Optical phase extractions based on reassigned continuous wavelet transform with application to simultaneous displacement and velocity measurement.

Instantaneous frequency extraction of a highly nonstationary optical interferometric fringe signal using continuous wavelet transform with Morlet wavelet often fails in the neighborhood of the null phase gradient. The present work reports that the optimal selection of the central frequency and time variance of the Morlet wavelet reduces the spread of wavelet energy to its adjacent bins, and the reassignment technique further sharpens the energy density and enhances accuracy of the extracted instantaneous frequency of the fringe signal. The developed algorithm is applied to a sinusoidal frequency-modulated fringe signal for which the mean square error percentage in normalized instantaneous frequency is determined to be 0.0032 Hz, which is significantly less than 0.0507 Hz obtained with a conventional continuous wavelet transform. Results are also compared with the existing phase stepping technique and found to be more accurate and free from any ripple like nonlinear error for sinusoidal fringe signals. The proposed technique is applied to a fringe signal obtained with a Michelson interferometer, generating displacement profiles that show advantages over those produced by the phase stepping technique. The applicability of the proposed technique is further extended to an arbitrary phase signal.