Uncertainty on fringe projection technique: A Monte-Carlo-based approach

Error estimation on optical full field techniques (OFFT) is millstone in the diffusion of OFFT. The present work describes a generic way to estimate overall error in fringe projection, either due to random sources (phase error, basically related to the quality of the camera and of the fringe extraction algorithm) or the bias (calibration errors). Here, a high level calibration procedure based on pinhole model has been implemented. This model compensates for the divergence effects of both the video-projector and the camera. The work is based on a Monte-Carlo procedure. So far, the complete models of the calibration procedure and of a reference experiment are necessary. Here, the reference experiment consists in multiple step out-of-plane displacement of a plane surface. Main conclusions of this work are: (1) the uncertainties in the calibration procedure lead to a global rotation of the plane, (2) the overall error has been calculated in two situations; the overall error ranges from 104 μm down to 10 μm, (3) the main error source is the phase error even if errors due to the calibration are not always negligible.

► Global fringe projection uncertainties have been calculated using Monte-Carlo method.
► The uncertainty evaluation include calibration aliasing for a pin-hole model.
► Two examples are given: a microscopic or a macroscopic case.
► For a typical macroscopic set-up, the total error is found to be 104 μm.
► The random error related to the phase is the principle error source.