Propagation of quantization error in a computer-generated hologram design algorithm

Abstract

One technique for designing Fourier holograms is an iterative algorithm wherein constraints are alternately placed on the reconstruction, or response, of the hologram and on the hologram itself. Although the ability of the algorithm to reduce quantization error is known,1 the relationship between the quantization scheme and quantization error as a function of iteration number has not been previously considered. A preliminary model for the propagation of quantization error within the iterative algorithm has been developed and is presented. The discussion is motivated using the dual-phase construction of a Fourier hologram.2 Dual-phase construction allows for the comparison of several different, but practical, quantization schemes, including minimum-distance quantization, closest-phase quantization, and polar quantization. Analyses indicate that the relative performance of the different quantization schemes changes as the number of iterations increases. Experimental verification of these results is presented.