Evaluating parametric uncertainty using non-linear regression in fringe projection

Optical coordinate measurement systems, such as fringe projection systems, offer fast, high-density measurements of arbitrary surface topographies. The versatility, speed and information density of fringe projection measurements make them attractive as in-situ measurement devices and autonomous inspection systems. However, the complex nature of the measurement process makes evaluating uncertainty from a fringe projection measurement complex – even in the hypothetical simple case where the accuracy of a measurement is limited only by the accuracy in the quantities that define a measurement from an indication; named system parameters here. In this paper, by validating a series of assumptions, a method to explore the uncertainty in the system parameters of a fringe projection system is given. The results of this investigation imply the common distortion model (the Brown-Conrady model) is not specific enough to the camera or projector of a fringe projection system to evaluate its uncertainty.