Open AccessGeneralized Fourier analysis for phase retrieval of fringe pattern
Author(s) -
Jingang Zhong,
Jiawen Weng
Publication year - 2010
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.18.026806
Subject(s) - fourier transform , short time fourier transform , phase retrieval , harmonic wavelet transform , non uniform discrete fourier transform , discrete fourier transform (general) , optics , fractional fourier transform , discrete time fourier transform , wavelet transform , phase correlation , spectral density estimation , fourier analysis , phase (matter) , window function , wavelet , algorithm , computer science , mathematics , physics , discrete wavelet transform , mathematical analysis , artificial intelligence , spectral density , telecommunications , quantum mechanics
A generalized Fourier analysis, by use of an adaptive multiscale windowed Fourier transform (AWFT), has been presented for the phase retrieval of fringe patterns. The Fourier transform method can be considered as a special case of AWFT method with a maximum window. The instantaneous frequency of the local signal is introduced to estimate whether the condition for separating the first spectrum component is satisfied for the phase retrieval of fringe patterns. The adaptive window width for this algorithm is determined by the length of the local stationary fringe pattern in order to balance the frequency and space resolution. The local stationary length of fringe pattern is defined as the signal satisfying the condition that whose first spectrum component is separated from all the other spectra within the local spatial area. In comparison with Fourier transform, fixed windowed Fourier transform and wavelet transform in numerical simulation and experiment, the adaptive multiscale windowed Fourier transform can present more accurate results of phase retrieval.