Theoretical modeling and numerical simulation of a light-field detector for x-ray differential phase contrast imaging

Most recently, a novel color-encoding light-field detector based on perovskite material has been demonstrated for x-ray differential phase contrast (DPC) imaging. However, it lacks performance evaluation and comparison between such a novel light-field detector and a widely used grating interferometer before applying it into medical imaging field.

This study aims at evaluating and comparing the DPC imaging performance of the light-field detector and the grating interferometer.

In this work, a mathematical signal model was developed for the color-encoding perovskite light-field detector designed for x-ray DPC imaging. Specifically, the beam refraction angle was modeled based on the changes in the emitted color within the standard CIE1931 color space. Upon it, noise responses were derived. Numerical simulations were conducted to compare the sensitivity and signal variance of the perovskite light-field detector with those of a generic grating interferometer system. Additionally, impacts of the polychromatic x-ray beam and the Compton scattering were also investigated.

It was found that the sensitivity of the perovskite light-field detector may surpass that of the grating interferometer if its color depth exceeds 30-bit (three 10-bit color channels). For perovskite light-field detectors, the signal noise increases as the detected refraction signal increases. In addition, polychromatic x-ray beam adds bias to the retrieved DPC signal, but has slight impact on the signal noise. Compton scattered x-ray photons could dramatically change the retrieved DPC signal.

This study demonstrates that the novel perovskite light-field detector may not be suitable for medical grade DPC imaging due to the inevitable Compton scatters. However, it might be a promising alternative to the grating interferometer in developing state-of-the-art scientific DPC imaging instruments for small sample ( $\le 2\mathrm{mm}$ ), in which the impact of Compton scatters could be ignored.