Doppler asymmetric spatial heterodyne (DASH) interferometry is a novel concept for observing atmospheric winds. This paper discusses a numerical model for the simulation of fringe patterns and a methodology to correct fringe images for extracting Doppler information from ground-based DASH measurements. Based on the propagation of optical waves, the fringe pattern was modeled considering different angular deviations and optical aberrations. A dislocation between two gratings can introduce an additional spatial modulation associated with the diffraction order, which was seen in laboratory measurements. A phase correction is proposed to remove phase differences between different row interferograms, which is the premise for calculating the average interferogram to improve the signal-to-noise ratio. Laboratory tests, simulation results, and Doppler velocity measurements indicate that a matrix determined in the laboratory can be applied to correct interferograms obtained from ground-based DASH measurements.