The automated and simultaneous extraction of multiple phase distributions and their derivatives continue to pose major challenges. A possible reason is the lack of proper data processing concepts to support the multiple wave mixing that needs to be introduced to make the configuration at a time sensitive to multiple phase components and yet be able to decrypt each component of the phase efficiently and robustly, in absence of any cross-talk. The paper demonstrates a phase estimation method for encoding and decoding the phase information in a digital holographic configuration. The proposed method relies on local polynomial phase approximation and subsequent state-space formulation. The polynomial approximation of phase transforms multidimensional phase extraction into a parameter estimation problem, and the state-space modeling allows the application of Kalman filtering to estimate these parameters. The prominent advantages of the method include high computational efficiency, ability to handle rapid spatial variations in the fringe amplitude, and non-requirement of two-dimensional unwrapping algorithms. The performance of the proposed method is evaluated using numerical simulation.


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