Application of two-dimensional warped discrete Fourier transform to nonlinear two-dimensional amplitude demodulation

Abstract

This study introduces a novel nonlinear two-dimensional (2D) warped discrete Fourier transform (WDFT) amplitude demodulation method that allows higher-resolution measurements on specific two-dimensional regions of interest. The specific application in this study addresses the need for the nonlinear 2D amplitude demodulation of fringe-wave fields acquired by a deformed Mach–Zehnder interferometer. The proposed method exploits the properties based on which the WDFT can obtain frequency spectra sampled at non-equidistant intervals and the symmetry of the Fourier transform. As a result, this 2D-WDFT-based method can be used to nonlinearly demodulate the amplitude of the 2D interference fringe wave field to obtain a high-resolution localized fringe envelope. This study describes the proposed analysis procedure and its application using this 2D WDFT-based demodulation scheme. Experimental verification of the proposed approach was conducted with the use of deformed Mach–Zehnder interferometry. The successful experimental validation proves the efficiency of the proposed algorithm for amplitude demodulation with dense sampling points located in the central part of the envelope. To the best of the authors’ knowledge, this is the first investigational report on a 2D nonlinear envelope demodulator.