Angular domain imaging of objects within highly - IEEE Xplore

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

257

Angular Domain Imaging of Objects Within Highly Scattering Media Using Silicon Micromachined Collimating Arrays Glenn H. Chapman, Member, IEEE, Maria Trinh, Nick Pfeiffer, Gary Chu, and Desmond Lee

Abstract—Optical imaging of objects within highly scattering media, such as tissue, requires the detection of ballistic/quasi-ballistic photons through these media. Recent works have used phase/coherence domain or time domain tomography (femtosecond laser pulses) to detect the shortest path photons through scattering media. This work explores an alternative, angular domain imaging, which uses collimation detection capabilities of small acceptance angle devices to extract photons emitted aligned closely to a laser source. It employs a high aspect ratio, micromachined collimating detector array fabricated by high-resolution silicon surface micromachining. Consider a linear collimating array of very high aspect ratio (200: 1) containing 51 1000 m etched channels with 102- m spacing over a 10-mm silicon width. With precise array alignment to a laser source, unscattered light passes directly through the channels to the charge coupled device detector and the channel walls absorb the scattered light at angles 0.29 . Objects within a scattering medium were scanned quickly with a computer-controlled axis table. High-resolution images of 100- m-wide lines and spaces were detected at scattered-to-ballistic ratios of 5 105 : 1, with objects located near the middle of the sample seen at even higher levels. At 5 106 : 1 ratios, a uniform background of scattered illumination degrades the image contrast unless recovered by background subtraction. Monte Carlo simulation programs designed to test the angular domain imaging concept showed that the collimator detects the shortest path length photons, as in other optical tomography methods. Furthermore, the collimator acts as an optical filter to remove scattered light while preserving the image resolution. Simulations suggest smaller channels and longer arrays could enhance detection by 100.

orders of magnitude greater and from which it is much more difficult to extract the structural information. The value in exploring optical imaging techniques is due to the fact that light has several important advantages over X-rays for noninvasive imaging of interior body structures. 1) Light is nonionizing at wavelengths in the visible to nearinfrared range ( 500-1200 nm). Thus, optical techniques could allow for greater monitoring frequency, enhancing early detection of cancer in areas such as mammography. 2) Unlike X-rays, the optical characteristics of tissue can be measured at varying wavelengths, providing important biomedical and functional information. 3) Optical imaging techniques are compatible with computer-aided tomography. 4) The advent of high-power laser diodes at a wide range of wavelengths offers the potential to exploit optical methods to create a small, portable, low-power scanning system. This paper investigates the use of a new type of optical tomography detection system. Angular domain imaging uses a silicon micromachined collimating array to restrict photons based on the source angle. We discuss the fabrication of the collimators, its testing with scattering mediums, and the computer simulation of the underlying principles.

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

II. EXISTING OPTICAL TOMOGRAPHY RESEARCH

I. INTRODUCTION

R

ESEARCHERS have spent many years seeking to develop optical detection techniques that will supplement or replace X-rays for imaging objects within tissue. Medical optical tomography techniques depend on the fact that light can penetrate tissue quite deeply, where some (but not much) is absorbed and most becomes heavily scattered. The key to successful optical imaging is separating the components of the light into: a) unscattered or slightly scattered light, which carries information about the structure of the tissue through which it passes, and b) highly scattered light, which is many Manuscript received November 18, 2002; revised February 10, 2003. This work wsa sponsored by the Natural Science and Engineering Research Council of Canada. The authors are with the Simon Fraser University, School of Engineering Science, Burnaby, BC V5A 1S6, Canada (e-mail: [email protected]). Digital Object Identifier 10.1109/JSTQE.2003.811286

Most optical tomography uses collimated laser beams as the light source to illuminate the tissue. As noted, light entering the tissue undergoes both absorption and scattering. In its simplest form, the laser beam intensity follows an exponentially decaying Beer–Lambert Law along its path through the media

where, for typical mammography values, the absorption cm , the scattering coefficient coefficient is cm , and the depth cm [1]. Light that is unscattered becomes “ballistic photons.” For this example, the ratio of scattered to ballistic photons (scattering ratio or level) is 6.7 10 : 1. Fortunately, most of the light is not scattered uniformly in all directions, but, instead, tends to divert mostly toward the laser beam’s direction of motion. This forward scattering creates an effective absorption anisotropic cm for the so called “quasi-ballistic coefficient, or 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 represents a significant target for detection in this research. Note that in practice, Monte Carlo simulation programs are needed to statistically calculate the paths, positions and directions of the emerging photons. One method under study uses time of flight, or time domain tomography, which measures transmitted light generated by femtosecond laser pulses and looks for the earliest arriving photons [2]. The ballistic/quasi-ballistic photons arrive first, having traveled the shortest distance, while scattered photons arrive hundreds of picoseconds later. A second technique, coherent domain imaging [3], or optical coherence tomography directs a reference beam to a detector at the system output to measure only photons in phase with the source beam, since the chaotic paths of scattered light generate random phases. Both techniques have successfully imaged objects buried inside thick tissue, but both methods have the disadvantage of requiring very expensive equipment and complex, sensitive setups. Collimated light sources and detector arrays have had a long history of investigation in optical tomography, especially in detection of mammary tumors. A simple collimator consists of a set of aligned apertures in two or more light blocking baffles. These aligned holes create a narrow angle of acceptance of incoming light, given by the angle formed between the hole diameter , and the collimator length . Thus, a collimator with 50- m holes and 10-mm length has an aspect ratio of 1: 200 and an acceptance angle of 0.29 (see Fig. 1). If a photon emerges from a scattering medium with an angle greater than the acceptance angle then it either fails to enter the collimator or becomes absorbed within it. Hence, only the ballistic and quasi-ballistic photons, undergoing no scattering or small scattering, will be detected. When very small acceptance angles are used, our work finds greatly enhanced detection which are competitive with existing methods but with a much simpler detection system, a methodology we call angular domain imaging. Most earlier collimator work consisted of detectors on the output of aligned pinholes, in two or more opaque baffle shields separated by long distances, achieving aspect ratios of 1: 10 to 1: 300 [4]. But the fact that these collimators were large made it difficult to measure multiple points. Because of the closely spaced holes, the light from one pair of pinholes would illuminate detectors at others. Thus, most recent work has used fiber optic cables as they can be bunched together to create an array of collimated detectors. However, for optical fibers, the acceptance angle is set by the differences in the index of refraction of the cable core and the cladding surrounding it, giving typical acceptance angles of 7 for core diameters of 20 m or less.

Fig. 2.

Silicon micromachined collimating array.

III. FABRICATION OF THE SILICON MICROMACHINED COLLIMATING ARRAY To obtain fine object resolution and detection, a collimating array must have relatively small holes with small spacing between them. In this design, as shown in Fig. 2, we used 51- m diameter holes with 102- m spacing to produce a parallel array of collimators with a predicted object resolution in the 100–200- m range. To observe an image, this collimator was aligned to a CCD detector in such a way that the hole spacings of 102 m matched the spacing requirement to be integer numbers of the CCD pixels. As a first approximation, the length of the array was set equal to the depth of the medium being investigated (which was 10 mm to give the needed aspect ratio). Each block of grooves covered 20 10-mm squares, fabricated on a 100-mm wafer. When combined with an encasement, these grooves became the silicon micromachined collimator 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 collimating structures can be best produced by micromachining. Micromachining is a technology that uses the fabrication methods of integrated circuit fabrication to create mechanical and optical structures of micrometer sizes. The large length of the array (10 mm) combined with the small hole size suggested that silicon surface micromachining could best generate the structure. For these initial experiments, only a linear collimating array was created. The basic steps of the collimator microfabrication are shown in detail in [5], [7]. These collimators started with a furnace silicon wafer oxidation (0.5- m-thick) which is then photolithographically patterned and etched with HF to create the masking layer of the collimator grooves (see Fig. 3). The silicon was etched in HF, HNO , and CH COOH [5] using the oxide openings to produce a groove width of 51 m after isotropic etching, with a 15- m undercut on each channel side (see Fig. 3). The oxide was then stripped leaving the grooved structure of Fig. 2. After fabrication, the wafer was cleaved into 20 10-mm sections along the cutting grooves between each section. For the first setup, a fresh silicon wafer was bonded to the etched wafer top, creating tubes in the collimator with half-circular cross sections (see Fig. 4). This method avoided the alignment process required to produce perfectly cylindrical holes. The half-circular holes 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. 5.

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

the holes were large enough that they covered several CCD detector pixels, and they caused no diffraction effects. The main disadvantage of half-circular holes at these sizes is that they produce different acceptance angles in different directions, so the collimation ratio is approximately twice the value in the vertical direction as in the horizontal direction. In a complete system, additional image processing (to extract more information) would be more difficult because of this asymmetry. But for these demonstration experiments, this constraint was not an issue. However, a design with special micromachined alignment structures is under fabrication which has created circular cross section collimators in tests with misalignments less than 2 m [5] for use in future research. Another issue that was of initial concern was the potential for reflected light from the silicon surface. Since silicon has a reflectivity of about 40%, it was initially considered that coating the surface with carbon would provide the best results by almost eliminating the reflectivity. Subsequent experiments have shown that this was not needed. The reason is that the isotropic etching does not produce a uniform optical surface in the grooves due to variations in the wet etching process. As a result the light is mostly scattered from the walls rather than reflected at shallow angles. With silicon’s 40% reflectivity, it only takes four such scatterings to reduce that scattered light to 2% of its initial intensity. Hence, there is no need at this point to add an absorption layer to the silicon. Other techniques can create collimators, the best alternative being combining fiber optic bundles from which the core is removed by etching leaving a set of hollow paths. The difficulty there is in maintaining the alignment of the holes [less than 4- m error 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 to offer considerable flexibility and control relative to others investigated to date.

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

One consideration in these microcollimators is diffraction effects. At 51- m, the current structures are 100 times larger than the 514-nm wavelength used. Furthermore, the 1-cm collimator length is only about 65% of the Rayleigh range (or Fresnel distance) for that diameter. As a result, light does not reach the far field diffraction pattern (see [5] for simulations). This combination means the diffractive spreading of the light is about the same as the collimator hole end diameter, and it is approaching the point where diffraction effects must be considered. The effect of diffraction would be to spread the light from ballistic photons (for a circular collimator roughly into an airy disk) so some would be absorbed by the collimator walls and, hence, reducing the amount of light collected by the detector. However while diffraction would smear the image within a given collimator, the walls mean it does not allow the diffracted light to be spread across several collimator holes. Hence, the resolution limit becomes no worse than the collimator hole size. IV. EXPERIMENTAL SETUP Determining the resolution of the objects being detected at various scattering levels was the main target of these experiments. To do this, a standard resolution test structure consisting and directions was fabricated of lines and spaces in both (see Fig. 5). The mask for these test structures was designed to show 51-, 102-, 153-, and 204- m line and space structures in both and directions. This design was chosen in the expectation that the 204 m would be clearly visible with the SMCA’s 102- m collimator hole spacing, the 102 and 153 m would be near the limits of detectability, and the 51 m would be below the detectable limit. These test patterns were fabricated from thin films (100 nm) of aluminum deposited on thin glass slides and then patterned photolithographically and aluminum-etched to obtain the structures. This process created test structures with an edge roughness of less than 2 m. In earlier experiments [7], test structure edge roughness was found to affect results when they were greater than the CCD pixel size. The optical experimental setup is shown in Fig. 6. For these experiments, the test object was attached to a 1-cm-thick glass cell which contained the liquid scattering medium. The cell was positioned adjacent to the SMCA array and a laser beam was directed through it, into the array (see Fig. 7). The collimating array was in turn adjacent to a monochrome CCD, with its end 0.5 mm from the detector surface (limited by the CCD’s packaging). In operation, the cell and sample would be moved on a precision axis (with 50-nm repeatability) stage under computer 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. 8. Top view of the image-taking portion of the experimental setup. 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 be maintained. This approach is similar to the scanning techniques used in a number of imaging systems. The detector used was a Texas Instruments TC245 with a 755 242 pixel screen, using only a 6.4 mm detection width. Each pixel occupies a 8.5- m (horizontal) by 19.75- m (vertical) area. The detector output could be displayed in real time or captured under computer control. An Electrim Corporation EDC 1000 image capture board allowed full control over the CCD parameters such as gain and exposure time. In the actual experimental setup (see Fig. 7), an argon ion mode was enlarged using a 10 laser running in the Keplerian beam expander, generating a 23 mm beam radius of nearly gaussian profile to illuminate the entire glass cell, SMCA and 6-mm-wide CCD. This maintains the illumination level within 4% over detector area. The argon ion laser was chosen only for its optical laser characteristics and would not be used if actual tissue were being scanned, as its green light (514 nm) would be too heavily scattered. During operation, other background illumination was almost fully removed to leave the laser as the only light source. The whole system was mounted on a vibration isolation table so that the measured drift of the laser alignment was 0.007 per day. The actual scanning system (see Fig. 8) required a precise alignment of the collimator to the laser and the CCD detector. The SMCA was mounted to give , , , and three axes of rotation control. For alignment, the CCD detector was put in a real time imaging mode, and the SMCA adjusted using the rotations until the laser light was seen replicating the collimator holes in the images. The collimator was then rotated so the holes

formed a straight line across the detector with less than one pixel spacing (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 reasonably stable. During the experiments, a computer program would capture the CCD image, then move the glass cell up an integer number of pixel spacings (typically three lines or 59.25 m), using the axis table, to take the next image. The program would also cut out the three pixel rows containing the image, and assemble all the rows of images to form a complete scanned image of the test object. In typical operations, 100 images were assembled per scan. Depending on the CCD exposure, scanning times would typically take from 1 to 2 min. The scanned images were processed in Adobe Photoshop to adjust for the nonrectangular nature of the pixels, creating an image with the correct horizontal and vertical aspect ratios. Thus, with this setup, it was possible to rapidly scan the SMCA across the test structures and investigate them. The scattering medium was created by mixing specific amounts of skim milk into deionized (DI) water to achieve the desired scattering level. Skim milk was chosen as it exhibits good scattering characteristics and has a low absorption coefficient [3]. Small amounts of milk were added to 20 mL of water until the scattering level desired was achieved. For example to achieve 1.428 10 : 1 (99.9993%) scattering ratio, 0.6 mL of milk was added to 20 mL of water. The optical glass cell of 10 10 50 mm was used to hold the scattering medium. The scattering level was calibrated by using an unexpanded laser beam and by measuring unscattered light within the glass cell filled with water, using a silicon power meter placed at a distance of 1 m from the cell. The same measure was then made with the cell filled with the scattering medium. The scattered beam was passed through a 3-mm-diameter hole at the output side of the cell to reduce the amount of scattered light reaching the detector. The scattering percentage was the fraction of the total light that was scattered, relative to the unscattered light detected with the scattering medium in place. The 2-mm-wide unscattered laser light hit the detector directly while the scattered light radiated through a wide angle, decreasing with the square of the distance. This light-intensity measurement was made in a darkened room and the background light signal was subtracted to achieve the final values. At the very highest

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

261

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 illumation at 0% (water), (d)15.39: 1 and (e) 1 10 : 1 scattering ratios, and (f) is a Pixelized version of (e).

2

scattering levels (where the unscattered light was reduced to 99.999 from its initial levels), the signal became very difficult to detect. At these higher levels, it became necessary to use a narrower 3-mm cell to measure the transmitted light and extrapolate to final values using the Beer–Lambert law. This extrapolation was confirmed over several scattering levels using both the 10- and 3-mm cell measurements. In these measurements, the absorption level was neglected as its coefficient is insignificant compared to the scattering value. This combination of computer-controlled optical setup, test objects, and scattering medium production allowed images to be taken over a wide range of scattering levels. V. EXPERIMENTAL MEASUREMENTS The aim of these experiments was to observe the test objects at various scattering levels until the objects could no longer be detected. As a first approximation, it was expected that the scattered light would increase as a uniform background intensity until that intensity exceeded the level contributed by the ballistic photons. Earlier experiments had confirmed this result with the detection of a simple knife-edge and larger test object. In these experiments, the test object was placed in the front (facing the laser) of the optical cell carrying the scattering medium. This location produced the maximum travel distance for the light in the scattering medium (a worst case scenario for scattering into the regions of the medium blocked from the laser light by the test patterns). Fig. 9(a) shows what the detector sees without the collimator in place, done at a 1: 1 scattering ratio, which is equally scattered and ballistic photon levels showing only a single 204- m

structure. Note how the image of the structure is of a very low contrast. Fig. 9(b) shows a first set of scanned images with the SMCA done using only water in the glass cell. This is a base image which indicates the best that the detector system can do without any additional processing of the image. Note that, not only are the largest 204- m test structures clearly visible, but the 153- and 102- m structures are also clearly visible. Unexpectedly, even the 51– m structures (the size of the holes) are visible, though with some distortion. This is because true structural information is actually given by each pixel in a collimator hole, as shown in Section VI’s simulations. What the collimator does is remove the scattered component but retains all the information of the light beam. Fig. 9, then, shows a sequence of the first SMCA scanned images at Fig. 9(c) 0% (water), Fig. 9(d) 16: 1, and (e) 1000: 1 or 99.9% scattering (i.e., one part in 10 was not scattered). Note that with the collimator the contrast level is almost unchanged as scattering increases at these levels, while Fig. 9(b) showed low contrast at only 1: 1 without the collimator. One interesting point is Fig. 9(e) at the 1000: 1 level which is a “pixelized” image of Fig. 9(d), that is the total intensity of all the pixels in each collimator hole is added up, then applied to the total area of the corresponding collimator hole. This pixelization was considered a simple improvement of the images but note that it actually does not give better images, in line with the simulation discussions. Also, note that all the images in this sequence have a set of collimator holes that were blocked. Subsequent inspections showed this was due to particles entering the structure during the assembly phase. The problems with the blocked holes [Fig. 9(c)] in this first generation 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 (e) 5.0 10 : 1 with the object at 60% of the medium thickness.

2

fabrication. Before assembling the collimators, both the etched and unetched chips were cleaned with an RCA clean (which removes organics) followed by an ultrasonic bath. The resulting improved collimator’s operation is shown in Fig. 10 ranging from zero scattering ratio to 5 10 : 1. Note how the whole width of the array is now clear with only one of the collimator holes transmitting less intensity than the others. This new collimator generated much better images, but again saw the image become barely detectable at the 1.9231 10 : 1 scattering ratio. At a 5 10 : 1 scattering ratio, an essentially uniform light level is seen [Fig. 10(e)], which is exactly the expected failure mode of the SMCA at high scattering levels. Fig. 10(f) shows the same scattering ratio (5 10 : 1) but with the objects located within the medium at 6 mm or 60% of the medium thickness. Note how the image is now easily detectable, showing that the front location is the worst case condition and that objects located within the scattering medium closer to the detector are detectable at much higher scattering levels. This result is understandable as an object in the center blocks with both the scattered and ballistic photons colliding with it. While not shown here, but done in [8], test objects placed at the SMCA end of the glass cell were always detectable because the test objects were directly blocking both scattered and ballistic light. This scattering ratio limitation very much suggested that much of the scattered light originated from the regions outside the collimator array, as the beam expander was creating a circular symmetry of illumination. By narrowing the beam with a slit of 0.25–mm width centered on the collimator, only light near the collimator could enter the scattering medium (see Fig. 11). Note how the 5.0 10 : 1 image [Fig. 11(a)]

210 : 1, (c) 3.125 210 : 1, (d) 1.9231 210 : 1 with no slit, and

now shows very clearly all the test pattern, as compared to the almost undetectable image in the corresponding Fig. 10(e) patterns without the slit. At ten times more scatter 4.999 10 : 1 [Fig. 11(b)], the image is still visible and, furthermore, a simple contrast enhancement significantly improves the image Fig. 11(d). Clearly, more complex image processing could improve this further. More importantly, note that in these images the 102– m objects are visible with the slit in place, while they are difficult to see without the slit at high scattering levels. Even the 51- m objects are somewhat detectable with the slit in place. This result indicates that the slit reduces the scattered light by at least 26 times, which is consistent with the improvement expected on the basis of the approximate 30 light reduction into the “scattering only” areas. Since the slit (or special optics to create a linear light beam) can be shrunk to at least 51 m, we could improve the detection by at least another five times. VI. MONTE CARLO MODELING OF ANGULAR DOMAIN IMAGING A. Introduction to Monte Carlo Simulation Monte Carlo simulation is a well established means of modeling the Boltzmann transport equation for photons in a scattering and absorbing medium. In this method, the path of each photon is simulated according to statistical parameters from the source to the detector. Based upon the properties of the scattering medium, the photon is moved a distance along its path. The photon’s trajectory is then altered according to a distribution of scattering angles and it is moved again. This

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

Fig. 11. SMCA improvement by narrowing beam with 0.25–mm slit at scattering ratios (a) 5.0 using basic contrast enhancement.

sequence repeats until the photon exits the scattering medium or is absorbed. The advantage of the Monte Carlo method is that it can be used to simulate arbitrarily complex geometries in absorbing and scattering mediums. However, this method does require substantial computational resources to simulate enough photons to have a statistically valid distribution. It is known that for many media the photon scattering distribution is not uniform. It has been shown by Jacques et al. [9] that the Henyey–Greenstein phase function [10] accurately describes the scattering of light in biological tissue. The important parameter of this phase function is , the cosine of the forward scattering angle, with values close to one representing a high degree of forward scattering. Many common biological tissues have a high degree of forward scattering, with values ranging from 0.79 to 0.98 for 633–nm wavelength photons [11]. There were two aims of this simulation. The first was to confirm that by observing only the small emission angle light, we are detecting the shortest path photons, just as in time domain tomography. The second was to verify the image improvement with a collimator length and determine what limits the resolution. B. Experiments Monte Carlo software originally developed by Jacques [12] was modified by Chu [8] to track the trajectories and pathlengths of photons exiting a homogenous scattering medium. This software was further modified to allow planar, absorbing objects to be placed within the scattering medium. Experiments were performed with this software to explore the effectiveness of filtering photons on the basis of exit angle for setups similar to those of the experiments. A Monte Carlo experiment was conducted to simulate the distribution of path lengths and trajectories of photons exiting a homogenous, 1-cm-thick, scattering medium from a uniform photon source of radius 0.0025 cm. The scattering medium was assigned properties similar to biological tissues with a value of 0.9 and a scattering level of 10 : 1. A 0.0025–cm radius shadow mask, axisymmetric with the photon source, was placed at the exit of the scattering medium. Fig. 12 shows a schematic of the simulation setup. Whereas the above experiment was conducted to determine the relationship between photon path length and exit angle for the scattering medium, a second Monte Carlo experiment was

263

210 : 1, (b) 4.999 210 : 1 as scanned, and (c) 4.999 210 : 1

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

conducted to determine the effectiveness of detecting objects within the scattering medium on the basis of photon exit angles. The simulation setup employed for the second experiment consisted of a uniform photon source of 0.01-cm radius, a 1-cm-thick, scattering medium with a value of 0.9 and a scattering ratio of 10 : 1, a 0.0025-cm radius shadow mask at the exit of the scattering medium, and a planar object of radius 0.00125-cm axisymmetric with the photon source. The object was placed at the front of the scattering medium (closest to the photon source). Photon quantities passing through photon density maps (radial bins axisymmetric with the uniform photon source) were measured at several planes on the exit side of the scattering medium. A shadow mask of radius 0.0025 cm, coincident with each photon density map, was employed to restrict the photons that were recorded. Fig. 13 shows a schematic of the simulation setup for the second Monte Carlo experiment. C. Results and Discussions The first Monte Carlo experiment was designed to examine the relationship between photon exit angle and photon path length through the scattering medium. Figs. 14 and 15 show the photon intensity and path length results for a simulation run with 10 photons. It can be seen in Fig. 14 that the photon intensity at the simulated 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 dividing the number of photons detected by the total number of photons launched 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. 15. Photon path length as a function of photon exit angle for a Monte Carlo simulation experiment of photon distribution in a scattering medium.

Fig. 13. Monte Carlo simulation setup to determine radial distribution of exit photons at photon density map plane = 1.

z>

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

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

in this experiment, 10 photons were launched from the source of which 943 photons were ballistic (which is close to the expected number of 1000 ballistic photons for the scattering level of 10 used). It can be seen in Fig. 15 that as the photon exit angle is decreased, the photon path length (normalized by the minimum possible path length of 1 cm) also decreases, showing that photons with small exit angles (little deviation from the original trajectory), have path lengths that are close to the minimum path lengths of the ballistic photons. The abrupt changes in normalized path length in Fig. 15 are due to the binning resolution of the photon density maps coupled with the low actual numbers of photons collected. This is an important proof of the angular domain imaging concept: by selecting the light with very little angular deviation we are selecting the shortest path length photons, just as occurs in coherence and time domain tomography. The second Monte Carlo experiment was designed to evaluate the effectiveness of filtering photons based on exit angle.

This simulation was conducted with 10 photons. Fig. 16 shows the photon intensity (normalized by the number of photons per unit area launched from the source) for planar photon density maps located at various distances on the exit side of the scattering medium. The two shadow masks together with the photon density map form a single collimating detector, capable of accepting photons within a narrow range of exit angles. It can be seen in Fig. 16 that the zero-length collimator case (when the cm) shows the highly planar photon density map lies at scattered signal in which it is very difficult to detect the presence of the 0.00125-cm radius object (half the diameter of the collimator hole). As the collimator length is increased, the image of the object’s shadow becomes more apparent. Note that for cases greater than 0.03 cm in length, the resolution of the image is set by the simulation bins, which would be equivalent to the CCD photodetectors (pixels) size, not the diameter of the collimating hole. This agrees with the experiments of Section V where 51- m objects were imaged even though the collimator hole spacing was 102 m. Thus, the collimator acts as an optical filter to remove scattered light while preserving the image, with a resolution limit set by the detector, not the collimator spacing. This also explains why the pixelization filter in Section V actually decreased image quality: it was removing resolution information. This simulation lacked sufficient photons to discuss what the resolution limits were when quasi-ballistic photons are the dominant factor, and to get that would take considerable increase in computational power. However, this cal-

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

265

Building either smaller diameter holes or longer collimators (up to 10 cm) is quite straightforward in microfabrication and that would improve the scattering rejection by 100 times. However, diffraction effects become important when the collimator holes approach about 50 times the wavelengths or collimator lengths exceed the Rayleigh range for that diameter, and those may limit resolution or decrease light detection levels. As noted enhanced image processing offers still more improvements. This result suggests that exceeding the current 1: 10 levels is quite feasible. Research is continuing on the SMCAs in these directions. Further Monte Carlo simulation software development is planned to allow larger number of photons, more complex geometries and diffraction effects to be simulated. Fig. 17. SNR for collimating detectors with lengths from 0.00 to 0.25 cm for a Monte Carlo simulation experiment with an embedded object at the front of the scattering medium.

culation is sufficient to show that the collimator hole spacing is not the limiting factor. What is not considered in this simulation is the diffraction effects from the objects within the scattering medium, which provides a limit to the resolution that depends on the object size and position. This means that making the holes smaller will not increase the resolution. The contrast ratio was examined by defining the total number of photons per unit area collected by the collimating detector in the unshadowed area as the signal and the photons per area collected in the shadowed area behind the object as the noise so that the signal-to-noise ratio (SNR) of the collimating array may be determined. Fig. 17 shows the improvement in SNR with increasing collimator length based on the results of the second Monte Carlo experiment. It can be seen that the SNR changes from 1.13 with a zero-length collimator to 13 with a 0.25-cm collimator. Beyond that length, the number of photons in the shadowed area was too small to be statistically reliable. This confirms the experimental result that at any given scattering level there is a collimator length beyond which, effectively, almost all of the scattered photons are removed and the contrast is at a maximum. VII. CONCLUSION The silicon micromachined collimating array proved to be a straightforward device capable of manufacturing with modest alignment equipment requirements. The current version of the SMCA shows acceptable detection of objects at levels of one part unscattered light in 5 10 parts scattered light. This result is approaching the 10 : 1 scattering ratios of the more complex time domain and coherence domain detection, but with much simpler equipment. Monte Carlo simulation programs designed to test the angular domain imaging concept showed the important requirement that the collimator removes scattered light and detects the shortest path length photons, as in other optical tomography methods. As in the experiments, image resolution is set by the detector pixel resolution, not by the collimator spacing or hole size. A number of improvements to this technique are being studied. With smaller slits, an improvement of 5–10 times is almost certain. Simple analysis also suggests that the scattering rejection varies with the inverse square of the acceptance angle.

REFERENCES [1] J. Beuthan, O. Minet, G. Muller, and V. Prapavat, “IR-Diaphanoscopy in medicine,” in Medical Optical Tomography: Functional Imaging Monitoring, SPIE IS11, G. Muler , Ed., 1993, pp. 263–282. [2] K. M. Yoo , B.B. Das, F. Liu, and R.R. Alfano, “Ultrashort laser pulse propagation and imaging in biological issue and model random mediasteps toward optical mammography,” in Medical 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 Zee et al., “Methods for measuring the optical properties of tissue samples in visible and near infrared wavelength range,” in Medical Optical Tomography: Functional Imaging and Monitoring, SPIE IS11, G. Muler et al., Eds., 1993, pp. 166–192. [5] M. S. Tank, “Development of a silicon micromachined collimator array to 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 interconnections: 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, “Micromachined silicon collimating detector array to view objects in hightly scattering medium,” Can. J. Electr. Comput. Eng., vol. 25, no. 1, pp. 13–18, 2000. [8] G. Chu, “Probing Structures in Scattering Medium Using a Silicon Micromachined Collimator Array,” B.A.Sc. thesis, School Eng. Sci., Simon Fraser 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 of HeNe laser light scattering by human dermis,” Laser Life Sci., vol. 1, pp. 309–333, 1987. [11] I. V. Yaroslavskil and V. V. Tuchin, “Light propagation in multilayer scattering media: Modeling by the Monte Carlo method,” Opt. Spectrosc., vol. 72, no. 4, pp. 505–509, 1992. [12] S. Jacques. (2001) Introduction to Biomedical Optics. Oregon Grad. Inst. [Online]. Available: http://omlc.ogi.edu/classroom/ece532/index. html

Glenn H. Chapman (S’72–M’80) was born on August 28, 1948. He received the B.Sc. degree in engineering physics and the M.Sc. degree from Queen’s University, Kingston, ON, Canada, in 1972 and 1975, respectively, and the Ph.D. degree from McMaster University, Hamilton, ON, Canada, in 1982. From 1980 to 1990, he was a Research Staff Member with the Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, where he worked on developing laser redundancy techniques for the Wafer Scale Integration project. Since 1990, he has been a Professor with the School of Engineering Science, Simon Fraser University, Burnaby, BC, Canada, specializing in the areas of large-area laser restructurable silicon systems, microfabrication technology, and micromachined sensors involving lasers. He is the author of 27 journal papers, 68 conference papers, two book chapters, and 20 patents. Prof. Chapman is a Senior Fellow of the British Columbia Advanced System Institute.

266

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

Maria Trinh was born on November 5th, 1978. She received the B.A.Sc. degree in systems engineering from Simon Fraser University, Burnaby, BC, Canada. She currently has three conference publications (two for SPIE Photonics West 2001 and 2002, and one for the 2002 IEEE Canadian Conference on Computer and Electrical Engineering) and a pending journal publication for the SPIE Journal of Microlithography, Microfabrication, and Microsystems.

Nick Pfeiffer was born on July 8, 1963. He received the B.A.Sc. degree in mechanical engineering from the University of British Columbia, Vancouver, BC, Canada, in 1988, the M.A.Sc. degree in engineering science, in 2001, from Simon Fraser University, Burnaby, BC, Canada, where he is currently pursuing the Ph.D. degree in the areas of optical tomography and angular domain imaging. He has served as senior management in several technology-based companies and is currently President 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 engineering physics from Simon Fraser University, Burnaby, BC, Canada, in 2001, and is currently pursuing the M.A.Sc. degree in biomedical engineering at the University of Toronto, Toronto, ON, Canada, where he is conducting research on intercellular communication systems for genetic circuits. He has two conference publications.

Desmond Lee is working toward the B.A.Sc. degree in systems engineering at Simon Fraser University, Burnaby, BC, Canada.