Statistical phase shifting step estimation based on continuous wavelet transform for high resolution interferometry metrology

A statistical phase shifting estimation for temporal phase shifting interferometry (PSI) based on continuous wavelet transform is proposed in this paper. The tests on numerical simulation and Moiré interferometry are performed for the validation. In the temporal PSI, the interferograms are reconstructed upon the assumptions of the accurate estimation of the shifted phase steps. The estimations are usually based on the experimental configuration of the phase shifting mechanism. Due to the calibration error and environmental errors, the phase steps are not constants and vary with time and introduce error in the phase reconstruction. To solve this problem, the researchers proposed different phase step estimation algorithms which explore both temporal (inter-frame) and spatial redundancies (intra-frame) in the data to estimate the shifted phase. Each algorithm imposes different constraints on the structure of the shifted phases. The accuracy of the estimated phase steps varies under different condition and also changes among different interferometers. The proposed methods can serve as a benchmark method for comparing the accuracy of the different phase steps estimation methods statistically.