Assessment of Fringe Pattern Decomposition with a Cross-Correlation Index for Phase Retrieval in Fringe Projection 3D Measurements

Phase retrieval from single frame projection fringe patterns, a fundamental and challenging problem in fringe projection measurement, attracts wide attention and various new methods have emerged to address this challenge. Many phase retrieval methods are based on the decomposition of fringe patterns into a background part and a fringe part, and then the phase is obtained from the decomposed fringe part. However, the decomposition results are subject to the selection of model parameters, which is usually performed manually by trial and error due to the lack of decomposition assessment rules under a no ground truth data situation. In this paper, we propose a cross-correlation index to assess the decomposition and phase retrieval results without the need of ground truth data. The feasibility of the proposed metric is verified by simulated and real fringe patterns with the well-known Fourier transform method and recently proposed Shearlet transform method. This work contributes to the automatic phase retrieval and three-dimensional (3D) measurement with less human intervention, and can be potentially employed in other fields such as phase retrieval in digital holography.