Design of a Scanning Optical Microscope forSimultaneous Large Field of View

and High ResolutionBenjamin Potsaid, John T. Wen, and Yves Bellouard

Center for Automation TechnologiesRensselaer Polytechnic Institute

Troy, NY 12180.Emails:potsaid,wen,bellouard @cat.rpi.edu

Abstract— In microsystems applications from micro-assemblyto biological observation and manipulation, the optical micro-scope remains one of the most important tools. However, itsuffers from the well known trade-off between resolution and fieldof view. Traditional solutions involve moving the sample underthe microscope using a moving stage or moving the microscopeitself, and switching between low and high magnification objectivelenses. In this paper, we present a new optical microscope designthat uses a 2-dimensional high speed, high precision steeringmirror system to scan the sample. By stitching the imagestogether as a mosaic, we have the potential to achieve both highresolution and large field of view. An experimental prototype hasbeen constructed to demonstrate the basic efficacy of the concept.However, in order to further improve the performance, systematicdesign of the optical, motion, and image acquisition subsystemsis needed. We present the design constraints and performancemetrics, and pose the design as a multi-objective optimization.By using a commercial optical design package, we show that itis possible to adjust the optical system parameters to improvespecific performance measures.

I. I NTRODUCTION

The optical microscope is an indispensable tool in theobservation and interaction with the micro-world, with appli-cations in micro-assembly, biological observation and manip-ulation, and inspection. With the introduction of solid stateimaging, inexpensive and powerful vision processing, andlow cost precision motion devices, new applications of theoptical microscope continue to emerge [1]. However, in itscommon form, the optical microscope suffers from the well-known problem of small field size at high resolution. Variousenhancements or modifications of the standard microscopehave been proposed to address this limitation. These solutionsgenerally add precision scanning capabilities to the microscopeby either moving the sample under the microscope with amoving stage, or moving the microscope over the sample.A large mosaic image of the object is then constructed bystitching together a sequence of small high resolution images[2]. These approaches are attractive since they can be adoptedto existing microscopes and there is no need for optical systemredesign. However, these types of scanning mechanisms tendto have low bandwidths because of the high precision require-ment, 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 mo-saic scope (SOMS). The motivation came from the micro-assembly and packaging activities at the Center for Automa-tion Technologies at Rensselaer Polytechnic Institute and theconceptual layout was inspired by a machine designed atEcolePolytechnic Federal de Lausanne (EPFL), for laser annealingshape memory alloy [3]. This concept was also proposed byY. Bellouard for the micromanipulation of cells [4]. The keyidea is a simple one: use a low mass steering mirror [5]–[7] positioned in themiddle of the optical path to scan theimages. The advantage of such an arrangement is obvious: alarge effective field of view at high resolution, no disturbanceto the sample, and high bandwidth operation. However, sucha system also poses significant challenges. In contrast to themoving stage or moving microscope designs, there is extensiveoff-axis imaging (i.e., images are obtained off the opticalaxis), which introduces distortion and image degradation [7].Careful optical design and even adaptive optical elements(lenses and mirrors) [8] may be necessary to achieve therequired performance in a given application. In this paper, wepresent relevant design constraints and performance metricsand pose the overall design as a multi-objective optimization.Preliminary results show that it is possible to improve specificperformance metrics by adjusting lens curvature and focallength, and lens position and orientation.

The rest of the paper will be organized as follows. Section IIpresents our current proof-of-concept implementation and re-sults, and discusses the performance limitation of the presentsetup. Section III discusses various performance metrics andposes the multi-objective optimization problem. Section IVpresents preliminary design results with a commercial opticalsystem design software, ZEMAX [9], used as the computationengine.

II. EXPERIMENTAL PROTOTYPE

The overall architecture of SOMS is shown in Figure 1.Light from the specimen is collected by the objective lensassembly and collimated into a beam. This beam reflects off

Fig. 1. Optical layout for the proof of concept prototype

the 2-D steering mirrors (shown schematically as a 1-D mirror)and is directed to the imaging optics to be focused onto thesurface of a CCD camera. An iris is used to increase the imagequality by blocking aberrated light.

Our first experimental setup [10], shown in Figure 2, wasbuilt using existing components available in our laboratory.The intent is to demonstrate the basic feasibility of the SOMSconcept instead of building a high performance system. Thebasic components of this system include: standard cataloglenses available from ThorLabs, a Sony XC-77BB CCD cam-era, Matrox Meteor II frame grabber, Cambridge technologiesgalvanometers and servo drivers, and a TI based DSP board.Figure 3 shows an example mosaic image of a gripper. Arudimentary correlation based image matching algorithm andKalman filter are used to extract the motion of the gripper tip,and the scanning pattern is automatically adjusted to track thetip and maintain it in the center tile. Figure 4 shows a videosequence of live cells obtained with our prototype system. Atemperature controlled chamber is constructed to ensure theliving condition for the cells. This sequence shows severalcell mitosis events occurring throughout the viewing field. Thecurrent practice in biology is to use a low-mag objective towait for mitosis to occur and then manually move the stageto locate the mitosis under the high-mag objective. Repeatedback-and-forth switching of the objectives may be necessary toaccurately locate the cell event of interest under the high-magobjective (due to the small field of view). This is challengingespecially for inexperienced users. SOMS not only offers thepossibility of automatically detecting the onset of mitosis andother events, but can be easily programmed to track and recordmultiple events at the same time. Automated quantitative cellanalysis using a moving stage has recently been proposed [11],[12]. However, the bandwidth of the overall system is stillconstrained by the response of the stage and the sensitivity ofthe cell specimen to motion.

A. Prototype Performance Evaluation

We have experimentally evaluated various optical perfor-mance metrics and compared them to simulated performancedetermined by the ZEMAX optical design software. Thiscross-validation with the design software is critical to buildconfidence in using such tools for design optimization.

The USAF 1951 calibration target is often used to ex-perimentally determine the resolving power of an optical

Fig. 2. Working Prototype of the SOMS

Fig. 3. Mosaic Micro-gripper Image taken with SOMS Prototype

system. The target has groupings of light and dark bands thatcreate a square wave contrast pattern. The spatial frequencies(measured in lines per mm) of these patterns increase (thelines get closer together) with the grouping number. Figure 5shows the target being imaged with the SOMS and Figure 6shows a closeup of the relevant region of the target. As seenin Figure 6, the highest frequency that still shows discernablecontrast 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 someof the tile boundaries. This is likely due to distortion andwill need to be compensated either optically or in imageprocessing.

The Modulation Transfer Function (MTF) is a widely usedcharacterization of the resolving power of an imaging system.It is basically like a Bode amplitude plot for spatially varyingpatterns. If the input to the imaging system is a sinusoidalcontrast pattern (in the object space), the output (in the imagespace) is also a sinusoidal contrast pattern, with the amplitudegain dependent on the input spatial frequency. MTF plots thisamplitude gain as a function of the input frequency. In general,as the spatial frequency increases, the output amplitude dropsoff. The MTF corresponding to our prototype system is shownin Figure 8 for both on-axis imaging as well as off-axis at(0.75mm,0.8mm), which corresponds to the location of Group7 Element 2 in the USAF 1951 target. The ZEMAX cutoffspatial frequency is about 152 lines per mm, which is thetheoretical maximum resolution. With noise and misalignment,

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 haveobtained experimentally.

We next compare the experimentally observed magnificationwith the simulation prediction. The dimensions of the patternson the calibration target are shown in Figure 7 wherexis the spatial sampling frequency that varies from group togroup. For Target 5 Element 1,x is 32 lines/mm. The actualtarget size is therefore 78.1µm×78.1µm (2.5/32 mm). Theobserved image of the target is 106×89 pixels, where eachpixel is 11µm×13µm, which results in a target image size of1161µm×1161µm. Therefore, the experimental magnificationis 1161/78.1 = 14.9. The magnification predicted by theZEMAX simulation is 15.2, which is very close to the experi-mental observation. The comparison between the experimentalresults and the simulation is shown in Table I.

III. O PTICAL SYSTEM DESIGN

In this section, we present various performance character-izations 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= 32lines/mm for Group 5

Description Experimental ZEMAX simulation

optical magnification 14.9 15.2

cutoff spatial freq. (lines/mm.) 144 152

TABLE I

EXPERIMENTAL AND SIMULATED PERFORMANCE

Fig. 8. ZEMAX simulated MTF of the experimental SOMS setup

Fig. 9. Coordinate frames and space domains

optimization for SOMS. Though at the present we focus onthe optical subsystem design, to achieve additional opticalperformance, the optical system design needs to be conductedconcurrently with the design of other subsystems, such asmotion control, thermal, and structural subsystems [13]–[15].We touch on some of the multi-disciplinary issues here, butthey will be more thoroughly addressed in our future effort.For the optical system design, a frequently used design metricis based on the optical path difference (OPD) (see Section III-B.2 below), which may be obtained via optical simulation ormeasured by using the Hartmann-Shack wavefront sensor [16].Other performance considerations such as diffraction limitedperformance, MTF, manufacturing tolerance, etc., also needto be taken into account in the design of a high performancesystem such as the camera system on the Mars Rover [17].In this section, we will discuss the static and dynamic designvariables, design constraints, and performance measures usedin our design optimization.

A. Design Variables

For each mosaic image, SOMS collects a series of imagetiles, ωi, i = 1, . . . ,M , in the overall workspaceΩ (seeFigure 9). We partition the design variables into two sets: staticcomponents,θs, that are fixed once the system is constructed(independent ofi) and dynamic components,θdi , that can beadaptively modified during the operation (fixed for eachi).

The static design parameters that will be used in the designoptimization include

• lens curvature• lens glass type• spacing between static lenses

• aperture diameters and locations• mirror diameter• CCD pixel size.

The dynamic parameters that will be adjusted based on theimage tile location are

• location of dynamic lenses• orientation of dynamic lenses• local displacement of the flexible mirror.

B. Performance Characteristics

1) Diffraction Limited Performance:When light propagatesthrough an opening, the edge effect leads to the interferencecalled diffraction (see Figure 10). A point source at infinityviewed through a circular aperture then becomes a disk (upto the first ring), called the Airy disk [18] (Figure 12 from[19] shows images of the Airy disks under different opticalimaging systems). The size of the Airy disk represents theultimate limitation to optical resolution in imaging. For a givenoptical system, the diameter of the Airy disk,DA, may beapproximately calculated as

DA = 1.22λ

NA

whereλ is the wavelength, NA is the numerical aperture of theoptical system (NA= nsina, wheren is the index of refractionand a is 1/2 of the angular aperture). Commercial opticalsystem design packages also typically have this calculationbuilt in. In our case, we writeDA for the ith image tile asDA(i, θs, θdi

).Now consider the imaging of a point source of light. To

create an image of this point, we need to convert the expandingspherical wavefront to a collapsing spherical wavefront. Therole of the optical system is to provide this transformationwhile preserving the relative positions of all the point sourceson the overall object to be imaged. If the converging wavefrontdeviates from a perfect spherical shape, then the light rays(perpendicular to the wavefront) will converge to a blur spotcausing a blurred image as illustrated in Figure 11, where thepossible image (CCD) plane placements and correspondingblur spot sizes are shown (denoted by A, B, and C). Thisdeviation from the spherical wavefront is typically caused bythe lens geometry. Due to manufacturability, lens surfaces arealmost always spherical instead of the ideal parabolic shape(for on-axis viewing; different shapes are needed for off-axisviewing). This leads to aberrations, characterized by sphericalaberrations, coma, astigmatism, field curvature, distortion, etc.For small deviation from the optical axis, the discrepancyis small, and the resulting aberration may be acceptable.But since we are performing extensive off-axis imaging, thegeometric aberration needs to be carefully managed. For agiven optical system, the blur disk due to geometric aberrationmay be obtained via ray tracing. Again, most of the opticaldesign software packages has this calculation built in. We willdenote the diameter of the blur disk for thei image tile asDB(i, θs, θdi

).

Fig. 10. Diffraction of Light through an Opening

Fig. 11. Blurring due to Optical Aberrations ( [19], Figure 5.4)

To ensure that the geometry of the optical system hasachieve the diffraction limitation (such an optical system iscalled diffraction limited), we impose the following constraintover all the image tiles

maxi

DA(i, θs, θdi) ≥ maxi

DB(i, θs, θdi). (1)

2) Optical Path Difference:Ray tracing captures blurringdue to optical geometry, but it does not contain the relativephase information between the rays. Such phase difference willalso lead to distortion of the wavefront. Lord Rayleigh noticedthat an imaging system would produce nearly perfect imagesif the optical path difference between all rays (hence thedistortion of the wavefront) is less than1/4 of the wavelength.Indeed, as shown in Figure 12, Airy disk with 1/4 wavelengthdifference in the optical paths is nearly indistinguishable fromthe perfect Airy disk, while distortion of the Airy disk becomesnoticeable when the optical path difference is larger. Theoptical path difference,∆op, can be calculated by finding theoptical path lengths of all rays and computing their maximumdifference. Optical design software packages usually havethis calculation built in. For our design, we impose this 1/4wavelength constraint (λ is usually taken to be 0.56µm):

maxi

∆op(i, θs, θdi) <

λ

4. (2)

3) Distortion: The diffraction limitation and optical pathdifference criteria are based on the consideration of a pointsource. Even if each single point source remains a perfect pointon the image plane, the relative spatial locations of the pointson an object need to be preserved to form an accurate image ofthe object. Distortion occurs when the transverse magnification

Fig. 12. Airy Disks under Different Imaging Systems [19]

Fig. 13. Characterization of Distortion

is a function of the amount of off-axis displacement [18], andapproximately increases with the cube of the field of view.Consider Figure 13, in whichd is the distorted distance of apoint in the field plane andd0 is the actual distance, then therelative distortion for that point is characterized by

γd(x, y) =d0 − d

d0. (3)

The absolute distortion (for theith image tile) is then

Rdi(x, y) = γd(x, y)√

x2 + y2. (4)

Let Sp be the pixel length:

Sp =Si

NCCD(5)

where Si is the CCD array size andNCCD is the numberof pixels on one side of the array (for simplicity, we assumea square array). To avoid postprocessing to correct for thedistortion, we require the worst case distortion to be less than1 pixel length:

maxi max(x,y)∈ωiRdi

(x, y)MSp

< 1, (6)

whereM is the magnification.4) Spatial Image Sampling:When two adjacent Airy disks

are separated by the radius of the disk,DA/2, they aredistinguishable. The CCD imager acts as a spatial samplerof these disks. In order to avoid aliasing, the spatial samplingfrequency has to be higher than the Nyquist frequency, whichis approximately4/DA (2 times the maximum spatial band-width, 2/DA). This then translates to the requirement that thepixel sizeSp is sufficient small:

Sp ≤ mini

DA(i, θs, θdi)

4. (7)

Description Desires

Coma aberration increases with the cube of thefield size

small field size

Scan time increases because more moves arerequired to cover an area as the field sizedecreases

large field size

A small mirror will clip the light beam, result-ing in reduced resolution

large mirror diameter

A large mirror increases the settling time of thegalvos

small mirror diameter

A bright illumination reduces the required ex-posure time

bright light

The cellular behavior can be modified or cellscan die under bright light conditions

dim light

TABLE II

TRADE-OFFS IN THE MULTI-OBJECTIVE DESIGN

5) Field Positioning Resolution:The steering mirror hascertain positioning uncertainty (at least as large as its encoderresolution). For theith image tile, denote the correspondingimage plane uncertainty by∆f . To ensure that the images tilescan be aligned without significant post processing, we requirethis uncertainty to be less than one pixel size at the imagesensor:

∆f < Sp. (8)

C. Performance Objectives

The performance objectives for the optical system arechosen to be

• System resolution,µ1, which is characterized by thereciprocal of the cut-off frequency of MTF.

• Size of the field of view,µ2.• Mosaic refresh rate,µ3.

Some of the trade-offs between these objectives are illustratedin Table II.

IV. PRELIMINARY OPTIMIZATION RESULTS

In this section, we present some preliminary results demon-strating the potential impact of the static and dynamic designparameters on the performance of SOMS. These results are ob-tained based on simulations using ZEMAX, which is an opticalmodeling, analysis, and optimization software package [9].Within ZEMAX, optical systems can be defined in terms ofsurfaces, optical materials, stop geometries, etc. The softwareis also flexible enough to support deformable mirrors, spatiallight modulators, and user defined optical systems. Models canbe defined parametrically and then optimized according to avariety of performance metrics using either global or localoptimization techniques. Many frequently used performancemetrics, such as blur spot diameter, OPD, and distortion arebuilt in, but more complex metrics can be assembled froma list of internally accessible variables to construct moresophisticated metrics as required.

We will present several examples to demonstrate the needfor a multi-objective optimization approach. First, the design

constraints and performance metrics described in Section IIIare evaluated for our prototype system. We then consider thefollowing 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 parametersto target one of the constraints: ratio between the diametersof 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 theoptimization tend to degrade, since they are not explicitlyconsidered. The results are shown in Table III and Figure 14.Column 1 shows the constraint (CON#), objective (OBJ#), andthe design variables (DV#). Column 2 describes the designconstraints and performance metrics. Column 3 shows thedesired performance level where appropriate. Performanceof our current prototype is shown in column 4, and theremaining columns show performance for the individuallyoptimized designs: design 1 has been optimized for CON1,while ignoring the other constraints, design 2 has only beenoptimized for CON2, and so on.

The results show that it is possible to improve any one of theconstraints, but doing so often degrades others. For example,if the radius of lens 3 is made slightly convex (Configuration2 in Figure 14), then the OPD improves, but the distortionand blur disk size degrades. Conversely, if the radius of lens3 is made slight concave (Configuration 3), then the distortionimproves, but the optical path difference degrades (note thelarge blur disk size in the figure and the corresponding lowresolution listed in the table). Also note that the scan timeincreases dramatically in case 4 because the smaller field ofview requires more mosaic tiles (11 mirror movements at 2.45ms each), to cover the entire workspace as compared to case1 (2 mirror movements at 2.9 ms each).

As another exploratory exercise, we have also investigatedthe possibility of dynamically moving one of the lenses foreach position in the scan pattern. In practice, the motion ofsuch a lens might be guided by a four or six bar mechanism.Lens 1 is allowed to translate in thex direction and rotateabout they axis independently for each scan position (i.e.,image tile). Table IV shows the performance results foroptimizing the OPD and Figure 15 shows the correspondinglens positions. The computation of the scan time uses theexperimentally observed mirror settling times as shown inFigure 16 for two different field sizes.

The results show that such an approach can improve theOPD. There is a modest increase in the Blur disk to Airydisk ratio, a significant improvement of about 50% for theresolution of the system, but a degradation of the distortion(which may be compensated through image processing).

Though the design optimization process has just begun, wehave developed a foundation in terms of design optimizationframework and computation environment. Our current goal is

Label Desc. Goal Exp 1 2 3 4 5

CON1 max(blur)/max(Airy) < 1 3.1 (2.5) * 6.3 137.5 3.1 3.1

CON2 max(OPD) < 14 1.5 0.9 (0.8) * 6.0 1.5 1.5

CON3 max(distortion) pixels < 1 53.1 93.9 129.7 (7.6) * 56.4 23.0

- max(distortion) % field - 3.6 3.7 4.7 3.3 4.0 3.6

CON4 CCD spatial sampling > 2 38.5 32.9 23.8 3.7 (73.7) * 16.7

CON5 field position resolution(pixels) < 1 0.46 0.44 0.31 0.84 0.89 (0.2) *

OBJ1 optical resolution l per mm - 105.0 95.0 100.5 8.2 105.0 105.0

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) - 5.8 5.8 5.8 5.8 27.0 5.8

DV1 Curve radius lens 3 (mm) - inf inf 22.1 -63.3 inf inf

DV2 Size of CCD pixel (µm) - 13.0 13.0 13.0 13.0 6.8 20

DV3 Focus Position (mm) - 45.5 45.1 40.4 50.8 45.5 45.5

TABLE III

OPTIMIZATION RESULTS FOR STATIC VARIABLESθs . * INDICATES WHICH CONSTRAINT WAS OPTIMIZED

Fig. 14. constraint 1 ray trace

to perform design iteration based on multi-objective optimiza-tion using ZEMAX as a computation engine and to implementthe next generation of SOMS based on the optimization result.

V. CONCLUSION

We have presented a new microscope concept that cansimultaneously achieve high resolution and large field ofview. A proof-of-concept prototype has been constructed todemonstrate the basic efficacy of this concept. However,

Fig. 15. Floating lens optimization example

since extensive off-axis imaging is required, further systematicdesign optimization is required. We present the relevant de-sign constraints, including aberration, optical path difference,distortion, spatial image sampling, and field position resolu-tion, and performance metrics, including resolution, field size,and image update rate. Initial optimization results using theZEMAX optical design package indicates the possibility toimprove certain design objective but possibly at the expense

Label Desc. Goal experimental float

CON1 max(blur)/max(Airy) < 1 3.1 3.0

CON2 max(OPD) < 14 1.5 1.0

CON3 max(distortion in pixels) < 1 53.1 70.2

CON3b max optical distortion % field - 3.6 4.8

CON4 CCD spatial sampling > 2 38.5 33.1

CON5 field position resolution(pixels) < 1 0.46 ??

OBJ1 optical resolution l per mm - 105.0 150.7

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, 0.0661mm)

DV2 rotation about y(frame B, frame C) - (0.0, 0.0) (0.0, 2.97)

TABLE IV

OPD OPTIMIZATION RESULTS FOR DYNAMIC PARAMETERS, θd

Fig. 16. Settling Times of the Motion System

of other objectives. We are currently pursuing a multi-objectiveoptimization 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 StateDepartment of Health. Their expertise and knowledge ofmicroscopy and cellular processes have contributed greatlyto the project. This research is also supported in part by theCenter for Automation Technologies under a block grant fromthe New York State Science and Technology Foundation.

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