Fundamental properties of spatial light modulators for Fourier transform applications

摘要

The performance of Fourier transform optical processors, e.g. optical correlators, beam steering systems, associative memories, etc., depends intimately both on the physical characteristics of the particular spatial light modulator (SLM) and on the particular algorithms that map the signal into the available modulation range of the device. For the most general Fourier systems the information/signal is complex-valued. This is an essential requirement for multi-spot beam steering systems and composite pattern recognition filters. Since practical and/or affordable SLM's only represent a limited range of values in the complex plane (e.g. phase-only or quantized phase), numerous approaches have been proposed and demonstrated for representing, approximating, encoding or mapping complex values to the available SLM states. The best approach depends on the space bandwidth product of the signal, the number of SLM pixels, the computation time of the encoding algorithm, the time available for the application, and the quality of the optical processor, as measured by an application-specific performance metric. Based on the low pixel count and the high cost per pixel of most current SLM's we argue for encoding algorithms that map one signal value to one pixel value, as opposed to group-oriented encoding. This maximizes the usable area of the frequency plane. We also recommend algorithms that maximize the fidelity over the entire frequency range as opposed to maximum diffraction efficiency/minimum mean squared error design. These ideas are illustrated with several simulated and experimental results for pseudorandom, minimum Euclidean distance, error diffusion and hybrid/blended encoding algorithms.