Optical EngineeringPerformance models of correlators with random and systematic phase errors
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Hybrid correlators are composed of numerous nonideal electronic and optical components that, to one degree or another, limit performance through unintended transformations of signals. Many of these eftects show up as phase errors at a spatial light modulator (SLM) plane. The errors can be described as random variables, or as systematic offsets from the correct phases, as appropriate. Sources of systematic phase errors include quantizing circuits, incorrect or nonlinear amplifier gain, limited range phase modulators and residual phase modulation of amplitude-mostly SLMs. Random phase errors arise from electronic noise and fabrication variations of SLMs. Several systematic and random filter plane errors are related through a single parameter that describes the amount of phase mismatch. A model of peak-to-noise ratio (PNR) is also presented that describes the combined effects of random and systematic errors. This expression contains the products of two functions, one that depends only on systematic, the other on random, phase mismatch. PNR is also a function of the number of pixels in the filter plane modulator and a normalized moment of the amplitude of the image spectrum. The model is useful for developing phase error budgets for correlation systems.