Sensitivity in X-ray grating interferometry on compact systems

Abstract

The optimization of compact X-ray grating interferometry systems is crucial for the progress of this technique in industrial devices. Here, an analytical formulation for the sensitivity of the phase contrast image acquisition is derived using previous results from noise analyses. Furthermore, experimental measurements of the sensitivity for different configurations are compared, providing further insight into the dependence on polychromatic radiation. Finally, strategies for the geometrical optimization are given.

Performance and optimization of X-ray grating interferometry

“…In the literature, α min has been referred to as the sensitivity [11,12]. As the sensitivity has also been defined differently [10,20], here α min is just referred to as the smallest detectable refraction angle.…”

“…For the differential phase-contrast image [1,2] of a grating interferometer, it can be shown [12] that the SNR is given by…”

“…However, the counterpart of long arrangements is the inverse quadratic relation with the flux for a given source and detector system. Taking into account both effects requires us to consider the timedependent α min [12]. Using equations (2.2) and (2.3) and the geometric relation s = d + l, for the Talbot interferometer, the factor p 2 /d becomes…”

“…The refraction angle α is geometry independent, and therefore the minimization of σ α can be used for the optimization of the geometry [11,12]. Here, σ α is defined as the smallest detectable refraction angle and is given by…”

“…For the optimization, the concept of the smallest detectable refraction angle is used, which has also been referred to as the resolution of the refraction angle [10] or the sensitivity [11,12].…”