ABSTRACT
This chapter presents modern techniques for phase demodulation of fringe patterns in digitalinterferometry. Phase demodulation is in general an ill-posed inverse problem; however, theintroduction of high spatial/temporal carriers turns this problem into a well-posed one. Phase-shifting interferometry (PSI) is analyzed using the frequency transfer function (FTF) formalism. The FTF allows easy comparison of phase-shifting algorithms (PSAs) in terms of signal-to-noise ratio, detuning, and harmonics distortion. We included popular few-step PSAs and analyzed them by their FTFs. Spatial-carrier interferometry is also included: Fourier demodulation, spatial-carrier phase-shifting, and spatial regularized quadrature filtering. The regularized phase-tracking (RPT) phase demodulates and unwraps single closed-fringe images. Unwrapping is trivial for noiseless wrapped phases. However, it is challenging for high phase-noise, multiple phase-jumps, and undersampled data. Well-known unwrapping methods are reviewed such as least-squares unwrapping, RPT-unwrapping, and temporal phase-unwrapping. Finally, wavefront analysis tests such as Ronchi, Moiré deflectometry, lateral shearing, Hartmann test, curvature sensing, and sub-Nyquist analysis are also included.
