A model for describing phase-converted image intensity noise in digital fringe projection techniques

Abstract

Digital fringe projection is a surface-profiling technique that is gaining popularity due to the increasing availability and quality of low-cost projection equipment and digital cameras. Noise in the pixel field of imaged targets induces error in the reconstructed phase and ultimately the surface profile measurement. In this paper, we present an approximate analytical probability density function for the estimated phase given an arbitrarily-correlated Gaussian pixel noise structure. This probability density function can be used to estimate the single point phase measurement uncertainty from easily obtainable pixel intensity noise statistics. We confirm the accuracy of the new model by comparing it to a Monte-Carlo simulation of the phase distribution. A complimentary graphics model is proposed which simulates the physical process of full-field phase measurement using a pin-hole camera model and three-dimensional point clouds of the measurement surface, allowing for another level of model verification.