X-ray Talbot interferometry, differential phase image

This m-file calculates the differential phase image measured by X-ray Talbot or grating interferometry

The differential phase image is calculated from 5 foreground and 5 background images measured by X-ray Talbot interferomerty. The sample was polypropylene sample. In the X-ray measurement, there were phase and amplitude gratings. The amplitude grating was used for scanning. The amplitiude grating in fringe scanning technique was moved five times. Therefore, M parameter is equal to 5. The measured images have size 1536 x 512 pixels (H x V). In other words, 1536 columns and 512 rows. The foreground and background images are encoded as unsigned 16 bit images with little endian byte order. The logic here is that intensity values for single pixel for different amplitude grating displacements produce sine curve. You could do sinusoidal fitting, but I use here Prof. Atsushi Momose approach. The intensity values in single pixel for 5 amplitude grating displacements are used to calculate complex number for this single pixel. The argumnet of this complex number can be calculated using angle function. You can then calculate argument for every pixel of foreground and background images. The argument of compelx number is actually angular value. The phase values or angles for foreground are stored in phase_image_fg. The phase values or angles for background are stored in phase_image_bg. The subtraction of phase_image_fg and phase_image_bg generates differential phase image. The final differential phase image is stored as double or 64bit real number image with little endian byte order as well. The raw images attached to this contribution were measured by laboratory of Prof. Atsushi Momose from Tohoku University in Sendai, Japan. You can try to calculate absorbtion or visibility (dark field) image from the image data.