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

Abstract

In order to measure the radial displacements of facets on surface of a growing spherical Cu 2-δ Se crystal with sub-nanometer resolution, we have investigated the reliability and accuracy of standard method of Fourier analysis of fringes obtained applying digital laser interferometry method. Guided by the realistic experimental parameters (density and orientation of fringes), starting from 2-dimensional model interferograms and using unconventional custom designed Gaussian filtering window and unwrapping procedure of the retrieved phase, we have demonstrated that for considerable portion of parameter space the non-negligible inherent phase retrieval error is present solely due to noninteger number of fringes within the digitally recorded image (using CCD camera). Our results indicate the range of experimentally adjustable parameters for which the generated error is acceptably small. We also introduce a modification of the (last part) of the usual phase retrieval algorithm which significantly reduces the error in the case of small fringe density.

New Insights into the Setting Processes of Glass Ionomer Cements from Analysis of Dielectric Properties

“…The digitally stored interferograms captured by a CCD camera (at sampling rate of 30 frames per second) were analyzed by a custom‐made computer program based on Fast Fourier Transform routine which extracts the mean phase values for each interferogram. Our modified algorithm improved the retrieved phase determination reliability and thus the theoretical resolution of sample dimension change to less than 0.3 nm . Real experimental resolution is however reduced to about 10 nm due to mechanical vibrations.…”

“…Our modified algorithm 24 improved the retrieved phase determination reliability and thus the theoretical resolution of sample dimension change to less than 0.3 nm. 25 Real experimental resolution is however reduced to about 10 nm due to mechanical vibrations. Their influence (on reliability of time-dependent phase changes reconstruction as well as on measurement resolution) is minimized by high sampling frequency and further original improvements in the phase unwrapping algorithm.…”

Possible burst-like facet growth mode at high temperatures

“…These refinements have enabled us to achieve nanometre resolution in vertical facet displacement. We have recently made new improvements to the method applied [26].…”

Effective procedure for determination of unknown vibration frequency and phase using time-averaged digital holography

“…by recording and analyzing the two dimensional interference patterns (fringes) created by reflection of laser beam from the object. If the object vibrates harmonically, the interference fringes locally change their phase according to the sinusoidal law, [20,21]. In order to minimize the effects of noise, we have calculated the phase differences between subsequent snapshots, and retrieved the particular phases ( ) ψ t from these differences.…”