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Robust phase-shifting algorithms designed for high-dynamic range in fringe-projection profilometry

Phase-shifting algorithms (PSAs) are usually derived for static or quasi-static conditions, where the temporal phase step is the only significant variation expected between successive frames. When these assumptions are valid, choosing the right algorithm often translates into faster acquisition times or robustness against systematic errors (such as detuning, random noise, and distorting harmonics). In practice, however, one may need to cope with dynamic conditions that require more complex phase-demodulation approaches. In this work, we present a PSA designed for robust quadrature filtering assuming temporal variations of the background and contrast functions. The frequency transfer function (FTF) formalism allows us to design its spectral response and to assess its robustness against systematic errors. This procedure is conceptually and computationally easy to generalize for many-step algorithms. Finally, a work-in-progress application for high-dynamic range (HDR) in fringe-projection profilometry is presented as proof of concept.