Comparative analysis of image pre-filtering techniques for phase-shifted noise-affected interferograms.

Phase-shifting techniques are one of the most promising strategies to extract the phase information and retrieve the parameters of interest (e.g., refractive index, beam collimation, object shape, deformations, thickness, focal length, etc.) from interferograms. However, traditional phase-shifting techniques suffer from both internal and external noise, which reduce measurement accuracy. This paper reports a comparative analysis of the three commonly used filtering techniques, namely, Fourier, windowed Fourier, and wavelet filtering for noise reduction and accurate extraction of phase information from phase-shifted interferograms. Toward this, two basic types of noise (additive and multiplicative noise) are introduced in the simulated interferograms and processed using the pre-filtering strategies. The effect of second-order harmonics in the presence of noise is also examined. In addition, experimental demonstrations of the real-life applicability of the analyses are provided using the interferograms recorded on coherent (Talbot) and incoherent (Lau) grating shearing interferometers. High accuracy in the measurement of defocusing error of the lens is obtained using the filtering strategies. Further inferences and insights are drawn in favor of the pre-filtering techniques.