IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 9, NO. 2, MARCH/APRIL 2003 257

Angular Domain Imaging of Objects Within HighlyScattering Media Using Silicon Micromachined

Collimating ArraysGlenn H. Chapman, Member, IEEE, Maria Trinh, Nick Pfeiffer, Gary Chu, and Desmond Lee

Abstract—Optical imaging of objects within highly scatteringmedia, such as tissue, requires the detection of ballistic/quasi-bal-listic photons through these media. Recent works have usedphase/coherence domain or time domain tomography (fem-tosecond laser pulses) to detect the shortest path photons throughscattering media. This work explores an alternative, angulardomain imaging, which uses collimation detection capabilities ofsmall acceptance angle devices to extract photons emitted alignedclosely to a laser source. It employs a high aspect ratio, microma-chined collimating detector array fabricated by high-resolutionsilicon surface micromachining. Consider a linear collimatingarray of very high aspect ratio (200: 1) containing 51 1000 metched channels with 102- m spacing over a 10-mm silicon width.With precise array alignment to a laser source, unscattered lightpasses directly through the channels to the charge coupled devicedetector and the channel walls absorb the scattered light atangles 0.29 . Objects within a scattering medium were scannedquickly with a computer-controlled axis table. High-resolutionimages of 100- m-wide lines and spaces were detected at scat-tered-to-ballistic ratios of 5 105: 1, with objects located near themiddle of the sample seen at even higher levels. At 5 106: 1ratios, a uniform background of scattered illumination degradesthe image contrast unless recovered by background subtraction.Monte Carlo simulation programs designed to test the angulardomain imaging concept showed that the collimator detects theshortest path length photons, as in other optical tomographymethods. Furthermore, the collimator acts as an optical filterto remove scattered light while preserving the image resolution.Simulations suggest smaller channels and longer arrays couldenhance detection by 100.

Index Terms—Angular domain imaging, lasers, micromachinedoptics, optical tomography, tissue optics.

I. INTRODUCTION

RESEARCHERS have spent many years seeking to de-velop optical detection techniques that will supplement

or replace X-rays for imaging objects within tissue. Medicaloptical tomography techniques depend on the fact that lightcan penetrate tissue quite deeply, where some (but not much)is absorbed and most becomes heavily scattered. The key tosuccessful optical imaging is separating the components ofthe light into: a)unscatteredor slightly scattered light, whichcarries information about the structure of the tissue throughwhich it passes, and b)highly scattered light, which is many

Manuscript received November 18, 2002; revised February 10, 2003. Thiswork wsa sponsored by the Natural Science and Engineering Research Councilof Canada.

The authors are with the Simon Fraser University, School of Engineering Sci-ence, Burnaby, BC V5A 1S6, Canada (e-mail: glennc@cs.sfu.ca).

Digital Object Identifier 10.1109/JSTQE.2003.811286

orders of magnitude greater and from which it is much moredifficult to extract the structural information.

The value in exploring optical imaging techniques is due tothe fact that light has several important advantages over X-raysfor noninvasive imaging of interior body structures.

1) Light is nonionizing at wavelengths in the visible to near-infrared range ( 500-1200 nm). Thus, optical techniquescould allow for greater monitoring frequency, enhancingearly detection of cancer in areas such as mammography.

2) Unlike X-rays, the optical characteristics of tissue canbe measured at varying wavelengths, providing importantbiomedical and functional information.

3) Optical imaging techniques are compatible with com-puter-aided tomography.

4) The advent of high-power laser diodes at a wide rangeof wavelengths offers the potential to exploit opticalmethods to create a small, portable, low-power scanningsystem.

This paper investigates the use of a new type of optical tomog-raphy detection system. Angular domain imaging uses a siliconmicromachined collimating array to restrict photons based onthe source angle. We discuss the fabrication of the collimators,its testing with scattering mediums, and the computer simula-tion of the underlying principles.

II. EXISTING OPTICAL TOMOGRAPHY RESEARCH

Most optical tomography uses collimated laser beams as thelight source to illuminate the tissue. As noted, light enteringthe tissue undergoes both absorption and scattering. In its sim-plest form, the laser beam intensity follows an exponentially de-caying Beer–Lambert Law along its path through the media

where, for typical mammography values, the absorptioncoefficient is cm , the scattering coefficient

cm , and the depth cm [1]. Light that isunscattered becomes “ballistic photons.” For this example,the ratio of scattered to ballistic photons (scattering ratio orlevel) is 6.7 10 : 1. Fortunately, most of the light is notscattered uniformly in all directions, but, instead, tends todivert mostly toward the laser beam’s direction of motion. Thisforward scattering creates an effective absorption anisotropiccoefficient, cm for the so called “quasi-ballisticor snake photons” (the ones that are mostly scattered forward).Since these quasi-ballistic photons also contain desired optical

1077-260X/03$17.00 © 2003 IEEE

258 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 9, NO. 2, MARCH/APRIL 2003

Fig. 1. Collimator separation of ballistic and scattered light.

information, their scattering ratio of about 10: 1 representsa significant target for detection in this research. Note thatin practice, Monte Carlo simulation programs are needed tostatistically calculate the paths, positions and directions of theemerging photons.

One method under study uses time of flight, or time domaintomography, which measures transmitted light generated byfemtosecond laser pulses and looks for the earliest arrivingphotons [2]. The ballistic/quasi-ballistic photons arrive first,having traveled the shortest distance, while scattered photonsarrive hundreds of picoseconds later.

A second technique, coherent domain imaging [3], or opticalcoherence tomography directs a reference beam to a detector atthe system output to measure only photons in phase with thesource beam, since the chaotic paths of scattered light generaterandom phases.

Both techniques have successfully imaged objects buriedinside thick tissue, but both methods have the disadvantage ofrequiring very expensive equipment and complex, sensitivesetups.

Collimated light sources and detector arrays have had a longhistory of investigation in optical tomography, especially in de-tection of mammary tumors. A simple collimator consists of aset of aligned apertures in two or more light blocking baffles.These aligned holes create a narrow angle of acceptance of in-coming light, given by the angle formed between the hole di-ameter , and the collimator length . Thus, a collimator with50- m holes and 10-mm length has an aspect ratio of 1: 200 andan acceptance angle of 0.29(see Fig. 1). If a photon emergesfrom a scattering medium with an angle greater than the accep-tance angle then it either fails to enter the collimator or becomesabsorbed within it. Hence, only the ballistic and quasi-ballisticphotons, undergoing no scattering or small scattering, will bedetected. When very small acceptance angles are used, our workfinds greatly enhanced detection which are competitive withexisting methods but with a much simpler detection system, amethodology we call angular domain imaging.

Most earlier collimator work consisted of detectors on theoutput of aligned pinholes, in two or more opaque baffle shieldsseparated by long distances, achieving aspect ratios of 1: 10 to1: 300 [4]. But the fact that these collimators were large madeit difficult to measure multiple points. Because of the closelyspaced holes, the light from one pair of pinholes would illumi-nate detectors at others. Thus, most recent work has used fiberoptic cables as they can be bunched together to create an arrayof collimated detectors. However, for optical fibers, the accep-tance angle is set by the differences in the index of refractionof the cable core and the cladding surrounding it, giving typicalacceptance angles of 7for core diameters of 20m or less.

Fig. 2. Silicon micromachined collimating array.

III. FABRICATION OF THE SILICON MICROMACHINED

COLLIMATING ARRAY

To obtain fine object resolution and detection, a collimatingarray must have relatively small holes with small spacingbetween them. In this design, as shown in Fig. 2, we used51- m diameter holes with 102-m spacing to produce aparallel array of collimators with a predicted object resolutionin the 100–200-m range. To observe an image, this collimatorwas aligned to a CCD detector in such a way that the holespacings of 102 m matched the spacing requirement to beinteger numbers of the CCD pixels. As a first approximation,the length of the array was set equal to the depth of the mediumbeing investigated (which was 10 mm to give the needed aspectratio). Each block of grooves covered 2010-mm squares,fabricated on a 100-mm wafer. When combined with anencasement, these grooves became the silicon micromachinedcollimator array (SMCA), which had a very high aspect ratio(200: 1) resulting in a small angle of acceptance (0.29).

Such high aspect ratio, small-hole,parallel aligned colli-mating structures can be best produced by micromachining.Micromachining is a technology that uses the fabricationmethods of integrated circuit fabrication to create mechanicaland optical structures of micrometer sizes. The large length ofthe array (10 mm) combined with the small hole size suggestedthat silicon surface micromachining could best generate thestructure. For these initial experiments, only a linear collimatingarray was created.

The basic steps of the collimator microfabrication are shownin detail in [5], [7]. These collimators started with a furnace

silicon wafer oxidation (0.5-m-thick) which is thenphotolithographically patterned and etched with HF to createthe masking layer of the collimator grooves (see Fig. 3). Thesilicon was etched in HF, HNO, and CH COOH [5] usingthe oxide openings to produce a groove width of 51m afterisotropic etching, with a 15-m undercut on each channel side(see Fig. 3). The oxide was then stripped leaving the groovedstructure of Fig. 2.

After fabrication, the wafer was cleaved into 2010-mmsections along the cutting grooves between each section. For thefirst setup, a fresh silicon wafer was bonded to the etched wafertop, creating tubes in the collimator with half-circular cross sec-tions (see Fig. 4). This method avoided the alignment process re-quired to produce perfectly cylindrical holes. The half-circularholes worked nearly as well as the fully circular ones because

CHAPMAN et al.: ANGULAR DOMAIN IMAGING OF OBJECTS WITHIN HIGHLY SCATTERING MEDIA 259

Fig. 3. SMCA masked layer to get 51-�m holes on 102-�m centers.

Fig. 4. Bonding of a cover chip to the etched section to create the siliconmicromachined collimating array.

the holes were large enough that they covered several CCD de-tector pixels, and they caused no diffraction effects. The maindisadvantage of half-circular holes at these sizes is that theyproduce different acceptance angles in different directions, sothe collimation ratio is approximately twice the value in thevertical direction as in the horizontal direction. In a completesystem, additional image processing (to extract more informa-tion) would be more difficult because of this asymmetry. Butfor these demonstration experiments, this constraint was not anissue. However, a design with special micromachined alignmentstructures is under fabrication which has created circular crosssection collimators in tests with misalignments less than 2m[5] for use in future research.

Another issue that was of initial concern was the potentialfor reflected light from the silicon surface. Since silicon hasa reflectivity of about 40%, it was initially considered thatcoating the surface with carbon would provide the best resultsby almost eliminating the reflectivity. Subsequent experimentshave shown that this was not needed. The reason is that theisotropic etching does not produce a uniform optical surface inthe grooves due to variations in the wet etching process. As aresult the light is mostly scattered from the walls rather thanreflected at shallow angles. With silicon’s 40% reflectivity,it only takes four such scatterings to reduce that scatteredlight to 2% of its initial intensity. Hence, there is no needat this point to add an absorption layer to the silicon. Othertechniques can create collimators, the best alternative beingcombining fiber optic bundles from which the core is removedby etching leaving a set of hollow paths. The difficulty thereis in maintaining the alignment of the holes [less than 4-merror in collimator to end to end alignment appears important(set by the pixel size)], and producing nonreflecting holes.Hence, at present the micromachining technique appears tooffer considerable flexibility and control relative to othersinvestigated to date.

Fig. 5. Imaging test structures of 51-, 102-, 153-, and 204-�m size.

One consideration in these microcollimators is diffraction ef-fects. At 51- m, the current structures are 100 times larger thanthe 514-nm wavelength used. Furthermore, the 1-cm collimatorlength is only about 65% of the Rayleigh range (or Fresnel dis-tance) for that diameter. As a result, light does not reach the farfield diffraction pattern (see [5] for simulations). This combi-nation means the diffractive spreading of the light is about thesame as the collimator hole end diameter, and it is approachingthe point where diffraction effects must be considered. The ef-fect of diffraction would be to spread the light from ballisticphotons (for a circular collimator roughly into an airy disk) sosome would be absorbed by the collimator walls and, hence, re-ducing the amount of light collected by the detector. Howeverwhile diffraction would smear the image within a given colli-mator, the walls mean it does not allow the diffracted light tobe spread across several collimator holes. Hence, the resolutionlimit becomes no worse than the collimator hole size.

IV. EXPERIMENTAL SETUP

Determining the resolution of the objects being detected atvarious scattering levels was the main target of these experi-ments. To do this, a standard resolution test structure consistingof lines and spaces in both and directions was fabricated(see Fig. 5). The mask for these test structures was designed toshow 51-, 102-, 153-, and 204-m line and space structures inboth and directions. This design was chosen in the expec-tation that the 204m would be clearly visible with the SMCA’s102- m collimator hole spacing, the 102 and 153m would benear the limits of detectability, and the 51m would be belowthe detectable limit. These test patterns were fabricated fromthin films (100 nm) of aluminum deposited on thin glass slidesand then patterned photolithographically and aluminum-etchedto obtain the structures. This process created test structures withan edge roughness of less than 2m. In earlier experiments [7],test structure edge roughness was found to affect results whenthey were greater than the CCD pixel size.

The optical experimental setup is shown in Fig. 6. For theseexperiments, the test object was attached to a 1-cm-thick glasscell which contained the liquid scattering medium. The cell waspositioned adjacent to the SMCA array and a laser beam wasdirected through it, into the array (see Fig. 7). The collimatingarray was in turn adjacent to a monochrome CCD, with its end0.5 mm from the detector surface (limited by the CCD’s pack-aging). In operation, the cell and sample would be moved on aprecision axis (with 50-nm repeatability) stage under com-puter control [8]. By moving the object, rather than the SMCA

260 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 9, NO. 2, MARCH/APRIL 2003

Fig. 6. Scanning direction of the test structures.

Fig. 7. Schematic of setup used for SMCA characterization.

and the laser beam, alignment of the array to the beam could bemaintained. This approach is similar to the scanning techniquesused in a number of imaging systems.

The detector used was a Texas Instruments TC245 with a755 242 pixel screen, using only a 6.4 mm detection width.Each pixel occupies a 8.5-m (horizontal) by 19.75-m (ver-tical) area. The detector output could be displayed in real timeor captured under computer control. An Electrim CorporationEDC 1000 image capture board allowed full control over theCCD parameters such as gain and exposure time.

In the actual experimental setup (see Fig. 7), an argon ionlaser running in the mode was enlarged using a 10Keplerian beam expander, generating a 23 mm beam ra-dius of nearly gaussian profile to illuminate the entire glasscell, SMCA and 6-mm-wide CCD. This maintains the illumi-nation level within 4% over detector area. The argon ion laserwas chosen only for its optical laser characteristics and wouldnot be used if actual tissue were being scanned, as its greenlight (514 nm) would be too heavily scattered. During opera-tion, other background illumination was almost fully removedto leave the laser as the only light source. The whole system wasmounted on a vibration isolation table so that the measured driftof the laser alignment was 0.007 per day.

The actual scanning system (see Fig. 8) required a precisealignment of the collimator to the laser and the CCD detector.The SMCA was mounted to give , , , and three axes ofrotation control. For alignment, the CCD detector was put ina real time imaging mode, and the SMCA adjusted using therotations until the laser light was seen replicating the collimatorholes in the images. The collimator was then rotated so the holes

Fig. 8. Top view of the image-taking portion of the experimental setup.

formed a straight line across the detector with less than one pixelspacing (8.5 m) error across the full array. The SMCA vertical( ) position was adjusted so the holes fit within three pixel lines,the minimum spacing. Once aligned, this setup was reasonablystable.

During the experiments, a computer program would capturethe CCD image, then move the glass cell up an integer numberof pixel spacings (typically three lines or 59.25m), using the

axis table, to take the next image. The program would also cutout the three pixel rows containing the image, and assemble allthe rows of images to form a complete scanned image of the testobject. In typical operations, 100 images were assembled perscan. Depending on the CCD exposure, scanning times wouldtypically take from 1 to 2 min. The scanned images were pro-cessed in Adobe Photoshop to adjust for the nonrectangular na-ture of the pixels, creating an image with the correct horizontaland vertical aspect ratios. Thus, with this setup, it was possibleto rapidly scan the SMCA across the test structures and investi-gate them.

The scattering medium was created by mixing specificamounts of skim milk into deionized (DI) water to achieve thedesired scattering level. Skim milk was chosen as it exhibitsgood scattering characteristics and has a low absorption coeffi-cient [3]. Small amounts of milk were added to 20 mL of wateruntil the scattering level desired was achieved. For exampleto achieve 1.428 10 : 1 (99.9993%) scattering ratio, 0.6 mLof milk was added to 20 mL of water. The optical glass cellof 10 10 50 mm was used to hold the scattering medium.The scattering level was calibrated by using an unexpandedlaser beam and by measuring unscattered light within the glasscell filled with water, using a silicon power meter placed at adistance of 1 m from the cell. The same measure was then madewith the cell filled with the scattering medium. The scatteredbeam was passed through a 3-mm-diameter hole at the outputside of the cell to reduce the amount of scattered light reachingthe detector. The scattering percentage was the fraction of thetotal light that was scattered, relative to the unscattered lightdetected with the scattering medium in place. The 2-mm-wideunscattered laser light hit the detector directly while thescattered light radiated through a wide angle, decreasing withthe square of the distance. This light-intensity measurementwas made in a darkened room and the background light signalwas subtracted to achieve the final values. At the very highest

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Fig. 9. Images from first generation collimator various scanning ratio (a) without collimator at 1: 1, (b) with collimator at 0% (water), (c) with wider illumationat 0% (water), (d)15.39: 1 and (e) 1�10 : 1 scattering ratios, and (f) is a Pixelized version of (e).

scattering levels (where the unscattered light was reduced to99.999 from its initial levels), the signal became very

difficult to detect. At these higher levels, it became necessaryto use a narrower 3-mm cell to measure the transmitted lightand extrapolate to final values using the Beer–Lambert law.This extrapolation was confirmed over several scattering levelsusing both the 10- and 3-mm cell measurements. In these mea-surements, the absorption level was neglected as its coefficientis insignificant compared to the scattering value.

This combination of computer-controlled optical setup, testobjects, and scattering medium production allowed images tobe taken over a wide range of scattering levels.

V. EXPERIMENTAL MEASUREMENTS

The aim of these experiments was to observe the test objectsat various scattering levels until the objects could no longer bedetected. As a first approximation, it was expected that the scat-tered light would increase as a uniform background intensityuntil that intensity exceeded the level contributed by the ballisticphotons. Earlier experiments had confirmed this result with thedetection of a simple knife-edge and larger test object. In theseexperiments, the test object was placed in the front (facing thelaser) of the optical cell carrying the scattering medium. Thislocation produced the maximum travel distance for the light inthe scattering medium (a worst case scenario for scattering intothe regions of the medium blocked from the laser light by thetest patterns).

Fig. 9(a) shows what the detector sees without the collimatorin place, done at a 1: 1 scattering ratio, which is equally scat-tered and ballistic photon levels showing only a single 204-m

structure. Note how the image of the structure is of a very lowcontrast. Fig. 9(b) shows a first set of scanned images with theSMCA done using only water in the glass cell. This is a baseimage which indicates the best that the detector system can dowithout any additional processing of the image. Note that, notonly are the largest 204-m test structures clearly visible, butthe 153- and 102-m structures are also clearly visible. Unex-pectedly, even the 51–m structures (the size of the holes) arevisible, though with some distortion. This is because true struc-tural information is actually given by each pixel in a collimatorhole, as shown in Section VI’s simulations. What the collimatordoes is remove the scattered component but retains all the infor-mation of the light beam.

Fig. 9, then, shows a sequence of the first SMCA scanned im-ages at Fig. 9(c) 0% (water), Fig. 9(d) 16: 1, and (e) 1000: 1 or99.9% scattering (i.e., one part in 10was not scattered). Notethat with the collimator the contrast level is almost unchanged asscattering increases at these levels, while Fig. 9(b) showed lowcontrast at only 1: 1 without the collimator. One interesting pointis Fig. 9(e) at the 1000: 1 level which is a “pixelized” image ofFig. 9(d), that is the total intensity of all the pixels in each colli-mator hole is added up, then applied to the total area of the cor-responding collimator hole. This pixelization was considered asimple improvement of the images but note that it actually doesnot give better images, in line with the simulation discussions.Also, note that all the images in this sequence have a set of colli-mator holes that were blocked. Subsequent inspections showedthis was due to particles entering the structure during the as-sembly phase.

The problems with the blocked holes [Fig. 9(c)] in this firstgeneration collimator were corrected by adding a new step in the

262 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 9, NO. 2, MARCH/APRIL 2003

Fig. 10. Images with second-generation SMCA at scattering ratios (a) 0% (water), (b) 7.143�10 : 1, (c) 3.125�10 : 1, (d) 1.9231�10 : 1 with no slit, and(e) 5.0�10 : 1 with the object at 60% of the medium thickness.

fabrication. Before assembling the collimators, both the etchedand unetched chips were cleaned with an RCA clean (which re-moves organics) followed by an ultrasonic bath. The resultingimproved collimator’s operation is shown in Fig. 10 rangingfrom zero scattering ratio to 510 : 1. Note how the wholewidth of the array is now clear with only one of the collimatorholes transmitting less intensity than the others. This new col-limator generated much better images, but again saw the imagebecome barely detectable at the 1.923110 : 1 scattering ratio.At a 5 10 : 1 scattering ratio, an essentially uniform light levelis seen [Fig. 10(e)], which is exactly the expected failure modeof the SMCA at high scattering levels. Fig. 10(f) shows the samescattering ratio (5 10 : 1) but with the objects located withinthe medium at 6 mm or 60% of the medium thickness. Note howthe image is now easily detectable, showing that the front loca-tion is the worst case condition and that objects located withinthe scattering medium closer to the detector are detectable atmuch higher scattering levels. This result is understandable asan object in the center blocks with both the scattered and bal-listic photons colliding with it. While not shown here, but donein [8], test objects placed at the SMCA end of the glass cellwere always detectable because the test objects were directlyblocking both scattered and ballistic light.

This scattering ratio limitation very much suggested thatmuch of the scattered light originated from the regions outsidethe collimator array, as the beam expander was creating acircular symmetry of illumination. By narrowing the beamwith a slit of 0.25–mm width centered on the collimator, onlylight near the collimator could enter the scattering medium(see Fig. 11). Note how the 5.010 : 1 image [Fig. 11(a)]

now shows very clearly all the test pattern, as compared to thealmost undetectable image in the corresponding Fig. 10(e) pat-terns without the slit. At ten times more scatter 4.99910 : 1[Fig. 11(b)], the image is still visible and, furthermore, asimple contrast enhancement significantly improves the imageFig. 11(d). Clearly, more complex image processing couldimprove this further. More importantly, note that in theseimages the 102–m objects are visible with the slit in place,while they are difficult to see without the slit at high scatteringlevels. Even the 51-m objects are somewhat detectable withthe slit in place. This result indicates that the slit reduces thescattered light by at least 26 times, which is consistent with theapproximate 30 improvement expected on the basis of thelight reduction into the “scattering only” areas. Since the slit(or special optics to create a linear light beam) can be shrunkto at least 51 m, we could improve the detection by at leastanother five times.

VI. M ONTE CARLO MODELING OF ANGULAR

DOMAIN IMAGING

A. Introduction to Monte Carlo Simulation

Monte Carlo simulation is a well established means ofmodeling the Boltzmann transport equation for photons ina scattering and absorbing medium. In this method, the pathof each photon is simulated according to statistical parametersfrom the source to the detector. Based upon the properties ofthe scattering medium, the photon is moved a distance alongits path. The photon’s trajectory is then altered according toa distribution of scattering angles and it is moved again. This

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Fig. 11. SMCA improvement by narrowing beam with 0.25–mm slit at scattering ratios (a) 5.0�10 : 1, (b) 4.999�10 : 1 as scanned, and (c) 4.999�10 : 1using basic contrast enhancement.

sequence repeats until the photon exits the scattering mediumor is absorbed. The advantage of the Monte Carlo method isthat it can be used to simulate arbitrarily complex geometriesin absorbing and scattering mediums. However, this methoddoes require substantial computational resources to simulateenough photons to have a statistically valid distribution.

It is known that for many media the photon scattering distri-bution is not uniform. It has been shown by Jacqueset al. [9]that the Henyey–Greenstein phase function [10] accurately de-scribes the scattering of light in biological tissue. The importantparameter of this phase function is, the cosine of the forwardscattering angle, with values close to one representing a highdegree of forward scattering. Many common biological tissueshave a high degree of forward scattering, withvalues rangingfrom 0.79 to 0.98 for 633–nm wavelength photons [11].

There were two aims of this simulation. The first was toconfirm that by observing only the small emission angle light,we are detecting the shortest path photons, just as in timedomain tomography. The second was to verify the imageimprovement with a collimator length and determine whatlimits the resolution.

B. Experiments

Monte Carlo software originally developed by Jacques [12]was modified by Chu [8] to track the trajectories and pathlengthsof photons exiting a homogenous scattering medium. This soft-ware was further modified to allow planar, absorbing objectsto be placed within the scattering medium. Experiments wereperformed with this software to explore the effectiveness of fil-tering photons on the basis of exit angle for setups similar tothose of the experiments.

A Monte Carlo experiment was conducted to simulate thedistribution of path lengths and trajectories of photons exitinga homogenous, 1-cm-thick, scattering medium from a uniformphoton source of radius 0.0025 cm. The scattering medium wasassigned properties similar to biological tissues with avalue of0.9 and a scattering level of 10: 1. A 0.0025–cm radius shadowmask, axisymmetric with the photon source, was placed at theexit of the scattering medium. Fig. 12 shows a schematic of thesimulation setup.

Whereas the above experiment was conducted to determinethe relationship between photon path length and exit angle forthe scattering medium, a second Monte Carlo experiment was

Fig. 12. Monte Carlo simulation setup to determine photon pathlengths andexit trajectories for a 1-cm-thick, homogeneous, scattering medium.

conducted to determine the effectiveness of detecting objectswithin the scattering medium on the basis of photon exit angles.

The simulation setup employed for the second experimentconsisted of a uniform photon source of 0.01-cm radius, a1-cm-thick, scattering medium with a value of 0.9 and ascattering ratio of 10: 1, a 0.0025-cm radius shadow mask atthe exit of the scattering medium, and a planar object of radius0.00125-cm axisymmetric with the photon source. The objectwas placed at the front of the scattering medium (closest tothe photon source). Photon quantities passing through photondensity maps (radial bins axisymmetric with the uniformphoton source) were measured at several planes on the exit sideof the scattering medium. A shadow mask of radius 0.0025 cm,coincident with each photon density map, was employedto restrict the photons that were recorded. Fig. 13 shows aschematic of the simulation setup for the second Monte Carloexperiment.

C. Results and Discussions

The first Monte Carlo experiment was designed to examinethe relationship between photon exit angle and photon pathlength through the scattering medium. Figs. 14 and 15 showthe photon intensity and path length results for a simulation runwith 10 photons.

It can be seen in Fig. 14 that the photon intensity at the simu-lated detector (located at the exit side of the scattering medium)increases in a linear fashion as the photon exit angle increases.The photon intensity in this figure was normalized by dividingthe number of photons detected by the total number of photonslaunched from the source. For the Monte Carlo simulation used

264 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 9, NO. 2, MARCH/APRIL 2003

Fig. 13. Monte Carlo simulation setup to determine radial distribution of exitphotons at photon density map planez >= 1.

Fig. 14. Photon intensity as a function of photon exit angle for a Monte Carlosimulation experiment of photon distribution in a scattering medium.

in this experiment, 10photons were launched from the sourceof which 943 photons were ballistic (which is close to the ex-pected number of 1000 ballistic photons for the scattering levelof 10 used).

It can be seen in Fig. 15 that as the photon exit angle is de-creased, the photon path length (normalized by the minimumpossible path length of 1 cm) also decreases, showing that pho-tons with small exit angles (little deviation from the original tra-jectory), have path lengths that are close to the minimum pathlengths of the ballistic photons. The abrupt changes in normal-ized path length in Fig. 15 are due to the binning resolution ofthe photon density maps coupled with the low actual numbersof photons collected. This is an important proof of the angulardomain imaging concept: by selecting the light with very littleangular deviation we are selecting the shortest path length pho-tons, just as occurs in coherence and time domain tomography.

The second Monte Carlo experiment was designed to eval-uate the effectiveness of filtering photons based on exit angle.

Fig. 15. Photon path length as a function of photon exit angle for a MonteCarlo simulation experiment of photon distribution in a scattering medium.

Fig. 16. Photon intensity as a function of radial bin location for collimatingdetectors with lengths from 0.00 to 0.25 cm for a Monte Carlo simulationexperiment with an embedded object at the front of the scattering medium.

This simulation was conducted with 10photons. Fig. 16 showsthe photon intensity (normalized by the number of photons perunit area launched from the source) for planar photon densitymaps located at various distances on the exit side of the scat-tering medium. The two shadow masks together with the photondensity map form a single collimating detector, capable of ac-cepting photons within a narrow range of exit angles. It can beseen in Fig. 16 that the zero-length collimator case (when theplanar photon density map lies at cm) shows the highlyscattered signal in which it is very difficult to detect the presenceof the 0.00125-cm radius object (half the diameter of the colli-mator hole). As the collimator length is increased, the imageof the object’s shadow becomes more apparent. Note that forcases greater than 0.03 cm in length, the resolution of the imageis set by the simulation bins, which would be equivalent to theCCD photodetectors (pixels) size, not the diameter of the col-limating hole. This agrees with the experiments of Section Vwhere 51- m objects were imaged even though the collimatorhole spacing was 102m. Thus, the collimator acts as an op-tical filter to remove scattered light while preserving the image,with a resolution limit set by the detector, not the collimatorspacing. This also explains why the pixelization filter in Sec-tion V actually decreased image quality: it was removing res-olution information. This simulation lacked sufficient photonsto discuss what the resolution limits were when quasi-ballisticphotons are the dominant factor, and to get that would take con-siderable increase in computational power. However, this cal-

CHAPMAN et al.: ANGULAR DOMAIN IMAGING OF OBJECTS WITHIN HIGHLY SCATTERING MEDIA 265

Fig. 17. SNR for collimating detectors with lengths from 0.00 to 0.25 cm fora Monte Carlo simulation experiment with an embedded object at the front ofthe scattering medium.

culation is sufficient to show that the collimator hole spacing isnot the limiting factor. What is not considered in this simulationis the diffraction effects from the objects within the scatteringmedium, which provides a limit to the resolution that dependson the object size and position. This means that making the holessmaller will not increase the resolution.

The contrast ratio was examined by defining the total numberof photons per unit area collected by the collimating detectorin the unshadowed area as the signal and the photons per areacollected in the shadowed area behind the object as the noiseso that the signal-to-noise ratio (SNR) of the collimating arraymay be determined. Fig. 17 shows the improvement in SNRwith increasing collimator length based on the results of thesecond Monte Carlo experiment. It can be seen that the SNRchanges from 1.13 with a zero-length collimator to 13 with a0.25-cm collimator. Beyond that length, the number of photonsin the shadowed area was too small to be statistically reliable.This confirms the experimental result that at any given scatteringlevel there is a collimator length beyond which, effectively, al-most all of the scattered photons are removed and the contrastis at a maximum.

VII. CONCLUSION

The silicon micromachined collimating array proved to be astraightforward device capable of manufacturing with modestalignment equipment requirements. The current version of theSMCA shows acceptable detection of objects at levels of onepart unscattered light in 510 parts scattered light. This resultis approaching the 10: 1 scattering ratios of the more complextime domain and coherence domain detection, but with muchsimpler equipment. Monte Carlo simulation programs designedto test the angular domain imaging concept showed the impor-tant requirement that the collimator removes scattered light anddetects the shortest path length photons, as in other optical to-mography methods. As in the experiments, image resolution isset by the detector pixel resolution, not by the collimator spacingor hole size.

A number of improvements to this technique are beingstudied. With smaller slits, an improvement of 5–10 times isalmost certain. Simple analysis also suggests that the scatteringrejection varies with the inverse square of the acceptance angle.

Building either smaller diameter holes or longer collimators (upto 10 cm) is quite straightforward in microfabrication and thatwould improve the scattering rejection by 100 times. However,diffraction effects become important when the collimator holesapproach about 50 times the wavelengths or collimator lengthsexceed the Rayleigh range for that diameter, and those maylimit resolution or decrease light detection levels. As notedenhanced image processing offers still more improvements.This result suggests that exceeding the current 1: 10levels isquite feasible. Research is continuing on the SMCAs in thesedirections. Further Monte Carlo simulation software devel-opment is planned to allow larger number of photons, morecomplex geometries and diffraction effects to be simulated.

REFERENCES

[1] J. Beuthan, O. Minet, G. Muller, and V. Prapavat, “IR-Diaphanoscopy inmedicine,” inMedical Optical Tomography: Functional Imaging Mon-itoring, SPIE IS11, G. Muler , Ed., 1993, pp. 263–282.

[2] K. M. Yoo , B.B. Das, F. Liu, and R.R. Alfano, “Ultrashort laser pulsepropagation and imaging in biological issue and model random media-steps toward optical mammography,” inMedical Optical Tomography:Functional Imaging Monitoring, SPIE IS11, 1993, pp. 425–439.

[3] H. Inaba, “Coherent detection imaging for medical laser tomography,”in SPIE IS11, 1993, pp. 317–347.

[4] P. van der Zeeet al., “Methods for measuring the optical properties oftissue samples in visible and near infrared wavelength range,” inMedicalOptical Tomography: Functional Imaging and Monitoring, SPIE IS11,G. Muleret al., Eds., 1993, pp. 166–192.

[5] M. S. Tank, “Development of a silicon micromachined collimator arrayto detect objects within highly scattering mediums,” M.Sc. thesis,School Eng. Sci., Simon Fraser Univ., Burnaby, BC, Canada, 2001.

[6] T. Wong, “An alternative approach to multi-chip module interconnec-tions: laser-welding micro cantilevers,” B.A.Sc. thesis, School Eng. Sci.,Simon Fraser Univ., Burnaby, BC, Canada, 1995.

[7] M. S. Tank, G. H. Chapman, and G. H. Chapman, “Micromachinedsilicon collimating detector array to view objects in hightly scatteringmedium,”Can. J. Electr. Comput. Eng., vol. 25, no. 1, pp. 13–18, 2000.

[8] G. Chu, “Probing Structures in Scattering Medium Using a Silicon Mi-cromachined Collimator Array,” B.A.Sc. thesis, School Eng. Sci., SimonFraser Univ., Burnaby, BC, Canada, 2000.

[9] L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,”Astrophys. J., vol. 93, pp. 70–83, 1941.

[10] S. L. Jacques, C. A. Alter, and S. A. Prahl, “Angular dependence ofHeNe laser light scattering by human dermis,”Laser Life Sci., vol. 1,pp. 309–333, 1987.

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Glenn H. Chapman (S’72–M’80) was born on Au-gust 28, 1948. He received the B.Sc. degree in engi-neering physics and the M.Sc. degree from Queen’sUniversity, Kingston, ON, Canada, in 1972 and 1975,respectively, and the Ph.D. degree from McMasterUniversity, Hamilton, ON, Canada, in 1982.

From 1980 to 1990, he was a Research StaffMember with the Lincoln Laboratory, MassachusettsInstitute of Technology, Lexington, where he workedon developing laser redundancy techniques for theWafer Scale Integration project. Since 1990, he

has been a Professor with the School of Engineering Science, Simon FraserUniversity, Burnaby, BC, Canada, specializing in the areas of large-area laserrestructurable silicon systems, microfabrication technology, and microma-chined sensors involving lasers. He is the author of 27 journal papers, 68conference papers, two book chapters, and 20 patents.

Prof. Chapman is a Senior Fellow of the British Columbia Advanced SystemInstitute.

266 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 9, NO. 2, MARCH/APRIL 2003

Maria Trinh was born on November 5th, 1978. Shereceived the B.A.Sc. degree in systems engineeringfrom Simon Fraser University, Burnaby, BC, Canada.

She currently has three conference publications(two for SPIE Photonics West 2001 and 2002, andone for the 2002 IEEE Canadian Conference onComputer and Electrical Engineering) and a pendingjournal publication for theSPIE Journal of Mi-crolithography, Microfabrication, and Microsystems.

Nick Pfeiffer was born on July 8, 1963. He receivedthe B.A.Sc. degree in mechanical engineering fromthe University of British Columbia, Vancouver, BC,Canada, in 1988, the M.A.Sc. degree in engineeringscience, in 2001, from Simon Fraser University,Burnaby, BC, Canada, where he is currently pursuingthe Ph.D. degree in the areas of optical tomographyand angular domain imaging.

He has served as senior management in severaltechnology-based companies and is currentlyPresident of Pfeiffer Consulting Inc., Mission, BC,

Canada. He has five conference publications.Mr. Pfeiffer is a member of the American Society of Mechanical Engineers.

He is licensed as a professional engineer (P.Eng.).

Gary Chu was born in Hong Kong, China, in 1978.He received the B.A.Sc. degree in engineeringphysics from Simon Fraser University, Burnaby,BC, Canada, in 2001, and is currently pursuingthe M.A.Sc. degree in biomedical engineering atthe University of Toronto, Toronto, ON, Canada,where he is conducting research on intercellularcommunication systems for genetic circuits.

He has two conference publications.

Desmond Leeis working toward the B.A.Sc. degreein systems engineering at Simon Fraser University,Burnaby, BC, Canada.