Comparative Study of Three Bayesian Filtering Approaches for Phase Step Estimation in Optical Interferometry

This paper presents three recursive Bayesian filtering approaches in phase shifting interferometry involving a piezoelectric device (PZT). The three approaches are extended Kalman filtering, unscented Kalman filtering, and particle filtering. These approaches estimate the phase steps imparted to the PZT in the presence of random noise. The advantage of recursive Bayesian filtering lies in its ability to determine the phase steps between 0 and radians without any prior calibration of the PZT. These approaches exhibit the possibility of real time tracking of the imparted phase steps to the PZT, a characteristic, currently not exhibited by any phase measurement algorithms. These algorithms are tested rigorously using simulated data in the presence of randomly distributed Gaussian noise. Experimental validations are also performed in a holographic interferometry optical set up to compare the performances of the three proposed approaches. Once the phase step is identified, the interference phase can be estimated using the least squares fitting approach.