Wavelet analysis of speckle patterns with a temporal carrier.

A novel temporal phase-analysis technique that is based on wavelet analysis and a temporal carrier is presented. To measure displacement on a vibrating object by using electronic speckle pattern interferometry, one captures a series of speckle patterns, using a high-speed CCD camera. To avoid ambiguity in phase estimation, a temporal carrier is generated by a piezoelectric transducer stage in the reference beam of the interferometer. The intensity variation of each pixel on recorded images is then analyzed along the time axis by a robust mathematical tool, i.e., a complex Morlet wavelet transform. After the temporal carrier is removed, the absolute displacement of a vibrating object is obtained without the need for temporal or spatial phase unwrapping. The results obtained by a wavelet transform are compared with those from a temporal Fourier transform.