1. Introduction

1.1 Optical projection tomography

In Optical Projection Tomography (OPT), a series of optical projections collected at several angles can be reconstructed to generate a two dimensional optical tomographic image of a sample [1]. In OPT sample composition and thickness is typically limited by scattering [2]. Several attempts have been made to overcome the effect of scattering including methods that utilize frequency domain [3], time gating [4–6], and angular domain [7] approaches. Despite the apparent difficulty in overcoming the effects of optical scatter, OPT remains a promising imaging modality as it can image endogenous tissue contrast as well as exogenous contrast agents in a non-destructive manner.

1.2 Trans-illumination projection imaging

In optical trans-illumination projection imaging, ballistic photons generate high image contrast, but at tissue thicknesses of 1-2 mm, very few ballistic photons survive [8]. Quasi-ballistic photons experience several scattering events as they traverse a sample, but they retain their forward trajectory. These photons are less informative than ballistic photons, but they can be utilized to generate a projection image of embedded targets. For thick samples (5-10 mean free paths), the population of quasi-ballistic photons is significantly greater than the population of ballistic photons. Consequently, a projection image acquired with quasi-ballistic photons can result in good image contrast and can be collected significantly faster than an image collected with ballistic photons. However, for turbid samples the majority of photons have undergone many scattering events, which significantly alters their trajectory from the initial forward direction. These scattered photons contain minimal information regarding the imaging target resulting in decreased image contrast.

1.3 Angular domain imaging

Trans-illumination imaging of turbid samples is highly dependent on the proportions of ballistic, quasi-ballistic, and scattered photons exiting the sample. Since ballistic and quasi-ballistic photons have undergone few scattering events, they lie near the axis of illumination. However, scattered photons have a near-isotropic angular distribution, and can be found exiting the sample at large angles with respect to the axis of illumination. This trajectory-based difference between photons of different scattering experience is the basis of angular domain imaging (ADI). One method for ADI involves the use of an Angular Filter Array (AFA, Fig. 1 ), an array of micro-channels (typically 80 μm x 80 μm x 2 cm) micro-machined from a silicon wafer [9,10]. Scattered photons are most likely to enter the AFA at high angles and are therefore attenuated by the walls of the micro-channels. Ballistic and quasi-ballistic photons pass through the AFA largely unattenuated. Monte Carlo simulation results have shown that photons near the axis of illumination have travelled the shortest paths [9]. The angular selectivity of the AFA is controlled by the aspect ratio of the micro-channels and properties of the micro-channel walls [11].

 

Fig. 1 a) Diagram of AFA: 80 μm x 80 μm x 2 cm (channel count and dimensions not to scale) b) SEM image (micro-channel opening view) of a Reflection-trapped AFA used to minimize internal reflections (top plate removed)

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The angular selectivity of the micro-channels can be approximated by the aspect ratio of the channel using the assumption that the channel walls act as perfect attenuators. In this limit, the angular selectivity for an 80 μm x 80 μm x 2 cm channel would range from < 0.22° for a photon trajectory limited to a plane parallel to a channel wall, to < 0.32° for a photon travelling between opposite corners within a channel. However, this approximation is inaccurate as a significant proportion of photons exiting the channel may undergo reflection events (up to three) [12]. To overcome internal reflections, a reflection-trapped AFA was designed with ridges on the channel walls (Fig. 1b) [12]. In the tested design, the ridge pattern was periodic along the channel length with an amplitude of 2.5 µm. The presence of the ridge pattern resulted in better performance through suppression of wall reflections and constrained the acceptance angle of each micro-channel to the range computed based on the geometry. Further improvement in reflection suppression can be obtained by the application of a sputtered layer of carbon on the channel walls.

The ADI method is advantageous compared to other trans-illumination imaging methods as it does not require complex instrumentation such as a pulsed laser or fast detector that have traditionally been used to reject scattered light. Furthermore, ADI can be used with continuous wave sources (e.g. diode laser), which avoid the low duty cycles associated with time and frequency domain measurements and the concomitant lower sensitivity and increased complexity [13]. Even with the use of simple instrumentation, ADI has been shown to resolve sub-millimeter targets in a scattering media of up to 6 reduced mean free paths [7].

1.4 Contrast and resolution

Previous analysis of an ADI system indicated that both object contrast and system resolution remained relatively constant over the central area of a cuvette that contained a turbid medium [7]. For example, for a 5 cm cuvette filled with 0.12% Intralipid, image contrast varied 15% when an absorptive target was positioned at a depth between 1 and 5 cm from the AFA. The system was also able to resolve a 150 μm target at every depth in a 5 cm cuvette filled with 0.1% Intralipid. However, the edges of the target were less defined when it was placed farther from the AFA. Until now, a constant system response (contrast and resolution) has been assumed for objects within the field of view of ADI systems. This assumption permitted us to use a standard reconstruction algorithm (filtered back-projection) in early work with angular domain optical projection tomography (ADOPT) [7]. In our previous work, absorbing targets were placed in the middle of a cuvette filled with a scattering Intralipid dilution. Image projections were collected at 200 angles spaced 1.8° apart and the image was reconstructed with a filtered back-projection algorithm. However, due to an uneven system response, we purposely limited the reconstruction of objects to the central area of the imaging plane.

1.5 Objective and approach

The objective of the work described here was to first evaluate the system response of ADOPT (object contrast and resolution) at a multitude of positions within the object plane (1 cm x 1 cm). The approach was to image three different sized attenuators translated across a grid of positions within the object plane. The resulting angular domain line profiles were analyzed to generate contrast and resolution maps of the system. In addition, resolution was measured by evaluating the line spread functions generated from a knife-edge. The second objective of the current work was to incorporate the system response information into an iterative image reconstruction algorithm and compare to conventional filtered back projection. An iterative algorithm was expected to minimize image artifacts arising from limited projection data and shadows resultant from the micro-channel walls when compared to filtered back projection image reconstruction. The iterative algorithm also provided a means to incorporate the position-dependant system response into the image reconstruction algorithm, which enabled enlargement of the usable field of view to include the entire imaging cuvette while improving contrast uniformity in the reconstructed images.

2. Experimental setup & methods

2.1 Illumination and detection

Figure 2 shows a schematic of the ADOPT setup. The illumination source was a CW laser diode (L808P1WJ, Thorlabs Inc.) emitting at 808 nm. The vertical divergence was corrected with an aspheric lens. The aspheric lens also focused the beam in the horizontal direction. A 1-mm pinhole was placed at the focal point to restrict the vertical height of the beam, and to improve the beam collimation. The beam was then expanded and collimated with two cylindrical lenses (f = −6 mm & f = 100 mm). The reflection-trapped AFA consisted of a series of 200 parallel micro-channels each 80 μm x 80 μm x 2 cm (Fig. 1b) [11]. The AFA was placed on a 6 degree of freedom jig to align the AFA with the collimated line of light. Detection was performed with a 16-bit linear CCD (TCE-1304-U, Mightex).

 

Fig. 2 Experimental setup, side view

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2.2 Imaging target

Three cylindrical absorbing targets were used to approximate point attenuators: a 0.7 mm diameter graphite rod; a 0.5 mm diameter graphite rod and a 0.2 mm diameter wire painted black. The targets were submerged in a 1 x 5 x 5 cm glass cuvette (1 cm path length) filled with 0.6% Intralipid solution, diluted from a 20% Intralipid stock solution. Intralipid is a fat emulsion that is used clinically and can also serve as a convenient and uniform scattering medium for optical imaging experiments [14,15]. The cuvette was placed 2 mm away from the AFA. The attenuation targets were translated across a grid of points within the imaging plane by a SCARA robot (E2C351, Epson). The 0.7 mm & 0.5 mm graphite rods were translated in 0.2 mm steps for a 46 x 46 scan. The 0.2 mm black wire was translated in 0.2 mm steps for a 48 x 48 scan. A blackened razorblade submerged in 0.6% Intralipid was used to measure the system resolution at 0.2 mm steps for a 43 x 43 scan. Extensive analysis was conducted with 0.6% Intralipid at 1 cm as it was previously determined to be the detection limit of the system (~6 reduced mean free paths) [7]. To illustrate the system performance at lower scattering levels, the 0.2 mm attenuating target was scanned at three different scattering levels, 0.5%, 0.55%, and 0.6% Intralipid all at 1 cm path length.

Three targets were used to obtain tomographic images and evaluate the performance of the reconstruction algorithm. One target consisted of a series of cylindrical rods with diameters 0.2, 0.5, 0.7 and 0.9 mm, submerged in a 0.6% Intralipid solution. This target was intended to evaluate the ability of the system to image objects of different size. A second target consisted of two Allen keys, 1.2 and 2 mm wide, submerged in a 0.6% Intralipid solution. The Allen key target was used to evaluate the performance of edge reconstructions in the system. The Intralipid targets were contained within the 1 x 5 x 5 cm glass cuvette, which was placed 2 mm from the AFA. The third target consisted of a grape suspended in air. The grape was ~2 cm in diameter, and extended beyond the field of view of the AFA. The grape was positioned so that it was 2 mm away from the AFA at its closest point. The seeds of the grape served as absorption targets. The grape target was used to simulate a typical biological sample, where the scattering and attenuation properties were unknown and non-uniform. All of the imaging targets were positioned and rotated with the SCARA robot.

2.3 Contrast and resolution analysis

The acquired signals of the rod targets and the blank images were first pre-processed with a morphological closing operation and a smoothing function to remove the shadows casted from the walls of the micro-channels. The shadows appeared as high frequency variations in contrast (Fig. 3a -blue). The smoothed signals of the rod targets were then normalized to the blank image (by division) with scattering media and no target to compute the transmittance. The negative of the common logarithm of the transmittance was then taken and resulted in absorbance (optical density).

 

Fig. 3 Graphite rod (0.5 mm in diameter) positioned near the center of the field of view, 7 mm from the AFA side of the cuvette. a) Raw subtracted signal (blue). Smoothed signal (red). Target position determined by algorithm (green). b) Gradient of smoothed signal.

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To evaluate image contrast and resolution at each position, the positions of the edges of the target were determined. A signal gradient was computed by using a moving cubic polynomial fit algorithm on the smoothed data. The moving polynomial fit method was found to be less sensitive to noise variations compared to our previous use of a numerical gradient algorithm [16]. The maximum and minimum of the gradient signal (Fig. 3b-pink) near the expected position of the target were used to identify the location of the target (Fig. 3a-green). Resolution was evaluated as the estimated width of the object which was determined by first measuring the pixel distance between the object edges in the image. As the pixels in the camera were 8 µm wide, the pixel distance was easily converted into a distance measurement. The positions of the object edges were also used to generate a pair of masks signifying the object and the background. Pixels lying within the two edges were included in the object mask while a comparably sized background mask was generated from pixels neighboring the object mask. The contrast was quantified by measuring the differences in optical density between the object and the background (Eq. (1).

The minimum resolution of the system was also evaluated at every point in the imaging plane using a blackened knife edge. The knife edge generated an edge response function. The derivative of the edge response function was evaluated with a moving cubic polynomial fit algorithm, to generate the line spread function [17]. The width of the line spread function (FWHM) was evaluated similarly to the width measurements of the point attenuators described above to yield system resolution measurements.

2.4 Tomographic image reconstruction

Projections were collected by rotating the imaging target with the SCARA robot between line scan acquisitions. For each target, 60 projections were collected at 6° intervals to cover 360°. The projections were preprocessed with a morphological closing operation and a smoothing function. Each projection was normalized (by division) to the dynamic range of the camera (2¹⁶) and the negative of the common logarithm of the signal was computed to obtain the attenuation. The attenuation-based sinograms were then used to reconstruct images with a filtered (Ram-Lak) back projection algorithm and an iterative algorithm.

The iterative algorithm employed a system-dependent forward model to generate sinograms of the reconstruction images. Using data from the calibration experiment where a 500 μm attenuating rod was translated in 200 μm steps at 46 x 46 locations, the line scans were decomposed into two signals, a quasi-ballistic signal and a background scatter signal. The quasi-ballistic signal was isolated with a similar edge detection method as the contrast and resolution experiment. However, as the previous edge detection method approximated the FWHM, the boundaries were extended slightly to include most of the quasi-ballistic signal. The magnitude of the quasi-ballistic signal was measured at each position to generate a weighting map (Q_j). As contrast was dependent on depth and independent of lateral position, the weighting map was averaged at each depth to generate a one dimensional depth dependent weighting matrix. The quasi-ballistic signal was then subtracted from the signal profiles to leave the background scatter signal, which was used to generate a two dimensional weighting matrix (S_ij).

In the forward model, each projection of the estimated sinogram (P_k,s, Eq. (2) at angle θ_k represented by the projection index k and camera pixel index s, was calculated as the linear superposition of the product of the estimated attenuation intensity (I(θ, i, j) Eq. (2) and the system response (Quasi-ballistic: Q_j, Scatter: S_i,j,s Eq. (2) acquired from individual attenuation targets located within the imaging volume (Eq. (2). The indices i, j, s represented the lookup position within the system response matrices. Although the system matrices were 46 x 46 elements, they were interpolated to achieve a finer grid spacing. For example, i and j ranged from 1 to 625 for a 625 x 625 pixel image. The quasi-ballistic signal was computed by integrating the product of the attenuation signals and the measured quasi-ballistic weighting function, along one ray directly in front of the camera pixel identified by s. To calculate the attenuation due to the background scattered signal, the attenuation at each pixel was multiplied by the background scatter weighting matrix. Since the targets were rotated within the cuvette, the system response was not expected to depend on sample rotation. We therefore used a rotational mapping to look up the image intensity (I(θ, i, j)). Bilinear filtering was used to improve the estimates.

A traditional ray-based attenuation approximation was used for the back-projection model. The differences between the measured sinogram and the estimated sinogram at a given projection angle and camera pixel (P'_k,s, Eq. (3) were back projected evenly along a line perpendicular to the detector onto the image estimate. After each projection, the resultant image estimate was rotated and remapped using bilinear filtering. The back projections for a given camera pixel were weighted to the number of pixels n(s) along the line of back projection.

Images were reconstructed with the following steps. (i) A master image estimate was initialized to zero attenuation at all locations. (ii) The master image estimate was forward projected to generate an estimated sinogram by Eq. (2). (iii) The difference between the estimated sinogram and the measured sinogram was computed, P'(θ,s). (iv) The difference sinogram was back projected to generate a new difference image estimate, which was added to the master image estimate. (v) Steps ii-iv were repeated until the maximal normalized pixel change in successive sinogram estimates was less than 0.02%.

3. Results and discussion

3.1 Contrast and resolution analysis

Figure 4a displays image contrast as a function of position for the 0.5 mm target. Contrast varied significantly with object depth, and minimally with lateral position. Contrast was averaged across all lateral positions at a given depth. The average contrast in OD at a given depth ranged from 0.01 to 0.29 for the 0.2 mm target, 0.02-0.68 for the 0.5 mm target, and 0.01-0.76 for the 0.7 mm target. Contrast was highest when the object was nearest the AFA, and degraded as the object neared the illumination side of the cuvette.

 

Fig. 4 (a) Position dependent contrast for 0.5 mm graphite rod in OD for a field of view 1 cm x 1 cm. (b) Depth dependent contrast for three different cylindrical targets: 0.7 mm-green, 0.5 mm-red, 0.2 mm-blue in a dilution of 0.6% Intralipid (c) Depth dependent contrast for 0.2 mm target at three different Intralipid dilution levels: 0.6%-blue, 0.55%-red, 0.5%-green. Depth was the distance measured from the AFA side of the cuvette.

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Figure 4b displays the mean contrast values as a function of imaging depth for three different sized targets. There was minimal difference between the 0.7 mm target and the 0.5 mm target. The 0.2 mm target had poorer contrast at every depth when compared to the 0.7 mm and the 0.5 mm target.

Figure 4c displays the mean contrast values as a function of imaging depth for a 0.2 mm rod submerged in three different concentrations of Intralipid (Fig. 4c blue-0.6%, red-0.55%, green-0.5%). There was minimal contrast difference between the 0.6% and 0.55% Intralipid targets. Contrast was highest for the 0.5% Intralipid target. This was expected as a larger proportion of quasi-ballistic photons will pass through a medium with lower scattering, resulting in a greater attenuation due to the target.

Figure 5a displays the measured width of the 0.5 mm target as a function of position. Overall the measured width varied minimally with target depth and lateral position. The measured width was 0.72 ± 0.09 mm for the 0.7 mm target, 0.59 ± 0.08 mm for the 0.5 mm target and 0.31 ± 0.11 mm for the 0.2 mm target. However, large localized variations in measured width were observed in the map in the lateral direction. Figure 5b displays the measured width of the 0.5 mm target at different lateral positions within a plane midway between the front and back surfaces of the cuvette. The large fluctuations at lateral positions nearby 2 mm and 7.5 mm present in both map and line graph were due to two defective channels. These localized variations could be eliminated with a defect-free AFA. As the attenuation target neared one of the defective channels, the edge detection algorithm misinterpreted the large gradient signal from the defective channel as the gradient signal from the edge of the target. This effect may result in either an overestimation or an underestimation of the target width, depending on the relative position of the target and the defective channel. This effect was more observable as the target was placed closer to the laser. This was expected as the contrast of the system is lowest near the laser.

 

Fig. 5 (a) Position dependent measured width for a 0.5 mm graphite rod (μm) for a field of view of 1 cm x 1 cm. (b) Measured width at different lateral positions for a depth at the center of the cuvette. (c) Resolution map computed from knife edge profiles for a field of view of 1 cm x 1 cm. (d) Line spread function for a knife (razor blade) positioned parallel to the lateral direction with the edge positioned at the center of the cuvette.

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Figure 5c displays a resolution map of the system, computed from the knife edge experiment. Figure 5d displays a line spread profile for an edge placed in the center of the imaging plane. Based on this measurement, the mean resolution of the system was 0.23 ± 0.03 mm. Similar to the width measurements most of the variations in the system resolution were due to the presence of defective channels. This estimate of the system resolution differed from previous experimental data, where a 150 µm target submerged in 0.6% Intralipid was resolved for a 1 cm path at 808 nm [18]. A small difference in measured resolution was expected as the resolution due to the differences in the measurement methods.

3.2 Target reconstructions

Figure 6 displays the cross sections of the imaging targets used to generate Figs. 7 and 8 . For Fig. 6, 720 projections were collected with the targets submerged in water (no scattering). The images were then reconstructed with a filtered back-projection method.

 

Fig. 6 Reconstructed images of absorbing targets a) 1.2 mm & 2 mm Allen key, b) 0.2 mm, 0.5 mm, 0.7 mm, 0.9 mm cylindrical rods in water and reconstructed with 720 projections using filtered back-projection. The reconstructed field of view was 1 cm x 1 cm.

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Fig. 7 Reconstruction of a 1.2 and 2 mm hex key with (a-c) iterative (d-f) filtered back-projection reconstruction. Images reconstructed from (a, d) 60 projections, (b, e) 30 projections, (c, f) 15 projections. The reconstruction field of view was 1 cm x 1 cm.

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Fig. 8 Reconstruction of 4 rods, 0.2 mm, 0.5 mm, 0.7 mm, 0.9 mm (a-c) iterative (d-f) filtered back-projection reconstruction. Images reconstructed from (a, d) 60 projections, (b, e) 30 projections, (c, f) 15 projections. The reconstruction field of view was 1 cm x 1 cm.

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Figure 7 displays several reconstructions of two Allen keys (2 mm and 1.2 mm width) with an iterative algorithm (Fig. 7 a-c) and the filtered back-projection algorithm (Fig. 7 d-f) with three different sets of projection data: (Fig. 7 a, d) 60 projections, (Fig. 7 b, e) 30 projections, and (Fig. 7 c, f) 15 projections. The filtered back-projection reconstructed circular objects for all projection data sets. Numerous image artifacts were apparent, these included streaking and ring artifacts. For example, a ring of image contrast was apparent near the center of the image in Fig. 7d, with a diameter of approximately ⅓ of the field of view. This image artifact was due to a defective channel. Alternatively, the iterative reconstruction method resulted in images with significantly lower appearance of image artifacts, and significantly better contrast for the attenuators. Furthermore, the ring artifact described for Fig. 7d was significantly suppressed.

Figure 8 displays several reconstructions of four rods (0.2 mm, 0.5 mm, 0.7 mm, 0.9 mm) with the iterative algorithm (Fig. 8 a-c) and the filtered back-projection algorithm (Fig. 8 d-f) with three different sets of projection data: (Fig. 8 a, d) 60 projections, (Fig. 8 b, e) 30 projections, (Fig. 8 c, f) 15 projections.

For both sets of absorbing targets, the filtered back-projection algorithm yielded poor image quality as the number of projections was too few to suppress image artifacts. The background had concentric ring artifacts due to uneven detector responses. In addition, the signal within a given target was heterogeneous. In contrast, the iterative reconstruction method (Fig. 7 a-c & 8 a-c) provided a smoother background, and eliminated most ring and streaking artifacts.

Figure 8 displays the case where an object (0.2 mm target) lies on the same radial position as a defective channel location. With 60 projections, the object was easily resolved with the filtered back-projection reconstruction method, but a bright ring was observed due to the presence of a defective channel in the AFA coincident with the radial position of the 0.2 mm target. For 15 and 30 projections, the 0.2 mm target was observed but it was also accompanied by ghosting along the ring consistent with the increment in rotation angle. The iterative method resulted in a suppression of the ring and ghosting artifacts caused by the defective channel and low projection count, respectively, but also suppressed the contrast of the 0.2 mm object. This result highlighted a potential tradeoff between suppression of image artifacts at the expense of image resolution for the iterative image reconstruction technique.

For the iterative image reconstruction, the fidelity of the shape of each reconstructed object decreased as the number of projections decreased. The absorbing objects were circular or slightly elliptical in cross section in the reconstructed images for 30 and 60 projections, but became highly elliptical or lobular for image reconstructions with 15 projections. Other differences in image quality were observed for the iterative reconstructions with 15, 30 and 60 projections (Fig. 8 a-c). For example, there was a subtle banding effect in the background signal along a radial trajectory upon which the objects were positioned. However, even in the presence of these artifacts, it is important to emphasize that with only 15 projections, the iterative reconstruction resulted in a qualitatively accurate reconstruction of the three largest attenuators (Fig. 8 c).

One assumption of the iterative algorithm was that the projections could be modeled as a linear superposition of point attenuators in the reconstruction estimates. In a scattering medium, image contrast was found to vary with object size [15]. As a result, a reconstruction algorithm based on object edges with a system matrix generated from knife edge projections may be more successful at reconstructing images with various sizes.

Figure 9a displays the measured sinogram (60 projections) of the 4 cylindrical rod target (0.2, 0.5, 0.7, 0.9 mm). The reconstruction estimate of the sinogram is displayed in Fig. 9b. Both sinograms display the variation of object contrast with projection angle. Contrast appeared higher when the object was closer to the AFA. The normalized average of the pixel by pixel absolute differences between the two sinograms was 13%. The vertical banding in the measured sinogram can be attributed to the variations in micro-channel efficiency across the AFA.

 

Fig. 9 a) Measured sinogram of a 4 cylindrical rods (0.2, 0.5, 0.7, 0.9 mm) with 60 projections. b) Reconstruction estimate of the measured sinogram

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Figure 10 displays a reconstruction of a central subregion of a transverse plane through a 2 cm diameter grape. The filtered back-projection (Fig. 10a) was able to reconstruct three of the four seeds; however, image contrast at the seeds was lower and there were many image artifacts compared to the result from the iterative reconstruction (Fig. 10b). Figure 10c shows a photograph of the seeds and surrounding medium after cutting the through the center of the grape. The grape target was less scattering than the attenuating rod and hex key submerged in Intralipid solution. This may explain the better performance of the filtered back projection method on the grape target compared to the Intralipid-based experiment.

 

Fig. 10 Reconstruction of a 2 cm diameter grape with 60 projections, a) filtered back-projection b) iterative reconstruction. c) Photograph of slice through grape. FOV = 1 cm x 1 cm

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The iterative algorithm was not optimized for the grape reconstruction as the imaging volume was >7 mm away from the edge of the AFA. In addition, the system matrix was experimentally measured with higher background scattering. Despite these issues, the iterative reconstruction algorithm appeared qualitatively superior to the filtered back-projection images of the grape when compared to the photograph (Fig. 10c). The performance of the algorithm at a different scattering level suggested that the iterative algorithm was robust against inaccuracies in the system matrix and may be suited to objects with heterogeneous scattering properties. This suggested that iterative ADOPT may provide a means to image complex structures such as biological specimens with higher accuracy than filtered back-projection.

4. Conclusions and future work

Image contrast and resolution for ADOPT were measured for an attenuating target positioned at a multitude of positions within the object plane. Contrast was found to vary significantly with depth, but minimally with lateral position. Contrast was greatest when the target was nearest to the AFA, and it decreased as the target neared the illuminated side of the cuvette. This effect was more apparent for larger objects. Resolution was found to vary significantly with lateral position and minimally with depth. At a given imaging depth, the estimated target width was found to vary periodically in the lateral direction, likely on account of the micro-channel walls.

The calibration scan generated a system matrix containing the system response to a point attenuator at every position within the object plane. This information was successfully incorporated into the forward model of an iterative image reconstruction algorithm. The cross section of a series of cylindrical rods (0.2, 0.5, 0.7, 0.9 mm) and a pair of hex keys (1.2, 2 mm) was reconstructed with the iterative algorithm and a filtered back-projection for comparison. The back projection method yielded an image with ring and streaking artifacts. The iterative algorithm reduced the ring artifacts considerably, and was more robust against the lack of projection data. The iterative algorithm was able to reconstruct images with 60 and 30 projections. With 15 projections, the attenuation targets were detected, but the reconstructed objects did not resemble the individual targets well. The filtered back-projection method was successful at reconstructing grape seeds within an intact 2 cm diameter grape, but the iteratively reconstructed image had greater contrast and noticeably reduced image artifacts. The iterative algorithm outperformed the filtered back-projection despite being optimized for a higher scattering level. The results suggested that iterative ADOPT is a useful non-destructive method for obtaining depth-resolved transverse images of weakly scattering biological samples up to 2 cm in diameter with potential for tomographic imaging of highly scattering tissue samples up to many millimeters (6 mm) in thickness.