Design of a Scanning Optical Microscope for Simultaneous Large Field of View and High Resolution

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1 Design of a Scanning Optical Microscope for Simultaneous Large Field of View and High Resolution Benjamin Potsaid, John T. Wen, and Yves Bellouard Center for Automation Technologies Rensselaer Polytechnic Institute Troy, NY s: {potsaid,wen,bellouard}@cat.rpi.edu Abstract In microsystems applications from micro-assembly to biological observation and manipulation, the optical microscope remains one of the most important tools. However, it suffers from the well known trade-off between resolution and field of view. Traditional solutions involve moving the sample under the microscope using a moving stage or moving the microscope itself, and switching between low and high magnification objective lenses. In this paper, we present a new optical microscope design that uses a 2-dimensional high speed, high precision steering mirror system to scan the sample. By stitching the images together as a mosaic, we have the potential to achieve both high resolution and large field of view. An experimental prototype has been constructed to demonstrate the basic efficacy of the concept. However, in order to further improve the performance, systematic design of the optical, motion, and image acquisition subsystems is needed. We present the design constraints and performance metrics, and pose the design as a multi-objective optimization. By using a commercial optical design package, we show that it is possible to adjust the optical system parameters to improve specific performance measures. I. INTRODUCTION The optical microscope is an indispensable tool in the observation and interaction with the micro-world, with applications in micro-assembly, biological observation and manipulation, and inspection. With the introduction of solid state imaging, inexpensive and powerful vision processing, and low cost precision motion devices, new applications of the optical microscope continue to emerge [1]. However, in its common form, the optical microscope suffers from the wellknown problem of small field size at high resolution. Various enhancements or modifications of the standard microscope have been proposed to address this limitation. These solutions generally add precision scanning capabilities to the microscope by either moving the sample under the microscope with a moving stage, or moving the microscope over the sample. A large mosaic image of the object is then constructed by stitching together a sequence of small high resolution images [2]. These approaches are attractive since they can be adopted to existing microscopes and there is no need for optical system redesign. However, these types of scanning mechanisms tend to have low bandwidths because of the high precision requirement, large dynamic mass of the mechanism, and possible disturbance to the specimen. The main goal of this paper is to present a new mosaic microscope design, which we call the scanning optical mosaic scope (SOMS). The motivation came from the microassembly and packaging activities at the Center for Automation Technologies at Rensselaer Polytechnic Institute and the conceptual layout was inspired by a machine designed at École Polytechnic Fédéral de Lausanne (EPFL), for laser annealing shape memory alloy [3]. This concept was also proposed by Y. Bellouard for the micromanipulation of cells [4]. The key idea is a simple one: use a low mass steering mirror [5] [7] positioned in the middle of the optical path to scan the images. The advantage of such an arrangement is obvious: a large effective field of view at high resolution, no disturbance to the sample, and high bandwidth operation. However, such a system also poses significant challenges. In contrast to the moving stage or moving microscope designs, there is extensive off-axis imaging (i.e., images are obtained off the optical axis), which introduces distortion and image degradation [7]. Careful optical design and even adaptive optical elements (lenses and mirrors) [8] may be necessary to achieve the required performance in a given application. In this paper, we present relevant design constraints and performance metrics and pose the overall design as a multi-objective optimization. Preliminary results show that it is possible to improve specific performance metrics by adjusting lens curvature and focal length, and lens position and orientation. The rest of the paper will be organized as follows. Section II presents our current proof-of-concept implementation and results, and discusses the performance limitation of the present setup. Section III discusses various performance metrics and poses the multi-objective optimization problem. Section IV presents preliminary design results with a commercial optical system design software, ZEMAX [9], used as the computation engine. II. EXPERIMENTAL PROTOTYPE The overall architecture of SOMS is shown in Figure 1. Light from the specimen is collected by the objective lens assembly and collimated into a beam. This beam reflects off

2 Fig. 1. Optical layout for the proof of concept prototype Fig. 2. Working Prototype of the SOMS the 2-D steering mirrors (shown schematically as a 1-D mirror) and is directed to the imaging optics to be focused onto the surface of a CCD camera. An iris is used to increase the image quality by blocking aberrated light. Our first experimental setup [10], shown in Figure 2, was built using existing components available in our laboratory. The intent is to demonstrate the basic feasibility of the SOMS concept instead of building a high performance system. The basic components of this system include: standard catalog lenses available from ThorLabs, a Sony XC-77BB CCD camera, Matrox Meteor II frame grabber, Cambridge technologies galvanometers and servo drivers, and a TI based DSP board. Figure 3 shows an example mosaic image of a gripper. A rudimentary correlation based image matching algorithm and Kalman filter are used to extract the motion of the gripper tip, and the scanning pattern is automatically adjusted to track the tip and maintain it in the center tile. Figure 4 shows a video sequence of live cells obtained with our prototype system. A temperature controlled chamber is constructed to ensure the living condition for the cells. This sequence shows several cell mitosis events occurring throughout the viewing field. The current practice in biology is to use a low-mag objective to wait for mitosis to occur and then manually move the stage to locate the mitosis under the high-mag objective. Repeated back-and-forth switching of the objectives may be necessary to accurately locate the cell event of interest under the high-mag objective (due to the small field of view). This is challenging especially for inexperienced users. SOMS not only offers the possibility of automatically detecting the onset of mitosis and other events, but can be easily programmed to track and record multiple events at the same time. Automated quantitative cell analysis using a moving stage has recently been proposed [11], [12]. However, the bandwidth of the overall system is still constrained by the response of the stage and the sensitivity of the cell specimen to motion. A. Prototype Performance Evaluation We have experimentally evaluated various optical performance metrics and compared them to simulated performance determined by the ZEMAX optical design software. This cross-validation with the design software is critical to build confidence in using such tools for design optimization. The USAF 1951 calibration target is often used to experimentally determine the resolving power of an optical Fig. 3. Mosaic Micro-gripper Image taken with SOMS Prototype system. The target has groupings of light and dark bands that create a square wave contrast pattern. The spatial frequencies (measured in lines per mm) of these patterns increase (the lines get closer together) with the grouping number. Figure 5 shows the target being imaged with the SOMS and Figure 6 shows a closeup of the relevant region of the target. As seen in Figure 6, the highest frequency that still shows discernable contrast between lines is approximately Group 7, Element 2 (indicated with white arrow), which has 144 lines per mm (about 7µm resolution). Also note the misalignment at some of the tile boundaries. This is likely due to distortion and will need to be compensated either optically or in image processing. The Modulation Transfer Function (MTF) is a widely used characterization of the resolving power of an imaging system. It is basically like a Bode amplitude plot for spatially varying patterns. If the input to the imaging system is a sinusoidal contrast pattern (in the object space), the output (in the image space) is also a sinusoidal contrast pattern, with the amplitude gain dependent on the input spatial frequency. MTF plots this amplitude gain as a function of the input frequency. In general, as the spatial frequency increases, the output amplitude drops off. The MTF corresponding to our prototype system is shown in Figure 8 for both on-axis imaging as well as off-axis at (0.75mm,0.8mm), which corresponds to the location of Group 7 Element 2 in the USAF 1951 target. The ZEMAX cutoff spatial frequency is about 152 lines per mm, which is the theoretical maximum resolution. With noise and misalignment,

3 Fig. 4. Mosaic Live Cell Image Sequence taken with SOMS Prototype Fig. 5. Mosaic of USAF 1951 calibration target the actual achievable resolution is typically less. Nevertheless, the simulated result matches closely with what we have obtained experimentally. We next compare the experimentally observed magnification with the simulation prediction. The dimensions of the patterns on the calibration target are shown in Figure 7 where x is the spatial sampling frequency that varies from group to group. For Target 5 Element 1, x is 32 lines/mm. The actual target size is therefore 78.1µm 78.1µm (2.5/32 mm). The observed image of the target is pixels, where each pixel is 11µm 13µm, which results in a target image size of 1161µm 1161µm. Therefore, the experimental magnification is 1161/78.1 = The magnification predicted by the ZEMAX simulation is 15.2, which is very close to the experimental observation. The comparison between the experimental results and the simulation is shown in Table I. III. OPTICAL SYSTEM DESIGN In this section, we present various performance characterizations of the optical system that we will use in the design Fig. 6. Zoom of USAF 1951 calibration target and dimensions Fig. 7. Size of USAF 1951 Target, x = spatial sampling frequency = 32 lines/mm for Group 5 Description Experimental ZEMAX simulation optical magnification cutoff spatial freq. (lines/mm.) TABLE I EXPERIMENTAL AND SIMULATED PERFORMANCE

4 aperture diameters and locations mirror diameter CCD pixel size. The dynamic parameters that will be adjusted based on the image tile location are location of dynamic lenses orientation of dynamic lenses local displacement of the flexible mirror. Fig. 8. ZEMAX simulated MTF of the experimental SOMS setup B. Performance Characteristics 1) Diffraction Limited Performance: When light propagates through an opening, the edge effect leads to the interference called diffraction (see Figure 10). A point source at infinity viewed through a circular aperture then becomes a disk (up to the first ring), called the Airy disk [18] (Figure 12 from [19] shows images of the Airy disks under different optical imaging systems). The size of the Airy disk represents the ultimate limitation to optical resolution in imaging. For a given optical system, the diameter of the Airy disk, D A, may be approximately calculated as Fig. 9. Coordinate frames and space domains optimization for SOMS. Though at the present we focus on the optical subsystem design, to achieve additional optical performance, the optical system design needs to be conducted concurrently with the design of other subsystems, such as motion control, thermal, and structural subsystems [13] [15]. We touch on some of the multi-disciplinary issues here, but they will be more thoroughly addressed in our future effort. For the optical system design, a frequently used design metric is based on the optical path difference (OPD) (see Section III- B.2 below), which may be obtained via optical simulation or measured by using the Hartmann-Shack wavefront sensor [16]. Other performance considerations such as diffraction limited performance, MTF, manufacturing tolerance, etc., also need to be taken into account in the design of a high performance system such as the camera system on the Mars Rover [17]. In this section, we will discuss the static and dynamic design variables, design constraints, and performance measures used in our design optimization. A. Design Variables For each mosaic image, SOMS collects a series of image tiles, ω i, i = 1,..., M, in the overall workspace Ω (see Figure 9). We partition the design variables into two sets: static components, θ s, that are fixed once the system is constructed (independent of i) and dynamic components, θ di, that can be adaptively modified during the operation (fixed for each i). The static design parameters that will be used in the design optimization include lens curvature lens glass type spacing between static lenses D A = 1.22 λ NA where λ is the wavelength, NA is the numerical aperture of the optical system (NA= nsina, where n is the index of refraction and a is 1/2 of the angular aperture). Commercial optical system design packages also typically have this calculation built in. In our case, we write D A for the ith image tile as D A (i, θ s, θ di ). Now consider the imaging of a point source of light. To create an image of this point, we need to convert the expanding spherical wavefront to a collapsing spherical wavefront. The role of the optical system is to provide this transformation while preserving the relative positions of all the point sources on the overall object to be imaged. If the converging wavefront deviates from a perfect spherical shape, then the light rays (perpendicular to the wavefront) will converge to a blur spot causing a blurred image as illustrated in Figure 11, where the possible image (CCD) plane placements and corresponding blur spot sizes are shown (denoted by A, B, and C). This deviation from the spherical wavefront is typically caused by the lens geometry. Due to manufacturability, lens surfaces are almost always spherical instead of the ideal parabolic shape (for on-axis viewing; different shapes are needed for off-axis viewing). This leads to aberrations, characterized by spherical aberrations, coma, astigmatism, field curvature, distortion, etc. For small deviation from the optical axis, the discrepancy is small, and the resulting aberration may be acceptable. But since we are performing extensive off-axis imaging, the geometric aberration needs to be carefully managed. For a given optical system, the blur disk due to geometric aberration may be obtained via ray tracing. Again, most of the optical design software packages has this calculation built in. We will denote the diameter of the blur disk for the i image tile as D B (i, θ s, θ di ).

5 Fig. 10. Diffraction of Light through an Opening Fig. 12. Airy Disks under Different Imaging Systems [19] Fig. 13. Characterization of Distortion Fig. 11. Blurring due to Optical Aberrations ( [19], Figure 5.4) To ensure that the geometry of the optical system has achieve the diffraction limitation (such an optical system is called diffraction limited), we impose the following constraint over all the image tiles max i D A (i, θ s, θ di ) max D B (i, θ s, θ di ). (1) i 2) Optical Path Difference: Ray tracing captures blurring due to optical geometry, but it does not contain the relative phase information between the rays. Such phase difference will also lead to distortion of the wavefront. Lord Rayleigh noticed that an imaging system would produce nearly perfect images if the optical path difference between all rays (hence the distortion of the wavefront) is less than 1/4 of the wavelength. Indeed, as shown in Figure 12, Airy disk with 1/4 wavelength difference in the optical paths is nearly indistinguishable from the perfect Airy disk, while distortion of the Airy disk becomes noticeable when the optical path difference is larger. The optical path difference, op, can be calculated by finding the optical path lengths of all rays and computing their maximum difference. Optical design software packages usually have this calculation built in. For our design, we impose this 1/4 wavelength constraint (λ is usually taken to be 0.56µm): max op (i, θ s, θ di ) < λ i 4. (2) 3) Distortion: The diffraction limitation and optical path difference criteria are based on the consideration of a point source. Even if each single point source remains a perfect point on the image plane, the relative spatial locations of the points on an object need to be preserved to form an accurate image of the object. Distortion occurs when the transverse magnification is a function of the amount of off-axis displacement [18], and approximately increases with the cube of the field of view. Consider Figure 13, in which d is the distorted distance of a point in the field plane and d 0 is the actual distance, then the relative distortion for that point is characterized by γ d (x, y) = d 0 d d 0. (3) The absolute distortion (for the ith image tile) is then Let S p be the pixel length: R di (x, y) = γ d (x, y) x 2 + y 2. (4) S p = S i N CCD (5) where S i is the CCD array size and N CCD is the number of pixels on one side of the array (for simplicity, we assume a square array). To avoid postprocessing to correct for the distortion, we require the worst case distortion to be less than 1 pixel length: max i max (x,y) ωi R di (x, y)m S p < 1, (6) where M is the magnification. 4) Spatial Image Sampling: When two adjacent Airy disks are separated by the radius of the disk, D A /2, they are distinguishable. The CCD imager acts as a spatial sampler of these disks. In order to avoid aliasing, the spatial sampling frequency has to be higher than the Nyquist frequency, which is approximately 4/D A (2 times the maximum spatial bandwidth, 2/D A ). This then translates to the requirement that the pixel size S p is sufficient small: D A (i, θ s, θ di ) S p min. (7) i 4

6 Description Coma aberration increases with the cube of the field size Scan time increases because more moves are required to cover an area as the field size decreases A small mirror will clip the light beam, resulting in reduced resolution A large mirror increases the settling time of the galvos A bright illumination reduces the required exposure time The cellular behavior can be modified or cells can die under bright light conditions TABLE II Desires small field size large field size large mirror diameter small mirror diameter bright light dim light TRADE-OFFS IN THE MULTI-OBJECTIVE DESIGN 5) Field Positioning Resolution: The steering mirror has certain positioning uncertainty (at least as large as its encoder resolution). For the ith image tile, denote the corresponding image plane uncertainty by f. To ensure that the images tiles can be aligned without significant post processing, we require this uncertainty to be less than one pixel size at the image sensor: f < S p. (8) C. Performance Objectives The performance objectives for the optical system are chosen to be System resolution, µ 1, which is characterized by the reciprocal of the cut-off frequency of MTF. Size of the field of view, µ 2. Mosaic refresh rate, µ 3. Some of the trade-offs between these objectives are illustrated in Table II. IV. PRELIMINARY OPTIMIZATION RESULTS In this section, we present some preliminary results demonstrating the potential impact of the static and dynamic design parameters on the performance of SOMS. These results are obtained based on simulations using ZEMAX, which is an optical modeling, analysis, and optimization software package [9]. Within ZEMAX, optical systems can be defined in terms of surfaces, optical materials, stop geometries, etc. The software is also flexible enough to support deformable mirrors, spatial light modulators, and user defined optical systems. Models can be defined parametrically and then optimized according to a variety of performance metrics using either global or local optimization techniques. Many frequently used performance metrics, such as blur spot diameter, OPD, and distortion are built in, but more complex metrics can be assembled from a list of internally accessible variables to construct more sophisticated metrics as required. We will present several examples to demonstrate the need for a multi-objective optimization approach. First, the design constraints and performance metrics described in Section III are evaluated for our prototype system. We then consider the following set of static design parameters: DV1: Radius of the front surface of lens 3 DV2: CCD pixel size DV3: Focal distance of the entire system measured from the front surface of lens 1. In our initial study, we use these three design parameters to target one of the constraints: ratio between the diameters of geometric optics blur disk and airy disk, OPD, distortion, CCD spatial sampling, and field position resolution. Of course, the constraints and performance indices not considered in the optimization tend to degrade, since they are not explicitly considered. The results are shown in Table III and Figure 14. Column 1 shows the constraint (CON#), objective (OBJ#), and the design variables (DV#). Column 2 describes the design constraints and performance metrics. Column 3 shows the desired performance level where appropriate. Performance of our current prototype is shown in column 4, and the remaining columns show performance for the individually optimized designs: design 1 has been optimized for CON1, while ignoring the other constraints, design 2 has only been optimized for CON2, and so on. The results show that it is possible to improve any one of the constraints, but doing so often degrades others. For example, if the radius of lens 3 is made slightly convex (Configuration 2 in Figure 14), then the OPD improves, but the distortion and blur disk size degrades. Conversely, if the radius of lens 3 is made slight concave (Configuration 3), then the distortion improves, but the optical path difference degrades (note the large blur disk size in the figure and the corresponding low resolution listed in the table). Also note that the scan time increases dramatically in case 4 because the smaller field of view requires more mosaic tiles (11 mirror movements at 2.45 ms each), to cover the entire workspace as compared to case 1 (2 mirror movements at 2.9 ms each). As another exploratory exercise, we have also investigated the possibility of dynamically moving one of the lenses for each position in the scan pattern. In practice, the motion of such a lens might be guided by a four or six bar mechanism. Lens 1 is allowed to translate in the x direction and rotate about the y axis independently for each scan position (i.e., image tile). Table IV shows the performance results for optimizing the OPD and Figure 15 shows the corresponding lens positions. The computation of the scan time uses the experimentally observed mirror settling times as shown in Figure 16 for two different field sizes. The results show that such an approach can improve the OPD. There is a modest increase in the Blur disk to Airy disk ratio, a significant improvement of about 50% for the resolution of the system, but a degradation of the distortion (which may be compensated through image processing). Though the design optimization process has just begun, we have developed a foundation in terms of design optimization framework and computation environment. Our current goal is

7 Label Desc. Goal Exp CON1 max(blur)/max(airy) < (2.5) * CON2 max(opd) < (0.8) * CON3 max(distortion) pixels < (7.6) * max(distortion) % field CON4 CCD spatial sampling > (73.7) * 16.7 CON5 field position resolution(pixels) < (0.2) * OBJ1 optical resolution l per mm OBJ2 Workspace Size (HxW mm) - 1.5x6 1.5x6 1.5x6 1.5x6 1.5x6 1.5x6 - field sized (H W mm) - 1.5x2 1.5x2 1.5x2 1.5x2 0.75x1 1.5x2 OBJ3 Mosaic Scan Time (ms) DV1 Curve radius lens 3 (mm) - inf inf inf inf DV2 Size of CCD pixel (µm) DV3 Focus Position (mm) TABLE III OPTIMIZATION RESULTS FOR STATIC VARIABLES θ s. * INDICATES WHICH CONSTRAINT WAS OPTIMIZED Fig. 14. constraint 1 ray trace Fig. 15. Floating lens optimization example to perform design iteration based on multi-objective optimization using ZEMAX as a computation engine and to implement the next generation of SOMS based on the optimization result. V. CONCLUSION We have presented a new microscope concept that can simultaneously achieve high resolution and large field of view. A proof-of-concept prototype has been constructed to demonstrate the basic efficacy of this concept. However, since extensive off-axis imaging is required, further systematic design optimization is required. We present the relevant design constraints, including aberration, optical path difference, distortion, spatial image sampling, and field position resolution, and performance metrics, including resolution, field size, and image update rate. Initial optimization results using the ZEMAX optical design package indicates the possibility to improve certain design objective but possibly at the expense

8 Label Desc. Goal experimental float CON1 max(blur)/max(airy) < CON2 max(opd) < CON3 max(distortion in pixels) < CON3b max optical distortion % field CON4 CCD spatial sampling > CON5 field position resolution(pixels) < ?? OBJ1 optical resolution l per mm OBJ2 Workspace Size (H W mm) - 1.5x6 1.5x6 OBJ3 Mosaic Scan Time - D D DV1 x offset (frame B, frame C) - (0.0mm, 0.0mm) (0.0mm, mm) DV2 rotation about y(frame B, frame C) - (0.0, 0.0 ) (0.0, 2.97 ) TABLE IV OPD OPTIMIZATION RESULTS FOR DYNAMIC PARAMETERS, θ d Fig. 16. Settling Times of the Motion System of other objectives. We are currently pursuing a multi-objective optimization approach for the full system design. ACKNOWLEDGMENT The authors would like to thank Richard Cole and Dr. Jacques Izard at the Wadsworth Center, New York State Department of Health. Their expertise and knowledge of microscopy and cellular processes have contributed greatly to the project. This research is also supported in part by the Center for Automation Technologies under a block grant from the New York State Science and Technology Foundation. REFERENCES [1] D. L. Farkas, B. Bailey, F. Lanni, and D. L. Taylor, New waves in light microscopy, in SPIE vol. 2137, 1994, pp [2] J. Zemek, C. Monks, and B. Freiberg, Discovery through automation, Biophotonics International, pp , May [3] Y. Bellouard, T. Lehnert, R. Clavel, T. Sidler, and R. Gotthardt, Laser annealing of shape memory alloys: A versatile tool for developing smart micro-devices iv, J. Phys., vol. 4, no. 8, pp , [4] Y. Bellouard, A flexible assembly station using enhanced vision control, Internal Document, Center for Automation Technologies, Rensselaer Polytechnic Institute, [5] J. Montagu, Two-axis beam steering systes, TABS, in Proc. of SPIE Vol. 1920, 1993, pp [6] X. Jiang, D. Laurin, D. Levesque, and D. Nikanpour, Design and fabrication of a lightweight laser scanning mirror from metal-matrix composites, in Proc. of SPIE Vol. 4444: Optomechanical Design and Engineering, A. Hatheway, Ed., 2001, pp [7] D. Weiner, Design considerations for optical scanning, in Proc. of SPIE Vol. 3131, 1997, pp [8] L. Sherman, O. Albert, C. Schmidt, G.Vdovin, G. Mourou, and T. Norris, Adaptive compensation of aberrations in ultrafast 3d microscopy using a deformable mirror, in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processinng VII, 2000, pp [9] ZEMAX Development Corp. [Online]. Available: [10] B. Potsaid, Y. Bellouard, and J. Wen, Scanning optical mosaic scope for micro-manipulation, in Int. Workshop on Micro-Factories (IWMF 02), Minneapolis, MN, 2002, pp [11] F. Ianzini, L. Bresnahan, L. Wang, K. Anderson, and M. Mackey, The large scale digital cell analysis system and its use in the quantitative analysis of cell populaionts, in 2nd Annual Int. IEEE-EMBS Special Topic Conf. on Microtechnologies in Medicine & Biology, Madison, WI, 2002, pp [12] F. Ianzini and M. Mackey, Development of the large scale digital cell analysis system (lsdcas), Radiation Protection and Dosimetry, pp , [13] P. Forney, Integrated optical design, in Proc. of SPIE Vol. 4441: Current Developments in Lens design and Optical Engineering II, R. Fischer, R. Johnson, and W. Smith, Eds., 2001, pp [14] M. Papalexandris, M. Milman, and M. Levine, Optimization methods for thermal modeling of optomechanical systems, in Proc. of SPIE Vol. 4444: Optomechanical Design and Engineering, A. Hatheway, Ed., 2001, pp [15] J. Melody and G. Neat, Integrated modeling methodology validation using the micro-precision interferometer testbed, in Proceedings of 35th Conference on Decision and Control, Kobe, Japan, Dec. 1996, pp [16] W. Jiang and H. Li, Hartmann-shack wavefront sensing ansd wavefront control algorithm, in Proc. of SPIE VOl. 1271: Adaptive Optics and Optical Structures, 1990, pp [17] G. Smith, E. Hagerott, L. Scherr, K. Herkenhoff, and I. J.F. Bell, Optical designs for the Mars 03 rover cameras, in Proc. of SPIE Vol. 4441: Current Developments in Lens design and Optical Engineering II, R. Fischer, R. Johnson, and W. Smith, Eds., 2001, pp [18] E. Hecht, Optics, 4th ed. Pearson Addison Wesley, [19] R. Fischer and B. Tadic-Galeb, Optical System Design. SPIE Press, McGraw-Hill, 2000.