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

Abstract

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.

Speckle reduction in holographic projection using temporal-multiplexing of spatial frequencies

“…By illuminating the SLM with a plane wave and, if nec essary, by using refractive optics such as a lens, the projected in tensity is generated across the fan-out plane [5]. During this pro jection process and due to the SLMs technical characteristics, the signal across the fan-out plane is characterized by [6,7]: i) Multiple replicas of the original projected intensity called diffraction orders resulting from the discrete nature of SLMs, ii) An envelope function modulates the diffraction pattern which depends on the finite size and the shape of the active area of the pixel, iii) A dc term, i.e. a bright spot arises in the center of each replica which originates from the light diffracted by the in active area between the pixels, 978-1-4799-1369-5/13 /$31.00©2013 IEEE iv) Speckle arise because in many cases of the iterative approaches the result is a phase distribution with a statistical property.…”

Multifocal multiphoton microscopy with adaptive optical correction

“…The phase mask corresponds to the Fourier transform of the desired intensity distribution. The ability of the SLM to represent complex--valued images enables intensive information processing functions using the Fourier transform properties of light (Cohn, 2001 …”

Spiking voltages for faster switching of nematic liquid-crystal light modulators

“…The increased on-axis light is a result of the expected decrease in diffraction efficiency with increase in spatial frequency. 10 In addition to speeding up the transition, movies of the diffraction patterns 11 show that spiking reduces both the time that the "ghost" or residual spot remains and the amount of energy that is scattered into the zero-order, on-axis spot.…”