Improved algorithm for processing grating-based phase contrast interferometry image sets

Grating-based X-ray and neutron interferometry tomography using phase-stepping methods generates large data sets. An improved algorithm is presented for solving for the parameters to calculate transmissions, differential phase contrast, and dark-field images. The method takes advantage of the vectorization inherent in high-level languages such as Mathematica and MATLAB and can solve a 16 × 1k × 1k data set in less than a second. In addition, the algorithm can function with partial data sets. This is demonstrated with processing of a 16-step grating data set with partial use of the original data chosen without any restriction. Also, we have calculated the reduced chi-square for the fit and notice the effect of grating support structural elements upon the differential phase contrast image and have explored expanded basis set representations to mitigate the impact.