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.

Digital fringe projection is a surface-profiling technique used for highly accurate noncontact measurements. As with any measurement technique, a variety of sources degrade to the measurement accuracy of the method. This paper presents an analytically-derived probability density function that explicitly models the surface height measurement error due to inevitable phase measurement error, and it includes the specific case of pixel noise inducing the phase measurement error that ultimately leads to the height estimation error. The accuracy of the model was validated through Monte-Carlo simulations of resultant height distributions subject to arbitrarily correlated pixel intensity noise and experimental digital fringe projection measurements where the pixel-by-pixel height uncertainty estimations were compared to the predictions of the derived model.

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Additive manufacturing (AM) processes are rapidly maturing and being adopted in numerous industrial sectors. One of the big challenges with many AM processes is the need for part quality control, either in post-manufactured assessment or in-situ during the build. This paper presents a low-cost structured light system (using camera and projector) that exploits digital fringe projection to achieve surface profiling of AM parts. Additionally, a probability density function of the surface profile is derived, helping the measurement process to provide the probabilistic support required for AM part quality control decisions. Results from a prototype system on AM parts are demonstrated.