Three‐dimensional spatial point computation in fringe projection profilometry

The demodulated phase in fringe projection profilometry (FPP) provides information about the (x,y,z)-coordinates of points of the observed object. However, the phase-to-coordinate conversion employing multiple cameras and projectors with different imaging models is not straightforward. This paper presents the following two contributions. First, a theoretical framework to investigate the triangulation problem in FPP is established. Seven representative triangulation methods commonly used in FPP are reviewed. Second, a generalized triangulation method is proposed for single-axis fringe projection supporting multiple cameras and projectors with lens distortion. The performance of the eight investigated triangulation methods is evaluated in terms of noise robustness and computation time by computer simulations and an experimental fringe projection optical setup. The results demonstrate that the mean dispersion approach yields the best performance, but vertical and horizontal fringes must be projected, while the new method is the most appropriate for single-axis fringe projection using multiple devices with lens distortion.