Modeling the measurement precision of Fringe Projection Profilometry

Three-dimensional (3D) surface geometry provides elemental information in various sciences and precision engineering. Fringe Projection Profilometry (FPP) is one of the most powerful non-contact (thus non-destructive) and non-interferometric (thus less restrictive) 3D measurement techniques, featuring at its high precision. However, the measurement precision of FPP is currently evaluated experimentally, lacking a complete theoretical model for guidance. We propose the first complete FPP precision model chain including four stage models (camera intensity, fringe intensity, phase and 3D geometry) and two transfer models (from fringe intensity to phase and from phase to 3D geometry). The most significant contributions include the adoption of a non-Gaussian camera noise model, which, for the first time, establishes the connection between camera's electronics parameters (known in advance from the camera manufacturer) and the phase precision, and the formulation of the phase to geometry transfer, which makes the precision of the measured geometry representable in an explicit and concise form. As a result, we not only establish the full precision model of the 3D geometry to characterize the performance of an FPP system that has already been set up, but also explore the expression of the highest possible precision limit to guide the error distribution of an FPP system that is yet to build. Our theoretical models make FPP a more designable technique to meet the challenges from various measurement demands concerning different object sizes from macro to micro and requiring different measurement precisions from a few millimeters to a few micrometers.