Aleatoric uncertainty quantification in digital fringe projection systems at a per-pixel basis

Digital fringe projection has a large number of applications from quality assurance, reverse engineering, to reconstructive surgery and digital entertainment. To date, there is no widely accepted approach to quantitatively assess accuracy and precision of these systems. Most of the relevant research focuses on accuracy (i.e. resemblance to the true object) rather than precision (i.e., aleatoric uncertainty of each measurement). In this work, we discuss the quantification of aleatoric uncertainty arising from camera noise and its propagation to the downstream measured 3D coordinates. For the first time to the authors' knowledge, we achieved high quality phase uncertainty quantification derived from multi-frequency fringe-pattern analysis at a per-pixel basis from a single scan given a well-calibrated system regarding the error of photometric parameters. The results indicate that, compared to the conventional phase uncertainty propagation model based on the intensity-independent camera noise assumption, the proposed uncertainty propagation model assuming intensity-dependent camera noise can achieve 7- to 10-fold improvement regarding phase uncertainty quantification. The proposed methodology could be used to estimate the point-wise error generated by a digital fringe projection scanner for the entire scanning region and from only a single scan.