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Chapter 4:
Quality-guided Phase Unwrapping and Refinement
In Chapters 2 and 3, the windowed Fourier ridges (WFRn) and windowed Fourier filtering (WFFn) algorithms are developed for exponential phase fields (T1 fringe patterns). They can be utilized to suppress noise and provide estimations of wrapped phase, local frequency, and fringe amplitude. If needed, higher-order derivatives of phase, such as curvature, can be obtained through numerical differentiation. In this chapter, wrapped phase maps (T2 fringe patterns) are unwrapped. Stimulated by the excellent denoising ability of the WFRn/WFFn demonstrated in Chapters 2 and 3, a phase-unwrapping approach based on denoising is explored. With quality guidance to rank the pixel priority for unwrapping, a WFRn/WFFnassisted and quality-guided (WFRn/WFFn-QG) phase-unwrapping algorithm is introduced. Because the WFRn/WFFn only provides suboptimal results, we will use congruence operation and least squares fitting (CO-LSF) as an optimal estimator to refine the unwrapped phase, even for locally higher order polynomial phase maps. In this chapter, 2D fringe patterns and 2D algorithms will be discussed, and the algorithms covered can be extended to higher dimensions.
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