Diffractive-optical-element design optimization of pattern-recognition filters

Abstract

Diffractive optical element (DOE) design techniques can be applied to the generation of pattern recognition filters for optical correlators, in which case the spatial light modulator (SLM) in the filler plane is thought of as a real-time DOE. The designer must first select the desired complex pattern recognition filter and then apply DOE design techniques to map the fully complex function onto the limited dynamic range SLM. To illustrate the procedure, we apply the techniques to the problem of implementing a matched filter with limited dynamic range Fourier plane SLM’s. We use computer simulations to evaluate the effectiveness of the technique. We quantify the performance by measuring the mean squared error between the ideal matched output and output from quantized filters. Numerical simulations indicate that the DOE method yields a significant improvement over direct quantization. The improvement in mean squared error comes, however, at the expense of light efficiency. The DOE technique has been applied to design of matched filters with binary phase, ternary phase, and phase-only SLM’s for coherent as well as incoherent optical correlators. The additional phase freedom in the incoherent design results in improved performance, but incoherent systems are limited to correlation with real positive reference scenes. A proof-of-principle laboratory experiment has been constructed to complement the numerical simulations.