Optimization of pupil design for point-scanning and line-scanning confocal microscopy

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1 Optimization o pupil design or point-scanning and line-scanning conocal microscopy Yogesh G. Patel, 1,* Milind Rajadhyaksha, 2 and Charles A. DiMarzio 1,3 1 Electrical & Computer Engineering Department, Northeastern University, 360 Huntington Avenue, Boston, Massachusetts 02115, USA 2 Dermatology Services, Department o Medicine, Memorial Sloan-Kettering Cancer Center, 160 East 53rd Street, New York, New York 10010, USA 3 Mechanical & Industrial Engineering Department, Northeastern University, 360 Huntington Avenue, Boston, Massachusetts 02115, USA *ypatel@ece.neu.edu Abstract: Both point-scanning and line-scanning conocal microscopes provide resolution and optical sectioning to observe nuclear and cellular detail in human tissues, and are being translated or clinical applications. While traditional point-scanning is truly conocal and oers the best possible optical sectioning and resolution, line-scanning is partially conocal but may oer a relatively simpler and lower-cost alternative or more widespread dissemination into clinical settings. The loss o sectioning and loss o contrast due to scattering in tissue is more rapid and more severe with a line-scan than with a point-scan. However, the sectioning and contrast may be recovered with the use o a divided-pupil. Thus, as part o our eorts to translate conocal microscopy or detection o skin cancer, and to determine the best possible approach or clinical applications, we are now developing a quantitative understanding o imaging perormance or a set o scanning and pupil conditions. We report a Fourier-analysis-based computational model o conocal microscopy or six conigurations. The six conigurations are point-scanning and line-scanning, with ull-pupil, halpupil and divided-pupils. The perormance, in terms o on-axis irradiance (signal), resolution and sectioning capabilities, is quantiied and compared among these six conigurations Optical Society o America OCIS codes: ( ) Conocal microscopy; ( ) Scanning microscopy; ( ) Conocal microscopy; ( ) Medical optics instrumentation; ( ) Optical design o instruments. Reerences and links 1. S. G. Gonzalez, M. Gill, and A. C. Halpern, eds., Relectance Conocal Microscopy o Cutaneous Tumors An Atlas with Clinical, Dermoscopic and Histological Correlations (Inorma Healthcare, London, 2008). 2. A. A. Tanbakuchi, J. A. Udovich, A. R. Rouse, K. D. Hatch, and A. F. Gmitro, In vivo imaging o ovarian tissue using a novel conocal microlaparoscope, Am. J. Obstet. Gynecol. 202(1), 90.e1 90.e9 (2010). 3. Y. Zhao, A. E. Elsner, B. P. Haggerty, D. A. VanNasdale, and B. L. Petrig, "Laser scanning digital camera or retinal imaging with a 40 degree ield o view," in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society o America, 2006), paper FMG5. 4. C. J. R. Sheppard and X. Q. Mao, Conocal microscopes with slit apertures, J. Mod. Opt. 35(7), (1988). 5. T. Wilson and S. J. Hewlett, Imaging in scanning microscopes with slit-shaped detectors, J. Microsc. 160(Pt 2), (1990). 6. A. A. Tanbakuchi, A. R. Rouse, J. A. Udovich, K. D. Hatch, and A. F. Gmitro, Clinical conocal microlaparoscope or real-time in vivo optical biopsies, J. Biomed. Opt. 14(4), (2009). 7. D. S. Gareau, S. Abeytunge, and M. Rajadhyaksha, Line-scanning relectance conocal microscopy o human skin: comparison o ull-pupil and divided-pupil conigurations, Opt. Lett. 34(20), (2009). 8. P. J. Dwyer, C. A. DiMarzio, and M. Rajadhyaksha, Conocal theta line-scanning microscope or imaging human tissues, Appl. Opt. 46(10), (2007). 9. P. J. Dwyer, C. A. DiMarzio, J. M. Zavislan, W. J. Fox, and M. Rajadhyaksha, Conocal relectance theta line scanning microscope or imaging human skin in vivo, Opt. Lett. 31(7), (2006). (C) 2011 OSA 1 August 2011 / Vol. 2, No. 8 / BIOMEDICAL OPTICS EXPRESS 2231

2 10. B. Simon and C. A. Dimarzio, Simulation o a theta line-scanning conocal microscope, J. Biomed. Opt. 12(6), (2007). 11. C. J. Koester, Scanning mirror microscope with optical sectioning characteristics: applications in ophthalmology, Appl. Opt. 19(11), (1980). 12. E. H. K. Stelzer and S. Lindek, Fundamental reduction o the observation volume in ar-ield light microscopy by detection orthogonal to the illumination axis: conocal theta microscopy, Opt. Commun. 111(5-6), (1994). 13. R. H. Webb and F. Rogomentich, Conocal microscope with large ield and working distance, Appl. Opt. 38(22), (1999). 14. K. Si, W. Gong, and C. J. R. Sheppard, Three-dimensional coherent transer unction or a conocal microscope with two D-shaped pupils, Appl. Opt. 48(5), (2009). 15. W. Gong, K. Si, and C. J. R. Sheppard, Optimization o axial resolution in a conocal microscope with D- shaped apertures, Appl. Opt. 48(20), (2009) (H.). 16. W. Gong, K. Si, and C. J. R. Sheppard, Divided-aperture technique or luorescence conocal microscopy through scattering media, Appl. Opt. 49(4), (2010) (H.). 17. J. T. C. Liu, M. J. Mandella, J. M. Craword, C. H. Contag, T. D. Wang, and G. S. Kino, Eicient rejection o scattered light enables deep optical sectioning in turbid media with low-numerical-aperture optics in a dual-axis conocal architecture, J. Biomed. Opt. 13(3), (2008). 18. J. T. C. Liu, M. J. Mandella, H. Ra, L. K. Wong, O. Solgaard, G. S. Kino, W. Piyawattanametha, C. H. Contag, and T. D. Wang, Miniature near-inrared dual-axes conocal microscope utilizing a two-dimensional microelectromechanical systems scanner, Opt. Lett. 32(3), (2007) (H.). 19. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968). 20. C. A. DiMarzio, Diraction, in Optics or Engineers (CRC Press, Boca Raton, FL, to be published). 1 Introduction Both point-scanning and line-scanning conocal microscopes have proven successul or imaging o human tissues, providing resolution and optical sectioning to observe nuclear and cellular detail. Both technologies are being translated or diverse clinical applications [1 3]. While traditional point-scanning is truly conocal and oers the best possible optical sectioning and resolution, line-scanning is partially conocal but may oer a relatively simpler and lower-cost alternative or more widespread dissemination into clinical settings. A line-scan is conocal in only one dimension (orthogonal to the line) but not in the other dimension (that is parallel). Consequently, the diraction-limited optical sectioning is ~20% weaker than that with a point scan [4,5]. However, with a reasonably high numerical aperture, the sectioning is suicient or imaging nuclear and cellular detail in human tissues such as, or example, the epidermis in skin and epithelium in ovaries [6,7]. O more serious consequence, is the loss o sectioning with increased imaging depth. The loss o sectioning and loss o contrast due to scattering is more rapid and more severe than with a point-scan. Interestingly, the optical sectioning and contrast with line-scanning conocal microscopy may be recovered with the use o a divided-pupil, as was experimentally discovered in human skin [8 10]. The divided-pupil coniguration was originally pioneered by Koester [11] and is similar to that o the theta microscope which was later developed by Stelzer and Webb [12,13]. More recently, Si et al., Gong et al. and Sheppard et al. reported a theoretical analysis o the divided-pupil coniguration with point-scanning, showing improvement in optical sectioning, compared to the ull-pupil coniguration, under certain detector conditions [14 16]. Liu et al., too, have reported analytical and experimental imaging results, showing stronger sectioning and enhanced contrast in deep tissue with their dual-axes point-scanning design, compared to a conventional single axis [17,18]. The dual axes design mimics the divided-pupil and theta microscope conigurations, in which the transmitter and receiver paths are separate and intersect only in the object plane (optical section). The ull-pupil is, o course, the standard coniguration, in which the transmitter and receiver paths are coaxial. The results to date indicate that the divided-pupil approach may oer improved imaging perormance in scattering tissues, compared to the ull-pupil, with either point-scanning or line-scanning. Moreover, as part o ongoing eorts to translate conocal microscopy or detection o skin cancer, we are exploring a simpler and lower-cost line-scanning coniguration [7 9] that may oer a practical alternative to currently available point-scanning technology. Thus, to determine the best possible approach or clinical applications, we are (C) 2011 OSA 1 August 2011 / Vol. 2, No. 8 / BIOMEDICAL OPTICS EXPRESS 2232

3 now developing a quantitative understanding o imaging perormance or a set o scanning and pupil conditions. In this paper, we report a Fourier-analysis-based computational model o conocal microscopy or six conigurations. The six conigurations are point-scanning and linescanning, with three pupil conditions which are ull-pupil, hal-pupil and divided-pupil. The ull-pupil coniguration is with transmitter and receiver through the same pupil. The hal-pupil coniguration is with transmitter and receiver through the same hal-pupil. Although not a practical coniguration, it provides useul insight into the degradation o perormance with hal o the circular aperture. The hal-pupil coniguration is important in understanding the improved out-o-plane rejection, however, not the best coniguration or optimal resolution. Finally, we consider a divided-pupil coniguration, with hal-pupils separated by an aperture divider, one-hal or transmission and the other or receiver detection. Comparative analysis o the hal-pupil and divided-pupil conigurations allows us to discriminate between the eects o reducing the numerical aperture and separating the two paths. The perormance, in terms o on-axis irradiance (signal), resolution and sectioning capabilities, is quantiied and compared among these six conigurations. We present results o integrated intensity in the coherent-transmission path and incoherent-receive path, which can be used to understand background speckle rom scattered light. 2. Theory Light propagation in the transmitter and receiver paths can be characterized using Fourier methods [19]. Speciically, the ield in the pupil plane o the objective lens is proportional to the Fourier transorm o the ield in the ield plane o the objective lens. For example, a uniorm plane wave in a circular aperture in the pupil plane is diracted so that it converges to orm an Airy pattern as the point-spread-unction (PSF) in the ield plane. We use the term ield plane or the object or image plane. Coherent light propagation is described by the Fresnel-Kircho integral: jkr jk e EField ( x, y, z ) EPupil ( xp, yp,0) dxpdy p 2 Aperture r (1) where the distance, r, is between (x,y,z ), the ield coordinates, and (x p,y p,0), the pupil coordinates. By taking the paraxial approximation o Eq. (1) and expanding the radial distance, r, we obtain the ield as a Fourier transorm: 2 2 ( ) ( xpx yp y ) jkz x y j2 jk jke 2 r z F Field (,, ) Pupil ( p, p,0) p p 2 z E x y z E x y e e dx dy (2) where the Fresnel radius, r F, is given by, r F 2 z. (3) We have assumed z is large enough to neglect a curvature term in x and y. In practice, this condition can be satisied by the use o a Franuhoer lens (see, e.g [20].). Equation (2) deines the relationship between the pupil unction and the ield unction in terms o a Fourier transorm (FT) pair. In order to calculate the ield at a location, z, other than the ield plane, a deocus parameter, Q, can be applied to the FT pair, where, 1 1 1, rf 2 Q. (4) Q z z o (C) 2011 OSA 1 August 2011 / Vol. 2, No. 8 / BIOMEDICAL OPTICS EXPRESS 2233

4 Equation (2) can be written with the deocus parameter: 2 2 ( x ) 2 2 y ( x ) ( ) p y xpx p yp y jkz j2 j2 jk jke 2z 2Q z Field Pupil p p p p 2 z E ( x, y, z ) e E ( x, y,0) e e dx dy. (5) The Fourier analysis allows or treating Eq. (3) and Eq. (5) in terms o spatial requencies, where the spatial requencies are deined as: xp yp x, y. z o z (6) o We can describe an optical system by saying that the image is the convolution o the object and the point spread unction (PSF). Equivalently, we can say that the FT o the object is multiplied by the transer unction to produce the FT o the image, where the transer unction is the FT o the PSF. For coherent imaging, we consider the object and image to be described by electric ields, and we call the PSF the coherent PSF. For incoherent imaging, the object and image are characterized by irradiance, and we use the terms incoherent PSF, and incoherent transer unction or optical transer unction. Thus optical systems can be analyzed by using only Fourier transorms, inverse Fourier transorm, and multiplication. 3. Fourier optics model The Fourier-analysis computational model was developed or two scanning modes, pointscanning and line-scanning. In each mode, we evaluated the perormance or three pupil conigurations: ull-pupil, hal-pupil and divided-pupil. In the ull-pupil, the transmitter and receiver path are through the entire pupil. For the hal-pupil coniguration, the transmitter and receiver path are through the same hal o the pupil. The hal-pupil is a useul intermediate step between the ull-pupil and divided-pupil coniguration. It provides the same pupil geometry as the divided-pupil, and thereore the same resolution, and beam proiles. It is not a practical approach to microscopy, but provides insight into resolution and sectioning. The divided pupil enhances contrast, because the transmitter and receiver paths are through opposite halves o the pupil, leading to rejection o light scattered by objects ar rom the ield plane at z. Fig. 1. Fourier-analysis computational model lowchart. A complete Fourier-analysis computational model lowchart, in three components, is shown in Fig. 1: (I) the transmission irradiance at the sample, (II) the receiver unction at the (C) 2011 OSA 1 August 2011 / Vol. 2, No. 8 / BIOMEDICAL OPTICS EXPRESS 2234

5 detector, and (III) the aperture coniguration at the pupil plane. Each row in Fig. 1 will be discussed in the ollowing sections Coherent-transmitter path For the transmitter s igure o merit, we compute the on-axis irradiance along the coherenttransmitter path o a conocal point-scanning or line-scanning microscope in order to optimize the proile o a Gaussian beam in a ull-pupil or divided-pupil. We deine the pupil diameter as D and the Gaussian beam diameter at 1/e 2 is h D. The variable parameter, the ill-actor, h, is the ratio o the 1/e 2 diameter o the Gaussian beam to the diameter (D) o the ull-pupil. From Fig. 1, on the transmitter side, we start with a coherent source, E Pupil (x p,y p,0), at the pupil plane (Ia) and compute the ield E Field (x,y,z ) in the ield plane (Ib) according to Eq. (5). The irradiance (Ic), is E Field (x,y,z ) 2, the square o the magnitude o the ield (Ib) Incoherent-receiver path For the receiver side, we use incoherent calculations because the detected signal is proportional to E 2. Incoherent analysis or a single unresolved scatterer is acceptable because we can use coherent or incoherent. For a collection o scatterers, which may be outo-ocus, to determine clutter, incoherent is the right approach. Thereore, we need the incoherent transer unction and the incoherent-point spread unction. The image in incoherent receiver is calculated by convolving the object irradiance with the incoherent-point spread unction (PSF). We thereore need a description o the receiver in the ield plane. In the absence o diraction, the receiver would be described as a geometrical optics image o the pinhole, or speciically a unction that is non-zero inside a inite radius. A complete description o the receiver unction is given as the convolution o this pinhole unction with the incoherent-psf o the optical system. Equivalently, in the pupil plane, we multiply the Fourier transorm o the pinhole unction by the incoherent transer unction. The pinhole unction is shown in Fig. 1(IIa), along with its Fourier transorm (IIb). Recalling that (1) the incoherent optical transer unction is the Fourier transorm o the incoherent PSF, (2) the incoherent PSF is the square o the coherent PSF, and (3) the coherent PSF is the inverse Fourier transorm o the coherent transer unction, we calculate the optical transer unction as shown in line III o Fig. 1. The coherent transer unction, given by the aperture or (IIIa) is inverse Fourier transormed to the produce the coherent PSF (IIIb). Next, we compute the magnitude squared o the coherent PSF to obtain the incoherent PSF and then Fourier transorm it to obtain the optical transer unction (IIId). We multiply this optical transer unction by the Fourier transorm o the pinhole (IIb) and inverse Fourier transorm to obtain the receiver unction (IV). Now we have the transmitter irradiance in (Ic) and the receiver unction in (IV). Multiplying these two, we obtain the sensitivity o the microscope (V) to a point target o scattering cross-section. We can then (1) examine the maximum value o this unction to determine signal strength, (2) measure its variation with x (or y) to determine transverse resolution, or (3) integrate it over all x and y to determine the response to a thin target. Finally, we can vary z o = z + z, and determine how the thin target signal degrades with deocusing, z, in order to evaluate sectioning ability. 4. Results We will deine all transverse distances in terms related to the pupil diameter, D. We have already mentioned the beam diameter, d = h D. In the divided-pupil coniguration we can vary the width o the divider, w = a w D, and the center position o the light source, (x c,y c ), given as x c = a x D and y c = a y D. In the ull-pupil coniguration, symmetry dictates that the center position o the Gaussian beam light source, (x c,y c ), is optimally set at (0,0) or maximum irradiance at the sample, as shown in the pupil plane o Figs. 2a, 2b, 2c. (C) 2011 OSA 1 August 2011 / Vol. 2, No. 8 / BIOMEDICAL OPTICS EXPRESS 2235

6 Transmission Image Irradiance y, Image Position, (μm) Transmission Pupil Irradiance y 1, Pupil Position, (mm) Coherent-transmitter path Numerous parameters are available or optimizing the coherent-transmitter path, such as image irradiance and peak irradiance, resolution, contrast and signal to noise ratio. The choice, o course, will usually be an optimum compromise among these parameters that will depend on the desired application and. For our work, optimization o the coherent-transmitter path is achieved by maximizing the image ield irradiance and peak irradiance. To maximize image ield irradiance, the goal is to optimize ill-actor, h, and xy-position (a x,a y ), or a given a w. I loss o power is eliminated, optimal h 1.00, however, a compromise is made by using h slightly greater than the h optimal to account or power Full-pupil point-scanning system The transmitter pupil irradiance (W/mm 2 ) and ield irradiance (W/μm 2 ) or varying ill actors, h, are shown in Fig. 2. The Gaussian beam is optimally centered at (a x = a y = 0) or maximum irradiance at the sample as shown in Fig. 2. We show three speciic cases, with an under-illed pupil (Fig. 2a), a moderately illed pupil (Fig. 2b), and an over-illed pupil (Fig. 2c). The corresponding transmitter irradiance maps are shown in Figs. 2d, 2e, 2, respectively. (a) h = 0.3 (b) h = 0.89 (c) h = 3.0 x x x 1, Pupil Position, (mm) x10 12 x x x, Image Position, (μm) (d) h = 0.3 (e) h = 0.89 () h = 3.0 Fig. 2. Transmission pupil and ield irradiance or a ull-pupil point-scanning system. With the Fourier-analysis computational model, the ill actor, h, is varied 0 h 5, and the on-axis image irradiance is plotted in Fig. 3a. For small values o h, (h < 1), as in Figs. 2a and 2d, we can integrate E Pupil (x p,y p,0) to ininity because it approaches zero beore reaching the edge o the aperture and a Gaussian-beam approximation is valid. To conirm the correctness o the Fourier analysis we veriy good agreement between the numerically computed on-axis image irradiance and this Gaussian approximation. The irradiance increases with increasing h because the image diameter o the Gaussian beam becomes smaller in inverse proportion to h 2. For large values o h, the Gaussian beam is approximately constant over the aperture and the image ield is an Airy unction. Again, image irradiance o the Airy unction agrees with the Fourier analysis. The irradiance decreases as h increases because the large Gaussian beam overills the pupil o the objective by increasing amounts. The diraction pattern does not change shape or size but the image irradiance decreases because the total power through the aperture decreases. Using the numerical computation, the optimum ill actor, h, is near the intersection o the computed Gaussian beam and uniorm source. More exactly, the optimum is at h = 0.89 and the ields shown in Figs. 2b and 2e are optimal. (C) 2011 OSA 1 August 2011 / Vol. 2, No. 8 / BIOMEDICAL OPTICS EXPRESS 2236

7 Fig. 3. Transmit on-axis image irradiance signal versus ill actor, h, or our conocal microscopy conigurations Full-pupil line-scanning system We analyzed the ull-pupil line-scanning coniguration using the same approach. The optimal position, (x c,y c ), or the line-source is again (0,0) by symmetry, with the computed optimum ill actor, h = 1.02, shown by the peak (o) in Fig. 3b. The pupil is slightly overilled to produce the highest on-axis irradiance in the image plane. This result is not surprising. As the Gaussian beam diameter at the pupil increases or the point-scanner, the area o the beam in the ield plane decrease according to 1/h 2. In line-scanning, it decreases according to 1/h. Thereore, optimization occurs at (o) or larger h Divided-pupil point-scanning system For the hal-pupil and divided-pupil conigurations, the coherent-transmitter path is the same, thereore the Fourier-analysis computational model or the coherent-transmitter path was repeated or only the divided-pupil coniguration o a point-scanning and line-scanning system. Now we need to optimize h and a x simultaneously. The optimal values are dependent on a w, but, a y = 0 still by symmetry. In the present work we consider a w = 0 to maximize transmitter area. The plot o the on-axis image irradiance or the divided-pupil point-scan is shown in Fig. 3c. The peak (o) or the computed divided-pupil point-scan on-axis image irradiance is at h = 0.66 with a x = For completeness, the Gaussian beam, uniorm source, and the ull-pupil point-scanning on-axis image irradiance are plotted. As expected, the peak is smaller than or the ull-pupil case. (C) 2011 OSA 1 August 2011 / Vol. 2, No. 8 / BIOMEDICAL OPTICS EXPRESS 2237

8 Divided-pupil line-scanning system The optimum ill actor, h, or the divided-pupil line-scanning system, as determined by the peak (o) in Fig. 3d is h = 0.52 with a x = The Gaussian beam, uniorm source, and the ull-pupil line-scanning on-axis image irradiance are plotted or comparison. Again, the optimal h is smaller or line-scanning than point-scanning as expected (Table 1). Table 1. Summary o the optimal ill-actor values and maximum on-axis image irradiance or each source and corresponding coniguration in the transmitter path Full-Pupil Coniguration Divided-Pupil Coniguration Point-Scanning h = 0.89, a x = 0, 63.7 W/mm 2 h = 0.66, a x = 0.35, 27.9 W/mm 2 Line-Scanning h = 1.06, a x = 0, 3.1 W/mm 2 h = 0.52, a x = 0.35, 1.5 W/mm Transverse resolution measurements Resolution is deined as the ability to discern that two objects are distinct. It depends on signal-to-noise ratio and desired statistics; thereore, it is complicated to deine exactly and no standard criterion exists. Whatever the choice o deinition or resolution, it can be computed rom the point spread unction (PSF) in the ield plane (V) as seen in Fig. 1. We arbitrarily choose to use the ull width at hal maximum (FWHM), which is the distance between the points where the irradiance is equal to 50% o the maximum irradiance, to determine the transverse resolution or a point-scan, Δx p, or line-scan, Δx l Transverse resolution or point-scanner The irradiance is plotted as a unction o transverse distance, x, or three point-scanning systems in ocus (z = 0μm) in Fig. 4 with a detector pinhole diameter, d pinhole = 2.5*d AiryDisc and NA = The transmitter image irradiance, the receiver unction in the ield plane, and the product are shown. For this pinhole (a typical choice), the transverse resolution is limited only by the transmitter beam diameter. The computed transverse resolution when in ocus is Δx p 0.22μm or the ull-pupil (h = 0.89), Fig. 4a, and Δx p 0.50μm or the hal-pupil and divided-pupil (h = 0.62), Figs. 4b and 4c. From Table 2, we observe that the transverse resolution remains consistent or hal-pupil or divided-pupil conigurations or all conigurations with dierent values o NA and d pinhole, given optimal ill actor, h, and x-position, a x. For a line-scan, the transverse resolution is better in all conigurations, irrespective o the pupil coniguration, NA, and d pinhole. The reason Fig. 4. Normalized image irradiance or point-scanning system, or z = 0μm with NA = 0.90, d pinhole = 2.5* d AiryDisc: (a) ull-pupil point-scan, (b) hal-pupil point-scan, and (c) divided-pupil point-scan. Note: See Fig. 6 or the same curves at z = 0.75μm. Table 2. Summary o transverse resolution measurements z = 0μm d pinhole = 0.1*dAiryDisc d pinhole = dairydisc [μm] NA = 0.50 NA = 0.90 NA = 0.50 NA = 0.90 Pupil Coniguration Δx p Δx l Δx p Δx l Δx p Δx l Δx p Δx l Full-Pupil Hal-Pupil Divided-Pupil (C) 2011 OSA 1 August 2011 / Vol. 2, No. 8 / BIOMEDICAL OPTICS EXPRESS 2238

9 or the improvement in transverse resolution relates to the ill actor o line-scanning (h = 1.02) versus point-scanner (h = 0.89). Because the coherent-transmitter path o the linescanner results in a larger h in the pupil, the corresponding PSF produces improved transverse resolution Optical sectioning measurements We begin our analysis o sectioning by examining how the signal, integrated over o x and y varies as the planar diuse object is moved out o ocus. We demonstrate this approach or a line-scanner, using the optimum ill actor, h, or a ull-pupil line-scan, h = 1.02, with NA = 0.90, and d pinhole = 2.5*d AiryDisc. Figure 5a shows results in the ield plane or the ull-pupil. The upper let panel shows the transmitter, which is a vertical line. The upper right shows the receiver unction, dominated by pinhole diameter, and the bottom let is the product. The lower right shows a slice through y = 0. The width is controlled by the transmitter because the pinhole is large. Fig. 5. Transverse resolution or line-scan, with h = 1.02, NA = 0.90, and d pinhole = 2.5* d AiryDisc or (a) ull-pupil coniguration (z = 0μm), (b) ull-pupil coniguration (z = 1μm), (c) hal-pupil coniguration (z = 1μm), (d) divided-pupil coniguration (z = 1μm). The most important characteristic o a conocal microscope is sectioning. Sectioning rejects out-o-ocus scatter and thereby increases contrast. Contrast is limited by all the light rom out o ocus. Thereore, optical sectioning can be characterized by integrating the signal over the area or dierent deocusing. The transmitter and receiver unctions become progressively wider when the target is out-o-ocus. Figure 5b shows that the broadening o the transmitter and receiver unctions leads to a reduced signal. The integral under the product (C) 2011 OSA 1 August 2011 / Vol. 2, No. 8 / BIOMEDICAL OPTICS EXPRESS 2239

10 is less than it is in Fig. 5a. Thus, out-o-ocus scattering contributes less to detected power than does in-ocus scatter. Fig. 6. Transmit Irradiance o point-scan, or z = 0.75μm with NA = 0.90, d pinhole = 2.5* d AiryDisc, (a) Full-Pupil Point-Scan, (b) Hal-Pupil Point-Scan, and (c) Divided-Pupil Point-Scan. NOTE: See Fig. 4 or the same curves at z = 0μm. Figure 5c shows the same or hal-pupil. Transverse resolution and axial sectioning are both worse because only ~1/2 o the aperture is used. However, the divided-pupil recovers the sectioning perormance. The transmitter and receiver are both centered on the axis in ocus, but are displaced in opposite directions with increasing distance as the object is moved out o ocus. Thereore, the product is lower than or the hal-pupil and its integral is lower as well. The eect is similar or the point-scan illustrated in Fig. 6. Quantitatively, the integrals are plotted or all conigurations in Fig. 7. The axial resolution (deined by the FWHM) or a ullpupil line-scanning coniguration (Δz sl 1.70μm) is better than or a hal-pupil coniguration (Δz sl 2.0μm), as expected. The loss in axial perormance with the hal-pupil is recovered in the divided-pupil line-scanning coniguration (Δz sl 1.30μm) providing better sectioning as more out-o-ocus light is suppressed by the conocal slit or pinhole. More importantly, Fig. 7 shows that the optical sectioning improves with the divided-pupil. In act it is even better than or the ull-pupil by a actor o six at z = 1μm. For the line source, even the axial resolution is improved with the divided-pupil coniguration. Fig. 7. The axial response or (a) point-scan and (b) line-scan or each coniguration. Table 3 summarizes the calculated axial resolution or each source and or all conigurations with dierent values o NA and d pinhole, given optimal ill actor, h, and x- position, a x. For a hal-pupil line-scan, with NA = 0.50 and d pinhole = 0.1* d AiryDisc, Δz sl = 2.50μm, which is greater than or a ull-pupil (Δz sl = 1.93μm) or divided-pupil (Δz sl = 1.65μm) coniguration. A point-scan or ull-pupil and divided-pupil is equal (Δz sl = 1.64μm or 0.50μm) or small d pinhole or all NA (NA = 0.50 or 0.90), respectively. As d pinhole increases, the optical section measurement o a point-scan improves as NA increases. For a line-scan with a small d pinhole, the optical sectioning is best in the divided-pupil coniguration. For large d pinhole o a line-scanner, the axial resolution is best in the ull-pupil coniguration, irrespective o the NA. (C) 2011 OSA 1 August 2011 / Vol. 2, No. 8 / BIOMEDICAL OPTICS EXPRESS 2240

11 Table 3. Summary o axial resolution measurements d pinhole = 0.1*dAiryDisc d pinhole = dairydisc [μm] NA = 0.50 NA = 0.90 NA = 0.50 NA = 0.90 Pupil Coniguration Δz sp Δz sl Δz sp Δz sl Δz sp Δz sl Δz sp Δz sl Full-Pupil Hal-Pupil Divided-Pupil Numerical aperture and pinhole diameter As the numerical aperture (NA) o the objective lens increases, the signal increases proportionately, as shown in Fig. 8a. The ull-pupil coniguration gives the largest signal regardless o source. The line-scan gives the smallest signal regardless o the pupilconiguration. As the pinhole diameter, d pinhole, increases, the irradiance increases, as shown in Fig. 8b. However, or values o d pinhole > 2.5*d AiryDisc the irradiance approaches an asymptote; the pinhole is collecting about the light scattering rom the ocused transmitter spot. 5. Discussion Fig. 8. Image Irradiance versus (a) numerical aperture at ocal plane, (b) pinhole diameter at ocal plane. We have presented a Fourier-analysis computational model or optimal pupil design o conocal microscopy. Note that the model is purely or pupil conigurations and does not explicitly account or object conditions. Thus, the inherent assumption is that the object is optically homogeneous and clear. In actual practice, the choice o pupil design or the best imaging perormance will depend on the optical properties o the desired object and application. In our particular application or imaging skin cancer, the eects o scattering and aberration must be considered. For optimization o the transmitter path or our system using the computational model, the optimum value or ill-actor, h, o the our conocal microscopy conigurations: (1) ull-pupil point-scanning, (2) ull-pupil line-scanning, (3) divided-pupil point-scanning, and (4) dividedpupil line-scanning are 0.89, 1.02, 0.66, and 0.52 respectively. Our results show the transverse resolution worsens rom the ull-pupil coniguration to the hal-pupil and divided-pupil conigurations, as expected in conocal microscopy. For optical sectioning, the divided-pupil coniguration is ideal, even outperorming the ull-pupil. Thereore, there is greater rejection o out-o-ocus light in the divided-pupil coniguration and higher contrast. The axial resolution degrades rom the ull-pupil to the hal-pupil coniguration, as expected. The divided-pupil recovers at least some resolution, and is even better than the ull-pupil coniguration in some cases. Even i resolution is worse, optical (C) 2011 OSA 1 August 2011 / Vol. 2, No. 8 / BIOMEDICAL OPTICS EXPRESS 2241

12 sectioning is always better with the divided-pupil coniguration. The image irradiance at the detector increases by several orders o magnitude as numerical aperture increases and to a lesser extent when the detector pinhole, d pinhole, increases. Exact values o resolution depend on numerical aperture (NA) and pinhole size. The divided-pupil recovers some or all the lost resolution, depending on NA and pinhole. Because the resolution o conocal microscope is naturally better than required or imaging subcellular detail in skin, the improved sectioning o a divided-pupil coniguration, and particularly a line-scanner, provides an improvement that is more important than the small degradation o resolution that arises rom using a raction o the aperture. Acknowledgments This research is supported by National Institutes o Health (NIH) grant R01-EB (C) 2011 OSA 1 August 2011 / Vol. 2, No. 8 / BIOMEDICAL OPTICS EXPRESS 2242