Synthesis of three-dimensional light fields with binary spatial light modulators

Computation of a binary spatial light modulator (SLM) pattern that generates a desired light field is a challenging quantization problem for which several algorithms have been proposed, mainly for far-field or Fourier plane reconstructions. We study this problem assuming that the desired light field is synthesized within a volumetric region in the non-far-field range after free space propagation from the SLM plane. We use Fresnel and Rayleigh-Sommerfeld scalar diffraction theories for propagation of light. We show that, when the desired field is confined to a sufficiently narrow region of space, the ideal gray-level complex-valued SLM pattern generating it becomes sufficiently low pass (oversampled) so it can be successfully halftoned into a binary SLM pattern by solving two decoupled real-valued constrained halftoning problems. Our simulation results indicate that, when the synthesis region is considered, the binary SLM is indistinguishable from a lower resolution full complex gray-level SLM. In our approach, free space propagation related computations are done only once at the beginning, and the rest of the computation time is spent on carrying out standard image halftoning.