Regularized phase shift estimation in X-ray grating interferometry

Abstract

A method for the estimation of the phase shift from beam deflection measurements in one direction is proposed in the context of X-ray grating interferometry. The common approach, which consists in simply integrating the measurements along this direction, produces typical line artifacts due to noise and missing information. Therefore, an algorithmic method is proposed, based on independence of measurement noise to differential phase and on the prior knowledge that the unmeasured phase derivatives are normally distributed over the field of view. This is shown to be equivalent to a Tikhonov regularization by a difference operator. A computationally tractable formulation of the optimal solution is derived. The method is demonstrated on experimental data and quantitatively evaluated by numerical simulations.