Fundamental properties of spatial light modulators for the approximate optical computation of Fourier transforms: a review

The performance of optical computers that include programmable Fourier optics depends intimately both on the physical characteristics of the particular spatial light modulator (SLM) and on the particular algorithms that map the ideal signal into the available modulation range of the SLM. Since practical affordable SLMs represent only a limited range of values in the complex plane (e.g., phase-only or quantized phase), numerous approaches have been reported to represent, approximate, encode or map complex values onto the available SLM states. The best approach depends on the space-bandwidth product (SBWP) of the signal, number of SLM pixels, computation time of encoding, the required response time of the application, and the resulting performance of the optical computer. My review of various methods, as applied to most current SLMs, which have a relatively low number of high cost pixels, leads me to recommend encoding algorithms that address the entire usable frequency plane and that emphasize the fidelity of the approximated Fourier transform over maximization of diffraction efficiency and minimization of approximation error. Frequency-dependent diffraction efficiency (due to pixel fill factor of discrete SLMs or resolution of spatially continuous SLMs) is also evaluated as a factor that can limit usable SBWP and possibly modify the choice of encoding method.