Reducing phase retrieval errors in Fourier analysis of 2-dimensional digital model interferograms

In order to measure the displacements of facets on a growing spherical Cu2−δSe crystal with sub-nanometre resolution, we investigated the reliability and accuracy of standard method of Fourier analysis of digital laser interferograms. Guided by realistic experimental conditions (two-dimensional (2D) interferograms), starting from 2D model interferograms and using original custom designed Gaussian filtering window and multistage unwrapping procedure of the retrieved phase, we demonstrate for a considerable parameter range the non-negligible inherent phase retrieval error due to non-integer number of fringes within the digital image. Our results indicate an intermediate parameter range where the error is acceptably small. We introduce an algorithm modification that significantly reduces the error, especially for low and high fringe densities. In the experimentally most common case of diagonal fringes the reduced error is an order of magnitude smaller than for nearly one-dimensional case within almost entire parameter space.