Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase calculation at discontinuities in fringe projection profilometry

Abstract Phase demodulation techniques from one fringe pattern have been widely studied because it can measure dynamic objects by capturing single image. These techniques mainly include Fourier transform (FT), windowed Fourier transform (WFT), and wavelet transform (WT). FT has been widely used to demodulate phase information from single deformed fringe pattern on smooth objects. However, for objects having discontinuities and/or large slopes, FT cannot obtain correct phase at the edges because of its global processing. WFT and WT have been applied to nonstationary fringe pattern analysis. Since local fringe information used to extract phase information, WFT and WT are better than FT for phase calculation at discontinuities and/or slopes. In this paper, we discuss the pro and con of the three methods on phase calculation at discontinuities and/or slopes. Simulated and experimental data are tested at edges in order to confirm which method is appropriate to measure objects having discontinuities by using one-frame fringe pattern acquisition method.

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