Simultaneous estimation of phase derivative and phase using parallel Kalman filter implementation

This paper proposes a technique for the simultaneous estimation of interference phase derivative and phase from a complex interferogram recorded in an optical interferometric setup. The complex interferogram is represented as a spatially varying autoregressive process in a given row or column at a time. The phase derivative is estimated from the poles of the transfer function representation of the autoregressive process. The poles are computed using the spatially varying autoregressive coefficients which are estimated by a computationally efficient Rauch-Tung-Striebel smoothing algorithm. The estimated phase derivative is used as a control input to a state space model designed for the phase estimation at each pixel. The unscented Kalman filter is utilized to deal with the nonlinear measurement process for the accurate estimation of the unwrapped phase. Numerical and experimental results substantiate the ability of the proposed method in handling noisy phase fringe patterns.