Characterization of the INFN proton CT scanner for cross-calibration of x-ray CT

Objective. The goal of this study was to assess the imaging performances of the pCT system developed in the framework of INFN-funded (Italian National Institute of Nuclear Physics) research projects. The spatial resolution, noise power spectrum (NPS) and RSP accuracy has been investigated, as a preliminary step to implement a new cross-calibration method for x-ray CT (xCT). Approach. The INFN pCT apparatus, made of four planes of silicon micro-strip detectors and a YAG:Ce scintillating calorimeter, reconstructs 3D RSP maps by a filtered-back projection algorithm. The imaging performances (i.e. spatial resolution, NPS and RSP accuracy) of the pCT system were assessed on a custom-made phantom, made of plastic materials with different densities ((0.66, 2.18) g cm−3). For comparison, the same phantom was acquired with a clinical xCT system. Main results. The spatial resolution analysis revealed the nonlinearity of the imaging system, showing different imaging responses in air or water phantom background. Applying the Hann filter in the pCT reconstruction, it was possible to investigate the imaging potential of the system. Matching the spatial resolution value of the xCT (0.54 lp mm−1) and acquiring both with the same dose level (11.6 mGy), the pCT appeared to be less noisy than xCT, with an RSP standard deviation of 0.0063. Concerning the RSP accuracy, the measured mean absolute percentage errors were (0.23+−0.09)% in air and (0.21+−0.07)% in water. Significance. The obtained performances confirm that the INFN pCT system provides a very accurate RSP estimation, appearing to be a feasible clinical tool for verification and correction of xCT calibration in proton treatment planning.


Introduction
Proton therapy (PT) is an established radiotherapy technique, thanks to its peculiar depth-dose profile (i.e. the Bragg peak) (Grau et al 2020). Although the high ballistic precision of PT represents its main advantage over photon treatments, it makes this technique more sensitive to uncertainties with respect to the planned target definition (Paganetti 2012). Hence, one of the current challenges in PT is the accurate description of body tissues, in terms of Relative (to water) stopping power (RSP), which finally determines the depth reached by protons inside the patient. The 3D RSP maps of the patients are currently calculated starting from the 3D Hounsfield unit (HU) map acquired with x-ray computed tomography (xCT), by means of semi-empirical methods. However, this conversion introduces non negligible uncertainties, which force to enlarge the irradiated volume by adding safety margins, of the order of 3%-3.5% of the proton range, around target volumes (Schneider et al 1996, Yang et al 2010.
Proton CT (pCT) provides in principle the potential for a direct and more accurate estimation of the RSP and hence for improved treatment planning. However, many technical challenges remain to be solved, which so far hindered the clinical application of pCT. The maximum available proton beam energy (i.e. about 230 MeV, corresponding to about 32 cm in water) could limit the size of the object to be imaged and thus restrict pCT to volumes or treatment sites below this range threshold. Furthermore, the eventual integration of pCT systems in the clinics would further increase the cost of PT equipment, which is the main drawback compared to conventional photon therapy. Finally, but likely most critical, pCT is still in the development phase and it will take time before pCT scanners will be certified for the clinical use (Takada et al 1988, Johnson et al 2016, Pettersen et al 2017, Esposito et al 2018, Civinini et al 2020, DeJongh et al 2021b, Bär et al 2022, Granado-González et al 2022. A recent study demonstrated that the ability to directly measure accurate RSP maps would enable pCT to be used for cross-calibration of the x-ray CT systems that are used for setting up the proton treatment plans (Farace et al 2021). This would be translated into a first clinical pCT application, without direct patient involvement. The purpose is to employ stabilised biological phantoms to mimic the proton beam interaction with human tissues. In fact, CT calibration is conventionally obtained by scanning a number of tissue equivalent materials, which have limitations in mimicking the radiobiological properties of real tissues and therefore introduce uncertainties in RSP estimation (Schaffner and Pedroni 1998). Trying to mitigate this issue, biological tissue samples were investigated for ex vivo validation (Möhler et al 2018, Xie et al 2018, Meijers et al 2020, Bär et al 2022. However, biological tissues are intrinsically heterogeneous, and uniform biological samples might be obtained only by homogenising tissue samples; this would mix all the different tissue components, modifying the tissue structure and properties, including the RSP. Considering such heterogeneity, it is expected that the most reliable RSP estimation would be directly obtained by pCT (DeJongh et al 2021a). The new calibration approach proposed in Farace et al (2021) relies on the possibility to acquire on the same biological phantom both the RSP and HU map, through the pCT system and the xCT system, respectively. By comparing the two tomographies voxel-by-voxel, a scatter plot is obtained (i.e. single-voxels RSP versus HU) and finally a cross-calibration curve can be extracted. Remarkably, once a reference pCT system is available, this procedure could be adopted by remote PT centres even when they are not equipped with a pCT system. This could be done by shipping a heterogeneous biological phantom to the remote centre, to be acquired with the xCT system to be calibrated, while having the corresponding RSP maps reconstructed from pCT measurements performed at the reference centre. The RPS map and the HU map are then processed and a calibration function specific for the remote xCT system can be extracted. The method was presented as a proof-of-principle in Farace et al (2021), deserving further improvements and refinements. In particular, the voxel-by-voxel comparison approach requires careful consideration of the differences between detectors and reconstruction algorithms of the two systems. Different levels of noise and spatial resolution are expected between the two tomographies. The different correlated blurring could introduce errors in the correlation between RSP and HU of each voxel. Therefore, understanding the imaging performances of the two systems is of paramount importance for a correct comparison of the two tomographies and for a correct estimation of the uncertainties in the extracted cross-calibration curve.
The present study aimed to assess the imaging performances of the INFN pCT system, in terms of spatial resolution, noise power spectrum (NPS) and RSP accuracy. This is a necessary preliminary analysis aiming at the implementation of the new procedure for cross-calibration of xCT. For this purpose, a custom-built synthetic phantom was proposed and imaged both with pCT and xCT systems at the Trento proton therapy centre (PTC).

pCT and xCT scanners and reconstructions
The INFN pCT system has been developed since 2006 in the framework of the PRIMA (PRoton IMAging) project funded by INFN (Civinini et al 2010, Scaringella et al 2013. The current system is a second generation apparatus and it is described in detail in Civinini et al (2020), with reconstruction methods updated in Scaringella et al (2023). The scanner is based on four planes of silicon micro-strip detectors, two upstream and two downstream with respect to the phantom to be imaged, which is placed on a remotely controlled rotating platform (figure 1). This configuration allows measuring the 3D coordinates and retrieving directions of the entry and exit points of each single proton in the phantom, required to reconstruct the most likely path (MLP) inside it (Schulte et al 2008). The residual energy of each proton is measured by a Cerium-doped Yttrium Aluminium Garnet (YAG:Ce) scintillating calorimeter, with a field of view (FOV) of 5 × 20 cm 2 . A distancedriven filtered back-projection algorithm (Rit et al 2013), taking into account the single proton MLP and the residual energy, is applied to reconstruct the phantom 3D RSP map.
The tomographies presented in this study were obtained with nine complete rotations of 0.9°angular steps, with acquisition rate of about 80-90 kHz. The total acquisition time for nine complete rotations is about 3 h. The total number of trigger events was 9 × 10 8 , assumed to be a good statistics for high quality image output (Scaringella et al 2023). The scans have been performed at the experimental beam line at the Trento PTC (Tommasino et al 2017) at the nominal proton kinetic energy of 211.2 MeV. To cover the entire FOV of the pCT system, a 2.5 mm tantalum plate is placed at the exit of the beam pipe to enlarge the beam, as described in Civinini et al (2020). In the filtered back-projection algorithm, a Hann filter may be used instead of the conventional rectangular window at Nyquist's frequency (defined as / s 1 2 with s the pixel spacing of the projections). The cut-off frequency of the filter (f cut ), expressed as a fraction of Nyquist's frequency ( f N ), can be adjusted in the range (0, 1). Since the reconstruction filter modulates the spatial frequency range both for signal and noise, we analysed image quality at different values of the filter parameter ( / f f cut N ), in order to find the best match of noise-spatial resolution tradeoff between pCT and xCT images and to build, at the same time, a lookup table useful for future applications.
The xCTs were acquired with a big bore Brilliance CT scanner (Philips Medical Systems, Cleveland, OH, USA) at the Trento PTC. To be closer to clinical scenarios, we decided to implement the standard acquisition protocol adopted for brain PT treatments. Namely, 120 kV x-ray beam with 0.563 scan pitch, 16 × 0.75 mm 2 collimation and 112 mAs exposure. This value of mAs was chosen in order to acquire the xCT images with a dose level comparable to that expected for the pCT statistics in this study: about 11.6 mGy, according to the dose estimation procedure described in Civinini et al (2017). To reconstruct the same FOV as the pCT system, the 512 × 512 acquisition matrix was reconstrued with a voxel size of 0.39 × 0.39 × 1.5 mm 3 , with the standard reconstruction kernel (UB). This voxel size is compatible with the ones normally used in the clinical protocol. A grid with the same dimensions was used for pCT reconstruction to facilitate the voxel-by-voxel comparison between proton and x-ray tomographies.

Image quality phantom
A specific phantom was designed and realised to investigate the pCT imaging performance in terms of spatial resolution, NPS and RSP accuracy (figure 2). The phantom has a cylindrical shape with 0.5 cm thick PMMA walls, 14 cm internal diameter and 13 cm height. Inside the phantom, five different cylindrical inserts of 3 cm Figure 1. The INFN pCT scanner with its main parts labelled: four tracking planes (T), the YAG:Ce calorimeter and the phantom on the rotating platform. The exit beam pipe is placed 413 cm far from the first tracker plane and is not visible in the image, but the beam direction is indicated by the blue arrow. The distance between the first and the second tracker plane, as well as the one from the third and fourth, has been set to 15 cm. The space left free between the second and third plane, where the phantoms have been installed, was 30 cm. diameter can be placed and fixed. Four synthetic plastic materials were chosen to resemble the density of different anatomical districts: Low-Density PolyEthylene (LDPE) (0.99 g cm −3 ), Acrylic (1.20 g cm −3 ), Delrin (1.41 g cm −3 ), Teflon (2.18 g cm −3 ). The fifth insert was made of beech wood that, as a low density (∼0.66 g cm −3 ) and inhomogeneous material, was exploited to preliminary and qualitatively probe the possible pCT system response to fatty and striated tissues which will be present in our future heterogeneous biological phantoms.
The phantom can be sealed on the top, in order to be employed with air or filled with (distilled) water. Hence, we could investigate the imaging performances at two different contrast-to-noise ratio levels. This allowed checking whether the response of the pCT system is linear, as is the case for the xCT system (Chen et al 2014)-that is, whether the spatial resolution of the system varies with the amount of noise and the contrast of the imaged object. Moreover, protons are expected to undergo different multiple-scattering in the two different background materials, resulting in different image quality.
Since all inserts were 6 cm high, the upper part of the cylinder was just air or water. In this way, homogeneous slices of water could be imaged to check the RSP value of water, that is the unity reference material, and the noise spectrum, as described in section 2.4.

Spatial resolution
The basic function that characterises the response of an imaging system is the modulation transfer function (MTF), which measures the spatial transfer characteristics of the system as a function of the spatial frequencies (Samei et al 2019).
Various methods have been proposed to measure the MTF, such as the use of slits, edges or bar pattern images (Samei et al 2019). In this study, the circular edges of phantom inserts were exploited to investigate the system response both symmetrically in the x-y plane and at different contrast and noise levels. This method was introduced by Richard et al (2012) and further refined by Chen et al (2014), and it was adapted in this study in the following way, both for pCT and xCT images.
(1) A squared region of interest (ROI), centred on the cylindrical insert and with a side twice the insert's diameter, was extracted in the x-y plane for each insert. The edge spread function (ESF) was thus constructed by recovering all the ROI pixel values as a function of their radial distance from the centre. Note that this approach assumes that the spatial resolution is homogeneous along the insert circumference and averages out the variations observed by Khellaf et al (2019) on simulated data with ideal trackers mainly.
(2) The ESF was then oversampled. This step allows the estimation of the so-called presampled MTF. Namely, the presampled MTF does not retain the typical MTF dependence on the signal pattern and on its relative location with respect to the detector grid. Hence, it is not affected by aliasing artefacts arising from the sampling step and it is a specific feature of the detector under study. In this way, the resolution values extracted from the presampled MTF should be independent of the voxel size, at least under the Nyquist theorem constraint (Buhr et al 2003). In the following analysis, the ESF was rebinned into one tenth of the voxel size in the x-y plane. This value has been provided in literature as a gold standard to avoid too noisy ESF, preserving at the same time the spatial frequency response (Samei et al 1998).
(3) The oversampled ESF obtained so far can be strongly affected by the noise of the imaging system. To avoid the resulting fluctuations, one should average the ESF over multiple slices. However, since a finite quantity of slices are available with our scanner, we introduced a regularisation on the ESF by imposing the monotonicity of the function. Actually, the monotonicity constraint is rephrased as a quadratic optimisation problem, as described in (Maidment et al 2003) and adapted through the Matlab ® (The MathWorks.Inc., Natick, MA, USA) algorithm for constrained nonlinear multivariable function.
(4) To further reduce the noise impact, the ESF was then averaged over three non-consecutive slices. The number of slices is limited by the pCT FOV size. In particular, three groups of three non-consecutive slices each were extracted and the ESFs were averaged within the same group (ESF mean ). As a first approximation, this procedure was adopted to estimate the variability of the MTF values obtained with the same procedure. Then, the following step was performed for each group.
(5) Differentiating the ESF , mean the line spread function (LSF) of the imaging system was obtained. By definition, the Fourier transform of the LSF is the MTF. As typically adopted for xCT systems (Samei et al 2019), the spatial resolution value was extracted from the spatial frequency corresponding to 10% of the MTF maximum value.

Noise power spectrum
The NPS was also investigated. The NPS magnitude reflects the level of stochastics fluctuations at each spatial frequency, and the integration for all nonzero frequencies yields the noise variance (Boedeker et al 2007). The shape of the NPS reveals the noise distribution in terms of spatial frequencies and the correlation between pixel values.
The 2D NPS was estimated through the method described by Boedeker et al (2007) and typically applied for conventional xCT scanners (Samei et al 2019). In order to investigate the noise characteristics across the entire FOV, nine 2.73 cm squared regions of interest (ROIs) were extracted within homogeneous water slices of the phantom as described in Samei et al (2019). Accordingly, the reliable NPS frequency range started at about 0.08 mm −1 and the noise was assumed to be wide-sense stationary within each small ROI.
The same ROIs were extracted for six slices along the rotation axis and subtraction of subsequent slices is performed for background removal before effectively calculating the NPS. This step allowed us to exclude the large-scale variations within each ROI. In fact, such variations are generally not considered noise, since they are not-stochastic. The choice of the background removal method has influence on the low-frequency domain of the NPS and the image subtraction method has been found to be one of the most accurate for xCT analysis (Dolly et al 2016). Hence, it was applied also for pCTs, to compare its response with the xCT one.
Finally, for ROI #i in a given z slice, the 2D NPS is defined as , is the value of the pixel at position (x, y) in the ith ROI, and I i mean, is the pixel mean value of the ith ROI, subtracted to remove DC components in the Fourier Transform. The 2D NPS of the nine ROIs were then averaged and translated into 1D radial NPS. To improve the accuracy, the 1D radial NPS was averaged over the six available water slices.

RSP accuracy
The RSP accuracy was estimated both in case of air-and water-filled phantom, in the following way. For each plastic insert of the phantom, a circular ROI with 2 cm diameter is extracted for each slice, centred in the insert to avoid boundary effects. The mean of the values in the ROI of the ith slice (RSP  170,190,210 MeV) to verify the robustness of the procedure. The targets were circular rods of the same materials of phantom inserts. In particular, rods of three different thicknesses (0.5, 1, 2 cm) were measured for each material, in order to exclude possible scattering effects due to the rod thickness. The RSP accuracy was also estimated for water. In this case, the circular ROI had a 4 cm diameter and RSP i mean, was averaged over six slices. The reference RSP value for water was the expected one for liquid water at room temperature (∼21°C) according to (NIST) .
In addition, the mean absolute percentage error (MAPE) of the pCT scanner was estimated as = with n the total number of inserts. Namely, = n 5 for pCT images of the phantom filled with water, while = n 4 in case of air-filled phantom, since no water RSP values are measured.

Results
The imaging performances (i.e. spatial resolution and NPS) were analysed both for xCT and pCT images of the phantom ( figure 3). Moreover, the accuracy of the RSP values reconstructed with the pCT was estimated in comparison with the MLIC measurements. As a first qualitative result, it was noticeable that both in xCT and pCT images the wood grains of the beech insert were clearly visible, validating a good response of the pCT system also to heterogeneous materials. In addition, some small air bubbles were distinguishable both in xCT and pCT with water background (figures 3(d)-(f)), proving that our system is sensitive even to 2 mm size details. The LDPE insert was not visible in pCT images with water background (figures 3(e), (f)), making it difficult to estimate the spatial resolution at the corresponding density. In fact, as reported in section 3.3, the RSP of LDPE was really close to 1, and thus the ESF was nearly flat.

Spatial resolution
The spatial resolution was estimated for all inserts but LDPE, both with air and water background, The spatial resolution and by varying the filter parameter ( / f f cut N ) in the range (0.45, 1). Values lower than 0.45 were not investigated, since common xCT scanners have spatial resolution values well above 0.4 lp mm −1 , that is the spatial resolution obtained with / f f cut N = 0.45. As reported in figure 4 and in the supplementary tables TS1, TS2, for all inserts, the pCT resolution was not the same in the two background cases, implying a nonlinear response of the imaging system, unlike xCT systems using a filtered back-projection technique. The impact of the Hann filter was the same in both pCT images, i.e. the smoothing effect of the filter was much more evident as the cutoff-frequency decreased and the spatial resolution decreased. In figure 4, it is clear that with filter parameter / f f cut N = 0.60, the spatial resolution of the pCT images with air background was compatible with the one of xCT for all the inserts, within the uncertainties. While in case of water background, the optimal cut-off parameter for the pCT-xCT comparison seemed to be / f f cut N = 0.65.

Noise power spectrum
The noise magnitude and distribution were analysed through the uniform water slices within the phantom. As expected, the Hann filter had an impact on the NPS of the pCT images. Decreasing the cut-off filter frequency increases the blurring of the images, as previously reported, and at the same time it reduces the noise magnitude. This is visible in figure 5(a) and, more quantitatively, in table 1, where the integrals of the NPS curves, i.e. the standard deviation, were listed for the filter parameter varying in the range (0.45, 1). For the comparison pCT-xCT, the HU values were linearly rescaled by a factor 1000 to ensure concordance of NPS units (i.e. RSP 2 mm 2 ). The standard deviation of the xCT was compatible with the one obtained with the pCT images with filter parameter 0.85, while it is greater than the one of pCT with filter parameter 0.65 by about 21%. The second effect of the filter application was the variation of the curve shape and especially of the frequency position of the NPS peak. In table 1, the peak position is reported as obtained from Gaussian fit of the peak region of the NPS curves with a confidence interval of 95%. As observed in figure 5(a), the peaks shifted toward lower frequency as the frequency parameter decreased. This variation was also visibly reflected in the noise appearance in the images, as reported in figures 5(b)-(d). The remarkable difference between the xCT and the pCT without applying the Hann filter clearly emerges from figure 5(a). With filter parameter equal to 0.65, the pCT frequency peak deviated from xCT by about 9% toward higher frequencies.

RSP accuracy
The MAPE was calculated both for air and water background pCTs, by varying the filter parameter ( / f f cut N ) in the range (0.45, 1) (table 2). It is noteworthy that all the MAPE values, for all the filter parameters and background cases, were compatible within uncertainties and are below 0.37%. For the filter

Discussion
The INFN pCT system has been repeatedly tested at the Trento PT Centre (Civinini et al 2020, Farace et al 2021 and the calibration and reconstruction procedures have been recently updated and verified (Scaringella et al 2023). We are now designing a new implementation of the pCT system in proton treatment planning, based on the direct comparison between pCT and xCT to construct a cross-calibration curve. The procedure, already proposed in Farace et al (2021), requires the pCT performance parameters to be extensively investigated as a preliminary step.
Therefore, in this study the imaging performance of the INFN pCT was investigated in terms of spatial resolution, NPS and RSP accuracy, through a custom-built, synthetic phantom. The phantom design is similar to the one already used in performance analysis of other particle CT systems (Johnson et al 2016, Volz et al 2021, Götz et al 2022. However, the possibility to fill the phantom with liquid water is a novelty, as a step toward more realistic clinical conditions and similarities to biological phantoms that will be used to further work on the cross-calibration curve. Moreover, by changing the background, we could investigate the linearity of the pCT response, relevant in the analysis of non-homogeneous, biological phantoms. As first qualitative results, the phantom pCT images correctly reproduced the phantom geometry, with no visible artefacts. Differences of RSP values below 1% were not distinguishable by simple visual inspection, as demonstrated also by the difficult identification of the LDPE insert in the water-filled phantom ( figure 3). However, small structures, such as air bubbles and wood grains, were clearly distinguishable, as they were in xCTs.
These aspects can be quantitatively assessed by means of the spatial resolution estimation. Exploiting the circular edges of the phantom inserts, the MTF was computed for each insert signal but the LDPE, both in air . Spatial resolution values for Teflon, Delrin, Acrylic, LDPE for pCT images reconstructed with different filter parameters ( / f f cut N ), both in case of water and air background. The blue and red coloured bands represent the spatial resolution value of xCT images for each insert with water or air background, respectively. and water background. The pCT images reconstructed with no Hann windowing had a clearly higher resolution than xCTs (figure 5). Moreover, both xCTs and pCTs were acquired at the same dose level (i.e. about 11.6 mGy), to compare their NPS. NPS is commonly assessed in xCT scanners characterization Table 1. Standard deviation of pixel values estimated from the integral of the NPS curves and frequency position of the NPS peak estimated through Gaussian fit, for pCT images reconstructed with different filter parameters ( / f f cut N ) and the xCT image. CT pCT ( (Samei et al 2019), and, to our knowledge, this article reports it for the first time for a pCT scanner. The noise magnitude (i.e. standard deviation) of pCT images reconstructed without Hann windowing is significantly higher than xCTs (table 1). In addition, the pCT noise spectrum is shifted toward higher frequency. This is directly reflected in the image appearance, with a visible finer grain noise, revealing a higher correlation between nearest voxels ( figure 5).
Furthermore, the pCTs were reconstructed with a Hann filter, varying the cut-off frequency to bring the imaging performance of the pCT system close to that of the xCT. As expected, the filter had a dual effect. On the one hand, it increased the blurring of the image, hence reducing the spatial resolution ( figure 4). On the other hand, it considerably decreased the noise magnitude of the image, i.e. the standard deviation, shifting at the same time the peak of the noise spectrum to lower frequencies ( figure 5, table 1).
Analysing the MTFs, it is noteworthy that the resolution level of the pCT system was different in the two background conditions (figure 4). This implies that the response of the system is nonlinear, in the sense that it depends on the level of noise and contrast, unlike the common xCT systems. The reason is the enormous impact of multiple scattering on proton trajectory compared to the x-ray one, and also its dependence on the traversed  material. In the case of insert-air contrast, the suitable Hann filter parameter value for matching pCT-xCT resolution is 0.60. On the other hand, the filter parameter value 0.65 is more suitable in the case of insert-water contrast. At the same time, the analysis of the NPS revealed that pCT has some potential for dose reduction in CT. In fact, adjusting the Hann filter so that the pCT had the same spatial resolution as the xCT ( / f f cut N = 0.65), at the same dose level the pCT images showed a lower noise magnitude than xCT ( figure 5(a)). As result, at the same dose level, there is no filter parameter matching both the xCT spatial resolution level and noise spectrum. Matching resolution levels and keeping the noise as low as possible would minimise errors in the voxel by voxel correlation of RSP and HU. As part of the work for the new calibration procedure based on the stabilised biological phantoms, we will investigate the impact of different resolution and noise levels between imaging modalities on the cross-calibration curve.
Varying the filter parameter value, we investigated the performance potential of the INFN pCT scanner. Recently,  compared two other prototype scanners using the same reconstruction algorithm without Hann windowing and the same spatial resolution metric but different beams and phantoms. Comparing the spatial resolution of their Dentin insert (RSP 1.495) in a blue wax body (RSP 0.980) with our Delrin insert (RSP 1.3652) in water (RSP 0.998), they obtained 0.62 lp mm −1 and 0.44 lp mm −1 for the pCT collaboration and ProtonVDA scanners, respectively, while we measured 0.72 lp mm −1 with the INFN scanner. However, the two phantoms had different materials and sizes (diameters of 18 cm blue wax in their study and 14 cm water + 1 cm PMMA in ours) and the insert distances from the phantom surfaces were different (about 3.2 and 3.5 cm), which are known to be two factors strongly influencing the spatial resolution in pCT (Krah et al 2018), together with many other factors such as beam quality and phantom positioning (Bopp et al 2014, Meyer et al 2020. Therefore, a direct comparison is not advisable. However, the obtained performance look-up tables allow us to easily adopt this analysis in future comparison between our pCT scanner and other xCT scanners for cross-calibration. Above all, the accuracy of the RSP values reconstructed by pCT is of paramount importance in the characterization of our system, in order to accurately verify the calibration of the xCT scanner or their eventual cross-calibration. The previous analysis of pure water cylinders showed an accuracy well below 1% (Scaringella et al 2023). In this study, with much more complex geometry and different material densities, the RSP accuracy was well below 1% (see supplementary material, tables 3 and 4). The resulting MAPE values were compatible within the uncertainties for all the filter parameters, revealing that there is no dependency to the filter windowing within the range of tested values. Moreover, they were compatible for all the inserts in both background cases, proving that even with different phantom density (air or water), and therefore different residual energies, the calorimeter response reconstructs the same RSP values. This is a finer check of the calibration procedure than the one described in Scaringella et al (2023). In addition, the MAPE values, although achieved with a small number of materials, are lower than the one reported in Dedes et al (2022) and Götz et al (2022) with the same reconstruction algorithm, demonstrating a praiseworthy response of our detectors and calibration procedure.
Finally, the results obtained in this study, through the updated calibration and reconstruction procedures, placed our pCT system among the others currently working with above-average RSP accuracy values and no clearly visible artefacts. The acquisition rate of 80-90 kHz is lower than the one achieved by other systems  and, together with a limited FOV, it makes direct patient application of the INFN pCT impractical. However, we are working on introducing the INFN pCT scanner as a clinical tool for a novel verification and cross-calibration approach in the proton treatment planning (Farace et al 2021), acquiring both pCT and xCT tomographies on heterogeneous biological phantoms.
Generally speaking, further improvements to the pCT system performances could result from adopting an iterative reconstruction algorithm. In principle, this might translate into a reduction of noise in both xCT and pCT images. However, as recently shown by Hansen et al (2016), distance-driven algorithms are able to produce high quality pCT images, with a strong reduction of computational time (i.e. about a factor 22). At the same time, the use of ions heavier than protons (i.e. helium or carbon ions) would allow improving spatial resolution and potentially reduce imaging dose. While dose reduction is an aspect of potential interest for future applications, the absorbed dose is not critical for the current study, being focused on phantom investigation.
In conclusion, the extensive analysis performed in this study confirms that our pCT is extremely accurate and it can be used as a reference RSP measuring method for the verification of the xCT calibration in proton treatment planning by scanning a dedicated phantom. Further work on the cross-calibration curve is required to choose the appropriate comparison condition between pCT and xCT scans. Finally, despite the nonlinear resolution, our data demonstrated that pCT could have some potential for dose reduction in CT.