Determining uncertainty in the functional quantities of fringe projection

Fringe projection systems can acquire a point-cloud of more than a million points in minutes while not needing to ever physically touch the measurement surface and can be assembled using relatively inexpensive off-the-shelf components. Fringe projection system can conduct measurements faster than their tactile counterparts and typically require less training to do so. The disadvantage of using a fringe projection system is the measurements are less accurate than alternative tactile methods – and typical methods to obtain an uncertainty evaluation within fringe projection require a tactile system as a comparator. Anterior to any measurement, fringe projection systems undergo a calibration, whereby the set of functional quantities (defined in this thesis as the system parameters) are found that define the measurement (the point-cloud) from the indication (a set of images). The accuracy of the estimated parameters will define the accuracy of any measurements made by the system. The calibration process does not evaluate any uncertainty of the estimated system parameters – the accuracy of the estimation of the parameters remains unknown, as is their exact effect on the measurement result. In this thesis, an investigation into the using the system parameters to evaluate the uncertainty of fringe projection measurements is made. Firstly, a method to localise the centre of ellipses in camera images with an uncertainty is given. This uncertainty is used to derive the uncertainty in the estimated system parameters. The uncertainty in the system parameters is tested by using the system parameters to measure known artefacts, a flatness artefact and two sphere-based artefacts, where the propagated uncertainty is tested against the measurement error. The accuracy of the system parameters are tested by comparing the measurement error of the measurements with measurements made on a commercial system, the GOM ATOS Core 300. In addition, an exhaustive study is undertaken on the calib