The general problem of a partially coherent synthetic aperture radar (SAR) imaging a scene that is subjected to random fade is considered. The impulse response, frequency response and response to extended random fields are formally derived. Explicit results are obtained using gaussian functions to describe the SAR, its coherence and the scene coherence. Results converge appropriately on known results for cases treated previously. New results are presented concerning all three classes of fading input scenes. The results are applied to the problem of SAR imagery of oceanic waves, with comments on certain aspects of Seasat-A SAR data as appropriate.