Approximated Wavefront Composition for Computer-Generated Holograms Based on Tiny Logic Operations

Abstract

Accelerating the calculation of computer-generated holograms (CGHs) is an urgent requirement for realizing practical electro-holography for three-dimensional (3D) displays. Although many algorithms have been developed for fast CGH calculations, sufficient acceleration of the CGH calculations is yet to be achieved. Simplifying CGH calculations using the redundancy of a hologram while recording a 3D image is a promising way for CGH acceleration. That is, the feature that a hologram can reproduce the 3D image almost correctly even if it was recorded with deviations originating from the approximation, etc., can be used to perform the CGH calculations rapidly. Therefore, this study proposes an approximation method for trigonometric functions, which have a heavy computational load and are heavily used in the composition process of the wavefronts emitted from a virtual 3D object such as point-light sources. The proposed method substitutes sin or cos functions with tiny logic operations that are expected to have lower computational loads than the normal functions for fixed or floating precision numbers. Numerical and optical experiments showed that the proposed method can calculate CGH 2.20 times faster on a central processing unit (CPU) and 8.43 times faster on a graphics processing unit (GPU) than the normal implementation, while maintaining sufficient image quality. The proposed method is not only effective in CPU and GPU implementations but also is expected to make a significant contribution to future circuit implementations for CGH-specific computers.