Abstract: Disclosed is a method of reconstructing a representative detailed phase image from a set of fringe pattern interferogram images of an object. The images are captured by an x-ray interferometer having a crossed diffraction grating. A set of captured fringe pattern interferogram images from the x-ray interferometer are provided, the set comprising no more than eight captured fringe pattern interferogram images. The method determines an estimate of an absorption parameter (a), two-dimensional amplitude modulation parameters (mx, my), and two-dimensional phase modulation parameters (?x and ?y) from a closed-form solution using the received set of captured fringe pattern interferogram images, and reconstructs the representative detailed phase image using the parameter estimates.