Fringe Pattern Analysis in Wavelet Domain

We present a full-field technique for single fringe pattern analysis based on wavelet transform. Wavelets technique is a powerful method that quantifies at different scales how spatial energy is distributed. In the wavelets domain, fringe pattern analysis requires spatial modulation by a high-frequency carrier. We realize the modulation process numerically by combining the fringe pattern and its quadrature generated analytically by spiral phase transform. The first application concerns the speckle denoising by thresholding the two-dimensional stationary wavelet transform (2D-swt) coefficients of the detail sub-bands. In the second application, the phase derivatives are estimated from the 1D-continuous wavelet transform (1D-cwt) and 2D-cwt analysis of the modulated fringe pattern by extracting the extremum scales from the localized spatial frequencies. In the third application, the phase derivatives distribution is evaluated from the modulated fringe pattern by the maximum ridge of the 2D-cwt coefficients. The final application concerns the evaluation of the optical phase map using two-dimensional discrete wavelet transform (2D-dwt) decomposition of the modulated fringe pattern. The optical phase is computed as the arctangent function of the ratio between the detail components (high-frequency sub-bands) and the approximation components (low-frequency sub-bands). The performance of these methods is tested on numerical simulations and experimental fringes.

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