shown in studies that used fluorescence imaging in combination with commercially available confocal scanning laser ophthalmoscopes (cslo) or flood retinal fundus cameras. Fluorescence images of axons and dendrites of retinal ganglion cells and capillaries have been shown after correcting for only the low order aberrations: defocus and astigmatism (Paques, Simonutti et al. 2006; Murata, Aihara et al. 2008; Walsh and Quigley 2008; Leung, Weinreb et al. 2011; Zhang, Zam et al. 2014). Some examples of these images are shown in Figure Figure Some example images of in vivo fluorescence retinal imaging in mouse eyes without AO. (a): Fluorescein angiography of retinal capillaries with a cslo (Paques, Simonutti et al. 2006); (b): Fluorescence image of retinal ganglion cell bodies with a flood-illumination retinal fundus camera, note the axons and dendrites were not labelled in this mouse strain (Murata, Aihara et al. 2008); (c): Fluorescence image of a retinal ganglion cell obtained with a cslo (Leung, Weinreb et al. 2011). Scale bars are shown in the individual image. Reproduced with permission from the following copyright holders: (a): Elsevier; (b) and (c): ARVO journals. Although image quality from the above studies was inferior compared to those with AO (described below), axons and dendrites from ganglion cells and capillaries could be 42

63 Chapter 1 Literature review sufficiently distinguished in most cases, especially in cslo images. It should be noted that all of the studies were performed on transgenic mice, due to the ease of obtaining transgenic strains that express fluorescent labels in retinal cells compared to rats. The fact that ganglion cell dendrites and capillaries could be resolved in rodent eyes without AO demonstrated the superior resolution ability of small animal eyes for in vivo retinal imaging. (In comparison, AO is essential to image retinal capillaries in the human eye.) With the aid of AO imaging, the lateral and axial image resolutions of these microscopic structures could be further improved (Geng, Dubra et al. 2012; Jian, Zawadzki et al. 2013; Schallek, Geng et al. 2013; Jian, Xu et al. 2014; Zawadzki, Zhang et al. 2015), allowing for more accurate measurement of cell sizes, capillary diameters and depth measurement, which are useful when measuring the microscopic retinal changes in disease progression or the monitoring treatment efficacy. AO imaging in rodent eye is described in more detail below Rodent eye imaging with AO Over the past few years, an increasing number of studies focused on AO in vivo imaging of the rodent retina. Almost all of these studies relied on fluorescence imaging of retinal cells and used scanning imaging modalities such as AOSLO and AO-OCT for improved image contrast (compared with conventional flood imaging which relies on intrinsic light scatter only). Biss et al. (2007) demonstrated a fluorescence AO scanning laser microscope to image the blood vessels and microganglia in transgenic mice. One strain expressed green fluorescent protein (GFP) in their microganglia, while intravenous injection of Evan s Blue dye was used to enhance the contrast of the blood vessels. Although they were able to show improvement of image quality (which was not as great as expected) with AO for capillaries and microganglia in fluorescence, the authors reported difficulty obtaining good quality SHWS spots in the mouse eye, possibly due to reflection from multiple retinal layers and the back of the crystalline lens. As a result, only partial wavefront correction was achieved (Biss, Sumorok et al. 2007). In addition, other similar studies also found distorted SHWS spots in rodent eyes compared to human eyes, potentially affecting the accuracy of wavefront sensing (Irving, Kisilak et al. 2005; de la Cera, Rodriguez et al. 2006; Bird, Kisilak et al. 2007). 43

64 Chapter 1 Literature review Geng et al. (2009) was the first to characterise in vivo lateral resolution in the rat eye using a fluorescence AOSLO. In vivo lateral resolution was determined by calculating the average full width at half maximum (FWHM) of the in vivo line-spread function, using in vivo and the corresponding ex vivo images of retinal ganglion cell dendrites (Geng, Greenberg et al. 2009). The authors found that, despite reaching a reported residual RMS of 0.05 µm for a mm pupil after AO correction, the lateral resolution (1.77 µm) was ~82% worse than the theoretical diffraction-limited linespread function (1.01 µm). They attributed this primarily to non-optimized defocus, which may arise due to the WFS and imaging light originating from different layers in a dioptrically thick rat retina (Geng, Greenberg et al. 2009). However, the SHWS spot quality was not shown in their study. In an effort to improve the SHWS spot quality in rodent eyes, Geng et al. (2011) used a large diameter WFS light that filled the pupil of the mouse eye, to decrease the depth of focus of the WFS beacon on the retina. Combined with careful focus control, a smaller spot could be formed on the desired retinal layer, leading to good quality SHWS spots in the mouse eye with their AOSLO system. Their efforts were recently rewarded with near diffraction-limited images of mouse retinal ganglion cells under fluorescence (Geng, Dubra et al. 2012), with an example image shown in Figure 1.21(a). Throughout their experiments, they kept the focus of the WFS light on the photoreceptor layer, and changed defocus alone when imaging other retinal layers such as the retinal ganglion cells. However, their AO images of photoreceptors without fluorescence in the mouse eye were of poorer contrast and resolution, compared to what is achievable in the human eye (Dubra, Sulai et al. 2011). With the ability to control the focus of the WFS beacon on the retina, another similar study also showed fluorescence AOSLO images of retinal pericytes in the mouse eye (Schallek, Geng et al. 2013), shown in Figure 1.21(b). 44

65 Chapter 1 Literature review Figure Some example AO images from the mouse eye. (a): Fluorescence image of ganglion cell body and processes obtained using an AOSLO (Geng, Dubra et al. 2012); (b): Fluorescence image of retinal capillaries and pericytes, labelled with colours, obtained using an AOSLO (Schallek, Geng et al. 2013); (c): Retinal B-scan from AO-OCT, AO image (yellow rectangle) is overlayed onto a standard OCT image (Jian, Zawadzki et al. 2013). Note the smaller scale bars in the first two images compared to the images without AO in Figure Reproduced with permission from the following copyright holders: (a): OSA publishing; (b): ARVO journals; (c): SPIE. In addition to AOSLO, Jian et al. (2013) showed an AO-OCT capable of obtaining AOcorrected B-scans and corresponding en-face images of the mouse retinal capillary bed at different layers without fluorescence, shown in Figure 1.21(c). Similar to the above studies that used variable focus control of the WFS light, the authors also positioned the focus of the WFS light on the outer retina (Jian, Zawadzki et al. 2013). More recently, widefield OCT and SLO were combined with AOSLO for precise 3-D localisation of fluorescence retinal cells in the mouse eye (Zawadzki, Zhang et al. 2015). Unlike the previous studies, the authors changed the focus of the WFS light to match the desired plane of imaging (Zawadzki, Zhang et al. 2015). However, this method lead to sometimes suboptimal wavefront sensing and correction, presumably due to the fact that 45

66 Chapter 1 Literature review the strongest reflection of the WFS light was from the vitreo-retinal interface and the photoreceptor layer (Geng, Schery et al. 2011). The above studies showed that there has been some success in AO imaging in rodent eyes when combining scanning AO imaging modalities with fluorescence. However, image quality obtained is not typically as high as would be expected from the substantially higher NA of the rodent eye, especially in reflectance AO imaging of more tightly packed structures such as the photoreceptor mosaic. This is possibly due to the effect that the dioptrically thick retina of rodent eyes has on the accuracy of wavefront sensing and hence AO image quality. This phenomenon had not previously been quantified prior to published work included with this thesis. In addition, pilot experiments (see Chapter 2) performed on the rat eye using flood AO imaging without the aid of fluorescence showed retinal images with poor contrast and resolution, as opposed to results obtained with scanning AO modalities. This shows that consistently obtaining high-resolution retinal images in rodent eyes is not yet routine and challenges still remain. The following section will describe these challenges in more detail. 1.9 Challenges of in vivo AO imaging in rodent eyes This section describes the challenges in wavefront sensing and in vivo flood AO imaging of rodent eyes, as a result of its dioptrically thick retina. Identifying and overcoming these challenges are the ultimate goals of this thesis, therefore the literature concerning potential methods to improve image quality in rodent eyes is also reviewed in the following section Challenges of wavefront sensing in rodent eyes The challenges to conventional assumptions in the field of ophthalmic imaging due to the dioptrically thick retina in rodent eyes were investigated in detail and methods proposed to address them were published in a peer-reviewed paper (Zhou, Bedggood et al. 2012), presented in Chapter 3. This section will provide a brief overview of the challenges of wavefront sensing in rodent eyes. Most studies that used a WFS light with variable focus control focused the WFS beacon on the outer retina close to the photoreceptor layer during wavefront sensing (Geng, Dubra et al. 2012; Jian, Zawadzki et al. 2013; Schallek, Geng et al. 2013), as this plane 46

67 Chapter 1 Literature review is thought to provide the greatest reflectance for infrared light (Geng, Schery et al. 2011). Images are then acquired from the layer of interest which is typically more anterior, and defocus alone is offset to account for the difference in depth. The assumption made with such an approach is that separation of the WFS and imaging planes induces a significant change only in defocus and not in higher order aberrations, and as such the difference in plane of regard can be compensated by adjusting defocus with minimal impact on the achieved image quality. This is often done in human AO retinal imaging with minimal observable drawback to image quality. However, since higher order aberrations also vary with the distance between the object and the optical system (the refractive components of the eye), if this distance becomes sufficiently large relative to the dimensions of the eye the only defocus assumption may no longer hold. In fact, since the dioptric thickness of the retina is ~11 D in the rat (Hughes 1979a; Geng, Greenberg et al. 2009) and ~30 D in the mouse (Schmucker and Schaeffel 2004a; Geng, Schery et al. 2011), much more than the ~0.7 D in the human retina, altering defocus alone may not compensate sufficiently for higher order aberrations at retinal planes other than the WFS plane. In addition, recall that longitudinal chromatic aberration (LCA) in rodent eyes is ~5.3 D for the rat (Millodot and Sivak 1978; Hughes 1979c), and ~7.7 D for the mouse (Geng, Schery et al. 2011) over a wavelength difference of 170 nm, compared to the ~1.8 D in the human eye over similar wavelength range (Geng, Greenberg et al. 2009). The large LCA in rodent eyes means that a large amount of defocus is required to compensate for the chromatic difference between the WFS and imaging light (or emitted fluorescence light), which often have significantly different wavelengths in AO imaging to allow efficient channel separations (Geng, Greenberg et al. 2009; Geng, Dubra et al. 2012; Jian, Zawadzki et al. 2013; Schallek, Geng et al. 2013). For example, the wavelength of the WFS light was 904 nm in a study of AO imaging in the rat eye (Geng, Greenberg et al. 2009), whereas the fluorescence emission peak wavelength used for imaging was 507 nm. Altering defocus alone to compensate for the wavelength difference in rodent eye imaging may not account for all higher order aberrations under the imaging light, even though the aberrations may appear well-corrected under the WFS light, because higher order aberrations vary non-linearly with refractive power. 47

68 Chapter 1 Literature review Another possible source of error is from the axial alignment of the DM with the exit pupil of the eye. In human imaging, there is little consequence when the DM is not precisely aligned with the exit pupil axially (Bedggood and Metha 2010). However, in the highly powered rodent eyes, small axial mis-alignment of the DM with respect to the eye s exit pupil may also contribute to an increase in residual aberrations, especially when the wavefront sensing and imaging planes are different. By quantifying the impact of these factors on aberration correction during wavefront sensing (Zhou, Bedggood et al. 2012), it is possible to further improve AO image quality in rodent eyes Challenges and advantages of flood AO imaging in rodent eyes As mentioned above, one of the advantages of scanning AO imaging modalities is that they are less susceptible to intra-ocular scatter. In comparison, flood AO ophthalmoscopes generally lack the ability to physically reject out-of-focus light during imaging, leading to reduced image contrast and resolution. However, scanning AO ophthalmoscopes typically obtain images limited to a rate of Hz (Roorda, Romero-Borja et al. 2002; Tam, Martin et al. 2010; Dubra and Sulai 2011; Geng, Dubra et al. 2012; Jian, Zawadzki et al. 2013; Pinhas, Dubow et al. 2013; Zawadzki, Zhang et al. 2015) due to the limitation imposed by the speed of the scanners. For example, AOSLO typically obtained images of the human retina at ~30 Hz over a 1 field (Roorda, Romero-Borja et al. 2002; Dubra and Sulai 2011; Pinhas, Dubow et al. 2013), although frame rates of up to 60 Hz have been shown over 1.5, by using the forward and return sweeps of the fast resonant scanner (Tam, Tiruveedhula et al. 2011). On the other hand, flood AO ophthalmoscopes have recently been shown to be capable of acquiring images at an order of magnitude faster than scanning AO modalities, owing to the development of detectors based on scientific complementary metal-oxide semiconductor (scmos) technology (Bedggood and Metha 2012; Bedggood and Metha 2013; Bedggood and Metha 2014). The scmos device used in the above studies is capable of imaging at 50 Hz at full frame (2560x2160 pixels) using a global shutter (i.e. all pixels are exposed simultaneously). Much higher frame rates are possible by 48

69 Chapter 1 Literature review restricting the region of interest in the vertical extent, while leaving the horizontal extent intact. For example, by restricting the vertical extent to around 200 pixels, a frame rate of 400 Hz could be obtained (Bedggood and Metha 2014). Further increase in frame rate to ~1000 Hz was possible by restricting the vertical field extent to 80 pixels (Bedggood and Metha 2013). The fast frame rate enabled detailed visualisation of the dynamics of individual blood cells as they traverse through the retinal capillaries in human eyes (Bedggood and Metha 2012), as well as the high frequency of cone intensity fluctuation due to pigment bleaching in response to light stimulation (Bedggood and Metha 2013). Flood AO imaging thus holds much promise in the study of the in vivo dynamics of microscopic structures, and as described above in section there are many advantages to imaging such structures in rodent eyes. However, as the pilot experiment in Chapter 2 will show, retinal image quality from the rat eye using flood AO imaging was poor when compared to the human eye. As later experiments in this thesis will show, these issues persisted despite implementation of methods described Chapter 3 to improve wavefront sensing accuracy. Therefore other methods were trialled to improve flood AO image quality in rodent eyes, which are described below Methods for improving flood AO image quality in rodent eyes In this section, a brief review of the possible methods to improve the quality of flood AO imaging is presented. The detailed implementations of these methods were published in two separate papers, which will be presented in Chapters 6 and 7. These methods are potentially applicable to other AO imaging modalities also Increasing image quality with HiLo imaging As described above, flood AO imaging suffers from the deleterious effects of intraocular scatter, which reduces both the contrast and resolution of AO images. In an effort to overcome the effects of light scattered from out-of-focus layers in flood-illumination fluorescence microscopy, Lim et al. (2008) proposed an imaging technique dubbed HiLo imaging. In brief, two images of the same region of interest are acquired either simultaneously or in rapid succession such that there is minimal difference in the optical 49

70 Chapter 1 Literature review state of the eye between the images. One image is acquired with uniform illumination, which is mainly used to derive the high-frequency component of the final image (hence the Hi in HiLo), while the other image is acquired using structured illumination (e.g. random laser speckle) which is mainly used to derive the low-frequency component (hence the Lo in HiLo). These images are then post-processed and integrated in frequency space in order to obtain a HiLo image. It has been shown in conventional light microscopy that HiLo imaging provides floodillumination images a kind of pseudo-confocality, or axial sectioning during postprocessing (Lim, Ford et al. 2011), due to the algorithm s ability to filter out out-offocus light with the original Hi and Lo images. Under certain conditions, the pseudo-confocality can rival the true confocality offered by a physical pinhole in scanning imaging systems (Lim, Ford et al. 2011). HiLo imaging thus offers the potential to improve image contrast in the highly powered rodent eyes during flood AO imaging, perhaps affording some of the axial sectioning capabilities and resulting resilience to scatter enjoyed by AOSLO. The details of HiLo imaging will be explained in Chapter 6, which presents an exploration of how this technique can be used with a flood AO ophthalmoscope (Zhou, Bedggood et al. 2014) Non-wavefront sensing AO imaging One method proposed to address the challenges in wavefront sensing in the rodent eye was to use image-based, or non-wavefront sensing AO (NS-AO) to completely eliminate the wavefront sensing step (Zommer, Ribak et al. 2006; Hofer, Sredar et al. 2011; Bonora and Zawadzki 2013; Jian, Xu et al. 2014; Wong, Jian et al. 2015). This technique makes direct use of some metric of image quality (Muller and Buffington 1974) to provide feedback for determination of the ideal state of the corrector in a trial and error optimisation approach. This can result in image quality similar or better than WFS-AO, after convergence of the NS-AO algorithm (Hofer, Sredar et al. 2011; Sulai and Dubra 2014). The typical long convergence time is the principal drawback of this method. 50

71 Chapter 1 Literature review NS-AO imaging has been incorporated into scanning modalities such as AOSLO and AO-OCT to obtain images of the photoreceptors, which rivaled or even exceeded the quality of WFS-AO images in the human eye (Hofer, Sredar et al. 2011; Wong, Jian et al. 2015). In addition, NS-AO-OCT was also used obtain B-scan and en-face images of the mouse retinal blood vessels and capillaries (Jian, Xu et al. 2014). The final image quality of NS-AO imaging depends largely on the selection of a suitable image quality metric (Fienup and Miller 2003). The metric should be sensitive to changes in the features of interest and should evolve in some sensible way with changes applied to the deformable mirror (e.g. showing a low increase to a peak and then a decrease in image quality beyond the peak). Since the above studies that incorporated NS-AO were performed with scanning modalities with confocal pinholes, they simply used the average or total frame intensity as the metric, since maximizing light through the confocal pinhole requires minimizing the width of the PSF. However, for a flood AO ophthalmoscope, using average or total frame intensity did not give robust convergence or good images from pilot experiments in this area, which is to be expected since changes in the aberrations, including defocus, ought not to alter average image brightness in a non-confocal system (Sulai and Dubra 2014). Therefore a suitable image quality metric must be established for flood NS-AO imaging. The potential of flood NS-AO retinal imaging was first proposed by Zommer et al. (2006), who outlined how image quality improvements might be achieved in model eyes with a simulated annealing algorithm. However, implementation of flood NS-AO to obtain in vivo retinal images of human and rodent eyes will be shown, for the first time, in a published paper Chapter 7 (Zhou, Bedggood et al. 2015). It will be shown that a different approach than Zommer et al. (2006) was used to maximise an image quality metric found to be more suitable to flood NS-AO imaging, which is a promising technique to improve flood AO image quality in the rodent eye. 51

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73 Chapter 2 Pilot experiment: in vivo flood AO imaging in a rat Chapter 2 Pilot experiment: in vivo flood AO imaging in a rat 2.1 Introduction This chapter describes the pilot experiment conducted on rat eyes using a portable flood AO ophthalmoscope initially designed for human and marmoset eyes, but modified to image the rat. The aim of this experiment was to test and document the imaging capability of the existing flood AO system on rat eyes. The findings of this pilot experiment informed and motivated the optical simulation investigations described in the next chapter. 2.2 Methods Animals used Long Evans rats were used since they are pigmented, and their retinas are less prone to light damage compared to the albino strains (Reuter and Hobbelen 1977), making them suitable for AO imaging. Three adult male rats (aged 8 to 11 weeks) were used and only the right eyes were imaged. All experimental procedures conform to the National Health and Medical Research Council (NHMRC) guidelines on the use of animals for scientific research (2008). All animal handling was performed according to the ARVO statement for the Use of Animals in Ophthalmic and Vision Research. Ethics approval (# ) for these experiments was obtained from the University of Melbourne Animal Ethics Committee Animal handling Prior to imaging, the rat was placed under general anaesthesia via intramuscular injection of ketamine and xylazine (60 and 5 mg/kg; Troy Laboratories Pty Ltd., Smithfield, NSW, Australia). The animal was given a maintenance dose of 50% the original dosage every 30 minutes until the end of the experiment. In addition to general anaesthesia, topical eye drops of a local anaesthetic (0.5% proxymetacaine hydrochloride, Alcaine, 5 mg/ml; Alcon Laboratories, Frenchs Forest, New South 53

74 Chapter 2 Pilot experiment: in vivo flood AO imaging in a rat Wales, Australia) and a mydriatic (0.5% tropicamide, Mydriacyl, 5mg/mL; Alcon Laboratories) were instilled in both eyes at the start of the experiment to eliminate the blink reflex and dilate the pupils. A rigid contact lens was placed on the eye being imaged to provide a clear optical surface and to reduce refractive error, while the other eye was kept moist throughout the experiment with an ophthalmic gel (0.3% hypromellose, GenTeal Gel, 3mg/g; Novartis Pharmaceuticals, North Ryde, New South Wales, Australia). The appropriate contact lens power was determined by retinoscopy and wavefront sensing, which agreed with the range given by Geng et al. (2009) of 0 to +20 D (Geng, Greenberg et al. 2009). After some trial and error, it was found that a rigid contact lens (Contact Lens Centre Australia, Clayton, Australia) with a total diameter of ~ 7 mm with a bicurve design, front optic zone diameter of 4 mm, base curve of 3.2 mm and power of ~+10 D performed the best. While we found that lens centration was not robust, with the lens drooping under its weight by about 1 mm and mislocalizing laterally by a similar amount, this settled into a stable position quickly on the eyes of all rats so that usable SHWS spots were obtained. After fitting the contact lens, the animal was securely wrapped in a disposable surgical mat to preserve body temperature, before being gently fastened to a simple small animal platform shown in Figure 2.1 (a redesigned small animal stage that allowed three-axes rotation was made for subsequent experiments and is shown in Chapter 5). During the experiment, body temperature of the rat was maintained with a circulating water heat pad that was secured underneath the platform. Whiskers on the right side of the rat were gently taped to avoid obstruction of the optical path for imaging. The rat s right pupil was then aligned approximately with the entrance pupil of the flood AO ophthalmoscope, and a trial lens was placed as close to the eye as possible to correct gross defocus refractive error prior to AO imaging. After the experiment, the animal was allowed to recover from the anaesthesia. 54

75 Chapter 2 Pilot experiment: in vivo flood AO imaging in a rat Figure 2.1. Small animal platform for the rat used in the pilot experiment. The platform was subsequently re-designed to allow for controlled 6-degree-of-freedom adjustments, as described and shown in Chapter Flood AO ophthalmoscope Figure 2.2 shows the setup of the primate (human/marmoset) flood AO ophthalmoscope adapted to image rat eyes for the pilot experiment. Note that the lenses and mirrors are labelled in the imaging channel only. There were seven mirrors (M1 to M7, excluding the deformable mirror (DM)) and three lenses (L1 to L3) in the imaging channel. M3 and M5 were curved mirrors, whilst the others were flat mirrors. The DM (Mirao 52d Imagine Eyes, France) had a diameter of 20 mm and 52 actuators, and enabled real-time (up to 15 Hz) aberration correction. The Shack-Hartmann wavefront sensor (SHWS) was constructed from a CCD camera ( CL, Pulnix America Inc., CA) attached to a Shack-Hartmann lenslet array of 0.4 mm pitch and 24 mm focal length (Adaptive Optics Associates, Cambridge, MA). The dashed-dot lines in Figure 2.2 indicate the light paths in the illumination channels for both the imaging and wavefront sensing (WFS) lights, whilst the dashed lines indicate the light paths in the imaging and WFS channels. The DM and SHWS lenslets were made optically conjugate to the exit pupil of the eye, whilst the AO imaging camera was made conjugate to the retina. A maximum retina field-of-view (FOV) of ~3 55

76 Chapter 2 Pilot experiment: in vivo flood AO imaging in a rat deg in diameter was obtained with this setup, and magnification was ~61x based on calculations made with a schematic rat eye. The AO imaging light source was a 670 nm laser diode (Model: RS ; MeshTel, aka Intelite, Inc. Genoa, NV, U.S.A.), passed through a 400 m long multimode optical fibre (FT400EMT, Thorlabs, Newton, NJ) to decrease coherence by way of modal dispersion, thereby reducing speckle contrast in images. Image acquisition of the AO imaging camera (Megaplus 4020C, Princeton Instruments, Trenton,NJ) was at 15 Hz with 5 ms exposure time, which was synchronised to the flash duration of the imaging light source. The WFS source was a super-luminescent diode (SLD) centred at 830 nm and pulsed at 15 Hz, which was synchronised to the CCD of the SHWS. The imaging and WFS light sources had powers of 360 μw and 12.5 μw at the cornea, respectively. At these levels and pulse frequency, the powers were within the maximum permissible exposure for 60 seconds of repetitive pulse exposure in humans (Delori, Webb et al. 2007). Due to the difference in wavelengths, the imaging and WFS lasers could be effectively separated by a dichroic beam splitter placed in front of the SHWS. 56

77 Chapter 2 Pilot experiment: in vivo flood AO imaging in a rat Figure 2.2. Primate flood-illumination AO ophthalmoscope adapted for imaging the rat in the pilot experiment. Some key components are indicated with red arrows. Dash-dot lines: light paths in the imaging and WFS light delivery channels; dashed lines: light path in the AO imaging and WFS channels; dichroic BS: dichroic (wavelength selective) beam splitter; DM: deformable mirror; Pellicle BS: 92/8 beam-splitters; SHWS: Shack-Hartmann wavefront sensor. The imaging light source was a 670 nm laser diode. The wavefront sensing light source was an 830 nm superluminescent diode. Intermediary lenses and mirrors were labelled as L# and M# in the imaging channel, respectively. M3 and M5 were curved mirrors, the rest were flat mirrors. Focal lengths of refracting/reflecting components: L1 = 125 mm, M3 = 500 mm, M5 = 200 mm, L2 = 100 mm, L3 = 400 mm. Pupil size: 3.75 mm for rat eye imaging (limited by clear aperture of the Mirao DM). During each imaging sequence, which usually took less than a minute, the total RMS wavefront errors and individual Zernike coefficients were displayed on a computer screen in real time. The AO loop would then be activated which would result in rapid reduction of the RMS wavefront errors due to correction of aberrations by the DM. Once the RMS wavefront errors reached a minimum, a quick succession of flashes was delivered from the imaging light source, and a movie (usually consisting of 25 frames) was captured by the imaging camera at up to 15 Hz. This sequence was then followed by a pause of a few seconds as buffered data was saved to the hard-drive. 57

78 Chapter 2 Pilot experiment: in vivo flood AO imaging in a rat To determine the best focal plane for the retinal vessels, different through-focus images were also captured by adding various amount of defocus to the DM during movie acquisition. Large retinal blood vessels could often be identified. The imaging field-ofview, as well as the pupil diameter of the AO ophthalmoscope were adjusted empirically throughout the experiment to obtain the best contrast for blood vessels. Due to the high magnification and small FOV of the rat eye using the current setup, navigating the retina during AO imaging could be challenging. To alleviate this problem, a low magnification retinal fundus photo of the rat s right eye was taken with a rodent fundus camera (Micron III, Phoenix Research Laboratories, CA) prior to the AO imaging session. The fundus photo was used as a guide to navigate the rat s retina during AO imaging. 2.3 Results and discussions The capability of the flood AO ophthalmoscope described in this chapter to obtain high resolution AO retinal images is demonstrated in Figure 2.3, which shows the retina from the left eye of a healthy human subject, 2 temporal to fixation. It can be seen that the photoreceptor mosaic and retinal capillaries from the same retinal area are clearly resolved under 670 nm light after AO correction. It should be noted that the focal length of L1 in the AO ophthalmoscope was 200 mm for human imaging, but this was the only modification made compared with the rat imaging set-up. The SHWS spot quality from the human eye was good, allowing consistently accurate wavefront sensing and correction by the DM. 58

79 Chapter 2 Pilot experiment: in vivo flood AO imaging in a rat Figure 2.3. AO images of human cone mosaic and capillaries from the left eye of a healthy human subject at 2 temporal to fixation. The images were contrast-stretched to fill their colour maps for display purposes. Scale bar = 50 µm. In contrast, Figure 2.4 shows a representative example of the best-corrected image of a large blood vessel in the rat, at a location superior to the optic nerve head. It can be seen from the contrast-stretched image that the blood vessel wall still appeared blurred after best AO correction. The striation of the nerve fibre layer is faintly visible towards the bottom right of the image. Repeated AO imaging on two other rats resulted in similar image quality. The optical media of the rats were confirmed to be nominally clear with direct ophthalmoscopy prior to AO imaging, ruling out gross media opacity as the cause for blurred images. 59

80 Chapter 2 Pilot experiment: in vivo flood AO imaging in a rat Figure 2.4. Representative best AO image of a large blood vessel in the rat eye in the pilot experiment. The image was contrast-stretched to fill the colour map for display purposes. Image quality is substantially worse than the human images acquired with the same system (Figure 2.3). Scale bar = 20 µm. Recall from the literature review that AO image quality from the rat eye was expected to be better than the human eye since the former has more than double the numerical aperture compared to the latter. However, the results from this experiment showed the contrary. In addition to blood vessels, attempts were also made to image photoreceptors in the rat without success. It is possible that this failure was partially due to the fact that the rat retina is has a much higher rod to cone ratio (100:1) (La Vail 1976) compared to human (20:1) (Hecht and Zajac 1974), and that rodents do not have a macula where the cones concentrate. Since rods do not waveguide (reflects light back in the same direction as it originates) as well as cones (Pallikaris, Williams et al. 2003), high contrast images of photoreceptors were difficult to be recorded using flood AO. The poor image quality shown in Figure 2.4 can be ascribed to a combination of factors, including intra-ocular scatter and poor wavefront sensing quality compared to that achieved for the human eye. In this experiment, the same wavefront sensing beam was used as for human eye imaging, which had a small diameter (<1 mm) to improve depth of focus for the SHWS beacon. Despite this, the SHWS spots were much blurrier in rat than in human eyes, with appearance similar to those shown by de la Cera et al. (2006) 60

81 Chapter 2 Pilot experiment: in vivo flood AO imaging in a rat in the mouse eye. Subsequently published systems in the field of rodent AO imaging (Geng, Schery et al. 2011) have instead employed a wide aperture input beam for the SHWS beacon (which fills the pupil of the animal), reflecting this beam from the deformable mirror on its way into the eye so that intrinsic SHWS spot quality improves as the AO-correction loop proceeds. In our pilot system, which lacked this feature, large refractive errors therefore acted to blur the SHWS beacon on the retina, such that each spot of the SHWS pattern was diffuse and low contrast, which frustrated individual centroid determination and reduced overall wavefront-sensing accuracy. Attempts were made to improve intrinsic SHWS spot quality by inserting different trial lenses as close to the eye of the rat as possible to correct for large defocus refractive error. However, despite these efforts only minimal improvement in the SHWS spot pattern was observed. Unfortunately, the SHWS spots were not recorded from this experiment. Improvement of the SHWS spot quality can be realised using a WFS light with a large diameter that fills the pupil, with an adjustable focus as recommended by Geng et al. (2011). This is shown in the design of the rat flood AO ophthalmoscope in Chapter 4. As a result of the blurry SHWS spots in the pilot system, the reported residual RMS wavefront error generally reduced from ~0.4 µm (after correction with a trial lens) to ~0.1 µm after AO as fit over a 3.75 mm pupil, (compared to the ~0.05 µm routinely obtained over a 6 mm pupil in the human eye). Although the residual RMS was not excessively high, it could be a spurious measurement from the degraded SHWS spots for all the reasons described above, and that actual wavefront quality was substantially worse than suggested by a wavefront RMS of 0.1 µm. In addition to the poor image quality, technical difficulties were experienced when aligning the animal s eye with the system using the simple small animal platform. Since the current flood AO ophthalmoscope lacked a pupil monitor, lateral alignment of the rat eye was achieved by observing the SHWS spots. The axial distance of the eye from the first element of the ophthalmoscope was measured with a simple ruler, which imparts an uncertainly of a few millimetres in axial matching of instrument and ocular pupil planes. Locating the desired retinal position to image proved difficult due to the fact that the simple small animal platform was not designed to rotate around the pupil. Due to these difficulties, using a low magnification fundus photo did not help very much with the identification of the retinal location that was seen through the small AO 61

82 Chapter 2 Pilot experiment: in vivo flood AO imaging in a rat ophthalmoscope field of view, making the exact location of, for example, the blood vessel in Figure 2.4 difficult to determine. These experiences stimulated the design and construction of a new small animal platform to address the above issues, and is described in Chapter Conclusion and outline of the following chapters This pilot experiment revealed several challenges when performing flood AO imaging on rat eyes: First, the SHWS spots were intrinsically of poor quality, as has been reported elsewhere in the literature (Irving, Kisilak et al. 2005; de la Cera, Rodriguez et al. 2006; Biss, Sumorok et al. 2007). Given that this issue was not much improved by trial lens prerefraction, it was posited that this is likely due to multiple planes of scatter separated throughout the large dioptric thickness of the rat retina (Geng, Schery et al. 2011). To explore and quantify the effect that a dioptrically thick retina has on aberration correction with wavefront sensing AO, and to allow the trial of potential optical design improvements to rectify this, computer-based optical modelling was performed using both rat and human schematic eyes under several commonly made assumptions in AO imaging (Zhou, Bedggood et al. 2012). The approach and results of these investigations have been published and are described in Chapter 3. Second, improvement in system design of the AO ophthalmoscope was need in order to improve the SHWS spot quality and address the alignment issues of the rat eye in an overall effort to improve the resolution of AO images. Guided by the lessons learned from the optical modelling chapter, a new flood AO ophthalmoscope was constructed specifically for the rat eye. The details of this are shown in Chapter 4. Using the new rat flood AO ophthalmoscope, results from optical modelling were validated using physical model eyes under conditions and manipulations similar to those explored in the optical modelling paper described in Chapter 3. In addition, AO imaging was attempted on the rat eye using the new flood AO ophthalmoscope, and the image quality was compared to this pilot experiment. These investigations are collectively described in Chapter 5. 62

83 Chapter 2 Pilot experiment: in vivo flood AO imaging in a rat Other methods that could potentially improve flood AO image quality in the rat eye were mentioned in the literature review. One of the methods that were explored here was HiLo imaging, which could be used to increase the contrast of flood AO images to better approach that available to confocal scanning methods. HiLo imaging was used in combination with the new rat AO system described in Chapter 4, and the result has been published in a peer-reviewed paper (Zhou, Bedggood et al. 2014), which is described in Chapter 6. In addition, flood AO image quality in the rat eye could be further improved using nonsensing adaptive optics (NS-AO; otherwise known as sensorless AO), which could be used to bypass the challenging wavefront sensing step all together. Details of flood NS- AO imaging have also been published in a peer-reviewed paper (Zhou, Bedggood et al. 2015), which is described in Chapter 7. Finally, the thesis concludes with a general discussion that provides an overview of the findings of this thesis and the future directions recommended for AO imaging of rodent and other highly powered eyes in Chapter 8. 63

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85 Chapter 3 Identifying limitations to adaptive optics image quality in rodent eyes using optical modelling Chapter 3 Identifying limitations to adaptive optics image quality in rodent eyes using optical modelling 3.1 Introduction As the pilot experiments described in the previous chapter show, conventional flood AO image quality from the rat eye remains inferior compared to the human eye, even though the rat eye has more than twice the numerical aperture. An optical modelling experiment was therefore carried out to determine the effect of some commonly held assumptions in the field of human AO imaging when those same assumptions are applied to the higher powered rodent eye. The details of this experiment have been published in a peer-reviewed manuscript which is attached in section 3.2 below (Zhou, Bedggood et al. 2012). Supplementary results that were not included in the paper due to space restrictions are also supplied in section 3.3. Note that the pilot experiment was carried out prior to the publication of focus optimization of the SHWS beacon in rodent eyes as described by Geng et al. (2011). As such, the degraded image quality could also be in part attributed to the quality of the SHWS beacon at the time of the experiment. Optimization of the SHWS beacon is described in the next chapter. 3.2 Paper 1: Limitations to adaptive optics image quality in rodent eyes Attached is a copy of the paper, published in Biomedical Optics Express in July 2012 and reproduced with permission from OSA publishing. 65

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100 Chapter 3 Identifying limitations to adaptive optics image quality in rodent eyes using optical modelling 3.3 Supplementary results for Paper 1 The figures shown in the manuscript above (Paper 1) were selected to most efficiently communicate the key ideas and findings for the purpose of the publication. However, due to space restrictions, some results were mentioned only in passing and corresponding figures were not included in the published manuscript. In this section results supplementing Paper 1 will be presented in detail Results from off-axis points for Fig. 8 in Paper 1 Fig. 8 of Paper 1 showed, for the on-axis case, the effect of error in axial positioning the AO corrector when there is also separation of the planes and wavelengths used for wavefront sensing and imaging. In Paragraph 3 of Section 3.4 in Paper 1 ("Combining the three sources of error to improve image quality") it was mentioned that off-axis points also showed similarly shaped curves to Fig. 8, without showing the actual data for off-axis points. The supplementary graph of Figure 3.1 provides this missing information. The solid curve is the same as the solid curve in Fig. 8 in Paper 1 above, whereas the dashed line shows the residual RMS from a location 10 off-axis. As mentioned in Paper 1, the 10 off-axis point shows a similarly shaped curve as the onaxis case, only shifted upward and horizontally (i.e. at increased axial offset). This means that best achievable image quality is worse and unable to reach the diffraction limit, and that ideal AO corrector axial position is slightly altered. 80

101 Chapter 3 Identifying limitations to adaptive optics image quality in rodent eyes using optical modelling Figure 3.1. Rat schematic eye: Effect of error in corrector position both on- and 10 off-axis. Wavefront sensing and AO correction was performed at 650 nm at the ILM. Imaging was performed at 475 nm at the outer retina, after optimizing for defocus only. For off-axis imaging, the performance curve is shifted both upwards and horizontally (i.e. axially). Optimal axial displacement of the corrector depends on eccentricity, following the general trends shown in Fig. 7 in Paper 1. It is worth noting that the 10 off-axis curve does not reach the diffractionlimit in this case. Dashed horizontal line indicates the Maréchal criterion (λ/14), below which diffraction-limited imaging is possible Reversal of component curves in Fig. 8 in Paper 1 In Fig. 8 of Paper 1, component curves were shown (dot-dash lines) which give the contributions to the overall spherical aberration of both a change in sensing wavelength alone (referred to as fixed plane in Fig. 8) and of a change in sensing plane along (referred to as fixed λ ). In paragraph 4 of Section 3.4 in Paper 1 ("Combining the three sources of error to improve image quality") it was mentioned that the direction of the slopes these component curves, were reversed upon reversal of the sign of displacement between the imaging/sensing planes or imaging/sensing wavelengths. This is an important feature of the residual aberrations arising from the combined manipulations, since it affects the best axial location to place the AO corrector. Figures 81

102 Chapter 3 Identifying limitations to adaptive optics image quality in rodent eyes using optical modelling 3.2 and 3.3 below show these reversals explicitly with change in imaging plane or imaging wavelength alone, respectively. Only residual spherical aberration (SA) is plotted since it is the dominant residual aberration for the on-axis case. The solid lines in Figures 3.2 and 3.3 are the same as the Residual SA componentfixed λ and Residual SA component-fixed plane lines in Fig. 8 of Paper 1, respectively. The dashed lines in Figures 3.2 and 3.3 show the reversal of the residual SA when either the imaging plane or wavelength is reversed. This feature of residual aberration has a significant effect on the corrector position at which minimum residual RMS occurs. Since any real eye will differ from the schematic eyes used to produce this data, the actual corrector position at which minimum residual RMS occurs must be found by trial and error in practice, but this modelling should provide a guide as to where to begin the search. Figure 3.2. Rat schematic eye: Effect of reversing sensing/imaging plane on residual SA at various AO corrector positions, while keeping wavelength unchanged at 650 nm. The relative geometry between the sensing and imaging planes sets the sign of the slope of the curve. 82

103 Chapter 3 Identifying limitations to adaptive optics image quality in rodent eyes using optical modelling Figure 3.3. Rat schematic eye: Effect of reversing sensing/imaging wavelength on residual SA at various AO corrector positions, while keeping retinal plane unchanged at the ILM. The relative offset between the sensing and imaging wavelengths sets the sign of the slope of the curve Testing the validity and robustness of the rat schematic eye results As mentioned in Paper 1, there is a certain degree of variability in the parameters of the rat eye reported in the literature that could potentially affect the modelling results. In order to test the validity and robustness of the conclusions, we systematically varied key parameters in the rat schematic eye and investigated the effect this may have on the residual aberrations. These include refractive error, anterior corneal curvature and asphericity of the cornea, as mentioned in paragraph 3 in the Discussion (Section 4) of Paper 1. The results are presented below Impact of modelling different values of refractive error The original (spherical-equivalent) refractive error of the rat schematic eye was D at the outer retina with a 3.5 mm entrance pupil. Refractive errors ±10 D of this were introduced by varying the axial length, while maintaining the retinal thickness at 170 µm. In each case, wavefront sensing was performed at the ILM while imaging at the 83

104 Chapter 3 Identifying limitations to adaptive optics image quality in rodent eyes using optical modelling outer retina using the same wavelength of 650 nm, compensating for defocus only. The residual RMS is plotted against the axial displacement of the AO corrector for both onand 20 off-axis. As shown in Figure 3.4, residual RMS changed only slightly on-axis, and by about 10% at 20 off-axis when the refractive error had been varied by ±10 D. This reflects the robustness of the rat schematic eye against refractive error, when residual aberration is considered. Figure 3.4. Rat schematic eye: Effect of corrector position in the presence of separation between imaging and sensing planes, after optimizing for defocus only. Refractive errors (RE) ±10 D from the original D (spherical equivalent) were introduced to show the robustness of the rat modelling results against refractive error. Residual RMS was plotted against corrector separation from the exit pupil, all other parameters are identical to Fig. 7 in Paper 1. Dashed horizontal line indicates the diffraction-limit, below which diffraction-limited imaging is possible Impact of modelling different values of anterior corneal curvature The anterior corneal curvature is another parameter that could potentially affect our results, since the cornea has been shown to counter the spherical aberrations from the crystalline lens (Campbell and Hughes 1981). To understand its effect on residual aberrations, it value was varied by two standard deviations either side of the mean value (Hughes 1979a) used in Paper 1, maintaining the same asphericity, while exploring the effects of shifting the image plane away from the wavefront sensing plane. 84

105 Chapter 3 Identifying limitations to adaptive optics image quality in rodent eyes using optical modelling Figure 3.5 shows the effect of imaging-sensing plane separation on residual aberrations, using the same wavelength (650 nm) for sensing and imaging similar to Fig. 3 in Paper 1. The sensing plane is fixed at the ILM while the imaging plane is varied towards the outer retina 170 µm away. The original corneal curvature used in Paper 1 was 2.97 mm, which was the mean value in Hughes (1979a) from 15 eyes. Using corneal curvature values two standard deviations either side from the mean, we calculated residual aberrations at two image locations: on-axis and 20 off-axis. Figure 3.5. Rat schematic eye: Effect of separation between imaging and sensing planes after optimizing for defocus, with various corneal curvature values. Original corneal curvature used in Paper 1 was 2.97 mm. Curvatures two standard deviations either side of the original value are also plotted here. It can be seen that residual RMS values using different corneal curvatures are similar in magnitude, with about 13% difference in value between 3.16 and 2.78 mm at the maximum separation of imaging planes at 20. Dashed horizontal line indicates the diffractionlimit, below which diffraction-limited imaging is possible. As Figure 3.5 shows, residual RMS values are similar between curvatures of 2.97 and 2.78 mm. Residual RMS values arising from modelling a shallower corneal curvature (3.16 mm) are higher than the other two curvature values, mainly due to increased residual spherical aberration. However, the relative (proportional) increase was less for the off-axis point compared to the on-axis point at the same retinal depths. For example, the relative increase of residual RMS between curvatures 3.16 mm and 2.78 mm is about 80% on-axis at 170 µm retinal depth, compared to about 13% at 20 off-axis at the same retinal depth. It is also worth noting that residual RMS falls below the 85

106 Chapter 3 Identifying limitations to adaptive optics image quality in rodent eyes using optical modelling diffraction-limit for all curvature values on-axis. This shows our results using the rat schematic eye are robust against change of corneal curvatures in the population Impact of modelling different values of anterior corneal asphericity The original rat schematic eye used in Paper 1 contained aspheric curvatures for all refracting surfaces, in line with anatomical data (Chaudhuri, Hallett et al. 1983). The asphericity of the anterior cornea could have an impact on the residual aberrations in our modelling since asphericity typically acts to reduce spherical aberration prior to any adaptive optics correction taking place (Smith, Bedggood et al. 2008). We therefore investigated the effect of a spherical cornea on our modelling and plotted results from both aspheric (filled symbols) and spherical (unfilled symbols) corneas in Figure 3.6 for the case of an error in the position of the imaging plane relative to the sensing plane. Similar to Figure 3.5 in the previous section, residual RMS from the separation of sensing and imaging planes, using the same wavelength, are plotted for various eccentricities. Figure 3.6 shows that in general, residual RMS increases very slightly with a spherical cornea at all eccentricities except on-axis. That is, although uncorrected spherical aberration of the eye could vary markedly between the two conditions, the residual RMS after AO in the presence of error in the imaging plane position was very small. The changes that were present are mainly due to an increase of residual spherical aberration when the anterior corneal curvature changes from aspheric to spherical (the contrary was actually true for the on-axis case). The small change in magnitude of residual RMS when changing the asphericity of the cornea tended to stay approximately constant in absolute terms at various eccentricities, so that the relative impact on residual RMS reduces with increase in eccentricity. Furthermore, diffraction-limited imaging was still achieved at both on- and 10 off-axis locations with both spherical and aspheric corneas. This shows our results using the rat schematic eye are robust against normal change of corneal asphericity in the population. 86

107 Chapter 3 Identifying limitations to adaptive optics image quality in rodent eyes using optical modelling Figure 3.6. Rat schematic eye: Effect of separation between imaging and sensing planes after optimizing for defocus, with aspheric and spherical corneas at various eccentricities. Note that an aspheric cornea was used in Paper 1. It can be seen that changing the corneal asphericity had only a small impact on the residual RMS values, confirming the robustness of the original reported findings for the rat schematic eye. Dashed line indicates the diffraction-limit, below which diffraction-limited imaging is possible. 3.4 Conclusion Adaptive optics imaging of rodent eyes is challenging, but nonetheless still potentially rewarding with their superior numerical aperture and subsequent promise of far better resolution. These modelling experiments identified some of the sources of residual aberration likely to be encountered under real-world imaging conditions. The effects of eccentricity, dispersion from choice of imaging and sensing wavelength, axial positioning of the corrector element and retinal image depth were systematically explored by modelling. The supplemental data presented in this chapter confirms that the rat schematic eye is robust against various changes in parameters and that our conclusions (and advice) can be relied upon. In light of the results from these experiments, modifications to the design of existing flood AO systems, such as correspondence between the plane and wavelength imaging/sensing, tight control over delivery of sensing light and precise axial alignment of the optical system, are recommended in order to improve AO image quality in rodent eyes. These 87

108 Chapter 3 Identifying limitations to adaptive optics image quality in rodent eyes using optical modelling recommendations were adopted in the construction of a new AO system dedicated for rat eyes. The next chapter will give a detailed description of this system. 88

109 Chapter 4 Flood illumination adaptive optics ophthalmoscope Chapter 4 Flood illumination adaptive optics ophthalmoscope 4.1 Introduction From the optical modelling paper (Paper 1) in Chapter 3, it was predicted that human eye imaging should be robust against axial positioning errors of the AO corrector and against differences in retinal depth and wavelength between the wavefront sensing and imaging lights. In contrast, the results predicted that retinal imaging in the higherpowered rat eye would be much less tolerant of these manipulations. The consequence of this was reflected in the reduced wavefront quality from the plane of interest for the rat schematic eye in the presence of these manipulations. In order to obtain good image quality from the highly-powered rat eye in practice, measures must be taken with the design of the AO ophthalmoscope to address these increased tolerance constraints. For instance, wavefront sensing and imaging lights should ideally be focused onto the same retinal plane and have the same wavelength. In addition, precise axial positioning of the eye can be enhanced by using a pupil monitor, thereby reducing positioning errors of the eye relative to the AO corrector. According to the modelling results from Chapter 3, these measures could go a long way to reduce or even eliminate residual aberrations in the highly powered eye, especially for off-axis imaging. Because the retina is a relatively poor reflector of light ( reflected) (Roorda, Miller et al. 2006), any AO ophthalmoscope should also minimise light loss as much as possible. Thus reflective imaging systems using mostly (spherical concave) mirrors are generally preferred over refractive lens-based systems (Bedggood and Metha 2010), since the former results in less light loss and less undesired back reflections. In addition to ocular aberrations, system aberrations should be minimised to ensure the best AO image quality is achieved. The dominant aberration of mirror-based AO ophthalmoscopes is astigmatism in the image plane, due to the off-axis nature of the required reflective telescope components (Webb, Hughes et al. 1987; Burns, Tumbar et al. 2007; Bedggood and Metha 2010). In theory, it is possible to use aspherical mirrors 89

110 Chapter 4 Flood illumination adaptive optics ophthalmoscope to reduce off-axis astigmatism, at least for small fields of view. However, due to the much higher cost of these mirrors, and the difficulties of alignment, spherical mirrors are still preferred. Astigmatism in the image plane introduced by the off-axis use of spherical mirrors reduces linearly with the increase in focal length, and quadratically with the decrease in the angle of incidence (Gómez-Vieyra, Dubra et al. 2009). For this reason, reducing the angle of incidence on spherical mirrors takes precedence over maximising focal length (Dubra and Sulai 2011). Due to the size of the mechanical mounts of the mirrors and other optical instruments in practice, an AO ophthalmoscope with the largest axial length possible should be used to reduce angle of incidence. In other words, spherical mirrors with longer focal lengths, arranged so that the angle of incidence is the smallest possible should be used to reduce astigmatism in the image plane. Apart from the image plane, design consideration should also be given to reduce astigmatism in the pupil conjugate planes (optical planes in the AO ophthalmoscope where the eye s pupil is imaged), where the wavefront sensor and deformable mirror are placed (Gómez-Vieyra, Dubra et al. 2009), thus improving the performance of wavefront sensing and subsequent correction. To achieve this, Gómez-Vieyra et al. (2009) showed that by folding two afocal telescopes in a non-planar configuration, it is possible to minimize astigmatism in all pupil conjugates as well as the image plane at one point of the field of view (a non-planar configuration is to be understood in contrast to a planar configuration, where the light path is contained within a single plane). More recently, Dubra and Sulai (2011) implemented the design concepts described in Gómez-Vieyra et al. (2009) as a mirror-based AOSLO with the reflective telescopes arranged in a non-planar configuration, which eliminated most system aberration in the final image plane as well as all pupil conjugate planes. They showed that by combining two telescopes folded at 90 to each other, which is the largest possible angle in a non-planar configuration, astigmatism accrued by one telescope can effectively be combined with the other to create what is essentially defocus aberration, which can then be corrected by adjustments in axial length. Recall from section 1.9 in the literature review that wavefront sensing is challenging in rodent eyes since early studies showed degraded Shack-Hartmann wavefront sensor (SHWS) spot quality (Irving, Kisilak et al. 2005; de la Cera, Rodriguez et al. 2006; 90

111 Chapter 4 Flood illumination adaptive optics ophthalmoscope Biss, Sumorok et al. 2007). This could be due to the dioptrically thick retina in the highly powered rodent eye as explained in a recent study by Geng et al. (2011). As a comparison, the change of focus needed to traverse the anterior to posterior retina of the rat and the mouse is ~11 D and ~30 D respectively (Geng, Greenberg et al. 2009; Geng, Schery et al. 2011), whereas only ~0.7 D is required for the human retina (Chan, Duker et al. 2006). Geng et al. (2011) showed a bimodal appearance of the SHWS spots in the mouse eye that worsened towards the edge of the pupil. They found that this occurred due to reflections of the WFS beam from the anterior and posterior retinal layers in the highly powered mouse eye, as a result of the small diameter of the WFS beam. A small WFS beam diameter is typically used in human AO imaging to increase the depth of focus so that the SHWS spots are less susceptible to focus and aberration artefacts on the first pass into the eye (Liang, Grimm et al. 1994). In order to overcome the bimodal spot patterns, they found that a large diameter WFS beam should be used, which filled the dilated pupil of the animal, to reduce the depth of focus in the mouse eye (Geng, Schery et al. 2011). In addition, the centre of the WFS beam was made hollow to avoid corneal reflection. Thus an annular WFS beam with a large diameter that fills the entrance pupil of the eye is required for good quality SHWS spots in the rodent eye. In this chapter, the design of a mirror-based, flood AO ophthalmoscope for the rat (called rat AO ophthalmoscope or simply AO system henceforth) is presented. The practical implementation of the aforementioned measures to reduce aberrations and improve the quality of the SHWS spots in the rat eye is also described in detail. The same rat AO ophthalmoscope was used in all subsequent experiments in this thesis. 4.2 ZEMAX modelling The design of the rat AO ophthalmoscope was first carried out using the optical design software ZEMAX (Zemax Development Corporation, Bellevue, Washington, USA) General aspects Before designing the system, the object and image spaces needed to be defined first. In order to simplify the design of the AO ophthalmoscope, the object point was taken to be on-axis at infinity such that a plane wavefront impinged upon the system (i.e. no schematic eye was used). This is equivalent to a flat wavefront emitting from a point 91

112 Chapter 4 Flood illumination adaptive optics ophthalmoscope source on the retina of an ideal eye, which is free of aberrations. The entrance pupil of the system was positioned where the exit pupil of the eye would be, one focal length away from the first element of the system, which was a 250 mm achromatic lens (see Figure 4.1 in section 4.2.4). Note that an achromatic lens, instead of a spherical mirror, was used as the first refracting element closest to the eye to improve system performance over the entire field-of-view (FOV), as demonstrated by Geng et al. (2012). The final image space of the system was defined at the location of the chargecoupled-device (CCD) of the retinal camera, where the light rays converge to form the image of the object point. The diameter of the entrance pupil was 3.75 mm, which is roughly the size of a dilated pupil of the rat eye. System magnification was chosen so that the pupil image size at the deformable mirror (DM) was 15 mm (x4 magnification), which corresponded to the usable area of the Mirao 52d DM from Imagine Eyes with 52 actuators (Imagine Eyes, Orsay, France). In addition, the pupil image size at the lenslet array of the SHWS was 7.5 mm (x2 magnification). The Ray Aiming feature in ZEMAX was enabled, and set to Paraxial. Ray aiming ensures the chief ray passes through the centre of the pupil, thus avoiding vignetting by a decentred pupil such as in the human schematic eye (vignetting occurred when all or part of the cone of light strikes the edge of an optical component or its mechanical mount). Although a decentred pupil was not used in the design of the AO ophthalmoscope itself, the Ray Aiming feature was enabled at all times to ensure consistency. The primary wavelength used for the design was 670 nm, which was the longest wavelength used in the real experiments. The shortest wavelength was 532 nm, which would provide maximum contrast for imaging blood vessels, due to strong absorbance by haemoglobin in erythrocytes (Tam, Martin et al. 2010). The vergence difference between these two wavelengths was ~0.25 D in the AO ophthalmoscope due to dispersion. The angles of eccentric beams were referenced to the entrance pupil of the system. The maximum FOV of the AO ophthalmoscope was 4.8, which could be obtained by 92

113 Chapter 4 Flood illumination adaptive optics ophthalmoscope passing the imaging beam through a multimode optical fibre (FT400EMT, Thorlabs, Newton, NJ) with a 400 µm core. Since ZEMAX models only the size of naked (i.e. unmounted) optical components, clearance for their mechanical mounts was also taken into account when tracing the eccentric light rays through the system to ensure vignetting did not occur at the mechanical mounts along the ray path over the entire FOV. It is also worthwhile to note that a three-dimensional map of the AO ophthalmoscope can be viewed in ZEMAX, which can be used to visualise the relative positions of the optical components. The coordinate of the system map is specified using the right hand rule, in which positive Z-axis (thumb) points towards the right, positive X-axis (index finger) points into the screen, and positive Y-axis (middle finger) points upwards Modelling optical surfaces The optical components of the AO ophthalmoscope were modelled in ZEMAX as different surfaces, whose properties and the properties of the optical medium immediately after them were specified by various parameters within the rows and columns of ZEMAX's Lens Data Editor. For example, each surface is represented by a row in the editor; the separation between two surfaces is specified by the Thickness column of the first surface, while the extent of a surface can be specified in the Semi- Diameter column. The ZEMAX program allows for tracing of real or paraxial light rays through all surfaces, according to the geometric or paraxial laws of optics respectively. Optical components were gradually added to the AO ophthalmoscope model, starting with the achromatic lens closest to the eye (see Figure 4.1 in section 4.2.4). A number of surface types were used in the modelling. Firstly, the Standard surface was used for optical components such as lenses and mirrors, and is the default surface type. However, the lens catalogue contained in ZEMAX can also be conveniently used to model real lenses with accurate metrology information provided by the lens suppliers. All lenses used were Thorlabs ( achromatic doublets with anti-reflection coating in the visible wavelength range ( nm). The most curved 93

114 Chapter 4 Flood illumination adaptive optics ophthalmoscope surfaces of the lens was pointed towards the collimated side of the beam to reduce spherical aberration. Secondly, the Zernike Standard Phase surface was reserved to model the deformable mirror. This surface can be used to simulate AO correction of the deformable mirror by optimising the individual Zernike terms which are used to specify it, and which result in the corresponding phase profile being implemented across the beam. Lastly, a Coordinate Break surface was used to change the angle of incidence of light rays on mirrors. This surface specifies that the components downstream of the break be tilted or decentred by a certain amount relative to the system before the Coordinate Break. For example, mirror surfaces were inserted with two Coordinate Breaks by default, one before the surface and the other after. In a non-planar system configuration, the angle of incidence of light rays on a mirror can be specified in the horizontal and/or vertical planes in the Coordinate Break before the mirror surface. The angle of reflection can then be automatically matched to that of the incidence Optimisation of angles of incidence The angles of incidence of beams on the spherical mirrors needed to be optimised in the non-planar design in order to reduce astigmatism simultaneously at the retinal and pupil conjugates. The metric chosen to quantify the effectiveness of the optimisation process was the root-mean-square (RMS) wavefront error at the respective conjugates. RMS wavefront error was chosen due to the ease of obtaining this measurement in ZEMAX, and the fact that it represented the total aberration present at a particular conjugate. For optimisation of aberrations in retinal conjugates, the object was placed at infinity, as described above. For optimisation of aberrations in pupil conjugates, the object was placed at the eye s exit pupil. The RMS wavefront error at an image plane was calculated using coefficients of individual Zernike terms (37 terms by default). The Zernike terms are measured over a default 64 x 64 square grid encompassing the circular entrance pupil. Note that the ordering of Zernike terms in ZEMAX differs slightly to the standard used in ophthalmic optics (Thibos, Applegate et al. 2002), and the coefficients are expressed in units of 94

115 Chapter 4 Flood illumination adaptive optics ophthalmoscope wavelengths and are normalized. However, all results were converted to the standard ordering (Thibos, Applegate et al. 2002) for reporting where applicable. Each retinal and pupil conjugate was optimised individually and in order along the ray path to minimise the aberrations of the entire AO ophthalmoscope. To achieve this, a draft AO ophthalmoscope with a planar design was constructed first with the essential components. Then the pupil or retinal conjugate in question was set to be the image plane, while all components downstream of that conjugate was deleted. During the optimisation process, the angles of incidence on the spherical mirrors that resulted in the least RMS wavefront error in the image plane was calculated using the optimisation function in ZEMAX (the angle of reflectance was automatically matched to the angle of incidence). The angles of incidence in both horizontal and vertical planes were optimised, resulting in the non-planar system configuration. In cases where the calculated angle of incidence was too small to accommodate the mounting hardware, it was manually increased by trial and error to ensure the RMS wavefront error remained small while leaving sufficient clearance for the mechanical mounts. After optimisation of the angles of incidence on spherical mirrors, the RMS wavefront error of the AO ophthalmoscope (before the DM was used to correct for aberrations) reached λ/144 at the DM (pupil conjugate), λ/102 at the SHWS (pupil conjugate), and λ/60 at the AO imaging camera (retinal conjugate), indicating diffraction-limited imaging was achieved surpassing the Maréchal criterion (Born and Wolf 1999) of RMS wavefront error λ/ Complete AO ophthalmoscope layout A bird s-eye view of the non-planar, flood-illumination rat AO ophthalmoscope showing the scaled dimension and location of the optical components is presented in Figure 4.1. Collimated light rays from the eye, representing a plane wavefront emanating from an on-axis retinal point, are refracted first by an achromatic lens (L1) with an anti-reflection coating for visible wavelengths ( nm), placed 250 mm away from the eye. As mentioned above, the purpose of the achromatic lens was to increase system field-of-view, and also reduce chromatic aberration, a similar design to the mouse AOSLO described by Geng et al. (2012). The ordering of the optical 95

116 Chapter 4 Flood illumination adaptive optics ophthalmoscope components in the direction of the propagation of light is (see figure caption for legend): L1 M1 CM1 Trial lens CM2 CM3 DM CM4 CM5 M2 BS L2. Figure 4.1. Scaled bird s-eye view of the rat AO ophthalmoscope using a non-planar design. The components that are at the initial and final system heights of 240 mm and 130 mm are labelled with black and red letters, respectively. The focal lengths (in mm) of the refractive and reflective components are also shown. Legend: L: lens; M: flat mirror; CM: curved (spherical) mirror; DM: deformable mirror; BS: beam splitter; P: pupil conjugate. Scale bar = 100 mm. Since the system adopted a non-planar design, some components appear overlapped in Figure 4.1. In order to illustrate the different height of the components, Figure 4.2 shows the front view of the AO ophthalmoscope, as seen from the imaged eye looking into the page. It can be clearly seen that the system height reduces most from CM2 to CM3. 96

117 Chapter 4 Flood illumination adaptive optics ophthalmoscope Figure 4.2. Front view of the AO ophthalmoscope as seen by the eye being imaged. The initial and final heights of the ophthalmoscope are also shown to the right. See Figure 4.1 in combination with this figure to understand the system layout and for legend. All lenses and spherical mirrors were separated by the sum of their focal lengths, forming three pairs of afocal telescopes. The initial system height was 240 mm from the optical bench, as shown in Figure 4.2 (The light delivery, widefield and pupil camera arms were all at a height of 240 mm. See Figure 4.3 for details). The angles of incidence on the reflective components of these telescopes are shown in Table 4.1. The first afocal telescope formed by L1 and CM1 was contained within the horizontal plane, with a horizontal angle of incidence (Ix) of -1.8, and vertical angle of incidence (Iy) of 0. The second pair of telescope formed by CM2 and CM3 was contained within the vertical plane, therefore at 90 to the first pair. The system height dropped from the initial 240 mm at CM2 to 110 mm at CM3, due to the vertical tilt of CM2. The system height then increased slightly to 130 mm, the final system height, at the DM. After the DM, the remaining components were confined within the horizontal plane at 130 mm high. This included the third pair of telescope formed by CM4 and CM5, and the remaining optical components of M2, BS, L2 and the imaging camera. In addition, the wavefront sensing arm (shown in Figure 4.3) was also at 130 mm high. 97

118 Chapter 4 Flood illumination adaptive optics ophthalmoscope Table 4.1. Focal length and angles of incidence onto the optical elements in the imaging path of the AO ophthalmoscope (L: lens; M: flat mirror; CM: curved (spherical) mirror; DM: deformable mirror). Optical element Focal length (mm) I x (degrees) I y (degrees) L M1 NA CM CM CM DM NA CM CM Flood illumination adaptive optics ophthalmoscope In this section, the hardware of the actual AO ophthalmoscope, including the illumination, wide-field and wavefront sensing arm are presented in detail. In addition, software control of the system is also described Flood AO ophthalmoscope layout The complete, scaled (1:1) physical layout of the flood-illumination AO ophthalmoscope is shown in Figure 4.3. All lenses used were achromatic doublets with a 2-inch (50.8 mm) diameter, with anti-reflective coating in the nm range to minimize light loss from reflection. Flat mirrors with 1- (25.4 mm) and 2-inch diameters were used to fold light rays. The spherical mirrors CM1 and CM2 were 75 mm in diameter, in order to accommodate an FOV diameter of 4.8. The remaining spherical mirrors, CM3 to CM5 were 2 inches in diameter. All mirrors were silver-coated to maximize reflection for visible and near-ir light. The focal lengths of all refractive and reflective components are labelled in Figure 4.3. The AO imaging arm designed in ZEMAX is flattened (i.e., all angles converted to the horizontal plane) and shaded in gray for visualization. Compared to Figure 4.1, which shows only the AO imaging arm modelled in ZEMAX, Figure 4.3 also shows other arms of the system, which are described below. 98

119 Chapter 4 Flood illumination adaptive optics ophthalmoscope Figure 4.3. Scaled (1:1) layout of the non-planar design flood-illumination AO ophthalmoscope, flattened for visualisation. The focal lengths (in mm) of the refractive and reflective components are also shown. Note that the distance between the two Fibre ports is not to scale. Lasers of various wavelengths (532, 593 or 670 nm) could be easily substituted as the imaging and WFS light sources. Legend: BS: 50(T)/50(R) wedge beam splitter; CM: curved (spherical) mirror; DM: deformable mirror; FM: flip mirror; M: flat mirror; P: unused pupil conjugate; Pellicle BS: 92(T)/8(R) pellicle beam splitter; SPR: spatial phase randomiser (see description in section ); WFS: wavefront sensing. FM labelled with an asterisk (*) indicates the flip mirrors used to switch between the wide-field (dashed line indicating light path) and AO arms. SPR 1 was only inserted to eliminate laser speckle when required. SPR 2 was used in all experiments to eliminate speckle in the WFS light. Gray area indicates the flattened ZEMAX diagram. Scale bar: 100 mm Illumination arm The illumination arm is shown on the left of Figure 4.3, where two separate illumination channels were used for the WFS and imaging lights. The WFS light source was one of three diode-pumped solid-state (DPSS) lasers (Altechna, Vilnius, Lithuania) with various nominal centre wavelengths (532, 593 and 670 nm). Since DPSS lasers are moderately coherent, they were used in conjunction with spatial phase randomizers (SPRs) (Md Lasers & Instruments, Inc, Pleasanton, CA) to modulate the time average coherence, and hence reduce speckle, in the SHWS spot images. The WFS lasers were arranged in a way so that the different wavelengths could 99

120 Chapter 4 Flood illumination adaptive optics ophthalmoscope be easily interchanged by using flip mirrors (not shown in Figure 4.3) without affecting system alignment. The vergence of the WFS light could be adjusted by inserting trial lenses in the Trial lens plane at the bottom left of Figure 4.3, which was made conjugate to the eye s pupil. The imaging light source was either a 532 nm DPSS laser (same manufacturer as the WFS laser) or a 670 nm laser diode (MeshTel, Genoa, NV, U.S.A.). The 670 nm laser diode was used for model, rat and human eye imaging to take advantage of its low amount of speckle, and the 532 nm wavelength was intended to be the imaging light for blood vessels in the rat eye in some of the experiments, due to its strong absorption by haemoglobin (Tam, Martin et al. 2010). The imaging light source was initially passed through 400 m of multimode optical fibre (FT400EMT, 0.39 NA, 400 μm core, Thorlabs, Newton, NJ). The optical fibre tip was nominally imaged onto the retina, resulting in an illuminated area subtending a diameter of ~4.8. The beam diameter at the pupil was ~4 mm, which filled the entire pupil of the rat eye. The 400 m length of multimode optical fibre was required to reduce the coherence of the imaging light sources by modal dispersion, hence reducing speckle in the final retinal image. However, it also led to ~75% 85% power loss for the imaging lights, which had a maximum output power of 350 mw and 100 mw respectively for 670 and 532 nm. The remaining power (~70 mw and 20 mw respectively for 670 and 532 nm) was found to be sufficient for model eye imaging using both wavelengths, but insufficient for in vivo imaging of the blood vessels in the rat eye using the 532 nm light. Due to the excessive light loss with the 400 m fibre, a much shorter, 2 m fibre (BFL37-200, 0.37 NA, 200 μm core, Thorlabs, Newton, NJ),was used for most in vivo experiments instead, which resulted in an illumination area of ~2.4 on the retina. Due to the much shorter length of the 2 m fibre, the output of the imaging light was found to contain excessive speckle. In order to reduce speckle in the imaging lights while using the 2 m fibre, another SPR could be inserted in the imaging light path as shown in Figure 4.3. The combined power loss of the imaging light through the 2 m fibre and the SPR was found to be ~20%. The remaining power was sufficient for in vivo imaging of the rat eye using either imaging wavelength. 100

121 Chapter 4 Flood illumination adaptive optics ophthalmoscope In AO retinal imaging, the wavefront sensing and imaging lights traditionally differ in wavelengths to allow efficient channel separation using dichroic mirrors. However, in the experiments in this thesis, the same wavelength for WFS and imaging was used whenever possible, as it was predicted by the modelling work in Chapter 3 that this could improve the AO image quality, particularly in the rat eye (Zhou, Bedggood et al. 2012). As a result, no dichroic mirrors were used in the AO ophthalmoscope. In order to avoid WFS light being coupled into the imaging camera, or the imaging light being coupled into the WFS camera due to their identical wavelength, the WFS and imaging lights were modulated in counter-phase at the camera frame rate of 15 Hz using a National Instruments programmable voltage controller (PCIe-6323, National Instruments, Austin, TX). To separate light between the different arms, a total of three beam-splitters (BS) (BSW16, Thorlabs, Newton, NJ) with 50% transmittance and reflectance were used in the illumination and AO imaging arms Wide-field imaging and pupil monitor arm Recall that in the optical modelling paper in Chapter 3, it was found that precise axial positioning of the highly powered rat eye was important for minimising residual aberrations, when the focus of the wavefront sensing and imaging lights were separated by the full retinal thickness. In order to precisely align the pupil of the eye with the system s entrance pupil, and to explore the retina of the rat in low magnification, an extra arm (called wide-field arm henceforth) was built with both a pupil and a (widefield) retinal camera (both were the same model, A102f, Basler AG, Ahrensburg, Germany). The wide-field arm consisted of separate light delivery and imaging paths from the AO arm, and are shown as dashed lines in Figure 4.3. These paths were enabled as needed through the use of appropriate flip mirrors (marked with an asterisk in Figure 4.3). The retinal areas on the pupil and wide-field retinal cameras were centred with the WFS and AO imaging cameras in the AO arm, respectively, so that alignment of the eye only needed to be performed once in the wide-field arm. The FOV of the wide-field retinal camera was approximately double that of the AO imaging camera. Several flip mirrors marked with asterisks in Figure 4.3 (*FM) were used to engage and disengage the wide-field arm. When aligning the animal at the start of the experiment, 101

122 Chapter 4 Flood illumination adaptive optics ophthalmoscope the flip mirrors were used to divert all light from the AO arm to the wide-field arm. Using flip mirrors instead of beam-splitters had two advantages. First, it limited light power that would be lost by sharing light with the AO arm. Second, it ensured minimal light power was required entering the eye, hence reducing the chance of damage to the retina of the rat. The pupil and wide-field retinal cameras were separated by a pellicle beam-splitter (BP108, Thorlabs, Newton, NJ), which transmits and reflects 92% and 8% of the light, respectively. The gain and exposure time of the two cameras were adjusted accordingly due to the unequal distribution of light power AO arm The illumination and imaging paths of the AO arm are shown in solid lines in Figure 4.3. The retinal FOVs were 2.4 (real rat eye) and 4.8 (model eye) using the 200 µm and 400 µm core optical fibres, respectively. Light reflected from the retina then traveled through the AO ophthalmoscope as described in the ZEMAX modelling section, before being split by a 50/50 beam-splitter into the WFS and AO imaging cameras. The SHWS was constructed from a CCD camera (Pike, Allied Vision Technologies, Stadtroda, Germany) with a Shack-Hartmann lenslet array of 0.4 mm pitch and 24 mm focal length (Adaptive Optics Associates, Cambridge, MA) attached, which operated at ~20 Hz during AO imaging. The magnification of the eye s pupil at the WFS was x2 and ~293 lenslets were used for wavefront sensing over a 3.75 mm pupil. The AO imaging camera was also a CCD (Megaplus 4020C, Princeton Instruments, Trenton,NJ) with 7.4 µm pixel sizes, capable of obtaining images at ~15 Hz. The actual exposure time of the camera during imaging was ~3 ms to minimize blur due to eye and breathing movements of the animal. Each pixel on the camera corresponded to ~0.2 μm in the rat eye, assuming an equivalent focal length for the eye of 3.3 mm (Hughes 1979a). The magnification of the rat retina at the CCD of the AO imaging camera was ~x39. To achieve the large vergence range required to image the dioptrically thick retina of the highly powered rat eye the AO imaging camera was placed on a ~60 cm railing, 102

123 Chapter 4 Flood illumination adaptive optics ophthalmoscope allowing rapid and accurate sliding of the camera back and forth to focus on retinal features at different depths. The movement of the camera was calibrated in dioptres, and a scale was placed next to the railing indicating the refractive error of the eye, and hence the dioptric power of trial lenses required to roughly focus the retinal feature onto the camera should it remain at its nominal position. A trial lens could then be placed in the Trial lens plane between CM1 and CM2 to correct for the refractive error, and the imaging camera returned to its nominal position for AO imaging. Returning the imaging camera to its nominal position ensured the WFS and imaging cameras were at the same vergence, hence minimizing non-common path errors as a result of moving the imaging camera away from its nominal position Alignment of components Before aligning the optical components, the WFS and imaging lasers were collimated. For alignment purposes, a 532 nm DPSS laser was used as the WFS light, whereas a 670 nm SLD was used as the imaging light. The different wavelengths made it easier to observe the light during alignment. The WFS laser was already highly collimated at its output; on the other hand, since the imaging laser was passed through the optical fibre, it was collimated by adjusting the collimating lens in the fibre port from which light was emitted. The 400 µm core optical fibre was used during alignment. Since the fibre tip was an extended object with 400 µm diameter, the diameter of the imaging laser beam increased with distance from the source, even though it was collimated. An adjustable aperture stop was therefore placed between the two lenses (f = 200 mm) immediately downstream to the perspex block (shown on the left of Figure 4.3) to vary the diameter of the imaging beam, so that a small diameter could be used during alignment. Co-axial alignment of the two lasers was critical to ensure wavefront sensing and imaging occurred at the same retinal location. Since the paths of the WFS and imaging lasers merge after the first beam splitter, they were aligned carefully to remain coincident several meters downstream, before the addition of other optical components. Care was also taken to ensure the WFS light remained co-axial with the imaging light at both pupil and retinal conjugates. Alignment of the two lasers was aided with two reference targets with the same height at different distances. The target closer to the beam splitter was made from a transparent acetate sheet that allowed transmission of the beam. The second target with identical pattern was made from printing paper. 103

124 Chapter 4 Flood illumination adaptive optics ophthalmoscope Alignment of the beams was achieved when they illuminated the centre of both targets. These reference targets were also used to ensure the centration of the beam after each component was added. Once the WFS and imaging lasers were aligned, the remaining optical components were added carefully using only the WFS light as the alignment light, and ensuring that their addition did not deviate the alignment beam when projected against a wall several metres away. Since alignment of the AO ophthalmoscope using a human eye was obviously impossible, a plane mirror was inserted at the eye s exit pupil plane. Using a plane mirror not only increased light efficiency as it reflected almost all incident light, but also allowed a plane wavefront to be used for the alignment. Lenses were centred using lens mount alignment plates (LMR1AP and LMR2AP, Thorlabs, Newton, NJ). At the centre of these alignment plates is a 1 mm wide pinhole, which allowed light to pass through the centre of the lens. This ensured accurate alignment was made when used in conjunction with the two reference targets placed downstream to the lens in question. As for mirrors, all were mounted on kinetic mirror mounts capable of angular adjustment of ± 3-4 from its nominally straight position (KM100 and KM200, Thorlabs, Newton, NJ). The DM was mounted on a custom-made mirror mount modified from a kinetic mirror mount from Thorlabs, so that it was capable of angular movement around its centre. Centration of light on curved mirrors was achieved subjectively by adjusting the kinetic mirror mount of the previous mirror Positioning of components at pupil conjugates Components such as the trial lens holder, the DM and the lenslet arrays for the SHWS needed to be accurately placed at the planes conjugate to the eye s exit pupil to ensure robust AO correction. To locate the pupil planes, an object was needed at the eye s exit pupil plane where the plane mirror was placed. Recall that the WFS light was used for alignment of the system. At the eye s exit pupil the WFS light had a diameter of ~3.5 mm, and that a plane mirror was placed at the exit pupil position of the eye during alignment. To help locate the pupil conjugates, an older plane mirror with scratches and some loss of silver 104

125 Chapter 4 Flood illumination adaptive optics ophthalmoscope coating was placed at the eye s exit pupil. The imperfection on the mirror was used as the object in the pupil plane. The final pupil conjugate was located first using the WFS camera, with the lenslet array removed. The WFS camera was positioned so that the CCD was at the final pupil conjugate. The WFS camera was then translated axially on a micrometer stage capable of moving at 0.01 mm increments axially, until the imperfections on the plane mirror came into focus subjectively. The axial translation was repeated several times, and the average position was used as the final pupil conjugate. The precision of this method was found to be ~1.5 mm i.e. displacing the WFS camera axially by >1.5 mm from the pupil conjugate plane would result in blurriness of the scratches on the plane mirror. The pupil conjugate at the DM was located next. The DM was also placed on a micrometer stage for fine axial translation. Prior to the alignment, the DM was deliberately offset slightly laterally (perpendicular to the beam) so that the edge of the mirror mount closest to the surface of the mirror was visible in the WFS camera. The DM was then translated axially until the edge of the mount was subjectively the sharpest. This process was also repeated several times, and the average value was taken to be the axial position of the pupil conjugate. After the optimum axial position was found, the DM was carefully moved back to its original lateral position. To locate the pupil conjugate at the trial lens holder in the imaging path, a similar procedure as for the DM was used. Since the trial lens holder was coupled with an aperture stop, which could be decreased in diameter, no lateral translation was needed to view the edge of the trial lens holder. The edge of the aperture stop was sharpened in the WFS camera by translating the trial lens holder axially. Once the positioning of the DM and trial lens holder was satisfactory, the lenslet array was attached back onto the WFS camera. The WFS camera was then carefully translated axially, so that the lenslet arrays rest at the pupil conjugate where the CCD of the camera was. To ensure the accuracy of this procedure, a fine marker was placed on the optical bench to indicate the position of the pupil conjugate. The alignment of the system and positioning of the components at pupil conjugates were repeated several times to ensure the lowest RMS wavefront error prior to AO correction was achieved. The final RMS wavefront error with the DM in its nominally 105

126 Chapter 4 Flood illumination adaptive optics ophthalmoscope flat state, measured by placing a flat mirror at the eye s exit pupil plane, was found to be ~0.05 µm at 670 nm over the full pupil of 3.75 mm, indicating diffraction-limited imaging according to the Maréchal criterion (Born and Wolf 1999). After AO correction was enabled, the residual RMS wavefront error of the system reached a low of ~0.02 µm at 670 nm over the full pupil Minimizing corneal reflection The WFS light had a large diameter (~3.5 mm) at the cornea. As mentioned above, such a large diameter was necessary to reduce the depth of focus of the WFS beam in a highly powered eye such as the rat. Several methods were used in order to avoid corneal reflection being coupled into the WFS and AO imaging cameras from such a large diameter beam. Firstly, a hollow centre was created in the WFS beam by inserting an opaque material (such as a piece of Blu-Tack ) adhering to a small piece of transparent acetate sheet. The diameter of the Blu-Tack was adjusted so that the central 2 mm of the beam was blocked to create an annular beacon. The acetate sheet/blu-tack unit was inserted in the WFS light path a few centimeters after the f = 125 mm lens in the WFS illumination arm on the left of Figure 4.3. It was found that such an annular beacon was needed mostly when imaging the eye on-axis, where the problem of the corneal reflection is most severe. Secondly, an extra afocal telescope was inserted just before the WFS camera as shown in Figure 4.3. An aperture stop with an adjustable diameter was placed one focal length away between the two lenses forming the telescope. Since light from the pupil of the eye was focused at the aperture stop, its diameter could be reduced in order to reject any unwanted reflection from the cornea and other retinal layers. Its initial diameter was at ~2-3 mm. During AO imaging, it could be reduced to as small as ~0.5 mm. It was found that after reducing the diameter of the aperture stop, the SHWS spots on the WFS camera were almost free of the artifact from corneal reflection. It should be noted that for optimum performance using the aperture stop, large refractive errors (> 2 D) from the eye were corrected first using trial lenses. This was necessary because the aperture stop is in a retinal conjugate, where the beacon from an eye with a large amount of refractive error will form a blur circle which then would become vignetted by the 106

127 Chapter 4 Flood illumination adaptive optics ophthalmoscope aperture. Refractive error of the eye was estimated by sliding the AO imaging camera on the railing as mentioned in section To minimize corneal reflection from the imaging light, a rectangular block of perspex, ~10 mm thick, was inserted just downstream to the fibre port where the imaging light was emitted, as shown on the left of Figure 4.3. The perspex block could be rotated at an angle so that the incidence beam was translated slightly from the centre of the cornea. This allowed light from the corneal reflection to be moved away from the imaging region. Rotation of the block did not change the angle subtended at the eye, and so did not change the region being illuminated. 4.4 Adaptive optics imaging procedure Developing a robust AO software control was not part of this thesis, as the software control of wavefront-based AO imaging had already been developed by members of this laboratory for an existing flood-illumination AO ophthalmoscope (Bedggood 2008). Integration of the software into the current AO ophthalmoscope was relatively straightforward, with the only modification needed being the addition of control for the pupil and wide-field retinal cameras. As such, this section describes the AO imaging procedure of a rat eye in a concise manner in two parts: alignment of the eye using the wide-field arm and AO imaging with the AO arm Alignment of the eye Details of the preparation of the rat prior to in vivo AO were described in the pilot experiment in Chapter 2. Briefly, the animal was anaesthetised and secured on a custom-made, stereotaxic small animal platform (a redesigned version is shown in Chapter 5). The stage was then secured to an aluminium frame attached to three Velmex BiSlides (Velmex Inc, Bloomfield, NY), which allowed three-axes (XYZ) translations with resolution of mm. A rigid gas-permeable contact lens was inserted into the eye being imaged to provide a clear optical surface. For alignment of the animal s eye, the wide-field arm was engaged by flipping up the three flip mirrors marked with asterisks in Figure 4.3. The WFS light was used to illuminate the pupil, which was imaged onto the pupil camera at a 1:1 magnification. The BiSlides were used for accurate movement of the animal axially and laterally, and 107

128 Chapter 4 Flood illumination adaptive optics ophthalmoscope the small animal platform was used to rotate the animal. The lateral alignment of the rat s pupil was achieved by observing the image in a live acquisition stream from the pupil camera. Axial alignment was achieved by subjectively sharpening the edge of the rat s pupil. Axial alignment experiments using the model eye suggested that the precision in axial alignment using this subjective method was ~1 mm. After the pupil was aligned, the WFS light was turned off, and the imaging light turned on to locate the retinal area of interest using the live acquisition stream of the wide-field retinal camera. The magnification of the retina at the wide-field camera was ~x22 (compared to ~x39 at the AO imaging camera). Once the eye was aligned, and the retinal feature of interest was centred on the widefield retinal camera, the flip mirrors were flipped down to disengage the wide-field arm while engaging the AO imaging arm AO imaging Prior to collecting data from an AO ophthalmoscope, the device must be calibrated to map wavefront distortions onto mirror command signals. In order to achieve this, the deformable mirror was first flattened by applying a set of pre-determined flat command signals (voltages) to the 52 actuators while measuring the wavefront using the SHWS. To verify that the DM was flattened, a plane wavefront was introduced to the system by inserting a new plane mirror (free of imperfection and scratches) at the eye s exit pupil position. The RMS wavefront error measured by the SHWS was ~0.05 µm when the DM was flattened. The flat command differs between different models of DM and the appropriate value was taken from the particular DM s manual. The AO ophthalmoscope was then calibrated using the flat wavefront. Briefly, calibration involved poking each actuator individually by applying a fixed command signal, and recording the displacement of the SHWS spots from their reference position when a flat wavefront was present. In this way, the interaction matrix relating actuator voltages to the mirror surface (or equivalently, SHWS spot displacements) was established. During an actual AO imaging session, an uncorrected wavefront would lead to displacement of the SHWS spots from their ideal locations. Such displacements were 108

129 Chapter 4 Flood illumination adaptive optics ophthalmoscope calculated and compared to the calibrated response function from each actuator using matrix algebra, assuming linearity within the system. This allowed the corresponding correction signal for each DM actuator to be calculated. Once the DM received the correction signal, the shape of the wavefront was altered by the actuators beneath the surface of the DM, and the new wavefront was measured by the SHWS again. This process repeated itself in real-time until the residual RMS wavefront error was sufficiently low (<λ/14) to allow diffraction-limited imaging, according to the Maréchal criterion (Born and Wolf 1999). Typically only a few seconds were needed for this to occur as the AO ophthalmoscope operated at ~20 Hz. Once the residual RMS wavefront error reached its minimum, the imaging camera was manually triggered in software. The imaging light was synchronized with the acquisition rate of the imaging camera and pulsed at counter-phase with the WFS light, so that AO correction and image acquisition occurred almost simultaneously to account for real-time variations in aberrations in in vivo imaging. The AO image sequence, as well as the corresponding wavefront data during image acquisition, were saved to the hard drive for future analysis. The typical number of frames acquired for each AO image sequence was 50, at a rate of ~15 Hz. 4.5 Conclusion The flood-illumination adaptive optics ophthalmoscope was presented in detail in this chapter. The system was used for the remaining experiments which involved conventional wavefront-based AO (WFS-AO) imaging, HiLo imaging and wavefront sensor-less imaging (NS-AO). The necessary modifications of the system to accommodate the latter two imaging techniques are described in the following chapters. 109

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131 Chapter 5 Validation of optical modelling results Chapter 5 Validation of optical modelling results 5.1 Introduction In Chapter 3 a peer-reviewed paper was presented showing optical modelling to predict the effect of eye power and retinal thickness on AO image quality for human and rat eyes. Image quality in these schematic eyes were compared at various eccentricities under three manipulations in AO imaging. A short description of these manipulations are reviewed as follows. In each manipulation the defocus term was varied to maximize image quality at the retinal plane of interest, as would be undertaken in any real AO ophthalmoscope: Manipulation 1: wavefront sensing and AO imaging at different retinal depths but the same wavelength. Manipulation 2: wavefront sensing and AO imaging at different wavelengths but the same retinal depth. Manipulation 3: AO imaging at a different (but fixed) retinal depth to wavefront sensing but the same wavelength, while offsetting the AO corrector axially from its nominal pupil position (i.e. Manipulation 1 together with error in the AO corrector position). Since these manipulations were performed in a software environment, they are termed virtual manipulations here. In contradistinction, corresponding manipulations performed using the real AO ophthalmoscope are termed physical manipulations. The virtual manipulations suggested that AO image quality in highly powered eyes should be significantly improved by matching the plane and wavelength for imaging with that for sensing, and ensuring that the deformable mirror is conjugate to the eye s pupil. Several factors could cause the predicted benefits of these changes to be unrealizable in practice. First, the entire AO ophthalmoscope used in the optical modelling was reduced to a phase plate in the exit pupil plane of the schematic eyes (where the retina was 111

132 Chapter 5 Validation of optical modelling results considered the object space). While this greatly simplified the modelling, it ignores system aberrations present in AO ophthalmoscopes in practice (by which the AO corrector is usually imaged onto to the eye s exit pupil). Second, we considered mostly point image formation in optical modelling, whereas extended images are captured in real AO ophthalmoscopes, which may have fieldvarying aberration profiles (anisoplanatism) (Bedggood, Daaboul et al. 2008). Third, we used residual wavefront RMS as our metric of image quality in optical modelling of the virtual manipulations. However, residual RMS after best AO correction for all the above manipulations is not accessible in a real AO ophthalmoscope. In fact, the Shack-Hartmann wavefront sensor (SHWS) should report minimal residual RMS (<0.05 µm) after best AO correction in practice (with good SHWS spot quality), regardless of the above manipulations. This is because the residual aberrations occurring as a result of those manipulations manifest only in the imaging arm of the system, and are not visible to the SHWS. A different quality metric based on the actual image is therefore needed in practice to quantify the effects of physical manipulations, as described in detail in the next section. Due to the above limitations of optical modelling, it is necessary to verify the modelling results with a real AO ophthalmoscope. This is achieved using physical replications of the virtual manipulations with physical model eyes. Similar to optical modelling, physical model eyes with different powers, 60 D (similar in power to a human eye) and 220 D (a physical alternative of a high-powered eye such as that of a rat), were used to evaluate the effect that eye power has on the final image quality under each experimental manipulation. Details of the physical manipulations, along with the model eyes used, are presented below. The results from physical manipulations are also compared to the corresponding virtual manipulations. Finally, the implications from the physical manipulations are presented in the context of improving the resolution of in vivo AO images in the rat eye using the floodillumination AO ophthalmoscope described in Chapter 4. Other methods to improve the AO image quality in rodent eyes are also introduced. 112

133 Chapter 5 Validation of optical modelling results 5.2 Methods The flood-illumination AO imaging system used for experiments in this chapter has been described in detail in Chapter 4. For experiments with model eyes, an aluminium frame mounted on Velmex BiSlides (Velmex Inc, Bloomfield, NY), which allowed calibrated three-axes (XYZ) translations and yaw rotation of the model eyes (see Figure 5.1), was used to hold the model eyes in place Construction of the physical model eyes All of the physical manipulation experiments in this chapter were performed using physical model eyes with powers of 60 D and 220 D. Figure 5.1 shows the assembled model eye, which was made of an adjustable pupil diaphragm (set to 3.5 mm in diameter) mounted in front of a lens holder, and an XY translational "retinal" mount behind the lens in a cage-mounting system (Thorlabs, Newton, NJ). A metal pole connected to the lens holder was used to secure the model eye in front of the AO system during imaging. A protractor at the base of the pole was used to measure (horizontal) eccentricity. In order to change the power of the model eye, aspheric plano-convex lenses with power of 60 D (f 17 mm) or 220 D (f 4.51 mm) were inserted into the lens holder, with the convex surface facing anteriorly to mimic the cornea of a real eye. The 60 D lens was intended to serve as the physical equivalent of the human schematic eye used in Chapter 2. The 220 D lens was intended to serve as a physical alternative to the rat schematic eye. Although the 220 D lens is less powerful than the rat schematic eye (which was about 300 D), it is still substantially more powerful than the 60 D lens which, as will be shown, impacts profoundly many important aspects of imaging performance. The difference in image quality as a result of the difference in power should be comparable to the predictions made by ZEMAX modelling using human and rat schematic eyes in Chapter

134 Chapter 5 Validation of optical modelling results Figure 5.1. Photos of the model eye constructed in a cage-mounting system using an adjustable pupil diaphragm, an aspheric plano-convex lens mounted behind the pupil, and an artificial retina taped onto an XY translational mount. (a) and (b): Side and frontal view of the model eye; (c): The model eye was secured to an aluminium frame mounted on the Velmex BiSlides in front of the AO system (red outline). A protractor at the base was used to measure (horizontal) eccentricity. Using the XY translational retinal mount allowed the same retinal area to be imaged even when the model eye was rotated off-axis (i.e. by bringing the same piece of artificial retina into any eccentric field of view). This allowed direct comparisons of image quality to be made between different eccentricities. As for the artificial retina itself, originally a small piece of printer paper with ink patterns was taped onto the retinal mount behind the lens. However, this effectively limited 'retinal features' to a single plane, making it impossible for some of the experiments described below which explores the consequences of imaging different layers of a thick retina. In order to construct an artificial retina with realistic dioptric depth, a two-layered design was used, as shown in Figure 5.2. The posterior layer was made of a piece of printer paper with ink patterns printed on the front surface. For the anterior layer, a transparent acetate sheet (refractive index 1.5) ~100 µm thick with ink patterns printed on the front surface was used. These were separated by a spacer (or two spacers, depending on the desired separation between the anterior and posterior layers), also made of a piece of transparent acetate sheet, with a hollow centre and no ink markings. 114

135 Chapter 5 Validation of optical modelling results The separation between the anterior and posterior ink patterns used in this experiment was 100, 200 and 300 µm (actual thicknesses). Note that the actual retinal thicknesses used in the virtual manipulations were 250 µm and 170 µm for the human and rat schematic eyes, respectively. Since the acetate sheet is about 100 µm thick, no spacer was needed for the 100 µm case as the ink patterns were printed on the front surface of the anterior layer; one spacer was used for the 200 µm and two were used for the 300 µm case. The three layers were held tightly together with a small amount of glue and mounted on the XY translational retinal mount. Figure 5.2. Diagrammatic representation of the dioptrically thick model retina. The posterior retina was made of a small piece of paper, with ink patterns printed on the surface. The spacer in the middle layer was made of a small piece of transparent acetate sheet, which is about 100 µm thick. The anterior retina was also made of a small piece of transparent acetate sheet with ink patterns printed on the anterior surface. The spacer was not used for the 100 µm retina, one spacer was used for the 200 µm retina, and two spacers were used for the 300 µm retina The physical manipulations This section gives detailed descriptions of the physical manipulations in this experiment. The order of the physical manipulations described here is the same as the virtual manipulations shown in Chapter

136 Chapter 5 Validation of optical modelling results Shifting imaging plane Figure 5.3 shows a diagrammatic representation of physical manipulation 1, in which the effect of varying the separation between the imaging and sensing planes at various eccentricities was investigated using the same sensing and imaging wavelength (670 nm), while correcting for defocus only. The purpose of this physical manipulation was to verify the effect on image quality predicted by the corresponding virtual manipulation 1 in Chapter 2. In Figure 5.3, the physical model eye is represented in Figure 5.3 as a square with an aperture stop anterior to the aspheric plano-convex lens, while the flat retina is represented as two vertical lines with the spacer in between. The position of the posterior retina was fixed to be close to plano in refractive error, while the anterior retina (with features printed on the anterior surface) was displaced by 100, 200 and 300 µm from the posterior retina as mentioned above. Figure 5.3. Manipulation 1: shifting imaging plane. The model eye was represented as a rectangular structure with an aperture stop anterior to the aspheric plano-convex lens and a dual-layered artificial retina. The spacer, which did not interfere with imaging, is shown as dashed lines. Wavefront sensing was performed at the posterior retina while imaging was at the anterior retina separated by 100, 200 and 300 µm from the posterior retina. Movement of the anterior retina is represented with horizontal dashed arrows. Eccentricities explored were 0, 2, 4 and 8, which was measured in system space using the protractor at the base of the model eye (see Figure 5.1). Higher eccentricities were not included due to the difficulty of obtaining quality SHWS spots at higher 116

137 Chapter 5 Validation of optical modelling results eccentricities in the 220 D model eye, since a flat retina was used and excessive astigmatism was present. It is noteworthy that the relative positions of the sensing and imaging planes were opposite in sign to those used in the virtual manipulation. This was because in the virtual manipulation, the wavefront-sensing (WFS) beacon was artificially placed on the inner-limiting membrane (ILM), where studies have shown to be one of the most reflective layers in the eye (Geng, Schery et al. 2011; Geng, Dubra et al. 2012). However, in experiments using the physical model eye, the SHWS spots were found to be brighter when placing the WFS beacon at the posterior retina, which was made of a piece of paper and therefore had higher reflectance. This difference does not affect the comparison of results between the physical and virtual manipulations, since it was the separation between the sensing and imaging planes that affected image quality repeating the virtual manipulations of Chapter 2 with the relative positions of sensing and imaging planes reversed showed a similar magnitude and trend for all 3 types of manipulations. To obtain a sharp image of the anterior retina, AO correction was first performed using the WFS beacon reflected from the posterior retina. Then, large defocus offset was subjectively adjusted to maximize the sharpness of the image for the anterior retinal target. This was accomplished by moving the retinal camera axially. Next, small defocus offset was adjusted objectively using a series of images obtained with finer steps of defocus offset applied to the adaptive optics correction. The optimal defocus offset corresponding to the best image was found using the objective image quality metric defined below. The final, optimised full frame images were collected for both model eyes at each retinal thickness and eccentricity for analysis. The image quality metric used for the objective optimisation of defocus was the coefficient of variation (CV All ) of all the pixels over a chosen region of interest (ROI; typically a square around 1 in size near the middle for the field of view), defined as: CV All σ = all Equation 5.1 µ all where σ all is the standard deviation of the intensity of all pixels in the ROI, and µ all is the mean intensity of all pixels in the same ROI. Therefore this image quality metric 117

138 Chapter 5 Validation of optical modelling results objectively measures the image contrast, and a higher value indicates better image contrast. Dividing the standard deviation by the mean made the metric less susceptible to intensity variations across different frames, which could be caused by small intensity fluctuations of the imaging light. The same method to optimise focus on features in the intended retinal layer was also employed in the other manipulations discussed below. It should be noted that this image quality metric is improved upon somewhat in Chapter 7 dealing with sensorless adaptive optics Shifting sensing wavelength Figure 5.4 shows the diagrammatic representation of physical manipulation 2, in which the effect of varying the wavelength of the wavefront sensing light, while keeping that of the imaging light the same, was investigated. As above, defocus was optimized by moving the camera to maximize image quality and then fine-tuned using finer defocus offset for the adaptive optics correction. The same eccentricities as manipulation 1 were used. Wavelengths of the sensing light are displayed as dashed blue and red lines symbolising the change. To limit any changes to the effect of the difference in wavelength alone, wavefront sensing and imaging were performed on a single plane (paper) with approximate refractive error of plano at 670 nm. Figure 5.4. Manipulation 2: shifting sensing wavelength. Wavefront sensing and imaging were performed on a single retinal layer (paper) in this case. The wavelength of the imaging light was fixed at 670 nm. The change in wavelength of the sensing light was represented as dashed blue and red lines. 118

139 Chapter 5 Validation of optical modelling results This manipulation was used as the physical verification of the predictions from virtual manipulation 2 in Chapter 2. One difference between the physical and virtual manipulations was that in the physical case, the wavelength of the sensing light was varied (λs = 670, 593 or 532 nm) while keeping the imaging wavelength the same (λi = 670 nm), whereas in the virtual case it was the imaging wavelength that was varied. The same wavelength was used as the imaging light in the physical manipulation since it had the highest power amongst all the laser light sources available at the time of the experiment. Due to the attenuation of power of the laser by the AO system, it was only practical to vary the wavelength of the sensing light. To check that this difference did not affect the comparison of results between the physical and virtual manipulations, the corresponding virtual manipulation of Chapter 2 was repeated with the wavelengths of sensing and imaging light reversed. The results showed a similar magnitude and trend for this manipulation, confirming that it is mainly the difference between λs and λi (Δλ) that affects image quality. Similar to manipulation 1, defocus was optimised first subjectively and then objectively, after the best initial AO correction was obtained for each Δλ and retinal eccentricity. The final, optimised full frame images were collected from both model eyes for analysis Shifting the axial position of the model eyes Figure 5.5 shows the third physical manipulation, where the axial position of the model eye was varied while wavefront sensing and imaging were performed on the posterior and anterior retinas, respectively, at eccentricities 0, 4 and 8. The refractive error of the posterior retina was close to plano, and was separated from the anterior retina by 200 µm by using a single spacer. 119

140 Chapter 5 Validation of optical modelling results Figure 5.5. Manipulation 3: shifting the axial position of the model eye. Wavefront sensing was performed at the posterior retina, while imaging at the anterior retina separated by 200 µm (a single spacer was used). The entire model eye was shifted towards (positive displacement) or away from (negative displacement) the AO system. The distance of the movement from the original pupil plane was measured with a vernier micrometer to the nearest mm. This manipulation was aimed to investigate a second-order effect on image quality where there was already a separation of 200 µm between the WFS beacon scatting layer and the retinal layer of interest. It was intended to be a physical verification of the corresponding virtual manipulation 3 in Chapter 2. In virtual manipulation 3, the AO corrector (virtual phase plate) was placed at the eye s exit pupil position. However, since a real AO ophthalmoscope was used in the physical manipulation, the AO corrector (deformable mirror) was imaged to a pupil conjugate at the head/eye-holder of the system. Since the mirror could not be moved freely due to the time-consuming process of re-alignment of the entire AO ophthalmoscope otherwise, offset of the AO corrector image from eye's pupil was accomplished by moving the model eye itself axially from -25 mm (away from the system) to +25 mm (towards the system). Calibrated movement was achieved using the Velmex BiSlide. As described above, defocus was optimised first subjectively and then objectively at each axial displacement and eccentricity. The final images for both model eyes were collected for analysis The challenge of wavefront sensing on acetate sheet Manipulations 1 and 3 relied on the effect of a thick retina, and were achieved by wavefront sensing at the posterior (paper) retina and imaging the anterior (acetate) 120

141 Chapter 5 Validation of optical modelling results retina. Manipulation 2, on the other hand, required sensing and imaging at the same plane. In order for the image features to look the same as for the other manipulations, wavefront sensing and imaging at the anterior (acetate) plane would be preferred. However, it was difficult to measure the wavefront arising from the acetate sheet using the Shack-Hartmann method, as explained below. First, the WFS beacon was reflected from both the front and back surfaces of the transparent acetate sheet, which is ~100 µm thick. Since the reflectivity of both surfaces of the acetate sheet was similar, this resulted in radial elongation of the SHWS spots from the centre of the lenslet array. The magnitude of the elongation of the SHWS spots, which is also observed in real eyes due to the dioptric thickness of the retina (Geng, Schery et al. 2011; Liu, Thibos et al. 2014), depends on the power of the eye and the radial distance of the spots from the centre of the lenslet arrays. As model eye power increases the elongated SHWS spots become twin-peaked (bimodal). Towards the edge of the pupil, reflections from the front and back layers of the acetate sheet separate into distinct spots, as shown in an example SHWS image for the 220 D model eye in Figure 5.6. Figure 5.6. Example SHWS image showing the bimodal appearance of the spots in a 220 D model eye with an artificial retina. The bimodal appearance becomes more distinct towards the edge of the pupil. In this particular example, the artificial retina was an acetate sheet. The spots closer to the centre were from the posterior surface of the acetate sheet, while the spots further 121

142 Chapter 5 Validation of optical modelling results away from the centre were from the anterior surface of the acetate sheet. A similar bimodal appearance was also observed with the dual-layer retina. For the 60 D model eye, the SHWS spots were elongated towards the edge of the pupil, but not noticeably bimodal, due to the small dioptric thickness (~ 0.4 D) of the acetate sheet in the 60 D model eye. For the 220 D model eye, the acetate sheet had a much larger dioptric thickness of ~5 D. Therefore the elongated SHWS spots quickly became bimodal towards the edge of the pupil. Wavefront sensing and correction could therefore be affected when the spot-finding AO algorithm used the averaged position of the elongated spots, or lock on to a mixture of the bimodal spots and reported spurious aberration measurements. Second, the acetate sheet provides a somewhat specular reflection, which would result in double pass aberrations being sensed by the SHWS. This is because the phase information of the eye in the WFS light, which passes the eye s optics twice, could be preserved at its first pass as it undergoes specular reflection from the smooth acetate sheet. On the other hand, light reflection from paper is largely diffuse, similar to that from the retina (see explanation in section 1.6.2). Therefore phase information of the eye in the WFS light at its first pass is largely lost as it reflects from the paper retina (Liang, Grimm et al. 1994), resulting in single pass aberrations being measured. The flood AO ophthalmoscope used in this work was not configured to account for double pass aberrations. Therefore wavefront sensing on the acetate sheet could introduce spurious aberrations especially off-axis. In an attempt to overcome the elongation of SHWS spots, an aperture stop was placed in the middle of the afocal telescope (conjugate to the retina) set immediately in front of the WFS camera (see system layout in Chapter 4). The diameter of the aperture stop was then reduced to block out the SHWS light scattered from the posterior retinal surface. However, this exercise was time-consuming and proved to be technically challenging since very careful manipulation of the position of the aperture stop was required, especially for off-axis imaging for both the 60 D and 220 D model eyes. Multiple WFS and AO imaging attempts were made until the best image quality could be obtained. This technique was used to obtain the Reference ROIs for manipulations 1 and 3 (see section 5.3), where wavefront sensing and imaging were performed on-axis only at the 122

143 Chapter 5 Validation of optical modelling results anterior retina (acetate sheet), where refractive error of the model eyes was set to as close to plano as possible to minimise double pass aberrations being sensed. Due to the technically challenging nature of wavefront sensing on acetate sheet, it was decided that for manipulation 2, a paper retina would be used instead. This lead to different ink patterns compared to manipulation 1 and 3. The difference in ink patterns did not affect results since the effect of the manipulations on the image quality of the ink patterns was compared within each manipulation, not across A suitable image quality metric In the virtual manipulations in Chapter 2, the computed residual wavefront RMS was used as the image quality metric for all manipulations. It was possible to obtain the residual RMS since the ZEMAX program provided such information. However, for the physical manipulations described above, it was not possible to collect residual RMS values from the SHWS, since (by design) these manipulations produced aberrations arising from the fact that sensing and imaging beams did not share the same path through the eye and system. In order to objectively quantify the final image quality, an optical quality metric based on the output images was needed. This metric should satisfy several requirements: 1. It should not be derived from the sensing beacon, since the design of the manipulations was such that the SHWS would always report good AO correction. 2. It should not be affected by intensity variations between images such as that caused by different eccentricities and retinal depths, or shot noise and read noise of the imaging camera. 3. It should return the measurement as a single number, so that comparison between images could be readily made and plotted. 4. It should agree with the subjective interpretation of image quality. Several image quality metrics were investigated using the resultant images from the physical manipulations, including average intensity, standard deviation and CV All. 123

144 Chapter 5 Validation of optical modelling results Average intensity and standard deviation were found to be unsuitable since they were affected by the intensity variations between images (failing the second requirement). On the other hand, CV All was used as a metric to measure optimal defocus, as mentioned above. However, CV All was found to be most reliable (best matched subjective judgement of image quality) when used to judge the quality of images obtained from the same eccentricity, such as several frames of the same ROI with different amounts of defocus. For comparison between images obtained from different eccentricities, CV All could give spurious results. For example, a well-corrected image at 0 eccentricity could have a similar CV All value to a poorly corrected image at 8, where the image features were smeared due to residual astigmatism, leaving a high contrast black band in the white background. A possible explanation for this is that CV All essentially measures overall image contrast, which could be similar between the well-corrected and the smeared images. To overcome the above challenge, an image quality metric known as mutual information (MI) was investigated. MI, also known as 'relative entropy', is a basic concept from information theory that measures the statistical dependence between two random variables (Maes, Collignon et al. 1997). In short, the intensity values of corresponding pixels in two images can be considered as random variables A and B. The MI value I(A, B) between the two images can be calculated by the following equation (Maes, Collignon et al. 1997): I( AB, ) = H( A) + H( B) H( AB, ) Equation 5.2 where H(A) and H(B) are the entropies of A and B, and H(A, B) is their joint entropy. I(A, B) is a single number that increases with increasing similarity between the two images. H(A) or H(B), and H(A, B) are defined as follows (Maes, Collignon et al. 1997), H( A) = p ( a)log p ( a) Equation 5.3 a a A H( AB, ) p ( ab, )log p ( ab, ) ab, AB A = Equation 5.4 where p A (a) is the marginal probability distribution of random variable A with intensity value a, and p AB (a, b) is the joint probability distribution of A and B with intensity AB 124

145 Chapter 5 Validation of optical modelling results values a and b. The above equations formed the basis of the Matlab algorithm that calculated MI for this experiment. MI has been shown to be a robust metric for registration of images even if acquired from different imaging modalities (e.g. registering MRI with CT data), since it makes no assumptions about the imaging process and is therefore quite general in nature (Wells, Viola et al. 1996; Maes, Collignon et al. 1997; Viola and Wells 1997). In addition, MI is not affected by intensity variation between images, making it possible to compare images obtained with different amount of illumination (Wells, Viola et al. 1996). From the definition above, MI can be used to calculate the similarities between two images and return a single number as a measurement the larger the MI value, the more similar two images are. Since it requires two images, a standard reference image was obtained by performing wavefront sensing and imaging at the same plane, with the same wavelength and zero axial offset of the eye. This in theory provides the best achievable image quality limited only by diffraction. In order to mitigate against anisoplanatic effects, the centre region of ~ within the reference image (reference ROI) was selected. Then, the corresponding resultant ROI (the region of interest obtained as a result of physical manipulation) was manually registered against the reference ROI for more precise alignment (guarding against minor translation, rotation or change of magnification). The reference-resultant ROI pair was used to generate the raw MI values, which were then normalised against the MI value obtained from the reference-reference ROI (reference ROI compared to itself which generates the highest MI value) for each manipulation. For manipulations 1 and 3, the reference ROIs were obtained by optimizing focus for details on the anterior (acetate sheet) retina. For manipulation 2, this was obtained on the single-layered (paper) retina, which had different features as described above. 5.3 Results and discussions This section shows the results and discussions from the three previously described physical manipulations using two physical model eyes with powers 60 D and 220 D, with comparison to the corresponding virtual manipulations from Paper 1 in Chapter

146 Chapter 5 Validation of optical modelling results Correlating MI to residual RMS using standard images Mutual information (MI) was used to quantify image quality resulting from the physical manipulations. On the other hand, image quality from the virtual manipulations were quantified using residual wavefront RMS. Since residual wavefront RMS cannot be obtained at the image plane for the physical manipulations, it is important to establish a relationship between these two metrics in order to draw comparison of the results from physical and virtual manipulations. To achieve this, the images (or rather, cropped regions of interest ROIs ) obtained at 0 eccentricity from the 60 D and 220 D model eyes were used as ideal or reference images, since they were considered diffraction-limited. Note that there were four such reference ROIs with different ink patterns, due to the different power (hence magnification) of the two model eyes, and the fact that manipulations 1 and 3 used the same ink pattern in each model eye, whereas manipulation 2 used a different ink pattern, as described in section (see Figure 5.7). For each of the four reference ROI s, increasing amounts of simulated virtual aberrations (up to 6th order Zernike terms) were used to create a series of seven simulated images (simulated ROIs) with progressively increasing amounts of blur. The sequence of artificial aberration profiles used was obtained in ZEMAX from the rat schematic eye by progressively increasing the horizontal eccentricity without any AO correction. The parameters used in the simulation were: wavelength = 650 nm, pupil size = 3.5 mm, focal length = 3.24 mm (rat schematic eye). These simulated ROIs were intended to be used to plot and appreciate the relationship between MI and residual RMS, since the former is unknown in adaptive optics vision science while the latter is commonly used. Appreciating this relationship facilitates interpretation of the results of physical manipulations presented below. Figure 5.7 shows the standard images in four rows. The left-most column contains the reference ROIs obtained from the 60 D and 220 D model eyes, which were already slightly blurred by diffraction. Note that reference ROI #1 for the 60 D and 220 D model eyes were used in physical manipulations 1 and 3, whereas reference ROI #2 for both model eyes were used in manipulation 2. The seven columns (numbered 1 7 on top of the figure) on the right contain the simulated ROIs, which have increased amount 126

147 Chapter 5 Validation of optical modelling results of blur towards the right due to increased amount of artificial aberrations as described above. The simulated ROIs in a given column were blurred by the same amount of artificial aberrations. The corresponding residual RMS and MI values are also shown above the images. The MI values were obtained as mentioned in Methods using the simulated-reference ROI pairs and then normalised against that of the reference-reference ROI pair, giving the reference ROI an MI value of 1.0. The residual RMS values for the simulated ROIs were obtained in ZEMAX as mentioned. For the reference ROIs, the residual RMS was set to zero, since it was considered aberration-free. Figure 5.8 shows the normalised MI values plotted against the residual RMS for each of the simulated ROIs in Figure 5.7. Images from the 60 D and 220 model eyes are shown in open and closed symbols, respectively. The columns of data points are numbered 1 7 corresponding to the column of simulated ROIs. It can be seen that for the 60 D model eye, normalised MI values decreased with the increase in residual RMS, but quickly plateaued for residual RMS > 0.2 µm. For the 220 D eye, on the other hand, normalised MI values decreased steadily with the increase in RMS, although the rate of decline was less for residual RMS > 0.4 µm. In addition, the shapes of the curves were similar for simulated ROIs from the same model eye. The above observations showed a non-linear relationship between MI and residual RMS values that could be dependent on the image feature, not the power of the model eye. This is because the same amount of artificial aberrations were applied to all four reference ROIs. Careful observation of the ink patterns from the 60 D model eye showed they were concentrated to the middle of the images, whereas ink patterns from the 220 D model eye were more evenly spread across the images. As a result of the concentrated ink patterns in the 60 D model eye, the blur induced by the simulated aberrations became less apparent as the residual RMS increased, leading to plateauing MI values. On the other hand, when the image features were more evenly spread, such as in the 220 D model eye, increases in residual RMS produced a relatively more proportional increase in perceived blurriness, and hence better correlation with MI values across a larger range of residual RMS values. 127

148 Chapter 5 Validation of optical modelling results Note that Figures 5.7 and 5.8 should be used as a guide only for the visualisation of the relationships between subjective and objective image quality. In real experimental results shown below, MI values could fluctuate somewhat for image qualities that appear similar subjectively, depending on imaging conditions such as eccentricity and retinal depth. 128

149 Chapter 5 Validation of optical modelling results Figure 5.7. Standard images with corresponding MI and RMS values, designed to illustrate the relationship between MI and residual RMS. Images from the 60 D (first two rows) and 220 D (last two rows) model eyes are shown. The ink patterns appear different due to reasons explained in the text. The ideal, or reference ROIs with the best image quality are on the left column. For each reference ROI, seven simulated ROIs using artificial aberrations (up to 6th order Zernike terms) measured from the rat schematic eye at increasing eccentricities are shown on the right columns (1-7). MI = mutual information values. RMS = root-mean-square value (in µm) of the first 28 Zernike coefficients (6th order), excluding piston, tip and tilt. Simulation wavelength: 650 nm, pupil size: 3.5 mm, focal length of eye: 3.24 mm. Scale bars: 60 D eye = 20 µm; 220 D eye = 10 µm. 129

150 Chapter 5 Validation of optical modelling results Figure 5.8. Normalised MI values plotted against residual RMS, from the simulated ROIs in Figure 5.7. For each simulated ROI, its MI value was normalised against that from the reference-reference ROI pair, which therefore had an MI value of 1.0. Open symbols: 60 D eye. Closed symbols: 220 D eye. The particular images that each column of data points corresponds to is labelled from #1 to #7 on the graph Results and discussions of physical manipulations This section shows the results of the three physical manipulations. Comparison between physical and virtual manipulations is described in detail in section Note that reference ROI refers to the region of interest in best-corrected AO image, resultant ROI refers to that as a result of the physical manipulations, and simulated ROI refers to that obtained with artificial aberrations in section above Manipulation 1: Shifting imaging plane In this manipulation, wavefront sensing was performed at the posterior artificial retina, while imaging at the anterior with the same wavelength (670 nm). The physical separation between the anterior and posterior layers of the artificial retina was 100 µm, 200 µm and 300 µm, while keeping the absolute position of the posterior retina fixed. The image quality of the resultant ROIs was represented by MI values, normalised to the reference ROI. The resultant ROIs as well as the reference ROI for the 60 D model eye can be visualised in Figure 5.9. The reference ROI was obtained with wavefront sensing and 130

151 Chapter 5 Validation of optical modelling results imaging on-axis at the anterior retina under the same wavelength (670 nm) and zero corrector displacement. The images were arranged with increasing physical separation between wavefront sensing and imaging planes (retinal thickness) down the columns, and increasing eccentricity across the rows. The corresponding normalised MI values are also shown beneath the images. Figure 5.10 shows the effect on image quality by shifting the imaging plane in the 60 D model eye, while compensating for defocus only. The normalised MI values of all resultant ROIs shown in Figure 5.9 are plotted against the retinal thickness. Note that the normalised MI value of the reference ROI has a value of 1.0, which is not plotted due to the scale of the graph. Various eccentricities are represented by different coloured markers. It can be seen from Figures 5.9 and 5.10 that for the 60 D model eye: 1. At a given eccentricity, image quality as assessed by MI values decreases by ~ 15% as the separation between wavefront sensing and imaging planes increases from 100 to 300 µm. 2. At a given retinal thickness, MI values decreased by ~20% from 0 to Subjective inspection of all resultant ROIs showed similar image quality when compared to the reference ROI. Interpretation of results: At a given eccentricity, the small decrease of MI values with increase in retinal thickness was consistent with the subjective lack of apparent image blur in Figure 5.9. Similar effects could also be seen in the first two simulated ROIs in the first row of the standard images in Figure 5.7, where a similar reduction in MI value (from 0.40 to 0.35) as a result of increased residual RMS (from 0.01 to 0.09 µm) resulted in only a small amount of subjective blur. Hence at a given eccentricity, the increase in residual aberrations was likely small with the increase in retinal thickness in the 60 D model eye. This observation is consistent with AO imaging in the human eye, which has approximately the same power, where a change of imaging plane after AO correction generally does not lead to a large reduction in image quality. 131

152 Chapter 5 Validation of optical modelling results At a given retinal thickness, the small amount of reduction of MI values with increased eccentricity was also consistent with the subjective lack of apparent image blur in Figure 5.9, which could be due to minimal amounts of residual aberrations present. Overall, for the 60 D model eye, separating the sensing and imaging planes by the full 300 µm only lead to a small reduction of image quality. This reduction was similar across all eccentricities trialled in this manipulation. As we shall see below, the same cannot be said for the higher powered 220 D eye. Figure 5.9. Reference and resultant ROIs obtained from manipulation 1 in a 60 D model eye. The ROIs are arranged with increasing eccentricity horizontally across, and retinal thickness vertically downwards. The reference ROI was obtained with AO sensing and imaging on-axis on the anterior retina under the same wavelength (670 nm) and zero corrector displacement. Normalised MI values are displayed below the ROIs. All images were contrast-stretched for display purposes. Scale bar = 20 µm in the reference ROI. 132

153 Chapter 5 Validation of optical modelling results Figure Effect of shifting imaging plane in a 60 D model eye after optimising for defocus. Image quality is represented by MI values (normalised against the reference ROI) on the vertical axis, while separation between wavefront sensing and imaging light, or retinal thickness (µm) is represented on the horizontal axis. Using the translation mount, the same feature was imaged on the artificial retina at various retinal eccentricities. Subjective judgement of the image quality for the 220 D eye can be made from the corresponding images in Figure 5.11, arranged in the same way as for Figure 5.9. In addition, Figure 5.12 shows the effect on image quality by shifting the imaging plane in the 220 D model eye, while compensating for defocus only. MI values have been normalised against the reference ROI, as was done for Figure Note that the ink pattern for the 220 D model eye was different compared to the 60 D model eye due to the higher magnification of the former. It can be seen from Figures 5.11 and 5.12 that for the 220 D model eye: 1. At a given eccentricity, MI values decreased dramatically as retinal thickness increased. The magnitude of the reduction from 100 µm to 300 µm was ~50% at 0, increasing to ~65% at 8. On average, MI values reduced by ~55% from 100 µm to 300 µm for all eccentricities. 2. At a given retinal thickness, the reduction of MI values was relatively mild from 0 to 8, ranging from ~5% at 100 µm, ~20% at 200 µm to ~30% at 300 µm. 133

154 Chapter 5 Validation of optical modelling results 3. Subjective inspection of the resultant ROIs at the same eccentricity showed similar trends as above. Resultant ROIs generally became more blurry with the increase in retinal thickness, whereas at the same retinal thickness, image quality appeared similar at 100 µm, but progressively worse at 200 and 300 µm with the increase in eccentricity. Interpretation of results: At a given retinal eccentricity, the above results showed that separating the sensing and imaging planes had a much larger negative impact on image quality in the 220 D model eye, compared to the 60 D model eye. Since all experimental conditions were equal for both model eyes (except for the ink patterns, which was not identical due to the difference in magnifications created by the difference in power), the different results were likely due to a larger accrual of residual aberrations in the 220 D model eye with increases in retinal thickness. Indeed, subjective inspection of the corresponding standard images (e.g. simulated ROI 1 vs 5) in Figure 5.7 showed a similar increase of blur as Figure 5.11 with a ~55% drop of MI (0.36 for simulated ROI 1, 0.18 for simulated ROI 5) value due to the increase in residual aberrations (0.01 µm for simulated ROI 1, 0.40 µm for simulated ROI 5). In addition, the larger reduction in MI values at higher eccentricity for the same increase in retinal thickness showed that residual aberrations increased with eccentricity. For the on-axis scenario, residual spherical aberration was most likely the dominant residual aberration affecting image quality. For off-axis scenarios, residual astigmatism was the most likely dominant residual aberration according to the corresponding virtual manipulation in Chapter 2, although the exact amount of each type aberration could not be determined in this experiment. At a given retinal thickness, the image quality was more stable with the increase in eccentricity, particularly at 100 µm, as can be seen subjectively in Figure At 200 and 300 µm, the image quality of the resultant ROIs were similar from 0 to 4, but more blurred at 6 and 8 possibly due to an increased amount of residual astigmatism as a result of the higher power of the model eye. Overall, for the 220 D model eye, separation of the sensing and imaging planes had a detrimental impact on image quality due to its higher power. This result was in stark 134

155 Chapter 5 Validation of optical modelling results contrast to the 60 D model eye, where the increasing separation between the two planes had a negligible effect on image quality at all eccentricities. Figure Reference and resultant ROIs obtained from manipulation 1 in a 220 D model eye. The ROIs are arranged with increasing eccentricity horizontally across, and retinal thickness vertically downwards. The reference ROI was obtained with AO sensing and imaging on-axis on the anterior retina under the same wavelength (670 nm) and zero corrector displacement. Normalised MI values are displayed below the ROIs. All images were contrast-stretched for display purposes. Scale bar = 10 µm in the reference ROI. 135

156 Chapter 5 Validation of optical modelling results Figure Effect of shifting imaging plane in a 220 D model eye after optimising for defocus. Similar to the 60 D eye, image quality is represented by MI values (normalised against the reference ROI) on the vertical axis, while separation between wavefront sensing and imaging light, or retinal thickness (µm) is represented on the horizontal axis. Using the translation mount, the same feature was imaged on the artificial retina at various retinal eccentricities Manipulation 2: Shifting sensing wavelength In this simulation, AO images were obtained by wavefront sensing and imaging on the same layer of retina. Different sensing wavelengths (λ = 532, 593, 670 nm) were used while the imaging wavelength was kept constant (λ = 670 nm). Note that the image features analysed for this manipulation appeared different from manipulation 1. The features were still small depositions of black ink, but here they were embedded within the matrix of a paper retina instead of on the surface of an acetate sheet. This was done because of the technical challenge of performing wavefront sensing and imaging on the acetate sheet as explained above in the Methods section Figure 5.13 shows the resultant ROIs from the 60 D model eye under manipulation 2 for subjective judgement of image quality. The reference ROI was also shown, which was obtained at Δλ = 0 nm at 0. The corresponding MI values from the reference-resultant ROI pairs were labelled below the images. The images were arranged with increasing eccentricity across the rows, and increasing wavelength offset (Δλ) down the columns. 136

157 Chapter 5 Validation of optical modelling results Figure 5.14 shows the normalised MI value plotted against Δλ at various eccentricities for the 60 D model eye. The MI values were normalised against the reference ROI, which has a value of 1.0 and therefore not shown in Figure It can be seen for from Figures 5.13 and 5.14 that, for the 60 D model eye: 1. At a given eccentricity, the MI value was generally stable with increase in Δλ, even at the highest eccentricity. 2. At a given Δλ, the MI values generally reduced by ~40% with from 0 to 8. The amount of reduction of image quality was similar across all Δλ. 3. Subjective judgement of the corresponding ROIs in Figure 5.13 showed that at a given eccentricity, the black ink pattern had similar quality across all Δλ, similar to what Figure 5.14 shows. At a given Δλ, the black ink pattern also appeared similar across all eccentricity. However, the brightness of the speckle pattern (from the paper retina) in the background of the images with the same Δλ appeared less distinct with the increase in eccentricity. This speckle artefact, which occurred on the paper retina, could explain the large reduction in MI values at a given Δλ with the increase in eccentricity, although the black ink pattern appear similar in all images. Interpretation of results At a given eccentricity, the relatively stable MI values with increasing Δλ was consistent with the subjective observation of the resultant ROIs in Figure The exception was the 2 case, whose MI value was much greater at Δλ = 0 nm before plateauing at Δλ = 77 and 138 nm, possibly due to the speckle artefact mentioned above. This discrepancy was considered to be experimental noise, since the black ink pattern appeared quite similar in clarity with increasing Δλ at a given eccentricity. This suggested that little residual aberrations were introduced due to the use of different sensing and imaging wavelengths in the 60 D model eye, an observation seen also in human eye AO imaging. At a given Δλ, speckle artefact (instead of residual aberrations) was likely the cause of the ~40% reduction of MI values with the increase in eccentricity. This is because if the reduction in MI values were caused by residual aberrations, then according to the 137

158 Chapter 5 Validation of optical modelling results standard images in Figure 5.7, even a lower reduction of e.g. 30% in MI value (simulated ROIs 1 vs 4) would result in an image so blurry that it would be impossible to distinguish the individual ink spots. Speckle artefact was unavoidable when the model eye was rotated increasingly off-axis since a paper retina was used in manipulation 2. Overall, for the 60 D model eye, wavelength difference between AO sensing and imaging light did not have a significant negative impact on image quality of the ink pattern. As we shall see below, the same cannot be said for the higher powered 220 D eye. Figure Reference and resultant ROIs obtained from manipulation 2 in a 60 D model eye. The images are arranged with increasing eccentricity horizontally across, and increasing Δλ vertically downwards. The reference ROI was obtained with AO sensing and imaging on-axis on the same layer of retina under the same wavelength (670 nm) and zero corrector displacement. All other images were also obtained on the same layer of retina. Normalised MI values are displayed below the ROIs. All images were contrast-stretched for display purposes. Scale bar = 20 µm in the reference ROI. 138

159 Chapter 5 Validation of optical modelling results Figure Effect of shifting wavefront sensing wavelength in a 60 D model eye after optimising for defocus. Image quality is represented by MI values in the vertical axis, normalised against the MI value of the reference ROI. The wavelength difference (Δλ) between the sensing and imaging light is represented on the horizontal axis (Δλ = 0, 77 and 138 nm). The imaging wavelength was 670 nm, while the sensing wavelengths were 532, 593 and 670 nm. The data point with Δλ = 0 at 0 was not represented here since this was the reference ROI, with a normalised MI value = 1.0. Figure 5.15 shows the reference and resultant ROIs from the 220 D model eye in physical manipulation 2, arranged in the same way as the 60 D model eye. The corresponding MI values are displayed below the images. Figure 5.16 shows graph of the effect of shifting the sensing wavelength while adjusting for defocus only in the 220 D model eye. The results were normalised against the MI value of the reference ROI, obtained at Δλ = 0 nm at 0 eccentricity, which has a value of 1.0 and therefore not shown in Figure It can be seen from Figures 5.15 and 5.16 that for the 220 D model eye: 1. At a given eccentricity, MI values decreased by an average ~20% with Δλ from 0 to 138 nm. The amount of decrease was similar from 0 to At a given Δλ, MI values decreased with eccentricity by an average ~25% from 0 to Subjective inspection of the resultant ROIs in Figure 5.15 showed that at a given eccentricity, the black ink pattern generally appeared more blurry with the 139

160 Chapter 5 Validation of optical modelling results increase in Δλ, similar to the observation from Figure At a given Δλ, the ink pattern also appeared more blurry with the increase in eccentricity, although the blurriness was more noticeable at 6 and 8. Speckle artefact was less pronounced in the images in Figure 5.15 compared to the 60 D model eye. Interpretation of results At a given eccentricity, subjective inspection of image quality from Figure 5.15, which showed an increasing amount of blur in the images with the increase in Δλ, was generally consistent with the trend of MI values in Figure The decline in image quality was likely due to an increase in residual aberrations with Δλ in the more powerful 220 D model eye. For the on-axis case, the main residual aberration was likely to be spherical aberration. For the off-axis cases, they were likely from residual coma and astigmatism, judging from the results of the corresponding virtual manipulation of the rat schematic eye presented in Chapter 3. This was consistent with the corresponding standard images (e.g. simulated ROIs 2 vs 3) in Figure 5.7, where a ~20% reduction in MI value due to residual aberrations resulted in a similar amount of image blur as Figure At a given Δλ, subjective judgement of the increased blurriness of the ink pattern with eccentricity in Figure 5.15 also agreed well with the decrease in MI values in Figure Unlike the 60 D model eye, speckle artefact was less pronounced in the resultant ROIs in the 220 D model eye. Therefore the likely cause of the reduction in MI values was increased residual aberration with eccentricity in the 220 D model eye. 140

161 Chapter 5 Validation of optical modelling results Figure Reference and resultant ROIs obtained from manipulation 2 in a 220 D model eye. The images are arranged with increasing eccentricity horizontally, and increasing Δλ vertically downwards. The reference ROI was obtained with AO sensing and imaging on-axis on the same layer of retina under the same wavelength (670 nm) and zero corrector displacement. All other images were also obtained on the same layer of retina. Normalised MI values are displayed below the ROIs. All images were contrast-stretched for display purposes. Scale bar = 10 µm in the reference ROI. 141

162 Chapter 5 Validation of optical modelling results Figure Effect of shifting wavefront sensing wavelength in a 220 D model eye after optimising for defocus. Image quality is represented by MI values in the vertical axis, normalised against the MI value of the reference ROI. The wavelength difference (Δλ) between the sensing and imaging light is represented on the horizontal axis (Δλ = 0, 77 and 138 nm). Similar to the 60 D model eye, the imaging wavelength was 670 nm, while the sensing wavelengths were 532, 593 and 670 nm. The data point with Δλ = 0 at 0 was not represented here since this was the reference ROI, with a normalised MI value = 1.0. Overall, for the high powered 220 D model eye, the wavelength difference between AO sensing and imaging light was responsible for the reduction in image quality. The amount of reduction was similar across all eccentricities trialled. This was in contrast to the much lower powered 60 D model eye, where the image quality stayed quite constant with increasing Δλ Manipulation 3: Shifting axial position of the model eye In this simulation, wavefront sensing was performed at the posterior retina, while imaging was performed at the anterior retina separated by 200 µm with the same wavelength (λ = 670 nm), in order to introduce a first-order error identical to manipulation 1. Then, AO images were obtained while varying the axial position of the model eye relative to the AO system, resulting in a relative offset of the eye s exit pupil with respect to the corrector (deformable mirror) conjugate, while correcting for defocus alone. 142

163 Chapter 5 Validation of optical modelling results Figure 5.17 shows the reference and resultant ROIs from the 60 D model eye, arranged with increasing eccentricity across the rows, and increasing axial displacement along the columns starting at zero from the middle row. The corresponding MI values are shown below the images. Ink pattern was identical to manipulation 1, where the resultant ROIs from the 200 µm retinal thickness were used as the resultant ROIs for the row representing corrector offset = 0 in Figure Figure 5.18 shows the effect of shifting the axial position of the model eye on image quality. The image quality metric, represented by the MI values normalised against reference ROI, was plotted against the relative axial displacement of the eye from its nominal zero offset position. Positive displacement values indicate movement towards the AO system and vice versa. It can be seen from Figures 5.17 and 5.18 for the 60 D model eye that: 1. At a given eccentricity, image quality generally stayed constant with the increase in relative axial displacement values, although MI values did reduced slightly at axial displacement of -25 mm. 2. At a given relative axial displacement, MI values generally reduced from 0 to 8 by an average ~16%. The amount of reduction was generally similar across different relative axial displacements. 3. Subjective inspection of the image quality from Figure 5.17 showed that at a given eccentricity, the ink pattern generally appeared little changed with the increase in relative axial displacement, except at the -25 mm row, where the images appeared slightly blurrier. At a given relative axial displacement, the ink pattern generally appeared to be of similar quality with the increase in eccentricity, with a small amount of distortion seen in the 8 column. Interpretation of results: At a given eccentricity, subjective judgement of image quality from Figure 5.17 generally agreed with objective image quality measurement using MI values in Figure Image quality was little changed with the increase in relative axial displacement, except for the extreme negative relative axial displacement at -25 mm. This asymmetrical effect of the relative axial displacement on image quality was likely due 143

164 Chapter 5 Validation of optical modelling results to the fact that best AO correction occurred when the model eye was placed slightly towards the AO system. Similarly, it has also been shown before that the best position for isoplanatism need not be at the pupil plane (Bedggood and Metha 2010). A similar effect was also shown in the corresponding virtual manipulation in Chapter 3, where the least residual RMS for the human schematic eye occurred when the AO corrector was moved ~10 mm posterior to the pupil plane. At a given relative axial displacement, the small reduction in image quality with increase in eccentricity was likely the result of small amount of residual aberrations. Subjective judgement of the image quality in Figure 5.17 showed that the this was more pronounced at 8. Overall, it can be seen that AO image quality was robust against typical axial position errors in the 60 D model eye. This is similar to observations in human AO imaging, where small axial alignment error of the eye does not affect image quality. In addition, displacement of the model eye away from the AO system resulted in worse image quality compared to displacement towards it. 144

165 Chapter 5 Validation of optical modelling results Figure Reference and resultant ROIs from manipulation 3 in a 60 D model eye. The images are arranged with increasing eccentricity horizontally across, and increasing relative corrector displacement from the pupil plane vertically from the middle row. The reference ROI was obtained with AO sensing and imaging on-axis on the anterior retina at the same wavelength (670 nm) and zero corrector displacement. All other images were obtained with the same wavelength (670 nm) sensing and imaging lights, separated by a 200 µm thick retina (sensing at the posterior, imaging at the anterior retina). Normalised MI values are displayed 145

166 Chapter 5 Validation of optical modelling results below the images. All images were contrast-stretched for display purposes. Scale bar = 20 µm in the reference ROI. Figure Effect of the relative axial position displacement in a 60 D model eye under manipulation 3, after optimising for defocus. The resultant image quality is represented by MI values on the vertical axis, normalised against the MI value of the reference ROI. Wavefront sensing was performed on the posterior retina, while imaging on the anterior retina separated by 200 µm using the same (λ = 670 nm) wavelength. The model eye was moved axially to achieve the relative axial displacement, which is represented on the horizontal axis. Figure 5.17 shows the reference and resultant ROIs from the 220 D model eye in manipulation 3, arranged in the same way as for the 60 D model eye. Image features were identical to manipulation 1, where the resultant ROIs from the 200 µm retinal thickness were identical to the resultant ROIs along the 0 mm row. Figure 5.20 shows the normalised MI values plotted against the relative axial displacement for the 220 D model eye, on the same scale as the 60 D model eye. It can be seen from Figures 5.19 and 5.20 that for the 220 D model eye: 1. At a given eccentricity, MI values were on average ~30% lower from 0 to ± 25 mm at 0, ~45% lower at 4 and ~60% lower at 8. The amount of reduction was similar for both positive and negative relative axial displacements at 0 and 4. At 8, the reduction was more at the negative axial displacements. 2. At a given relative axial displacement, the MI values generally reduced from 0 to 8 by an average of ~40%. However, the reduction varies with the sign of 146

167 Chapter 5 Validation of optical modelling results axial displacement: about 7% at 0 mm displacement; ~55% at negative relative axial displacements and ~37% at positive relative axial displacements. 3. Subjective inspection of the images in Figure 5.19 showed that at a given eccentricity, the images became more blurry with relative axial displacement, especially at the negative relative axial displacements. At a given relative axial displacement, the images became more blurry with increased eccentricity, particularly from 4 to 8. Interpretation of results: At a given eccentricity, subjective inspection of the image quality in Figure 5.19 was consistent with the decline in MI values in Figure Similar percentage reduction in MI values due to residual aberrations resulted in similar amount of blur in the standard images in Figure 5.7. Therefore the reduction in image quality was likely to be the result of residual aberrations caused by the relative axial displacement of the model eye, while sensing and imaging on a separate plane. At the highest eccentricity of 8, the image quality was much worse at the negative axial displacements, similar to the observation for the 60 D model eye. At a given relative axial displacement, the reduction in MI values with increase in eccentricity was also consistent with the subjective inspection of image quality. This reduction in image quality was likely to be caused by residual aberrations as a result of the high power of the 220 D model eye. In addition, image quality worsened more rapidly at negative relative axial displacements, affirming the observation from the 60 D model eye that best AO correction likely occurred when the model eye was placed slightly towards the AO system. Overall, it can be seen that for the high powered 220 D model eye, more precise axial placement of the eye was required to avoid residual aberrations while sensing and imaging on separate planes. The tolerance (maximum displacement before significant reduction of image quality) of relative axial displacement for the 220 D model eye likely reside within the ± 5 mm range, according to the curves in Figure This was in contrast to the 60 D model eye, where the tolerance of relative axial displacement was likely much larger (within ~± 15 mm). 147

168 Chapter 5 Validation of optical modelling results Figure Reference and resultant ROIs used for manipulation 3 in a 220 D model eye. The images are arranged with increasing eccentricity horizontally across, and increasing relative corrector displacement from the pupil plane vertically from the middle row. The reference ROI was obtained with AO sensing and imaging on-axis on the anterior retina under the same wavelength (670 nm) and zero corrector displacement. All other images were obtained with the same wavelength (670 nm) sensing and imaging lights, but separated by a 200 µm thick retina (sensing at the posterior, imaging at the anterior retina). Normalised MI values are displayed 148

169 Chapter 5 Validation of optical modelling results below the images. All images were contrast-stretched for display purposes. Scale bar = 10 µm in the reference ROI. Figure Effect of the relative axial position displacement in a 220 D model eye under manipulation 3, after optimising for defocus. The resultant image quality is represented by MI values on the vertical axis, normalised against the MI value of the reference ROI. Similar to the 60 D model eye, wavefront sensing was performed on the posterior retina, while imaging on the anterior retina separated by 200 µm using the same (λ = 670 nm) wavelength. The model eye was moved axially to achieve the relative axial displacement, which is represented on the horizontal axis Summary of results and general discussion The above results showed that in general, the 60 D physical model eye was much less susceptible to the effect of all physical manipulations compared to the 220 D. All experimental parameters being equal, the difference in power between the model eyes was likely to result in larger amounts of uncorrected residual aberration in the 220 D model eye. This is because aberration components such as astigmatism, coma and spherical aberrations scale rapidly with eye power (to the first, second and third powers, respectively) (Smith and Atchison 1997), and so the amount of residual aberrations should be significantly higher with the 220 D compared to the 60 D model eye, under the same manipulations. For this reason, AO imaging in human eyes, which has an equivalent power of ~60 D, does not suffer markedly from reduced image quality under the same imaging conditions of the physical manipulations. That is, the typical retinal thickness, typical range of wavelengths used, and typical errors in corrector position are 149

170 Chapter 5 Validation of optical modelling results not expected to cause noticeable loss in image quality. However, for higher-powered eyes such as the rat, which has an equivalent power of ~300 D, the results presented here suggest that uncorrected residual aberrations due to the above factors in fact are more detrimental to image quality Comparison between virtual and physical manipulations The above results showed a similar trend to those from the corresponding virtual manipulations in Chapter 3 using the human and rat schematic eyes, although there residual RMS was used as the image quality metric instead of mutual information (MI). Note that an increase in residual RMS and a decrease in MI values indicate reduction in image quality. For the human schematic eye, Figures 2, 4 and 6 in Paper 1 in Chapter 3 showed that residual RMS did not exceed the diffraction limit for any of the three virtual manipulations for eccentricities 12. Similarly, subjective comparison of the resultant ROIs from the 60 D model eye showed largely similar image quality under the three physical manipulations. However, physical manipulation 3 did result in a slight worsening of image quality with negative relative axial displacement compared to positive values. On the other hand, since the rat schematic eye has an equivalent power of ~300 D, about 40% more than the 220 D physical model eye, direct comparison between the virtual and physical manipulations of the respective eyes is not strictly possible. Instead, the results between the rat schematic eye and the 220 D (physical) model eye can be compared qualitatively. Firstly, virtual manipulation 1 showed that for the rat schematic eye (Fig. 3 in Paper 1), residual RMS was within the diffraction-limit (Maréchal criterion: RMS < λ/14 indicates diffraction-limited imaging) for the entire retinal thickness at eccentricities 10. This was in contrast to physical manipulation 1 for the 220 D model eye, which showed a significant reduction in image quality with retinal thickness for all eccentricities (maximum 8 ), and therefore cannot be said to have remained diffractionlimited. Note that at higher eccentricities (> 10 ) in virtual manipulation 1, residual RMS did rise above the diffraction-limit as retinal thickness increased in the rat 150

171 Chapter 5 Validation of optical modelling results schematic eye. However, for physical manipulation 1, eccentricities > 8 was not tested with the physical model eye due to the technical difficulty described in section Overall, both virtual and physical manipulations 1 showed that deterioration of image quality was more rapid in the higher-powered eyes with the progressive separation of retinal depth of sensing and imaging lights. The image quality in the 220 D physical model eye appeared to deteriorate more rapidly with the increase in retinal thickness in manipulation 1 than did the rat schematic eye. Secondly, virtual manipulation 2 with the rat schematic eye (Fig. 5 in Paper 1) showed that residual RMS increased rapidly with the difference between sensing and imaging wavelengths to beyond the diffraction-limit at all eccentricities. In addition, the rate of increase of residual RMS was more rapid with increase in eccentricity. Similarly for the corresponding physical manipulation, worsening of the image quality was also seen in the 220 D model eye with increased wavelength difference. However, the rate of worsening was similar for all eccentricities trialled in the physical manipulation. Overall, both virtual and physical manipulations 2 showed deterioration of image quality was more rapid in the higher-powered eyes with the separation of sensing and imaging wavelength. The image quality in the 220 D physical model eye showed a less rapid deterioration with wavelength difference than did the rat schematic eye for manipulation 2. Thirdly, virtual manipulation 3 with the rat schematic eye showed a rapid increase in residual RMS with the relative axial displacement of the corrector from the eye s pupil plane, and that diffraction-limited imaging was only possible over a small (1 mm) range of relative axial displacement. Similarly, physical manipulation 3 with the 220 D model eye also showed a rapid worsening of the image quality with the increase in relative axial displacement, although the rate of deterioration was likely less than the rat schematic eye due to the lower power of the former. In addition, since the 220 D physical model eye had a lower power than the rat schematic eye, a larger range of displacement (± 25 mm) was used for the former than that for the latter (± 2 mm). Overall, both virtual and physical manipulations 3 showed deterioration of image quality was more rapid in the higher-powered eyes with the axial displacement of the pupil position relative to the corrector. The 220 D physical model eye performed better 151

172 Chapter 5 Validation of optical modelling results than the rat schematic eye for manipulation 3, implying that a larger tolerance of axial displacement error exists for the former Explanation of discrepancies of results for high-powered eyes The above comparison showed that virtual and physical manipulation results were similar for the lower-powered eyes. However, some discrepancies were noted in the results for the higher-powered eyes. Since the rat schematic eye is ~40% more powerful than the 220 D model eye, virtual manipulations with the rat schematic eye should have resulted in a more rapid deterioration in image quality than all of the physical manipulations with the 220 D model eye. The above comparison showed that was the case for manipulations 2 and 3. However, for manipulation 1, physical manipulation with the 220 D model eye resulted in apparently more rapid deterioration in image quality than the corresponding virtual manipulation with the rat schematic eye. This discrepancy could be a result of differences between the schematic and model eyes other than their different equivalent power; and differences between virtual and physical manipulations shown below. Firstly, the model eyes were constructed with only a plano-convex, aspheric lens and a pupil diaphragm as shown in Figure 5.1. On the other hand, the schematic eyes shown in Chapter 3 were more realistic, consisting of aspheric surfaces, a separate cornea and lens, and a gradient-index refractive profile for the lens. It has been shown in the human eye that the cornea and lens tend to contribute in opposite sign to total eye aberration thus improving performance in many cases (Artal, Berrio et al. 2002). A gradient index lens has been shown to better predict both monochromatic and chromatic aberrations of real eyes (Campbell and Hughes 1981; Liou and Brennan 1997), and to improve isoplanatism for retinal imaging (Bedggood and Metha 2010) compared to a homogenous equivalent lens. Therefore simplifying the refractive elements of the eye to a single lens in the physical model eye is expected to increase residual aberrations both on- and off-axis with the physical manipulations, especially for the higher powered 220 D eye. Secondly, the physical model eyes were made with flat retinas, as opposed to the curved retinas in the schematic eyes. It has been shown that a curved image surface reduces the amount of aberrations including astigmatism and coma, and increases off-axis imaging 152

173 Chapter 5 Validation of optical modelling results sharpness (Rim, Catrysse et al. 2008). In addition, astigmatism rises linearly with axial error and quadratically with field position (Smith and Atchison 1997). Therefore a flat retina was likely to increase the amount of residual astigmatism in the model eyes, towards the edge of the image in off-axis imaging, especially for the 220 D eye. Lastly, an actual AO ophthalmoscope was used for the physical manipulations, whereas only a phase plate was used for the virtual ones. Although aberrations were corrected by the DM in the physical manipulations, these corrections may not be as perfect as in the virtual manipulations, especially for higher order aberrations. In addition, while an isolated schematic eye can be highly isoplanatic, this performance can be lost in combination with an AO ophthalmoscope due to interaction between the uncorrected spherical aberration of the eye and the refractive elements of the AO telescope (Bedggood and Metha 2010). Despite these differences, the results from the three physical manipulations largely confirmed the conclusions drawn previously from the three corresponding virtual manipulations. That is, AO image quality in the human eye is robust against differences in imaging depth and wavelength compared to the wavefront beacon, and to positioning errors of the AO corrector. On the other hand, image quality appears to decline sharply with each of these manipulations in a high-powered eye such as the rat eye. 5.4 In vivo AO imaging of rat eyes Methods Since the current AO ophthalmoscope (shown in Chapter 4) was built with the intention of improving image quality for rat eyes, we also attempted AO imaging of the rat eye while taking into account the results of the physical and virtual manipulations. Hence efforts were made to ensure wavefront sensing and imaging were performed on the same retinal plane and wavelength, and the relative axial displacement of the eye s pupil was as close to zero as possible. The details of these are described below. In vivo AO imaging was attempted on the eyes of 3 healthy Long Evans rats (male and female), aged from 2 to 6 months, on 3 occasions - a representative example is shown in this chapter. The aim was to image blood vessels and photoreceptors without the aid of fluorescence. All animal handling was performed according to the ARVO statement for 153

174 Chapter 5 Validation of optical modelling results the Use of Animals in Ophthalmic and Vision Research. Ethics approval was obtained from the University of Melbourne Animal Ethics Committee. The anaesthesia and handling of the rat and fitting of a rigid contact lens have been described in detail in the pilot experiment in Chapter 2. For this experiment, the anaesthetised rat was gently fastened to a re-designed stereotaxic small animal platform shown in Figure The small animal platform, when secured on the aluminium frame attached to the Velmex Bislide (see Figure 5.1), allowed translation and rotation of the rat along all three axes for eye alignment. While not critical, an attempt was made to align the animal in the stage so that the pitch, yaw and roll axes intersected as close as possible to its pupil centre. This made it easier when aligning with the ophthalmoscope and centring the rat s retinal region of interest. Figure Photos of the custom-made, stereotaxic small animal platform for the rat. It was constructed to allow rotation around the x- ( pitch axis, represented by (1)), y- ( roll axis, represented by (2)), and z- ( yaw axis) axes. The inner barrel allows translation along the y- axis (3), whereas a horizontal scale allowed translation along the x-axis (4) to align the pupil with the z-axis. The axes are shown in both the side view (a) and front view (b) of the stage. A limitation of the platform is that rotations along these axes are not independent since they do not all intersect at the centre of the pupil. After roughly aligning the rat eye with the ophthalmoscope, the axial and lateral positions of its pupil, which was illuminated with the WFS light, were fine-tuned using the Velmex Bislide while observing the live pupil image from the pupil camera. An annular WFS beacon with 3.5 mm inner diameter, and 4 mm outer diameter was used in order to reduce the depth of focus of the beacon on the retina (Geng, Schery et al. 2011), 154

175 Chapter 5 Validation of optical modelling results maximising the likelihood that the beacon came from a single retinal layer. Then, while observing the live retinal image in the wide-field retinal camera with the imaging light on, the rat was positioned so that the desired retinal location was centered on the camera. In addition, the refractive error of the rat eye fitted with the rigid contact lens was estimated subjectively by inserting trial lenses in the pupil plane prior to the widefield retinal camera while observing the clarity of the retinal image. Next, the flip mirrors shown in Chapter 4 were flipped down to disengage the wide-field arm, while engaging the AO imaging arm. The SHWS spots were sharpened by focusing the input WFS beam using trial lenses inserted into the pupil plane in the light delivery arm (marked Trial lens in the light delivery arm in Figure 3 of Chapter 4). Then, the bulk of low-order refractive error of the rat eye was corrected with trial lenses inserted into the AO imaging arm (marked Trial lens in the imaging arm in Figure 3 of Chapter 4) before closing the AO loop to correct for the remaining measurable aberrations. Multiple images were then acquired at 15 Hz with 3 ms exposure using the AO imaging camera. The imaging light was a 670 nm laser diode (MeshTel, Genoa, NV, U.S.A.), passed through 2 m of multimode optical fibre (BFL37-200, 0.37 NA, 200 μm core, Thorlabs, Newton, NJ), which resulted in a field-of-view in the rat eye of ~2.4 (system space). The WFS light was a diode-pumped solid-state (DPSS) laser, with the same nominal wavelength of 670 nm. Speckle in the imaging and WFS lasers was reduced by passing the light through spatial phase randomisers (SPR) as mentioned in Chapter 4. The imaging and WFS lasers were pulsed in anti-phase at 15 Hz, with powers of 360 μw and 12.5 μw at the cornea, respectively. The anti-phase pulsing was necessary to ensure efficient separation of WFS and imaging lights when using the same wavelength for sensing and imaging. At these light levels and pulse frequency, the powers were within the maximum permissible exposure (MPE) for 60 seconds of repetitive pulse exposure (Delori, Webb et al. 2007). 155

176 Chapter 5 Validation of optical modelling results Results and discussions Typical SHWS spots from the rat Figure 5.22 shows typical SHWS spot patterns from the rat retina with a rigid contact lens, after correction with trial lenses but before AO correction. The size of the annular wavefront beacon is the same for both images in Figure Figure 5.22(a) shows the typical SHWS spots when the WFS beacon was reflected from the wall of a large blood vessel (this vessel is shown in Figure 5.23(a)). The SHWS spots appear to be of good quality and well-focused, unlike the blurry appearance obtained in the pilot experiment (similar to those shown by de la Cera et al. (2006)). However, some scintillation of spot brightness was observed during wavefront sensing due to movement of the spot on the retina from the breathing artefact of the rat, and blood flow within the vessel. Some of the spots also appear elongated towards the pupil edge. Figure Typical SHWS spots from the rat eye with the use of a rigid contact lens. (a): When the WFS beacon was reflected from the wall of a large blood vessel; (b): When the WFS beacon was reflected from a featureless part of the retina. Both images were obtained before AO correction and contrast-stretched for display purposes. Figure 5.22(b) shows the typical SHWS spots when the WFS beacon was reflected from a featureless part of the retina of the rat eye. Compared to Figure 5.22(a), the spots appear much larger in size. The larger size of the SHWS spots (compared to Figure 5.22(a)) was likely due to reflection of the WFS beacon from the dioptrically thick retina of the rat. However, each spot was still distinct, as opposed to the blurry 156

177 Chapter 5 Validation of optical modelling results appearance seen in the pilot experiment. Similar to Figure 5.22(a), some elongation of the spots still occurred towards the pupil edge. The typical residual RMS for the rat eye after best AO correction was ~ µm over a 3.5 mm pupil, compared to ~0.02 µm for the physical model eyes with the same pupil size. In addition, AO imaging was also attempted on the human eye prior to the rat experiment to verify the ability of the AO ophthalmoscope to perform in vivo imaging. Residual RMS from the human eye with a 3.5 mm pupil after AO correction was ~0.04 µm, under imaging wavelength of 670 nm. Note that for a 670 nm imaging light, the image is considered diffraction-limited when the residual RMS is < 0.05 µm. From the above results, it can be seen that the rat AO ophthalmoscope was capable of achieving diffraction-limited imaging in both model and human eyes. For the rat eye, the SHWS spot was significantly improved compared to those obtained in the pilot experiment, which had similar appearance to those shown by de la Cera et al. (2006). However, AO correction in the rat eye was close to, but not within the diffraction limit, reaching a residual RMS of ~ µm. This was possibly due to a combination of poorer SHWS spot quality towards the pupil edge, and the presence of breathing artefact from the rat under general anaesthesia Retinal image quality from the rat Figure 5.23(a) shows an example of the best-corrected image quality obtained from a rat eye. The residual RMS was ~0.10 µm, and the corresponding SHWS spots were shown in Figure 5.22(a). The image is an average of 25 registered frames and contraststretched for display purposes. The imaged area was just superior to the optic nerve head, and a large blood vessel (~20 µm in diameter) can be seen in the image. As a comparison, a representative example of the best corrected AO image of a blood vessel from the rat eye from the pilot experiment (shown in Chapter 2) using the previous generation flood AO ophthalmoscope designed for primates is also shown in Figure 5.23(b), averaged over 20 frames and contrast-stretched for display purposes. The pilot image was obtained with 830 nm and 670 nm as the sensing and imaging light, respectively. No annular WFS beacon was used, and there was no pupil camera in the primate AO ophthalmoscope. The WFS beacon was positioned on the retina just 157

178 Chapter 5 Validation of optical modelling results adjacent to the blood vessel, in the centre of the image. The reported residual RMS was also ~0.10 µm. However, due to the poor SHWS spot quality (not recorded but similar to those shown by de la Cera et al. (2006)), the measurement of the residual RMS was likely inaccurate. Figure Comparison of best corrected AO images from the rat AO ophthalmoscope and pilot data from the primate AO ophthalmoscope. (a): Image from the rat AO ophthalmoscope; (b): Pilot data from the primate AO ophthalmoscope, adjusted to the same size to account for system magnification difference. Sensing wavelengths were 670 nm and 830 nm for (a) and (b), respectively. Imaging wavelength was 670 nm for both (a) and (b). The coefficient of variation values (CV All ) were calculated for the regions of interest marked by the same size of white squares in each image, which contain similar features. CV All 0.21 in (a), and 0.18 in (b), indicating better image contrast in the former. Both images were contrast-stretched to fill their colour map for display purposes. Scale bar = 20 µm in both images. In fact, it can be seen subjectively that image quality was better in Figure 5.23(a), obtained with the rat AO ophthalmoscope. The edge of the vessel is more defined compared to that from the pilot experiment. In addition, image quality was also quantified objectively by calculating coefficient of variation (CV All ) values for the regions of interest (ROI) marked by the white squares in both images, which contain similar features (blood vessel). Recall that in section , the concept of CV All was introduced as an image quality metric that measures image contrast (higher CV All = better contrast), defined by the standard deviation of all pixels over the mean of all pixels in the ROIs. The CV All value for the ROI in Figure 5.23(a) was ~0.21, compared to ~0.18 in Figure 5.23(b), indicating better image contrast for the blood vessel in the former. 158

179 Chapter 5 Validation of optical modelling results The subjectively and objectively better image quality in Figure 5.23(a) was likely the result of performing wavefront sensing and imaging with the same wavelength and retinal layers, and more accurately positioning of the rat eye axially using the rat AO ophthalmoscope. Although image quality of large blood vessels could be improved using the rat AO ophthalmoscope, image quality in the rat was still below expectation based on experience with human imaging, especially given the fact that the numerical aperture in the rat eye is more than twice as that as the human eye with dilated pupils (Geng, Greenberg et al. 2009). For reference, Figure 5.24 shows cone images 2 superior to the fovea from a healthy human eye, obtained using the same AO ophthalmoscope as the rat images in Figure Residual RMS for the human eye image is ~0.04 µm over a 3.5 mm pupil, indicating diffraction-limited imaging. Retinal cones can be clearly distinguished in the image, showing the capability of the rat AO ophthalmoscope to obtain diffraction-limited images in vivo. Note that this image is also shown in the HiLo paper in Chapter 6. Figure Retinal cone image from a healthy human eye obtained using the rat AO ophthalmoscope. Image was obtained approximately 2 superior to the fovea, averaged over 30 frames and linearly stretched to fill the colormap for display purposes. The fovea is towards the bottom of the image. Pupil size = 3.5 mm. Scale bar = 30 µm. 159

180 Chapter 5 Validation of optical modelling results Although human cones could be imaged above, it was not possible to obtain AO images of capillaries or photoreceptors in the rat using the current AO ophthalmoscope. The reasons for this remain unclear, but was possibly due to intra-ocular scatter from the ocular media and the retina using flood-illumination, the low contrast of blood vessels using 670 nm as the imaging light and the poor waveguide property of the photoreceptors, which were dominated by rods in the rodent eye (La Vail 1976; Fekete and Barnstable 1983; Szel and Rohlich 1992) Summary of results and general discussion The current AO images of the rat eye showed superior image quality compared to the pilot image, which was obtained with the primate AO ophthalmoscope described in Chapter 2. The following factors, verified by physical manipulations on model eyes, likely led to the improved image quality: 1. The same wavelength was used for sensing and imaging, compared to a Δλ of 160 nm ( ) in the pilot experiment. 2. Refined focusing of the WFS beacon on the retina, as well as performing wavefront sensing and imaging as much as possible on the same plane, due to the WFS beacon being reflected from the wall of the large blood vessel. 3. More accurate axial positioning of the rat s eye using a pupil monitor. Although there was improvement of AO image quality compared to the pilot data, obtaining diffraction-limited AO correction in the rat eye was still challenging using the current rat AO ophthalmoscope, with residual RMS in the range of ~ µm. This could be due to a combination of factors, including excessive movement of the rat from the breathing artefact, and elongation of the SHWS spots towards the edge of the pupil. Using an annular WFS beacon and correction of the input WFS beam with trial lens did improve the SHWS spot quality in the rat eye, but further improvement of the spot quality could be achieved by correcting the input WFS beam with AO, as routinely done in AOSLO systems (Geng, Dubra et al. 2012). However, this approach proved technically infeasible for the flood AO system used for this experiment. 160

181 Chapter 5 Validation of optical modelling results Given that the rat has more than double the numerical aperture (NA) compared to the dilated human eye, one would expect much better image resolution after AO correction (Geng, Greenberg et al. 2009). However, despite the modest improvements obtained, flood AO image quality from the rat was still markedly inferior compared to what is routinely achieved from the human eye with the same hardware and software. Some of the possible explanations for the inferior image quality from the rat, in addition to the challenging wavefront sensing step mentioned above, are provided below. Firstly, the AO retinal image of the rat in Figure 5.23(a) was obtained with 670 nm, which did not give good contrast for blood vessels. Much better contrast of the blood vessels could be achieved with a shorter wavelength, due to the absorption of shorter wavelength by haemoglobin (Tam, Martin et al. 2010). The experiments described in the following chapters therefore used 532 nm as the imaging light. Similarly, contrastenhancing agents could also be used to improve the image quality of retinal capillaries and retinal ganglion cells, as shown by previous experiments (Geng, Dubra et al. 2012; Schallek, Geng et al. 2013; Zawadzki, Zhang et al. 2015). In addition, the lack of a confocal pinhole in the flood AO ophthalmoscope meant that the light scattered from shallower retinal layers such as the retinal nerve fibre layer in the rat eye could drown out features from deeper retinal layers such as smaller blood vessels, capillaries and photoreceptors, which could be resolved with AOSLO systems (Geng, Greenberg et al. 2009; Geng, Dubra et al. 2012). In order to overcome the challenge of intra-ocular scatter in flood AO ophthalmoscopes, a pseudo-confocal imaging technique called HiLo microscopy, which has been developed specifically for flood imaging microscopes (Lim, Chu et al. 2008; Santos, Chu et al. 2009; Lim, Ford et al. 2011), was next trialled. HiLo imaging has been shown to produce pseudo-confocal images with quality rivalling that of a scanning system in some microscopy applications, and could therefore improve AO retinal image quality for the rat. As for the challenging wavefront sensing step, it can be forfeited all together in sensorless AO, which we termed non-sensing AO (NS-AO). NS-AO iteratively corrects the aberrations based on the improvement of AO image quality upon progressive perturbations of the deformable mirror (Muller and Buffington 1974; Fienup and Miller 2003; Hofer, Sredar et al. 2011; Jian, Xu et al. 2014; Wong, Jian et 161

182 Chapter 5 Validation of optical modelling results al. 2015). NS-AO in vivo imaging has been shown in scanning AO ophthalmoscopes previously for both human and mouse eyes (Hofer, Sredar et al. 2011; Jian, Xu et al. 2014; Wong, Jian et al. 2015). However, it has not been incorporated into a flood AO ophthalmoscope. The details of HiLo imaging and NS-AO experiments is presented alongside peerreviewed papers in the next two chapters. 162

183 Chapter 6 Improving adaptive optics image quality using HiLo imaging Chapter 6 Improving adaptive optics image quality using HiLo imaging 6.1 Introduction As described in the literature review in section 1.6.4, the contrast of image structures derived from flood AO systems is generally lower than confocal scanning AO images of the same retinal regions, because the confocal pinhole acts to reject nearly all light scattered from out-of-focus retinal planes. This is a major advantage of confocal scanning systems over flood imaging systems. However this comes the cost of generally slower imaging speeds, aggravated by the interaction of the scanned spot with eye motion to generate intra-frame distortions that are difficult to unwarp (Cooper, Sulai et al. 2016). What is desired is a method that combines the fast, undistorted full-frame advantages of flood-based imaging with the enhancements in contrast that comes from rejecting 'outof-focus' scattered light. A recently developed imaging technique known as HiLo microscopy has been proposed to do just that, and initial demonstrations have shown that this technique can provide pseudo-confocality and improve image contrast in floodillumination microscopes (Lim, Chu et al. 2008; Santos, Chu et al. 2009; Mertz and Kim 2010; Lim, Ford et al. 2011; Mertz 2011; Ford, Lim et al. 2012; Michaelson, Choi et al. 2012). In this chapter, HiLo imaging is explained in detail and results are presented following incorporation of this technology into the rat flood AO ophthalmoscope in an attempt to improve image contrast in the rat eye. The results have been published as a peerreviewed journal paper (Zhou, Bedggood et al. 2014), which is attached below. 6.2 Paper 2: Improving high resolution retinal image quality using speckle illumination HiLo imaging Below is a copy of the paper, published in Biomedical Optics Express in August 2014 and reproduced with permission from OSA publishing. 163

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201 Chapter 7 Improving adaptive optics image quality using non-sensing AO Chapter 7 Improving adaptive optics image quality using non-sensing AO 7.1 Introduction As shown in Chapter 5, wavefront sensing of the rat eye remains challenging even after the implementation of an annular WFS beacon with adjustable focus. One (somewhat radical) solution to the difficult wavefront sensing step is to forfeit it altogether and instead use a technique variably called wavefront sensorless AO, imaged-based AO, or, as in this thesis, non-sensing AO (NS-AO). These names reflect the fact that the method relies solely on the AO image itself to provide feedback to the DM to correct for aberrations. In the dioptrically thick rodent eye in particular, NS-AO has the potential for additional advantage in bypassing the large non-common path errors created by differences in wavelengths and planes of focus between the WFS and imaging lights, as shown in in the paper presented in Chapter 3 (Zhou, Bedggood et al. 2012). NS-AO has its origin in astronomy (Muller and Buffington 1974), and has recently been incorporated into scanning AO ophthalmoscopes for both human and rodent in vivo imaging (Hofer, Sredar et al. 2011; Bonora and Zawadzki 2013; Jian, Xu et al. 2014; Wong, Jian et al. 2015). NS-AO has also been incorporated into a flood AO ophthalmoscope (Zommer, Ribak et al. 2006) for model eye imaging. However, in vivo imaging in the human or rat eye has not been shown before using this technique in a flood AO ophthalmoscope. This chapter presents a peer-reviewed journal paper (Zhou, Bedggood et al. 2015) that describes the implementation of NS-AO in the rat flood AO ophthalmoscope shown in Chapter 4. By implementing NS-AO, it was hoped that AO image quality could be improved in the rat eye when compared to the WFS-AO images shown in the previous chapters. 7.2 Paper 3: Contrast-based sensorless adaptive optics for retinal imaging Below is a copy of the paper, published in Biomedical Optics Express in September 2015 and reproduced with permission from OSA publishing. 181

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