Investigating numerical reconstruction quality and sparsity constraints on the holographic fringe pattern in digital holography

Abstract

In this paper, we investigate quality factors of numerical reconstruction with a small number of signals based on sparsity from a holographic fringe pattern. Holographic fringe pattern generated by Fresnel diffraction is a complex amplitude and sparse distribution in frequency domain. The sparsity of holographic fringe pattern could play a key role in reconstruction quality assessment in compressive holography. In this paper we have investigated sparsity constraint on holographic fringe pattern which influences the overall quality of numerically reconstructed data. In addition, we have investigated reconstruction quality for various subsampling methods including uniform sampling, random sampling, variable density sampling, and magnitude-based sampling. Experiments have been conducted to evaluate reconstruction qualities on sparsity constraints and sampling patterns. Experimental results indicate that the way to extract the sparse signals could significantly affect the quality of the numerical reconstruction in digital holography and visually plausible reconstruction could be obtained with a sparse holographic fringe pattern.