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Chapter 7:
Demodulating a Single Closed Fringe Pattern
In Chapter 6, fringe pattern denoising (FPDen) processes that input a noisy closed fringe pattern and output a clean one are outlined. In this chapter, we will explore fringe pattern demodulation (FPDem) processes that input a noisy or clean closed-fringe pattern and output a noisy or clean phase map. Fundamental problems withFPDemare discussed in Section 7.1. In FPDem, some algorithms require fringe patterns to have zero background, and some algorithms further require fringe patterns to have unit amplitude. For this reason, background removal and amplitude normalization are introduced in Section 7.2. Three FPDem approaches are discussed: (1) a transform-based approach, including the WFR2 algorithm and quadrature transform; (2) a decoupled spatial approach, including a frequency-guided sequential demodulation method and its fast version; and (3) an integrated spatial approach, including regularized phase tracking and its variations. These FPDem approaches are introduced in Sections 7.3, 7.4, and 7.5, respectively. The focus on these three approaches largely reflects their relevance to the author’s experiences in the field and does not negate the importance of the other algorithms. Many other FPDem algorithms will be briefly covered and linked to these three approaches, and interested readers are encouraged to refer to Ref. 1. Algorithms are introduced and simulation examples are provided to better understand their performances. The demodulation of experimental fringe patterns is given in Section 7.6, and the discontinuity problem is briefly discussed in Section 7.7.
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