Review of fringe pattern phase recovery using the 1-D and 2-D continuous wavelet transforms

Improving speed and precision of local frequency analysis using Gaussian ridge interpolation for wavelet and windowed Fourier ridge algorithms

“…A second topic which would be interesting to revisit is the approach used by Watkins and others [8], where the phase is reconstructed based on the extracted frequency information without the need to perform phase unwrapping. Any of the methods described for instance in [32] can be used to that end.…”

“…Any of the methods described for instance in [32] can be used to that end. This approach was partly abandoned because a good precision required much more analysing frequencies as compared to phase unwrapping based techniques [8]. However, the current algorithm essentially removes this barrier now.…”

“…While many fringe analysis techniques exist already, there is a continued interest in applying new algorithms capable of getting better results in the face of increasing noise levels. In that respect, wavelet ridge techniques (WR) and windowed Fourier transform techniques (WFR) are taking the fore-front [8,9]. However, especially for the windowed Fourier transform technique, analysis time can become prohibitive.…”

“…The obtained frequency values however are discrete and correspond to the analysing frequencies which were evaluated. Thus, if a better precision is required, more frequencies need to be analysed and a longer evaluation time immediately follows (as mentioned in a recent review on WR [8] and on WFR in [9]). The focus in the current paper will be on how to reduce the amount of frequencies required to perform this analysis without sacrificing the precision on the local frequency estimation through an interpolation on the ridge.…”

Hilbert-Huang processing and analysis of complex fringe patterns

“…Typical tasks encountered during fringe pattern processing and analysis include noise reduction (denoising), background elimination (detrending), intensity distribution normalization and fringe phase/amplitude demodulation. Single-frame fringe analysis methods traditionally employ Fourier transform (FT) [12][13][14], windowed Fourier transform (WFT) [15][16][17][18][19], discrete/continuous wavelet transform (D/CWT) [20][21][22][23][24][25][26][27], S-transform (ST) [28][29][30][31], regularized phase tracking (RPT) [32][33][34][35][36][37][38][39][40] or spatial carrier phase shifting (SCPS) [41][42][43][44].…”