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 opti cs depends intimately both on the physical characteristics; of the particul ar spatial light modulator (SLM) and on the particular algorithms that map the ideal signal into the available modulation range of the SLM. Since prac tical affordable SLMs represent only a limited range of values in the compl ex plane (e.g., phase-only or quantized phase), numerous approaches have be en reported to represent, approximate, encode or map complex values onto th e available SLM states. The best approach depends on the space-bandwidth pr oduct (SBWP) of the signal, number of SLM pixels, computation time of encod ing, the required response time of the application, and the resulting perfo rmance 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 f requency plane and that emphasize the fidelity of the approximated Fourier transform over maximization of diffraction efficiency and minimization of a pproximation error. Frequency-dependent diffraction efficiency (due to pixe l fill factor of discrete SLMs or resolution of spatially continuous SLMs) is also evaluated as a factor that can limit usable SBWP and possibly modif y the choice of encoding method. (C) 2001 Society of Photo-Optical Instrume ntation Engineers.