Tomography of dark‐field scatter including single‐exposure Moiré fringe analysis with X‐ray biprism interferometry—A simulation study

Abstract

In this work we present tomographic simulations of a new hardware concept for X-ray phasecontrast interferometry wherein the phase gratings are replaced with an array of Fresnel bi-prisms, and Moiré fringe analysis is used instead of "phase stepping" popular with grating-based setups.Methods: Projections of a phantom consisting of four layers of parallel carbon microfibers is simulated using wave optics representation of X-ray electromagnetic waves. Simulated projections of a phantom with preferential scatter perpendicular to the direction of the fibers are performed to analyze the extraction of small angle scatter from dark field projections for: 1) bi-prism interferometry using Moiré fringe analysis;2) grating interferometry using phase stepping with 8 grating steps; and 3) grating interferometry using Moiré fringe analysis. Dark field projections are modeled as projections of voxel intensities represented by a fixed finite vector basis set of scattering directions. From the simulated projection data, an iterative MLEM algorithm reconstructs the coefficients of a fixed set of seven basis vectors at each voxel representing the small angle scatter distribution.Results: Results of reconstructed vector coefficients are shown comparing the three simulated imaging models. The single-exposure Moiré fringe analysis shows increase in noise because of 1/8th the number of projection samples but also is obtained with less dose and faster acquisition times. Furthermore, replacing grating interferometry with bi-prism interferometry provides better CNR. Conclusion:The simulations demonstrate the feasibility of the reconstruction of dark-field data acquired with a bi-prism interferometry system. With the potential of higher fringe visibility, bi-prism interferometry with Moiré fringe analysis might provide equal or better image quality to that of phase stepping methods with less imaging time and lower dose.

X‐ray bi‐prism interferometry—A design study of proposed novel hardware

“…In our previous paper, 32 we performed simulations using wave optics to evaluate X‐ray phase‐contrast imaging with grating interferometry using phase stepping and with bi‐prism interferometry using single‐exposure Moiré fringe analysis. Results of reconstructed vector coefficients of small‐angle scatter showed that bi‐prism interferometry with single‐exposure Moiré fringe analysis has an increase in noise compared to grating interferometry using phase stepping because of one‐eighth the number of projection samples but provides better contrast‐to‐noise ratio (CNR) due to better photon flux with less dose and faster acquisition times.…”

An Analytical Algorithm for Tensor Tomography From Projections Acquired About Three Axes

“…In our work we performed simulations evaluating the model of [8], [67] with the reconstruction of coefficients for a fixed basis set of 7 vectors. The coefficients were reconstructed from Moiré fringe analysis of single-exposure dark-field projections obtained from X-ray bi-prism interferometry [69]. Wieczorek et al [12] modified the forward model [8], [67] to develop an anisotropic X-ray dark-field tomography (AXDT) method by replacing the discretization of the scatter function as a fixed basis set of vectors at each voxel with a spherical harmonic expansion.…”

“…In our previous work we performed simulations evaluating the reconstruction of the coefficients for a fixed basis set of 7 vectors from Moiré fringe analysis of projections of a single-exposure of dark-field scatter obtained from X-ray bi-prism interferometry [69]. To obtain a tensor representation would have involved performing a second step of fitting the estimated vector coefficients to an ellipsoidal representation of the tensor at each voxel [8], [67].…”