Denoising a Single Closed Fringe Pattern

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In previous chapters, the first three types of fringe patterns, from which the phase is either easy to extract (T1 and T3 fringe patterns) or has already been extracted (T2), are discussed in detail. Our focus now shifts to a single closed fringe pattern with neither phase shifting nor carrier (T4). The process of retrieving the phase from a closed fringe pattern—usually called fringe pattern demodulation (FPDem)—is our major task and will be the focus of Chapter 7. Because noise often affects the success of demodulation, fringe pattern denoising (FPDen) is examined first in this chapter. FPDen can be realized in either the spatial domain, or a transformed domain. For continuity with previous chapters, adaptive windowed Fourier filtering (AWFF2) is introduced first in Section 6.1 to denoise a closed fringe pattern in the windowed Fourier domain. In the spatial domain, it is intuitive and effective to smooth a fringe pattern along the fringe orientation, which is the main idea of oriented filtering. To make oriented filtering possible, fringe orientation should be estimated first—this process is introduced in Section 6.2. Three forms of oriented filters, oriented partial differential equations (PDEs), adapted coherence enhancing diffusion (ACED), and spin filters are described in Section 6.3. The AWFF2 and ACED are compared in Section 6.4, representing transformed domain filters and spatial domain filters, respectively. 2D filters are emphasized and developed, as they can be easily extended to higher dimensions.