A theory of the effect of hard limiting and other distortions upon the quality of microwave images

Abstract

This paper adds quantitative confirmation to the assertions of previous writers that the phase of the signal received in the aperture contains the preponderance of the information useful for image formation. An easily calculable metric is established for judging the extent of the alteration of an image due to an arbitrary distortion of the signal in the aperture or of the imaging kernel in the signal processor. Given some known or measurable amplitude or phase nonlinearity in the detector at the front end of the measurement system, it is possible to judge whether such nonlinearity is tolerable or whether it must be removed. Subjective viewing tests confirm the validity of the metric. High angular resolution microwave images are used to test the theory. It is demonstrated that hard limiting the input signals to a phased array preserves much of the image integrity; amplitude-only information, on the other hand, destroys it. Only one bit of phase information sometimes suffices. Two bits of signal phase and 2-bit phase quantization of the exponential kernel in the signal processor results in an extraordinarily simple signal processor that produces surprisingly good imagery.