Optical artefact characterization and correction in volumetric scintillation dosimetry

Interactions of scintillation light within the scintillator tank change the light distribution that is measured by the camera and therefore constitute the first source of error to be dealt with by any correction algorithm. Scintillation light undergoes scattering as it travels through the scintillator. In addition, it can be reflected at the tank wall, and its path can be altered by refraction through the window–air interface. Each of these interactions changes the light distribution that is measured by the camera.

Although scintillators are designed to be transparent to their own light emissions, scintillation photons experience Rayleigh scattering and additional scattering due to absorption and re-emission as they pass through the scintillator. The result of this scattering is a blurring of the measured light distribution that is independent of the camera's focus settings. This blurring may be particularly problematic when measuring steep dose gradients and highly heterogeneous radiation fields such as proton Bragg peaks, where blurring leads to a broadening of the Bragg peak and a decrease in its height.

Previous work in volumetric scintillation dosimetry has shown that blurring due to photon scatter can be corrected by deconvolving a point spread function (PSF) from the images (Kirov et al 2005, Ponisch et al 2009). These studies obtained the PSF by assuming a functional form of the PSF and then fitting the parameters of the function based on a comparison between the measured and expected scintillation light projections. While this approach provided reasonable results, the PSF was not derived from any measurement or calculation.

Refraction changes the path of light as it travels from one medium to another. Refraction at the interface between the LS solution and the tank window is minimal because the materials' indexes of refraction are similar. However, refraction at the window–air interface is significant, leading to a shift in the expected positions of individual pixels and an increase in the apparent size of objects or light sources within the tank.

Another challenge associated with measuring light from a large volume with a lens-camera system is perspective, the decrease in an object's apparent size with its increasing distance from the lens. Telecentric lenses can be used to acquire images without perspective, but these lenses can only acquire light from an area as large as the diameter of the primary lens. In the case of a large detector such as the one in this study, the weight and cost of a telecentric lens large enough to measure the entire detector would be substantial. If non-telecentric optics are used for quantitative measurements, the size of objects must be scaled by their distance from the lens.

The scintillation light from the detector is collected and transmitted to the CCD chip by a compound optical lens, which introduces additional artefacts, including vignetting, lens distortion, and blurring due to the PSF of the lens.

Vignetting is the decrease in a camera's measurement efficiency with distance from the image centre, and is typically classified as mechanical, optical, or natural. Mechanical and optical vignetting are caused by the physical obstruction of light in the optical train and can be prevented by appropriate selection of the lens settings. Natural vignetting is caused by the divergence of light as it travels from the lens to the image sensor. The degree of natural vignetting varies with the lens and camera design, but it is present in most cameras and must be corrected for accurate quantitative light measurement over the entire image.

Lens distortion is the nonlinear mapping of radial distance in image space that results from imperfect lens design. It is typically either 'barrel distortion,' in which the image is magnified at the centre relative to the edges, or 'pincushion distortion,' in which the image is magnified at the edges relative to the centre. Modern scientific lenses are designed to minimize lens distortion, but no lens is perfect.

In addition to the blurring caused by light scattering in the scintillating medium, the lens itself also introduces blurring to the optical system. As a result, the blurring in the scintillator detector is a combination of two PSFs, one from scattering in the scintillator and one from the lens.

The CCD chip is the final source of error in the image acquisition chain. CCD chips are subject to various sources of noise, including photon noise, dark noise, and readout noise. An additional source of noise is stray radiation, including gamma rays and secondary neutrons, protons, and nuclear fragments. The CCD can be exposed to these stray particles, which may deposit their energy within individual pixels, leading to transient spikes or streaks in the images.

The detection system used in this study consists of a cubic tank containing a volume of LS solution, with a CCD camera for measuring the light distribution in the tank (figure 2). The LS solution serves as the detection medium and also as the attenuating phantom. The LS solution used in this study is BC-531 (Saint-Gobain Crystals, Hiram, OH), which consists of scintillating molecules in a mixed solvent of linear alkyl benzene and 1,2,4-trimethylbenzene. The density of the scintillator is 0.87 g cm⁻³, and its refractive index is 1.47. Its light emission peak is centred at 425 nm, its light output is 59% of the output of anthracene, and the decay time of the principal scintillation light emission is 3.5 ns. A scintillator-to-water proton range scaling factor of 0.902 was calculated for BC-531 using the Monte Carlo package MCNPX version 2.7.0 (Walters et al 2002).

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The tank walls are made of opaque polyvinyl chloride (PVC), except for one wall, which is made of clear polymethyl methacrylate (PMMA). This PMMA wall serves as a window through which the camera views the light emission from the scintillator. The tank and camera are connected by a light-tight housing, also constructed of PVC, which isolates the detector optics from ambient light. The tank dimensions are 20 × 20 × 20 cm³, and the camera is located 70 cm away from the tank. To reduce reflections from the grey PVC tank walls, the interior walls of the tank were covered with a lining of black polymer. The surface of this polymer was roughened by hand with sandpaper to further reduce reflections. Reflections at the LS-air interface at the top of the tank were avoided by filling the tank until the LS-air interface was above the region viewed by the camera.

The CCD camera used in this study is the Luca^EM S 658M (Andor Technology, Belfast, Northern Ireland). The CCD resolution is 658 × 496 pixels, and the physical pixel size is 10 µm. The camera digitizes optical signals at 14 bits and is capable of measuring 37 full frames per second. The chip is cooled to −20 °C via an on-board thermoelectric cooling system. An objective lens (JML Optical Industries, Rochester, NY) with an effective focal length of 25 mm was fitted to the camera, and the focus and aperture were set to 0.82 m and f/5.6, respectively, resulting in a focal depth of 11.6 cm centred on the scintillator tank.

2.2.1. CCD artefacts

2.2.2. Lens artefacts

Vignetting. Natural vignetting is approximated by the 'cos⁴(θ) law of illumination' (Ray 1994), which states that the degree of vignetting is proportional to cos⁴(θ), where θ is the angle between the optical axis and the ray from the exit pupil of the lens to the measurement point on the imaging sensor (figure 3). The vignetting value for a given pixel (i,j) can therefore be calculated by the equation

$$\begin{equation} V_{i,j} = \cos ^4 ( {\theta _{i,j} } ) = \frac{{a^4 }}{{\big( {a^2 + d_{i,j}^2 } \big)^2 }} \end{equation} \tag{ 1 }$$

where a is the distance from the exit pupil to the principal point (the point where the optical axis meets the image sensor), and d_i,j is the distance from the principal point to pixel (i, j). Depending on the lens design, the distance a may differ significantly from the focal length. In the event that the parameter a is not known, it can be approximated by the ratio of the object-space focal distance to the measured object-space pixel size at the focal plane. The cos⁴(θ) rule is only strictly valid for thin lenses, and some commercially available lenses diverge significantly from this behaviour (Goldman 2010). However, the cos⁴(θ) rule provides a simple analytical model of vignetting that is effective in many cases. Those desiring a more accurate vignetting correction can use alternate vignetting models, such as those proposed by Litvinov and Schechner (2005) or Goldman (2010).

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The vignetting in our lens-camera system was measured by analysing flat field images. These were acquired by attaching a diffusing filter to the front of the lens and acquiring images of the centre of a flat screen computer monitor at close range. Several flat field measurements with different camera orientations were averaged together to reduce the impact of any non-uniformities in the monitor output. The resulting flat field was fit to a cos⁴(θ) function using least squares optimization. The effective pixel size of the camera was known, allowing d_i,j to be calculated precisely. Because the distance a was not known for the lens used in this study, the fit of the cos⁴(θ) function consisted of fitting the parameter a of equation (1). The vignetting in the detector system was corrected by scaling each image by the cos⁴(θ) function determined by the fit.

Lens distortion. One approach to solving the lens distortion problem is to calibrate a lens and map its distortion modes. Camera calibration methods using vanishing points and vanishing lines to identify the camera focal length have been extensively developed (Caprile and Torre 1990, Wang and Tsai 1990), and calibration techniques for determining lens distortion have been developed for machine vision applications (Tsai 1992, Zhang 1999). In this study, lens distortions were measured and corrected using the Camera Calibration Toolbox for Matlab (Bouguet 2010), which is an implementation of the previously cited camera calibration techniques. It was used to develop a model of the camera's intrinsic and extrinsic parameters, including focal length, principal point, and lens distortions, based on multiple images of a checkerboard pattern at different orientations. The lens distortion was modelled using the second-order symmetric radial distortion model used by Zhang (1999). The calibrated distortion model was then used to restore the rectilinearity of each image acquired with the detector.

Lens PSF. In the simplifying case of a perfect (aberration-free) lens, the PSF is produced by the diffraction of light from the source as it travels through the lens aperture, and is equivalent to the Fraunhofer diffraction pattern of the aperture. Real lenses diverge from this ideal behaviour, as the PSF is broadened by imperfections in the optical system.

The PSF of a lens with a fixed focal length can be described as a function of six variables, including the wavelength of the light, the image coordinates (x and y), the lens aperture, the distance from the lens to the object (z), and the back focal distance (Shih et al 2012). In the case of the detector described here, the light wavelength, lens aperture, and back focal distance are fixed. This leaves the lens-object distance and the image coordinates as the variable parameters of the PSF. Because the lens-object distance is constrained to the inside of the scintillator tank, the lens PSF is essentially a three-dimensional (3D) function with a unique value for every point in space within the scintillator tank.

The PSF of the entire system consists of the convolution of the lens PSF and the PSF due to light scatter within the scintillator:

$$\begin{equation} {\rm PSF}_{{\rm sys}} ( {x,y,z} ) = {\rm PSF}_{{\rm scatter}} ( {x,y,z} )*{\rm PSF}_{{\rm lens}} ( {x,y,z} ). \end{equation} \tag{ 2 }$$

While PSF_lens is technically a function of the 3D location inside the scintillator tank, in practice its variation may be small enough over the region of interest that an invariant PSF_lens could be assumed as a first-order approximation. Because of the expected small variation and the difficulty of measuring PSF_lens at multiple locations, we assumed an invariant PSF_lens in this study. We leave as future work the determination of the spatial variation of PSF_lens.

PSF_lens was measured using the method described in ISO standard 12233 for measuring the resolution of photographic cameras (ISO 2000). This process involves three steps.

• 1.  
  Photograph a slanted edge formed by the interface between black and white regions.
• 2.  
  Measure the edge-spread function (ESF) perpendicular to the slanted line. Repeating this measurement at multiple locations along the slanted line allows the ESF to be determined with a resolution greater than the camera resolution.
• 3.  
  Take the derivative of the ESF to obtain the line-spread function, which is the one-dimensional equivalent of the PSF.

The test pattern was formed by joining a black strip of plastic to a white strip along a carefully machined straight edge. This pattern provided the required ESF and was chemically compatible with the scintillator solution. This test pattern was affixed to a rigid surface and viewed at an angle with the camera to produce the requisite slanted edge. The measurement of PSF_lens in air was compared to the measurement of PSF_sys performed in the scintillator tank, as described in section 2.2.3.

2.2.3. Scintillator tank artefacts. Refraction and perspective

Refraction and image perspective both affect the location and apparent size of objects and light sources within the tank. Because of this interconnection, refraction and perspective are corrected simultaneously. We developed a first-order correction for refraction and perspective based on the simplifying assumption that our camera system is a pin-hole camera. As shown in figure 4(a), any photon created along the line $\overline {MC}$ is projected onto the point X in the camera focal plane. Therefore, the apparent size and location of an object depends on its distance away from the focal plane. The presence of the scintillator solution creates an additional change in the object's apparent size and location. As shown in figure 4(b), refraction changes the direction of the photon track and thus changes the observed position of the photon origin. In addition to change of location, the change in apparent pixel size causes a change in the pixel value in the CCD image.

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Refraction and perspective are corrected analytically based on the pin-hole camera assumption. The index of refraction of the LS is 1.47 and that of the acrylic tank is 1.49. Since refraction at the LS-window interface is very small, only refraction at the window–air interface is considered in the correction. Considering that most of the photons are created along the proton track, the goal of the correction is to translate the image from the focal plane to the plane of the proton track.

First, the coordinate of each pixel in the camera plane is mapped to the proton track plane using Snell's law and trigonometric identities. Based on the coordinate translation map, the ratio of the pixel area at the proton track plane to that at the focal plane is calculated for each pixel. The pixel value at the proton track plane is then normalized by dividing each pixel value by its corresponding area ratio. For example, if the area ratio is smaller than 1, the normalized pixel value will be higher than the measured value. The normalized pixel values with the translated coordinates are then used to interpolate to the final pixel value at the proton track plane.

Photon scatter. The final step of our artefact correction is to address photon scatter in the scintillator. We adapted the method described in section 2.2.2 to measure PSF_sys for the scintillation detector. The test pattern was placed in the scintillator tank, and the light source for the photograph was produced by exciting the scintillator with an ultraviolet lamp (F15T8/BLB, General Electric Lighting) with a 368 nm emission peak. This ensured that the wavelength of light used for the measurement was the same as that of the light produced during LS irradiation. The PSF_sys measurement was repeated with the test pattern placed at a distance of 3, 10 and 16 cm from the tank window in order to evaluate the relationship between scatter and the distance travelled through the scintillator.

The low-intensity tail of the measured PSF was fit to an exponential function. This preserved the shape of the PSF and prevented the noise in its low-intensity tail from propagating to the images during blurring correction. Blurring in the detector was corrected by deconvolving the measured PSF from the detector images using the Lucy–Richardson deconvolution algorithm (Biggs and Andrews 1997).

For each source of error, our goal was to describe the magnitude of error it caused and the effectiveness of our correction method for mitigating it. Thereafter, we used gamma analysis to identify the correction steps that played the greatest role in restoring the images to the original dose distributions.

Proton pencil beams of four energies (85.6, 100.9, 144.9, and 161.6 MeV) were used for in-depth testing of the optical artefact corrections. Depth-light profiles were plotted for qualitative comparison of the measured and calculated distributions. The overall effectiveness of the optical artefact corrections was evaluated by comparing raw and corrected CCD measurements with Monte Carlo dose calculations.

Two-dimensional gamma analysis (Low et al 1998) was performed to quantify the agreement between the CCD images and the corresponding projections of the Monte Carlo dose distributions. The analysis included all pixels in which the reference distribution was at least 5% of the maximum value. This analysis was performed with the uncorrected and corrected images and with each one of the corrections left out to show its contribution to the overall correction process.

Gamma analysis was also performed on the corrected images with the analysis parameters varying from 1% to 3% dose difference and from 1 to 3 mm distance to agreement. Beginning at the commonly used gamma analysis criteria of 3% dose difference and 3 mm distance to agreement, we decreased both of these parameters until the passing rate for at least one of the beam energies dipped below 95%, which we set as the limit for 'acceptable agreement' between the measured and calculated distributions.

While it is common practice to use a percentage of the maximum dose as the dose difference criterion for gamma analysis, we elected to use a percentage of the local dose at each pixel as the dose difference criterion. We consider this to be appropriate for this study because the maximum dose in a proton Bragg peak is much higher than the average dose in the region, and the use of a percentage of the maximum dose would be too generous of a dose difference criterion, limiting the utility of gamma analysis for comparison of dose distributions.

Proton beam measurements with the scintillator detector were carried out at the MD Anderson Cancer Center Proton Therapy Center, Houston on the scanning beam gantry. The detector was aligned isocentrically on the treatment couch, and mono-energetic proton pencil beams were directed into the scintillator tank perpendicular to the camera axis at a depth of 10 cm from the tank window. Pencil beams were also delivered at depths of 5 and 15 cm from the tank window in order to evaluate the variation in light scatter with distance travelled through the scintillator. The experimental setup is shown in figure 5. Nominal proton beams of the four energies named above were delivered and measured separately. A total of 220 monitor units, as described in Gillin et al (2010), was delivered for each beam energy. The CCD camera acquired images at 2 frames per second, so that each proton beam was delivered over the course of two images.

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3D dose distributions were calculated for the beam energies named above using the Monte Carlo radiation transport code MCNPX, version 2.7d (Waters et al 2002) with validated phase space models of the specific scanning beam nozzle being used (Sawakuchi et al 2010). The voxel size was set to 1 mm perpendicular to the beam direction, and it varied from 1 to 0.1 mm in the beam direction, with higher resolution in the steep-dose-gradient region around the Bragg peak.

Scintillators exhibit a nonlinear response to ionizing radiation with varying linear energy transfer, a phenomenon called ionization quenching. This phenomenon causes an under-response of the scintillator in the Bragg peak because of the steep increase in linear energy transfer in the Bragg peak region. To account for this effect in the comparison between the Monte Carlo and CCD data, we applied a quenching model to the Monte Carlo dose data to obtain the scintillating radiation output. The parameters for this model were determined in a previous study by our group for the same detector configuration (Robertson et al 2013).

3.1.1. CCD noise

The dark current of the CCD camera was evaluated by calculating the mean pixel value and standard deviation over the entire frame for a range of exposure times (figure 6). As expected, the dark noise increased linearly with time. This is illustrated by a linear fit to the data, with an R² value of 0.9992. The baseline dark signal pixel value for the CCD is 510. The dark current offset is corrected during background subtraction.

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3.1.2. Stray radiation

The spatial median filter effectively removed single-pixel spikes caused by stray radiation (figure 7). The mean number of transient spikes and streaks in the test images decreased from 3 to 0 after the median filter was applied. The median filter did not significantly affect the shape of the underlying light distribution.

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3.2.1. Vignetting

The cos⁴(θ) vignetting model provided a good approximation to the measured vignetting behaviour of the camera (figure 8).The fit to equation (1) yielded a value of a = 26.5 mm, which matches well with the lens focal length of 25 mm and the approximation of a based on object-space parameters, which was 26.9 mm. While the cos⁴(θ) model did not perfectly match the measured signal fall-off, the agreement is considered sufficient for the purposes of this study. The under-response due to vignetting measured for this detector was as great as 4% at the corners of the image, with 7.8% of all pixels under-responding by 3% or more. After the vignetting correction was applied, 99.8% of pixels in the flat field image were within 1% of the pixel value at the centre of the image.

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3.2.2. Lens distortion

As expected, the lens distortion model obtained from the calibration process showed very little distortion in the centre of the field of view. Pixels at the edges of the field of view could be displaced by as much as 2 pixels, which corresponds to a measurement error of 0.6 mm (figure 9). The small magnitude of these distortions illustrates the quality and appropriateness of the lens selected for this detector.

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3.2.3. Lens PSF

3.3.1. Refraction and perspective

3.3.2. Photon scatter

PSF_sys was found to be a sharp peak with very steep fall-off, dropping to 0.015% within 10 pixels from the centre. At a distance of 8 pixels from the centre, the noise contribution was significant enough that, while the PSF continued to decrease on average, it no longer decreased monotonically. In order to extend the range of the measured PSF beyond 8 pixels, the low-intensity tail was fit to a decreasing exponential function. This allowed the measured PSF to be extrapolated to a distance of 64 pixels from the centre.

To our surprise, there was no substantial difference between the PSF_sys measurements performed at different depths in the scintillator. In addition, the measured PSF_lens was equivalent to the measured PSF_sys (figure 10). This suggests that PSF_lens is the primary contributor to PSF_sys in our detector, with PSF_scatter making a negligible contribution. The invariance of PSF_sys with depth in the scintillator tank is confirmed by comparison of the lateral profiles of proton pencil beams delivered at depths of 5, 10, and 15 cm from the tank window. After correction for perspective, attenuation, and inverse-square intensity fall-off, there was no substantial difference between the profiles (figure 11).

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The corrected CCD light distribution on the beam's central axis exhibited a clear improvement in agreement with the Monte Carlo light distribution in comparison to the uncorrected CCD light distribution (figure 12). The light distributions all exhibited decreased signal in the Bragg peak due to quenching, as described in section 2.3.2.

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Gamma analysis was used to compare the scintillation light measurements from the LS detector system with the projected scintillation light distributions calculated using Monte Carlo methods. The minimum gamma analysis parameters that provided 'acceptable agreement' were 2%/2 mm and 3%/1 mm. The gamma analysis pass rates for the varying gamma criteria are given in table 2 for each of the four beam energies. The gamma pass maps with the 2%/2 mm criteria are shown in figure 13 for the 85.6 and 144.9 MeV proton beams.

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The gamma analysis clearly demonstrates the effectiveness of the optical artefact corrections applied to the CCD data. With the common gamma criteria of 3%/3 mm, the average passing rate rose from 85.6% for the uncorrected light distributions to 99.7% for the corrected distributions. Using the more stringent criteria of 2%/2 mm, the difference was larger, rising from 65.9% for the uncorrected distribution (figure 13, top) to 98.2% for the corrected distribution (figure 13, bottom) on average.

To evaluate the contribution of each step in the overall correction process, the gamma analysis was repeated with each of the corrections omitted. The results are shown in table 3. The contribution of the spatial median filter, vignetting, and lens distortion corrections was minimal. The refraction correction was larger, and the greatest proportion of the overall correction was contributed by the blurring correction.

We determined that blurring from the lens was the primary source of the overall PSF, while light scatter in the scintillator was negligible. This was contrary to our expectations, as previous studies assumed that light scatter was the primary source of blurring. This result suggests that the scintillator BC-531 effectively meets the desirable criteria of transparency to its own light emissions. It also highlights the importance of using high-quality optics in order to obtain the narrowest possible PSF.

While unexpected, this finding is fortuitous, as it renders unnecessary the use of different PSFs for different depths within the scintillator tank. While photon scatter proved to be insignificant in this study, we wish to emphasize that this result is valid only for the scintillator BC-531, and that the level of scattering in other scintillators has not yet been evaluated for this application. The primary significance of this finding is that blurring due to the lens is non-negligible and requires separate treatment from blurring due to light scatter.

In our results, the areas that most frequently failed the gamma analysis were the low-dose edges, where noise and offsets in the background level have a much larger influence than they do on the beam axis. This is a result of our decision to use a percentage of the local pixel dose in our gamma analysis rather than a percentage of the maximum dose, as is commonly used in radiation therapy dose evaluation. The local dose difference is a stricter criterion, which provides more meaningful comparisons in low-dose regions. Had we chosen to use a percentage of the maximum dose, the pixels in these low-dose areas would have passed.

The vignetting and lens distortion corrections showed little contribution to the gamma pass rate in this study, and in some cases they even caused a small decrease in the passing rate. However, the value of these corrections should not be overlooked. The vignetting and lens distortion corrections are largest at the edges of the image, and because our dose distributions included very little data near the image edges, these corrections appeared to have little effect. That being said, the use of low-distortion lenses and telecentric lenses could render lens distortion and vignetting corrections unnecessary, especially considering that the data at the tank edges are likely to be less important than the data in the centre.

The spatial median filter had a small negative effect on the gamma pass rates. This is unsurprising given the tendency of median filters to blur sharp edges. However, this effect was small, and gamma analysis is not sensitive to the spikes and streaks that the median filter is designed to remove. The median filter may prove to be more important when multiple cameras are used to obtain a 3D reconstruction of the light distribution, as high-intensity spikes could interfere with 3D reconstruction algorithms.

The central-axis light signal data shown in figure 12 reveal an imperfect match between the Monte Carlo calculations and the corrected CCD data. The disagreements may come from several possible factors, including noise in the CCD measurements as well as imperfections in the correction factors and Monte Carlo calculations. The refraction and perspective corrections only apply analytically to one plane within the detector, and the light signal outside of that plane cannot be completely corrected for these phenomena. However, we believe that in the current study, this limitation was not observed because the dose was concentrated along a single narrow pencil beam.

The most notable disagreement between the CCD and Monte Carlo data was in the maximum light intensity at the Bragg peak, which differed by ±3%. This variation was unsurprising, given the sharpness of the proton Bragg peak and the high spatial resolution of the data. An additional source of error in the Bragg peak height came from the quenching parameters applied to the Monte Carlo dose calculations to obtain the Monte Carlo light distribution. In a previous study, we reported that this quenching calculation method was accurate to within ±5% (Robertson et al 2013), and the maximum errors in that study were in the Bragg peak. This source of uncertainty alone is sufficient to explain the deviations between the Monte Carlo and CCD peak light values. Further efforts to decrease the error in the quenching correction process are underway.

An additional source of error in the correction factors is the difficulty of exactly measuring the PSF. Our method allowed us to measure the PSF with twice the spatial resolution of the CCD camera, but this resolution was still coarse compared to the sharp peak of the PSF. We selected the peak value of the PSF by fitting a Gaussian function to the immediately surrounding data points, but this method only provides an approximate peak value. The actual peak value may vary by as much as a factor of 2, which could change the results of the blurring correction. However, our results match the Monte Carlo data well, suggesting that our measured PSF was sufficiently close to the actual PSF to provide an accurate blurring correction for this detector system. An alternative approach for analytically calculating the lens PSF based on the lens prescription (Shih et al 2012) may provide improvements in accuracy while also facilitating the use of a PSF that varies with position inside the tank.

Reflection of the scintillation light is a source of artefacts that was not dealt with directly in this study. Reflections may occur at any interface between the scintillator and the tank wall, the tank window, or the air above the scintillator. Reflections have been problematic in previous studies involving volumetric scintillation dosimetry (Beddar et al 2009, Ponisch et al 2009, Kirov et al 2005). Reflections are highly dependent on the geometry and materials of the scintillator tank, and are difficult to correct through image processing. We believe that the best approach to minimize artefacts due to reflection is to prevent them through careful detector design, such as we did in the steps described in section 2.1.