Transfer functions for partially coherent systems with applications to SAR

An impulse response function and a transfer function applicable to partially coherent systems are presented. The general formulation is applied to synthetic aperture radar imaging systems to derive closed form results. Properties are derived for partially coherent systems that describe performance dependance on system phase and amplitude match to input signal characteristics, and to system and signal partial coherence. Such systems are shown to be energy conservative in the event of coherence variations. Output spectral properties that describe the dependance of multiplicative Rayleigh noise on input signal coherence, system coherence and phase match are presented. It is shown that the mean output from a SAR for a random distributed scene input is not dependent on system focus, system coherence or scene coherence, whereas imagery of scene detail is dependent on these parameters.