2D phase-unwrapping algorithms (PUAs) are commonly used to obtain a continuous phase map from the sawtooth-shaped phase map. However, implementing PUAs can be time consuming, and the accuracy of those algorithms may be low if there is heavy noise. In this paper, we develop a simple and robust PUA based on the transport of intensity equation (TIE). In our method, the TIE was solved using the fast cosine transform, and a phase correction operation was introduced after the TIE was solved. Because of the phase correction operation, the proposed method can obtain a satisfactory unwrapping result even in a notably hash noise condition. The simulation and experimental results are presented to validate the effectiveness of the proposed method. The detailed software package can be found at https://ww2.mathworks.cn/matlabcentral/fileexchange/68493-robust-2d-phase-unwrapping-algorithm.

This paper proposes a new interferometric method to measure the phase modulation characteristics of a liquid crystal spatial light modulator (LC-SLM). In our proposed method, the beam was incident perpendicular to the SLM and the combined grayscale pattern loaded into the SLM consisted of three parts. The left part was a blazed diffraction grating, and the two right parts were grayscale with different constant values. The gray value in the downward section remained constant at zero, while it gradually increased from 0 to 255 in the upward section. By changing the gray value of the combined grayscale loaded on the LC-SLM, different sheared fringe patterns, generated by the interference between the constant phase-modulated beam and the +1 order diffracted beam of the blazed grating, could be obtained. The phase modulation value could then be calculated using only one sheared fringe pattern. As a result, our proposed method can reduce the effect of environmental vibration or air turbulence and improve measurement precision. The experimental results are presented to validate the method's potential.

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