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

Abstract

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 RayleighSommerfeld 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.

Calculation of the scalar diffraction field from curved surfaces by decomposing the three-dimensional field into a sum of Gaussian beams

“…Here, U and a are vectors that have lengths T and N, respectively; G is a T × N matrix. Note that the total number of parallel Gaussian beams used in the decomposition is equal to N (the degree of freedom of the signal space), that is, MK N. We form the system matrix G as G g 11 r − s 11 jg 12 r − s 12 j…jg MK r − s MK (21) and the coefficients vector a as a a 11 ; a 12 ; …; a MK T :…”

“…(24). The mentioned expression, which is based on the Rayleigh-Sommerfeld diffraction model, gives the scalar 3D field corresponding to a modulated Gaussian window function quite accurately even for nonparaxial cases [8,21].…”

Full-complex amplitude modulation with binary spatial light modulators

“…Thus, there is a limit to the degree of blurring we can tolerate. It is well known that the light field produced by a pixellated SLM consists of diffraction orders, which are shifted, modulated, and dispersed versions of each other, so they essentially carry the same information [15,29,30]. The order that has the lowest frequency content is called the central order.…”

“…One approach is to devise coding methods such that the ideal complex-valued CGH that generates a desired light field is encoded in a CGH that is suitable for writing on the physical SLM [5,6]. Many different encoding methods for multilevel amplitude-only, multilevel phase-only, and binary SLMs have been proposed [7][8][9][10][11][12][13][14][15]. In these methods, when the observation region is considered, the actual SLM behaves like a lower-resolution full-complex SLM.…”

Non-iterative phase hologram computation for low speckle holographic image projection

“…Many algorithms are proposed for various SLM types. [18,19] investigate the CGH computation for amplitude-only and amplitude mostly SLMs, while [20,21] explore the binary SLM case. Most algorithms, however, are proposed for phase-only SLMs, due to their superior light efficiency and multilevel modulation capability [22][23][24][25][26][27].…”