Iterative synthesis of binary inline Fresnel holograms for high-quality reconstruction in divergent beams with DMD

Abstract

Aim of this paper is formation of single focused diffraction order using binary amplitude modulation for digital micromirror device (DMD) applications. This can be achieved by using inline binary Fresnel holograms with divergent incident beam. However, extremely low reconstruction quality and diffraction efficiency of such holograms, synthesized by conventional means, prevent it. Here, we present new iterative method of synthesis of binary inline Fresnel holograms with much higher image reconstruction quality and diffraction efficiency compared to standard technique of hologram direct calculation. Synthesis procedure was carried out in two stages. The first stage of the new technique is based on Gerchberg-Saxton algorithm with two principal differences. First one is that synthesized diffractive optical element (DOE) is not a phase one, but an inline binary amplitude hologram. And second difference is that incident wavefront is spherical instead of a plane one. The second stage includes an application of the direct search with random trajectory method which greatly improves hologram characteristics by consequent processing of every pixel in it. The resulting binary inline Fresnel holograms in comparison to ones, synthesized using direct calculation method, have up to 11 times lower reconstruction error and up to 4 times higher diffraction efficiency. Results of optical reconstruction using DMD also demonstrate superiority of the new approach.