3D Compton scattering imaging: study of the spectrum and contour reconstruction

TL;DR

This paper explores 3D Compton scattering imaging, demonstrating that contour reconstruction of electron density maps is feasible using first- and second-order scattered data, with successful implementation on synthetic and Monte Carlo data.

Contribution

It introduces a mathematical framework for contour reconstruction from first- and second-order Compton scattering data, highlighting the structural smoothness of second-order radiation and its implications.

Findings

Second-order scattered radiation is smoother than first-order.

Contours are primarily encoded in first-order scattering data.

Reconstruction scheme is validated on synthetic and Monte Carlo data.

Abstract

3D Compton scattering imaging is an upcoming concept exploiting the scattering of photons induced by the electronic structure of the object under study. The so-called Compton scattering rules the collision of particles with electrons and describes their energy loss after scattering. Although physically relevant, multiple-order scattering was so far not considered and therefore, only first-order scattering is generally assumed in the literature. The purpose of this work is to argument why and how a contour reconstruction of the electron density map from scattered measurement composed of first- and second-order scattering is possible (scattering of higher orders is here neglected). After the development of integral representations for the first- and second-order scattering, this is achieved by the study of the smoothness properties of associated Fourier integral operators (FIO). The second-order scattered radiation reveals itself to be structurally smoother than the radiation of first-order indicating that the contours of the electron density are essentially encoded within the first-order part. This opens the way to contour-based reconstruction techniques when using multiple scattered data. Our main results, modeling and reconstruction scheme, are successfully implemented on synthetic and Monte-Carlo data.