Frequency guided methods for demodulation of a single fringe pattern with quadratic phase matching

Hilbert-Huang processing and analysis of complex fringe patterns

“…Moreover the departures from uniform sinusoidal intensity distribution deteriorate the quality of fringe pattern phase/amplitude demodulation. The common solution is to filter out the noise/background term and normalize the fringe pattern prior to applying the phase extraction algorithm especially in the single and two frame approaches, e.g., the regularized phase tracking [32][33][34][35][36][37][38][39][40], Gramm-Schmidt ortonormalization [69][70][71], and the implicit smoothing splines (ISS) method [72] (most recent algorithm [72] requires single normalized fringe pattern as an input, the noise component does not need to be treated at preprocessing stage). Several normalization solutions have been proposed over the last decade.…”

“…Typical tasks encountered during fringe pattern processing and analysis include noise reduction (denoising), background elimination (detrending), intensity distribution normalization and fringe phase/amplitude demodulation. Single-frame fringe analysis methods traditionally employ Fourier transform (FT) [12][13][14], windowed Fourier transform (WFT) [15][16][17][18][19], discrete/continuous wavelet transform (D/CWT) [20][21][22][23][24][25][26][27], S-transform (ST) [28][29][30][31], regularized phase tracking (RPT) [32][33][34][35][36][37][38][39][40] or spatial carrier phase shifting (SCPS) [41][42][43][44].…”