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.

We report our experimental results of phase shifting shadow moiré with a constant but unknown phase step to estimate both the wavefront phases and the phase step. The method allows phase retrieval from phase shifting interferograms even though the calibration data of the phase shifter are unknown. Compared with the traditional shifting shadow moiré method, the proposed algorithm is insensitive to the height dependent effects, which is the main systematic source of error in phase shift shadow moiré when reconstructing surfaces from fringe patterns. Experiments show that the proposed method can effectively minimize the effects of the phase shifting errors and possesses a superior performance to existing typical phase shifting algorithms in the shifting shadow moiré technique.

We propose a phase unwrapping method for general interferometric applications. The proposed method relies on a derivative Zernike polynomial fitting (DZPF) technique where the phase is approximated as a combination of Zernike polynomials. The fitting coefficients are then estimated using the least squares method. Thus the phase unwrapping problem is reduced to the calculation of these coefficients. Because of the full field operation, the proposed method is fast and efficient. In addition, the method directly provides the desired phase without the need to compute the misalignment errors further. The method combines the phase unwrapping and the wavefront fitting process. Simulation and experimental results are presented to validate the method's potential.

A triple-frequency color fringe-projected technique is presented to measure dynamic objects. Three fringe patterns with a carrier frequency ratio of 1:3:9 are encoded in red, green, and blue channels of a color fringe pattern and projected onto an object's surface. Bidimensional empirical mode decomposition is used for decoupling the cross talk among color channels and for extracting the fundamental frequency components of the three fringe patterns. The unwrapped phase distribution of the high-frequency fringe is retrieved by a three-step phase unwrapping strategy to recover the object's height distribution. Owing to its use of only a single snapshot, the technique is suitable for measuring dynamically changing objects with large discontinuity or spatially isolated surfaces.

A method combining the spatial and temporal fringe analysis techniques is proposed to extract the phase from shadow moiré interferogram with random phase shift. The proposed method first determines the grating translation difference based on the spiral phase transform technique. Then the initial phase shift is estimated. After that a generalized iterative least-squares method is developed to retrieve the accurate phase map using three interferogram frames. The proposed method relaxes the restriction on phase shift calibration between frames and provides stable and correct convergence in a fast way. Simulation and experiment demonstrate the effectiveness of this method. It shows our method possesses a superior performance than the existing typical phase-shifting algorithm. The proposed method is suitable for phase-shifting shadow moiré.