Commissioning of a solid tank design for fan-beam optical CT based 3D radiation dosimetry

Objective. Optical computed tomography (CT) is one of the leading modalities for imaging gel dosimeters used in the verification of complex radiotherapy treatments. In previous work, a novel fan-beam optical CT scanner design was proposed that could significantly reduce the volume of the refractive index baths that are commonly found in optical CT systems. Here, the proposed scanner has been manufactured and commissioned. Approach. Image reconstruction is performed through algebraic reconstruction technique and iterated using the fast iterative shrinkage-thresholding algorithm (FISTA) algorithm. Ray tracing for algebraic reconstruction was performed using an in-house developed ray tracing simulator. A set of Sylgard® 184 phantoms were created to commission spatial resolution, geometric deformity, contrast-to-noise ratio (CNR), and scan settings. Main Results. The scanner is capable of a 0.929 mm−1 spatial resolution, observed at 200 iterations, although the spatial resolution is highly dependent on the number of iterations. The geometric distortion, measured by scanning a needle phantom with the prototype scanner as well as a conventional x-ray CT was found to be within <0.25 mm. The CNR was found to peak between 65 and 190 occurring between 50 and 100 iterations and was highly dependent on the region chosen for background noise calculation. The proposed scanner is capable of scanning and reading out slices in less than 1 min per slice. Significance. This work displays the viability of a fan-beam optical CT scanner with minimal index matching using ray-traced algebraic reconstruction.


Introduction
Radiation therapy (RT) is a non-surgical approach to treating cancerous tumors. The damage from high-energy particles does not discriminate between cancerous and healthy tissue, meaning tumor-targeted delivery of radiation is required to effectively treat cancer as well as spare healthy tissue. As the precision of treatment increases, so does the demand for effective dosimetric tools to verify the accuracy of tumor-targeted treatments. Three-dimensional dosimeters offer an accurate and robust way to verify complex dose distributions within a volume.
Three-dimensional dosimeters are often a composition of radio-sensitive chemicals that have been set in some material matrix such as gelatin, or plastic. The radio-sensitive chemicals react in a known and measurable way to the absorbed dose. It has been shown that three-dimensional dosimeters have the potential to be an exceptional tool for three-dimensional dose verification (Jackson et al 2015). One of the pervasive concerns for three-dimensional dosimeters is how to quickly and accurately read out the absorbed dose information from the dosimeter can be performed.
The three main read out methods are magnetic resonance imaging, x-ray computed tomography (CT), and optical CT (Baldock et al 2010). Optical CT became a possible candidate for scanning three-dimensional dosimeters in 1996 when Gore et al showed that optical CT could be used to scan PAG polymer gel dosimeters Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. (Gore et al 1996). Subsequent works have produced a large variety of scanner designs and methods (Doran et al 2001, Oldham et al 2001, Wuu et al 2003, Krstajić and Doran 2006, Sakhalkar and Oldham 2008, Campbell et al 2013, Deene 2019. Typically, optical CT systems utilize a standard filtered back projection (FBP) technique to reconstruct images. While FBP is an ideal reconstruction method for conventional x-ray CT, it can be challenging to use in optical CT due to the introduction of light refraction. The FBP reconstruction assumes a straight ray path from the source to the detector. This assumption necessitates that refractions in the ray path are heavily reduced or removed in optical CT systems. One of the most prevalent techniques to reduce refractive artifacts is an index matching bath (Gore et al 1996, Wolodzko et al 1999, Xu et al 2004, Krstajić and Doran 2007, Campbell et al 2013. Refractive baths can be cumbersome, messy, and undesirable to work with, as they are typically a large volume (1-15 l) of some chemical mixture (water, glycerol, propylene glycol, etc) that has to be maintained and monitored, else mixtures can separate or evaporate over long scanning periods which results in refractive mismatches and image artifacts Yatigammana 2012, Deene 2019).
Previously published works produced an optimized scanner geometry that allowed for a large reduction in the need for index matching (Chisholm et al 2015, Ogilvy et al 2020. In the work of Ogilvy et al, the optimization process simulated thousands of design geometries, tracking ray paths, ray intensity, and overall attenuation. The designs were scored based on metrics that would influence overall image quality, and a 'best' geometry was found. The purpose of this work is to manufacture and commission the 'best' geometry scanner. The prototype CT scanner manufactured in this work is unique in that it features a solid acrylic block with minimal index matching fluid (5 -30 ml), and does not require rays to travel a direct path from source to detector. This scanner uses a modified version of the ray tracing simulator, created during the design phase, to implement the algebraic reconstruction technique and iteratively reconstructs images with the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) algorithm.
In this work, we manufacture and commission the prototype scanner. The focus of the commissioning was the establishment of the scanner's performance characteristics relating to geometric distortion, spatial resolution, contrast-to-noise ratio (CNR), and scan settings. This work shows that a prototype optical CT scanner that reduces refractive index matching baths to <30 ml and incorporates ray-path tracing into its reconstruction is capable of reconstructing high-quality images.

Scanner design
The design rationale and methodology have been discussed in-depth in a previously published paper (Ogilvy et al 2020). The fan-beam is created using an 635 nm diode laser (Edmund Optics., Barrington, NJ, USA). Briefly, the laser is aligned to a 60°line-generating Powell lens using a TECHSPEC® Optical Cage System (Edmund Optics., Barrington, NJ, USA). Before entering the Powell lens, the laser passes through a slit to reduce the thickness of the resulting fan-beam.
The fan-beam then enters a 290 mm long solid acrylic (Poly(methyl methacrylate)) block. The front face of the block is machined into a 61 mm radius semi-circle to shape the beam towards a 104 mm diameter bore hole. A 101.6 mm (4in) diameter dosimeter is placed in the cavity of the bore (figure 1(a)). By use of a radial shaft seal (CR39932, SKF; Toronto, ON, CA), a very small volume of refractive index matching fluid is suspended in the gap between the dosimeter and the block ( figure 1(b)). All of the surfaces that rays transmit on the scanning plane of the block are sanded and polished to reduce scatter from scratches or scuffs.
The detector array forms a continuous 256 mm line, consisting of five 64-element photodiode arrays (S8865 Series, Hamamatsu; Hamamatsu City, Japan). The rear wall of the block was machined such that the detector arrays can be seated directly against the acrylic without a collimator. Each of the 320 photodiode elements have an active area of 0.8 mm by 0.7 mm, with a 0.1 mm spacer between each active area. Dosimeter rotation and vertical motion are performed by a pair of motion-controlling stages (ESP300, Newport; Irvine, CA, USA) which operate from beneath the dosimeter.
The lack of collimators on the detectors introduces a high sensitivity to stray light entering the system. To minimize this, the entire scanner system is contained within a light-tight box. It is expected that considerable noise would be introduced if the scanner were used on scattering dosimeters, therefor analysis is restricted to absorption-based dosimeters.
The dosimeter containers were constructed from a transparent, 4.000' outer diameter by 0.125' wall thickness cast acrylic tube (ePlastics, San Diego, CA, USA). The tube was then cut to a 7 cm height and fitted with a base. The benefit of manufacturing containers from a long continuous tube is that the containers do not have seams often found during plastic manufacturing, which can be a large source of scatter.
The optics of the scanner were designed for use with FlexyDos3D dosimeters (Deene et al 2015). However, FlexyDos3D dosimeters have unfavorable qualities for performing commissioning experiments. The dose response of FlexyDos3D dosimeters exponentially decays with time (<120 h), and over time the background attenuation increases (Deene et al 2015, Høye et al 2015. An ideal commissioning phantom would be reusable and unchanging between uses. The material of choice for commissioning was Sylgard® 184, which makes up 95% of a FlexyDos3D dosimeter by weight and has nearly identical optical properties. Sylgard® 184, commonly referred to as polydimethylsiloxane (PDMS), is made of a 10:1 mixture of a silicone elastomer and curing agent. Any attenuation added to a phantom was done using Silc Pig TM Black (Smooth-On, Macungie, PA, USA), a pigment designed to dye silicone products.

Reconstruction
The gold standard for CT reconstruction was FBP up until the last decade, when there has been a rapid increase in the use of iterative reconstruction techniques for image formation (Willemink and Noël 2018). For the current scanning system, the lack of straight-ray geometry renders filtered back-projection an incompatible method of image reconstruction. During the design phase of the research, it was determined that an algebraic reconstruction technique (ART) could be used to reconstruct without straight-ray geometry as long as ray paths are known. The system matrix used in the iterative reconstructing algorithm is built in-house and based on the ray-tracing simulator created for the scanner design optimization (Ogilvy et al 2020). In 2021, Guenter et al identified several viable algorithms for CT imaging (Guenter et al 2022). Of those, the FISTA has high performance when a stopping condition is unknown, and can be run to higher number of iterations without fear of over-iterating. In this work the FISTA algorithm was chosen to be used throughout the commissioning of the proposed scanner in order to minimize the effects of iteration stopping number on subsequent image analysis.

Ray tracing
To perform reconstruction, an accurate ray tracing system matrix must be generated that characterizes the path a ray will take to arrive at a specific detector. A ray tracing system matrix generator for the optical CT scanner was coded in Matlab (MathWorks Natick, MA, USA). The geometry and optical properties of the scanner are simulated such as material refractive index, material linear attenuation coefficient, block length, bore hole position, laser position, laser polarity, ray intensity, etc. During ray tracing, 400 000 rays are generated over a 60°a rc such that they are evenly distributed at a projected line. Each ray travels through the simulated scanner, and the refraction is calculated using Snell's Law. In the ray tracer, located where the physical detector array would be, are 1280 simulated virtual detectors. Each virtual detector has a width of 0.2 mm, that is, a quarter of the width of the physical detecting elements. Of the 400 000 simulated rays, only the rays closest to the centers of each virtual detector are chosen for input into the system matrix, meaning only 1280 ray paths are used. The system matrix tracks the path length of those 1280 rays, and stores the length traveled through each pixel of the 512 × 512 image.

Geometric distortion
A needle phantom was created to characterize any geometric distortion of the scanner. A set of needles were arranged in a grid pattern and cured into a blank Sylgard® 184 mixture. The scan was performed with water filling the gap between the block and the phantom container. The true position of the needles was determined by scanning the needle phantom with a Lightspeed RT 16 (GE Medical Systems Chicago, Illinois) x-ray CT scanner at 120 kVp, 1.25 mm slice thickness, and a field-of-view of 250 mm at the isocenter. Axial scans were then performed using the prototype scanner to compare the needle position against the x-ray CT. Each needle was segmented into a region of interest (ROI), converted to binary, and the MATLAB centroid function was used to find the cross-sectional midpoint of each needle.

Spatial resolution
Spatial resolution was commissioned by creating a Sylgard® 184 phantom, where a circular column was molded from a precisely machined rod. The mold was then back-filled with a dyed Sylgard® 184 mixture (figure 2). After scanning the phantom and reconstructing the image, the centroid of the high-attenuation insert is found and the distance from the centroid is calculated for each pixel. The edge spread function (ESF) of the region of circular attenuation with well-defined geometry is found by fitting a cubic spline to the edge data, and the derivative of the ESF returns a line spread function (LSF). Applying a fast-Fourier transform to the LSF results in the modulation transfer function (MTF).

Verification of attenuation coefficient linearity
Verification of the scanner's attenuation coefficient linearity was preformed by comparing the scanner's measured attenuation coefficients of a dyed water solution to a spectrophotometer measurement of the same solution. A water solution was used as the reference image for the prototype scanner, and as the background measurement for the spectrophotometer. A concentrated mixture of water and Patent Blue VF dye (Sigma-Aldrich; Oakville, ON) was created and incrementally added to the scanner's dye-water solution each trial. Between trials, an aliquot mixture was saved to be scanned by the spectrophotometer. The transmission percentage was found for each of the optical scanner and the spectrophotometer. The optical density was calculated by taking the negative natural logarithm of the measured transmission. The optical densities were then converted to the linear attenuation coefficient by dividing the optical density value by the distance traversed by the interrogating optical beam.

Results and discussion
3.1. Geometric distortion Commissioning of the geometric distortion was performed using a needle phantom that was scanned using both the prototype scanner as well as a conventional x-ray CT scanner. The cross-sectional midpoint was determined for each needle, and compared between the optical and x-ray scans (figure 3). It was found that needle alignment was <0.25 mm for all of the needles.
The reconstruction was repeated with an intentionally incorrect system matrix. The system matrix used assumed that paraffin oil (n = 1.467) was placed in the bore gap rather than water (n = 1.332). This mismatch worsened the center-of-intensity agreement to <0.4 mm. The mismatch experiment was repeated with an assumed gap material of acrylic matching fluid (n = 1.4887), and the center-of-intensity agreement continued to worsen to <0.5 mm. The average center-of-intensity agreement across all 18 needles was 0.121 mm, 0.208 mm, and 0.230 mm for the water, paraffin oil, and acrylic matching fluid trials respectively. It was found that the needle alignment mismatches occurred most at the periphery of the phantom which was expected as the periphery is reconstructed from rays that undergo more refraction.

Spatial resolution
Commissioning of the spatial resolution was performed using a phantom with a cylindrical region of high intensity ( figure 4(a)). The MTF was measured from the edge of the high-attenuation region ( figure 4(b)). When performing iterative reconstruction, the number of iterations can greatly affect the clarity of an edge (figure 4(c)), as well as the noise in a system (Kak and Slaney 2001). During this experiment, reconstructions were performed with a varied number of iterations (table 1), and as expected a larger number of iterations corresponded to a higher spatial resolution up to 200 iterations. Due to the highly-varied nature of data on either side of the edge, some improvement to the spatial resolution can be found by cropping the data around the edge. The data was cropped using the Korea Aerospace Research Institute (KARI) method as outlined in Viallefont-Robinet et al (2018), and considerable improvements were seen in the spatial resolution (Viallefont-Robinet et al 2018) for the MTF 50 . The KARI method helps to reduce the impact of noise, and ROI non-uniformity to the MTF calculation by calculating where to trim the over-sampled ESF based on the second derivative of the LSF (knee point). The best spatial resolution (MTF 50 ) was found to be 0.929 mm −1 after 200 iterations (figure 4(d)), and 1.412 mm −1 at 200 iterations for MTF 20 . A higher number of iterations did not show improvement in the spatial resolution. For reconstructions with less than 80 iterations, the conditions in the KARI method for cropping would not result in a reasonable edge, so those iteration numbers were disregarded.
As radiotherapy treatments advance, efforts to safely decrease planning target volume (PTV) increase (Kron 2008). Typical PTV margins for precise radiation treatments such as stereotactic radio surgery can be as low as 1 mm (Jhaveri et al 2019), and can range from 3 to 5 mm for treatments such as stereotactic body radiation therapy (SBRT) (Liu et al 2020). A sub-millimeter spatial resolution benchmark is all but required for a modern 3D dosimetry system. The PTV margin is functionally a sum of positioning errors (patient motion, treatment accuracy, etc), and one of the hopes is that 3D dosimetry systems will be used to further reduce the PTV margins of treatments. Thus, sub-millimeter spatial resolution would require a potential scanner to be capable of scanning a dosimeter with more spatial accuracy than currently permitted in the most precise radiation treatments. The MTF values found by the proposed scanner confirm that the scanner performs with submillimeter spatial resolution.

Verification of attenuation coefficient linearity
A dyed solution was chosen for this experiment, because of it's relative simplicity. The downside of using a comparatively large volume to measure the transmission values of the dye solution is that the range of testable linear attenuation values is relatively small compared to, for example, the more complex finger phantom method which itself has associated drawbacks (Oldham et al 2003, Jordan 2013. The transmission measurements found by the scanner were calculated from the collected sinograms to avoid influence from the reconstruction algorithm. The dye phantom was scanned 10 times per trial. The transmission values found for each of the 10 slices were averaged together. The two central detectors (160 and 161) had their transmission values averaged together, and the corresponding optical density was divided by the vessel diameter (10.16 cm) to produce the linear attenuation coefficients. The scanner showed linearity in attenuation coefficients with a slope of 0.906 when compared with a spectrophotometer (figure 5) and is consistently linear from 0 to 0.6 cm −1 , indicating that the scanner can be used for relative dosimetry applications. Figure 3. Needles arranged in a grid pattern were fixed in Sylgard® 184 with water in the bore gap. (a) A cross-sectional slice from the x-ray CT can be seen. The image has been cropped and resized such that the x-ray image can be compared to optical CT. (b) A crosssectional slice from the proposed optical CT scanner. (c) The two images are overlaid, where x-ray CT is the blue channel, optical CT is the red channel, and their overlap appears magenta.

Scanning parameters
The scanner photo-diodes and motor system have a number of programmable settings that can affect the resulting image. The detector array has an adjustable exposure time for the photo-diode elements. During a scan, forward projections are collected continuously at two different alternating exposure times. The two collections are then used to calculate a detector floor offset. A fleet of tests were performed considering the detector exposure times and axial motor speed. It was found that the scanner is capable of collecting slices in less than 45 s without a considerable introduction of electronic noise.
The two exposure times chosen were 4.64 ms, and 6.73 ms. It was found that at least 5 projections collected per degree was ideal for scanning when considering scan time and noise. To insure that 5 projections are collected per degree, the axial motor rotates at 17.6°s −1 , whilst continuously collecting transmitted laser  intensity. A total of 1830 projections are collected at each of the exposure times. After a slice has rotated 360°, the detector memory is read out to the computer while the motors move to the next slice. During the scan-settings tests, it was found that the prevalence of detector noise is most prominent on the detectors that are collecting heavily refracted rays. As more projections are used per slice, and as the detectors are exposed for longer acquisition times, the noise of refracted-ray detectors is not reduced at a proportional amount compared to rays that experience less refraction. It can be seen in figure 6 that the peripheral rays of the fan arc have their noise reduced by a similar amount as the central rays, rather than scaling multiplicatively.

Contrast and noise
The contrast was commissioned using the same phantom that was created to commission spatial resolution. Due to the iterative nature of ART, the noise level in images depends on the number of iterations used during reconstruction. The contrast was compared using the CNR defined by: , 1 sig bkgd bkgd Figure 5. A comparison of the linear attenuation coefficients measured of a dyed water solution by the prototype optical CT scanner and a spectrophotometer. A linear relationship can be seen with a slope of 0.906. Figure 6. A 360°scan was collected on a blank Sylgard® 184 phantom. The projections were binned and averaged into 0.5°steps. The average response of each detector was found, as well as the standard deviation of each detector. Shown is the standard deviation as a percent of the mean for each of the 320 detector elements. It can be seen that the highest standard deviations are found near the periphery of the detector array where ray paths have experienced more extreme refraction. The 5-projection collection took 42 s to collect and the 20-projection collection took 209 s to collect.
where μ is the mean of a defined ROI. The CNR was calculated at ascending numbers of iterations, using multiple ROIs from the background (figure 7(a)). It can be seen that the CNR peaks around 50-100 iterations before falling slightly ( figure 7(b)). The range of maximum CNR was between 65 and 190, and was highly dependant on where the sample region for the background is taken. It can be seen that the noise texture is influenced by the proximity to highly attenuating structures (figure 7(c)), thus affecting the CNR value. Noise characterization can be challenging in iterative reconstruction systems. Specifically, with the FISTA algorithm higher iterations result in a smoothing effect. The smoothing effect can be clearly seen in the corners of the square insert of figure 7(a) where the corners have become rounded. An additional biproduct of the smoothing means that a scan of a blank PDMS phantom would result in a reported noise of zero, which is not accurate.

Detector interpolation: exemplar-based inpainting
In this work, one of the detector arrays contains a series of 3-5 faulty detectors, resulting in collection errors within these elements. The collection error propagates into a large ring artifact during image reconstruction. Ring artifact removal in sinogram space can be a difficult task, as simple linear or geometric interpolation does not sufficiently consider the sinusoidal motion of scanned objects. Because the ring artifact region is well defined, the exemplar-based image inpainted technique (EBIIT) was chosen to fill in the faulty region (figure 8). The technique was designed by Criminisi et al and focuses on saving edge clarity in the target region (Criminisi et al 2003). The data collected by the faulty detectors bisects the circular insert in figure 4(a). While EBIIT prioritizes edge clarity, it is believed that the edge warping of the circular insert on the left and right are the result  of EBIIT limitations. In preliminary reconstructions with linear interpolation, results provided a worse image than EBIIT.

Conclusion
A prototype optical CT scanner was manufactured based on the optimized and simulated design of a previous work (Ogilvy et al 2020). The design focuses on a large reduction in the need for refractive index matching by physical design, and iterative reconstruction that accounts for refraction in the ray path. Each iteration of the FISTA algorithm takes about 0.9 s to complete, meaning a 200 iteration reconstruction is performed in around 3 min. The prototype scanner was commissioned and found to have a maximum spatial resolution of MTF 50 = 0.929 mm −1 which peaked around 200 iterations. The scanner has a linear response to attenuation. The geometric distortion was measured by comparing needle alignment between the prototype scanner and an x-ray CT machine. Center-of-intensity needle alignment was <0.25 mm for all 18 needles. It was found that the scanner can collect as quickly as 45 s per slice, but can be run slower to reduce electronic noise. Regardless of settings, electronic noise was found most prevalent on detectors that receive heavily refracted rays. The contrast of the system peaks around 50-100 iterations, and the CNR peak has a wide range (65-190) which depends heavily on the sampling region for the background attenuation.
The future of this work may be to categorize a set of reconstruction algorithms that perform best in specific scenarios and focus on either spatial resolution, contrast, or noise. It is believed that the FISTA algorithm will not be the optimal algorithm for all cases, and further investigation into reconstruction algorithms is required. Another potential future to this work could be introducing more complicated design geometries that further reduce the scanner size, and allow for optical collection via CCD.

Data availability statement
The data that support the findings of this study are openly available at the following URL: https://osf.io/dwvsn/ ?view_only=b1fa330f52a6406797d1b36653991703. Data will be available from 13 February 2023.