Direct unwrapped phase estimation in phase shifting interferometry using Levenberg-Marquardt algorithm

An algorithm for the direct unwrapped phase estimation from the linearly phase shifted interferograms is presented. The temporal fringe intensity along each pixel is represented as a function of fringe amplitude, phase step and the searched phase. These parameters are estimated in the nonlinear least squares sense using the Levenberg-Marquardt algorithm. The proposed method allows the masked interferograms to be handled using a pixel selection approach to provide the appropriate initial conditions at a given pixel utilizing the estimated parameters at one of its neighboring pixels, which results in direct unwrapped phase estimation. Simulation results are provided to evaluate the performance of the proposed method as a function of noise power, spatially varying phase step, number of interferograms and phase step detuning error. The experimental results are also provided in the case of a holographic interferometry setup.