An image reconstruction method for differential phase contrast imaging includes receiving data corresponding to a signal produced by an X-ray detector and corresponding to X-rays that passed through a subject and a grating system to reach the X-ray detector. The method also includes performing a fringe analysis on the received data. The fringe analysis includes a non-integer fringe fraction correction utilizing one or more adapted basis functions in the Fourier domain to determine one or more Fourier coefficients. A differential phase image of the subject is generated by utilizing the one or more Fourier coefficients.