XTI - differential phase, absorption, visibility images-3-rd

Calculation of differential phase, absorption, and visibility images acquired by grating interferometry using fast sinus fitting.

This program is dedicated to the X-ray Talbot Interferometry or XTI or grating inteferometry. This program calculates differential phase, absorption and visibility images, but it is using Levenberg-Marquardt sinusoidal fit. The Levenberg-Marquardt algorithm for fitting sinusoidal function uses Jacobians to find amplitude, phase and offset of sinusoidal function. The sinusoidal function is defined as a*sin(t + b) + c, where a is the amplitude, b is the phase shift and c is the offset. The differential phase image is defined as b_fg - b_bg, where b_fg is the phase shift for foreground with sample and b_bg is the phase_shift for background without sample. The absorption image is defined as c_fg/c_bg. So, it is the ratio between sinusoidal curve offset for foreground to the sinusoidal curve offset for background. Finally, the visibility image is defined as (a_fg/c_fg) / (a_bg/c_bg) for each pixel. To speed up Levenberg-Marquardt algorithm, I rewrote all matrices into the 1D matrix form. In addition, I am using matrix multiplication on the solely 1D matrices and matrix inversion calculation applied on the solely 1D matrices. Here, I am using only for cycles. I do not use matrix character of Matlab here, because this algorithm is designed as example for C++ code using only 1D arrays and for cycles. This algoritm was designed for speed up. It takes something more than 60 seconds to calculate all images using i7-8750H CPU. This algorithm is appropriate for reconstruction X-ray phase imaging data coming from X-ray grating interferometry and real time imaging.

The data attached to this m-script were measured in the laboratory of Prof. Atsushi Momose from Tohoku University in Sendai and his colleagues Y. Wu-san and H. Takano-san.