A synthetic aperture radar (SAR) achieves a high azimuth resolution by illuminating targets with multiple pulses and using the Doppler history to synthesize a large antenna. When combining the pulses, it is normally assumed that the targets are stationary, and that their reflectivity is independent of time. The topic of this thesis is the processing of SAR images where the the targets have a time-dependent reflectivity. One can imagine, for instance, a ship rolling in a rough sea. One possible way of processing such targets is described by R. Keith Raney. The goal of this thesis is to provide a well structured introduction into Raney's formalism on partially coherent targets, and to investigate a focusing strategy for scenes where the targets have different coherence times. The image formation processes of a synthetic aperture radar is thoroughly discussed, and a one-dimensional model of the azimuth dimension is introduced. Raney's formalism is compared to this model and found to be formally correct. A partially coherent point target is simulated, and Raney's formalism is tested for the purpose of target detection in the presence of scene partial coherence. It is shown that the whole system, including partial coherence in both scene and processor, behaves as a Gaussian low-pass filter weighted by the scene autocorrelation function and the processor coherence function
