Performance and optimization of X-ray grating interferometry

Abstract

The monochromatic and polychromatic performance of a grating interferometer is theoretically analysed. The smallest detectable refraction angle is used as a metric for the efficiency in acquiring a differential phase-contrast image. Analytical formulae for the visibility and the smallest detectable refraction angle are derived for Talbot-type and Talbot-Lau-type interferometers, respectively, providing a framework for the optimization of the geometry. The polychromatic performance of a grating interferometer is investigated analytically by calculating the energydependent interference fringe visibility, the spectral acceptance and the polychromatic interference fringe visibility. The optimization of grating interferometry is a crucial step for the design of application-specific systems with maximum performance.

Sensitivity-based optimization for the design of a grating interferometer for clinical X-ray phase contrast mammography

“…The visibility decay produced as the Talbot order is increased is caused by the corresponding reduction in the spectral acceptance of the interferometer. This trend is confirmed by the formula derived in [29] for polychromatic visibility, as can be seen on the second column of Table 3. The difference in absolute values between the latter and our calculations is due to the fact that this formula assumes perfect spatial coherence and gratings, whereas our simulations take into account the finite focal spot size [34], limited grating heights, grating wafer thicknesses and detector stopping power.…”

“…A π phase grating was selected for our optimization procedure, since for Talbot orders higher than 1, the use of a π/2 grating causes a significant visibility drop due to the sign inversion of the fringes for some energies of the input spectrum. This negative effect becomes more relevant as the Talbot order increases, while for Talbot order one it conversely causes a slight visibility improvement, because the sign inversion does not occur in this case [29]. However, the latter improvement is so small that can be disregarded.…”

Diagnostic Accuracy of Quantitative and Qualitative Phase-Contrast Imaging for the ex Vivo Characterization of Human Coronary Atherosclerotic Plaques

“…Recently, other investigators reported a way to solve this (32), and new x-ray detector systems are currently under development (27).…”

Improving radiation dose efficiency of X-ray differential phase contrast imaging using an energy-resolving grating interferometer and a novel rank constraint

“…The interferometer system used in this study was operated at the first fractional Talbot order, at which the fringe visibility of the diffraction fringe pattern drops gradually when the beam energy deviates from the designed operation energy of the interferometer. At higher fractional Talbot orders, the fringe visibility may reach zero at multiple energy levels [12,13]. In practice, however, the width of an energy bin width is always finite, and the energy resolution of the PCD is always limited, As a result, these theoretical zero-crossings of the visibility-energy curve are usually smeared out with polychromatic x-ray radiations.…”

“…Therefore, an optimal energy bin width should be selected to balance the drops in fringe visibility and the number of detected photons within the selected energy bin [10,11]. While it is straightforward to search for an optimal energy window when the system is operated at the first Talbot order, the definition of an optimal energy window may become tricky when the system is operated at higher Talbot orders [12,13] due to the existence of multiple local maxima and minima in visibility-energy response curve.…”