Determination of interferometer phase distributions by use of wavelets

Abstract

A new technique for directly extracting phase gradients from two-dimensional (2-D) interferometer fringe data is presented. One finds the gradients by tracking the maximum modulus of the continuous wavelet transform of the fringe data and the phase distribution that is obtained, with a small error, by integration. Problems associated with phase unwrapping are thereby avoided. The technique is compared with standard methods, and excellent agreement is found. In common with Fourier-transform methods, the technique is capable of extracting the full 2-D phase distribution from a single image.

Two-dimensional wavelet transform for reliability-guided phase unwrapping in optical fringe pattern analysis

“…We note that a r ∝ 1 ω [4,5,10,12,17,18], where ω is the local frequency of the fringe pattern. From Eq.…”

“…(10), we can realize that the modulus of the 2D WT coefficients calculated by using the first daughter wavelet definition is not only proportional to the modulation B but also to the scale parameter a r . Because a r is inverse proportional to the local frequency ω [4,5,10,12,17,18], the modulus value of W 1r b x ; b y ; a r ; θ at the local area with a low frequency is enlarged, which makes the modulus not good enough to represent the reliability of the phase data. From Eq.…”

“…The one-dimensional (1D) WT is introduced to analyze a fringe pattern for its multiresolution ability and good spatial localization ability [4,5,[8][9][10][11][12]. It outperforms the FT method in some cases because FT always operates globally in the whole spatial domain.…”

Wavelet-transform analysis of spectral shearing interferometry for phase reconstruction of femtosecond optical pulses

“…All the time and frequency information of the signal shows readily apparent on the two topographies; therefore, one could directly read out the phase at the corresponding frequency in the phase topography. This phase retrieval technique has been verified in reference [11][12][13].…”

Determination of height profile from a two-dimensional fringe signal using a two-dimensional continuous wavelet transform

“…Since 1983, the Fourier transform has been as the most commonly used phase distribution calculation technique according to the literature. On the other hand, CWT was applied as a simulation for the fringe projection technique for the first time in 1999 and it has been frequently used since [6]. In particular, noisy images, taken from a fringe pattern with one carrier frequency, are analyzed successively with 2D CWT [7,8].…”