Statistical searching of deformation phases on wavelet transform maps of fringe patterns

A wavelet transform (WT) analysis is presented to obtain the deformation phases from the fringes with non-uniform carrier frequency, which may appear in the pattern of varied-periodic fringes generated in displacement measurement. Based on the phase maps of the Morlet WT coefficients distributed in a space-scale spectrum, a statistical processing is carried out to search the compacted density of the phase intervals over the scale, and from that the phase modulations related to the object deformation can be determined. Numerical simulation demonstrates the validity of the pattern-processing technique, and the experimental results show the applications to the measurement of the in-plane displacement by the digital speckle pattern interferometry (DSPI) and the measurement of the out-of-plane deflection by the projecting Moiré fringes.