Optimal Pupil Design for Confocal Microscopy Yogesh G. Patel 1, Milind Rajadhyaksha 3, and Charles A. DiMarzio 1,2 1 Department of Electrical and Computer Engineering, 2 Department of Mechanical and Industrial Engineering, Northeastern University, 440 Dana Building, 360 Huntington Avenue, Boston, MA 02115 3 Department of Dermatology, Memorial Sloan-Kettering Cancer Center, 160 East 53 rd Street, New York, NY 10022 ABSTRACT Confocal reflectance microscopy may enable screening and diagnosis of skin cancers noninvasively and in real-time, as an adjunct to biopsy and pathology. Current instruments are large, complex, and expensive. A simpler, confocal line-scanning microscope may accelerate the translation of confocal microscopy in clinical and surgical dermatology. A confocal reflectance microscope may use a beamsplitter, transmitting and detecting through the pupil, or a divided pupil, or theta configuration, with half used for transmission and half for detection. The divided pupil may offer better sectioning and contrast. We present a Fourier optics model and compare the on-axis irradiance of a confocal point-scanning microscope in both pupil configurations, optimizing the profile of a Gaussian beam in a circular or semicircular aperture. We repeat both calculations with a cylindrical lens which focuses the source to a line. The variable parameter is the fillfactor, h, the ratio of the 1/e 2 diameter of the Gaussian beam to the diameter of the full aperture. The optimal values of h, for point scanning are 0.90 (full) and 0.66 for the half-aperture. For line-scanning, the fill-factors are 1.02 (full) and 0.52 (half). Additional parameters to consider are the optimal location of the point-source beam in the divided-pupil configuration, the optimal line width for the line-source, and the width of the aperture in the divided-pupil configuration. Additional figures of merit are field-of-view and sectioning. Use of optimal designs is critical in comparing the experimental performance of the different configurations. Keywords: confocal microscopy, Fourier optics, point-scanning, line-scanning, full-pupil, divided-pupil 1. INTRODUCTION In the United States, over one million new cases of skin cancer are diagnosed per year, but many more are suspected. Because biopsy is the only currently accepted method of confirming a diagnosis, over 5 million biopsies are performed to detect these one million cancers [1-3]. These biopsies cost the U.S. healthcare system over $1.5 billion [1-3]. Reducing the need for biopsy in the 80% of cases which are found to be benign could eliminate most of this cost. Confocal reflectance microscopy may enable early noninvasive screening and comparable diagnosis of skin cancers in real time with and minimize the need for biopsies. The confocal reflectance point-scanning microscope [Figure 1] was developed by Marvin Minsky to create an image of a plane within a turbid specimen while blocking out-of-focus light [4-5]. In Minsky's invention the sample was moved to accomplish scanning. This system achieved the ability to image sections throughout a specimen noninvasively. A confocal microscope uses a point source of light to illuminate a point within a specimen. The scattered light from this focused point is then collected onto a detector through a point aperture. The collected light forms an image from that point with sharp axial and lateral resolution. The size of the detector and illuminated point Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XVII, edited by Jose-Angel Conchello, Carol J. Cogswell, Tony Wilson, Thomas G. Brown, Proc. of SPIE Vol. 7570, 75700P 2010 SPIE CCC code: 1605-7422/10/$18 doi: 10.1117/12.842862 Proc. of SPIE Vol. 7570 75700P-1
are matched such that light not from the point of focus is blocked and the detector receives light only from the plane of focus. Figure 1: Confocal reflectance point-scanning microscope optical system layout. The confocal reflectance line-scanning system [Figure 2] is similar to a point-scanning system expect instead of a focused point within a specimen, a focused line is illuminated onto a specimen. Instead of a point illumination and detection through a pinhole, the plane being imaged is scanned with a focused line and detected through a confocal slit (i.e. a line slit). The line source is formed by a cylindrical lens between the laser source and objective lens. The line is formed in one direction and an image is formed in real-time using a scanner. Figure 2: Confocal reflectance line-scanning microscope optical system layout. There are two types of confocal reflectance line-scanning, the divided-pupil objective lens aperture, pioneered by Charles Koester [6-7], and the full-pupil confocal reflectance line-scanning system introduced by GJ Brakenhoff and K. Visscher [8-10]. Proc. of SPIE Vol. 7570 75700P-2
We present a Fourier-analysis computational model and compare the on-axis irradiance of a confocal point-scanning microscope in both full-pupil and divided-pupil configurations, optimizing the profile of a Gaussian beam. We repeat both calculations with for a confocal line-scanning microscope, which focuses the source to a line, in fullpupil and divided-pupil configurations. 2. FOURIER-ANALYSIS COMPUTATIONAL MODEL The amplitudes and phases of all the light rays reaching the image plane can be characterized using Fourier methods. Fourier analysis allows for treating optical processes in terms of spatial frequencies [11]. Therefore this type of analysis can be used for modeling the aperture and objective lens in a confocal scanning system. A pictorial representation of Fourier analysis in a lens system is shown in Figure 3. The field in the pupil plane (Σ p ) is the Fourier transform of the field in the front focal plane of the lens, which is the object (Σ o ) or image plane. Figure 3: Illustration of Fourier analysis in a lens system. The pupil plane (Σ p ) points become the Fourier transform at the back focal plane of a lens, which is the object (Σ o ) or image plane. Fourier analysis schematic shows the pupil plane (Σ p ) where a uniform plane wave is diffracted at the front focal point of the lens and then converges to form the far-field diffraction pattern at the back focal plane, or object/image plane (Σ o ) of the lens (depending on the direction of light and how the imaging system is being used). The object plane, Σ o, also called the transform plane, is where the far-field diffraction electric-field pattern (distribution) is displayed. Since optical systems generally involve two-dimensional components and light, the Fourier transform pair can be generalized in two dimensions as Equation (1) and its FT as Equation (2), where the quantities k x and k y are the angular spatial frequencies along the two corresponding axes. The object scatters waves, which are collected by the lens, and the parallel bundles of rays are brought to convergence at the back focal plane [12]. The pupil plane mask is known as the aperture function: (1) and the object plane distribution is the Fourier transform of the pupil field distribution: Proc. of SPIE Vol. 7570 75700P-3
(2) 2.1 SYSTEM CONFIGURATION The Fourier analysis computational model evaluated two scanning modes: (1) a point-scanning confocal reflectance microscope and (2) a line-scanning confocal reflectance microscope. In addition, the model evaluated two pupil configurations: (1) full-pupil configuration [Figure 4] and (2) divided-pupil configuration [Figure 5]. Figure 4: Full-Pupil Configuration Figure 5: Divided-Pupil Configuration The full-pupil configuration allows for illumination and detection with the entire pupil of the objective lens. This configuration leads to good resolution; however, there is greater acceptance of multiply scattered light [13-15]. The divided-pupil configuration illuminates half of the objective lens and collects from the other half. This configuration looses optical sectioning due to using only ½ the NA of the objective lens; however, it regains performance with ability to filter out multiply scattered light [13-15]. 2.2 MODELING PARAMETERS In addition to the scanning modes and pupil configurations, there are several parameters that are accounted for in the model. The first of these parameters is the wavelength, λ, which we stipulated to be 632nm and 830nm, corresponding to the 632nm HeNe laser (Melles Griot), and 830nm laser diode (Micro Laser Systems, Inc.) of our system. The lens diameter for the full-pupil or divided-pupil is d and the Gaussian beam at 1/e 2 is h. d. The variable parameter, the fill-factor, h, is the ratio of the 1/e 2 diameter of the Gaussian beam to the diameter (d) of the full-pupil or divided-pupil, depending on the configuration modeled. In the divided-pupil configuration, aw, is the width of the divider, where aw = width/d. The center position of the light source, x c, is given as x c = position/d. Proc. of SPIE Vol. 7570 75700P-4
We present a Fourier-analysis optics model and compare the on-axis irradiance of a confocal point-scanning or linescanning microscope in both pupil configurations, optimizing the profile of a Gaussian beam in a full-pupil or divided-pupil. 3. RESULTS We will show that the optimal value of fill-factor, h, is 0.90 for full-pupil point-scanning and 0.66 for the dividedpupil. For line-scanning, the fill-factors are 1.02 for full-pupil and 0.52 for the divided-pupil. 3.1 FULL-PUPIL POINT-SCANNING CONFIGURATION We compare the computed point-scan on-axis image irradiance values to a calculated Gaussian source and a uniform source at varying h values, [Figure 7]. For fill factor h=0.3, [(O), Figure 7], the pupil irradiance and image irradiance is shown in Figure 8. The Gaussian approximation is good for small values of h as Figure 7 shows good correlation of on-axis image irradiance for the Gaussian source (. ) and the computed point-scan on-axis image irradiance curve ( ) for fill factor values, h < 1. As h becomes larger, (h>1), the Gaussian approximation does not hold because there is diffraction due to truncation of the Gaussian source. The uniform source, ( === ), shows good correlation of on-axis image irradiance to the computed point-scan on-axis image irradiance curve ( ) for fill factor values, h > 2 [Figure 7]. For fill factor h=3.0, [(Δ), Figure 7], the pupil irradiance and image irradiance is shown in Figure 9. For large values of h, the uniform source correlates well to the point-scan image irradiance, however, there is a great loss of power in the image plane. Figure 7: Graph shows the on-axis image irradiance for computed line-scan, Gaussian, and uniform sources. Proc. of SPIE Vol. 7570 75700P-5
Figure 8: Pupil & Irradiance for h = 0.3 Image Figure 9: Pupil & Irradiance for h = 3.0 Image The optimum fill factor, h, value seems to be near the intersection of the computed Gaussian source and Uniform source. We show the pupil plane irradiance and image plane irradiance for the optimum fill factor, h = 0.9, [( ), Figure 7], and the horizontal slice through the respective plane showing the beam profile and peak irradiance, [Figure 10]. Figure 10: Pupil & Image Irradiance for h = 0.9, and the horizontal slice through the respective plane showing the beam profile and peak irradiance. Proc. of SPIE Vol. 7570 75700P-6
3.2 FULL-PUPIL LINE-SCANNING CONFIGURATION In the full-pupil line-scanning configuration, the optimum fill factor is h=1.02. The pupil is slightly overfilled to produce the highest on-axis irradiance in the image plane. Figure 11 shows the pupil & image plane irradiance and a horizontal slice through the respective plane. The plot of the maximum on-axis image irradiance of the computed line-scan ( ) for varying fill factor values is shown in Figure 12, with Gaussian source (. ) and Uniform sources ( === ) as comparison. Figure 11: Pupil & Image Plane Irradiance, with corresponding horizontal slice through plane for fullpupil line-scanning configuration. Figure 12: Graph shows the on-axis image irradiance for computed line-scan, Gaussian, and uniform sources. 3.3 DIVIDED-PUPIL POINT-SCANNING CONFIGURATION The Fourier analysis computational model was repeated for the divided-pupil configuration for a point-scanning and line-scanning system. Figure 13 shows the pupil and image plane irradiance and the horizontal slice through the respective plane for h=0.66. The plot of the on-axis image irradiance signal for the divided-pupil point-scan is shown in Figure 14. Proc. of SPIE Vol. 7570 75700P-7
Figure 13: Pupil & Image Plane Irradiance, with corresponding horizontal slice through plane for fullpupil line-scanning configuration. Figure 14: Graph shows the on-axis image irradiance for computed line-scan, Gaussian, and uniform sources. 3.4 DIVIDED-PUPIL LINE-SCANNING CONFIGURATION The Fourier analysis computational model evaluation for the divided-pupil configuration line-scanning system determined the optimum fill factor value to be h=0.52. Figure 15 shows the pupil and image plane irradiance and the horizontal slice through the respective plane for h=0.52. The plot of the on-axis image irradiance signal for the divided-pupil point-scan is shown in Figure 16. Figure 15: Pupil & Image Plane Irradiance, with corresponding horizontal slice through plane for fullpupil line-scanning configuration. Figure 16: Graph shows the on-axis image irradiance for computed line-scan, Gaussian, and uniform sources. 4. CONCLUSIONS We have presented a Fourier-analysis computational model in optimal pupil design for confocal microscopy. We presented optimum parameters for four confocal microscopy configurations: (1) full-pupil point-scanning, (2) fullpupil line-scanning, (3) divided-pupil point-scanning, and (4) divided-pupil line-scanning. We have shown the Proc. of SPIE Vol. 7570 75700P-8
optimal value of fill-factor, h, is 0.90 for full-pupil point-scanning and 0.66 for the divided-pupil. For line-scanning, the fill-factors are 1.02 for full-pupil and 0.52 for the divided-pupil. In future work, additional parameters we will consider are the optimal location of the point-source beam in the divided-pupil configuration, the optimal line width for the line-source, and the width of the aperture in the dividedpupil configuration. Use of optimal designs is critical in comparing the experimental performance of the different configurations. ACKNOWLEDGEMENTS This work was supported in part by Gordon-CenSSIS, the Center for Subsurface Sensing and Imaging Systems, under the Engineering Research Centers Program of the National Science Foundation (Award Number EEC- 9986821). Special thanks to Dr. John Haller & Dr. Yantian Zhang, for the support of the National Institute of Biomedical Imaging and Bioengineering (NIBIB) at the National Institute of Health (NIH). The primary author received funding through the Integrative Graduate Education and Research Traineeship (IGERT) in the area of Nanomedicine at Northeastern University. REFERENCES [1] National Cancer Institute, American Cancer Society, 2008 statistics [2] www.cancer.gov/statistics [3] http://seer.cancer.gov/statfacts [4] Confocal scanning microscope, M Minsky Rapport technique, Patent, (1955). [5] Memoir on inventing the confocal scanning microscope, M Minsky, SPIE Milestone Series MS, VOL 131, pages 7-17, (1996). [6] CJ Koester, Scanning mirror microscope with optical sectioning characteristics: applications to ophthalmology, Appl.Opt. 19, 1749 1757 (1980). [7] CJ Koester, High efficiency optical sectioning with confocal slits, Trans. R. Microsc. Soc. 90, 327 332 (1990). [8] GJ Brakenhoff and K Visscher, Confocal imaging with bilateral scanning and array detectors, J. Micros. 165, 139 146 (1992). [9] GJ Brakenhoff and K Visscher, "Novel confocal imaging and visualization techniques," in Micro 90: Proceedings of the Royal Microscopical Society Conference, H. Y. Elder, ed. Chapter 9, (Hilger, London, 1990). [10] Visscher, K., G. J. Brakenhoff, and J. J. Krol. Micromanipulation by "multiple" optical traps created by a single fast scanning trap integrated with the bilateral confocal scanning laser microscope. Cytometry. 14: 105-114, 1993. [11] M. Born, E. Wolf. Principles of optics. 7 th Edition. Cambridge University Press, Cambridge. 1999. [12] E. Hecht. Optics. 4 th Ed. Addison-Wesley, New York. 2002. [13] PJ Dwyer, CA DiMarzio, JM Zavislan, WJ Fox, and M Rajadhyaksha, "Confocal reflectance theta line scanning microscope for imaging human skin in vivo," Optics Letters 31, 942-944 (2006). [14] PJ Dwyer, CA DiMarzio, and M Rajadhyaksha, "Confocal theta line-scanning microscope for imaging human tissues," Applied Optics 46, 1843-1851 (2007). [15] DS Gareau, S Abeytunge, and M Rajadhyaksha, "Line-scanning reflectance confocal microscopy of human skin: comparison of full-pupil and divided-pupil configurations," Optics Letters 34, 3235-3237 (2009). *ypatel@ece.neu.edu, Phone: (617) 373-8570, Fax: (617) 373-7783 Proc. of SPIE Vol. 7570 75700P-9