A perturbation method is presented for reconstructing phase from uncorrupted amplitude measurements in synthetic aperture radar (SAR) imaging via a wave equation governing SAR data and a Riccati equation that relates the amplitude and phase functions of SAR data. The two wave equations governing SAR data at two temporal frequencies of the radar signal are combined to derive a method to reconstruct complex phase errors, i.e., fading as well as loss of coherence, that vary linearly with respect to the radar signal's temporal frequencies.<>