XTI - differential phase, absorption and visibility images

This m-script calculates differential phase, absorption, and visibility images acquired by X-ray Talbot or grating interferometry.

This m-script takes M=5 foreground and M=5 background images obtained by fringe scanning technique in X-ray Talbot interferometry or grating interferometry. The M=5 is the number of steps in fringe scanning technique or M=5 movements of amplitude grating. Each raw image for foreground (fg) and background (bg) has size of 1536 x 512 pixels (H x V). The raw foreground and raw background images are encoded as unsigned 16 bit integers. In each pixel, 5 intensity values for foreground and 5 intensity values in background generate sinusoidal curve for foreground and background. This sinus curve for foreground and background is fitted with sinus function using Levenberg-Marquardt method. The difference between phase of sinus fit for foreground and phase of sinus fit for background generates differential phase image (b_fg - b_bg). The absorption image is the ratio beteween sinus fit offset for foreground and sinus fit offset for background (c_fg / c_bg). Finally, the visibility image is calculated according to the (a_fg/c_fg) / (a-bg/c_bg). The sinus function for foreground is a_fg * sin(t + b_fg) + c_fg, and for background is a_bg * sin(t + b_bg) + c_bg. So, a is here amplitude, b is the phase, and c is the offset. The foreground and background raw images were measured by Prof. Atsushi Momose laboratory at Tohoku University in Sendai.