Comparison of reconstruction algorithms in lens-less Fourier transform digital holography

Abstract

The different reconstruction algorithms are investigated and the reconstructed images are presented in lensless Fourier transform digital holography. The most employed three algorithms, all based on the fast-Fourier-transform, are: the convolution algorithm, the angular spectrum algorithm, and the Fresnel algorithm. With the convolution algorithm and angular spectrum algorithm, there is an optimal reconstruction distance where the pass-band range of the transfer function is the largest. Then the whole reconstructed image with the highest resolution can be acquired. When the distance is different from the optimal distance, the size of the reconstructed image may vary with the distance and may disappear from the field of view in some cases. In order to obtain the whole image, two methods are proposed. However, at this time the resolution of the reconstructed image becomes lower. When the distance is smaller than the optimal distance, the whole image can be obtained, but the resolution of the image also decreases. The Fresnel algorithm is performed by using a single fast-Fourier-transform. With Fresnel algorithm, the same reconstructed images can be obtained with the different reconstruction distances and the reconstruction is better than with the convolution algorithm and the angular spectrum algorithm.