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 calibration, including applying curvature, specificity and parameter stability tests on the non-linear regression used within calibration. The sphere-based measurements were found to not be robust enough against measurement noise in fringe projection to be able to provide information on errors caused by the system parameters. This thesis raises questions as to the appropriateness of using sphere-based measurements to represent the performance of a fringe projection system. The flatness measurements made using the estimated system parameters achieved an accuracy of approximately 30 "μm" across a 300 "mm"×140 "mm" flatness artefact, which is similar to measurements made by the commercial system. However, the estimated uncertainty was unable to explain all measurement discrepancy between the fringe projection measurements and the tactile measurements. The result specificity test indicated poor specificity of the mathematical model of fringe projection, namely the camera pinhole model with Brown-Conrady distortion. It is concluded that the level of accuracy of the mathematical model has become a limiting factor in the accuracy of fringe projection measurements, instead of the accuracy of the inputs to the calibration. Therefore, the uncertainty of the system parameters cannot be used to evaluate an uncertainty of a measurement made using a fringe projection system

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 calibration, including applying curvature, specificity and parameter stability tests on the non-linear regression used within calibration. The sphere-based measurements were found to not be robust enough against measurement noise in fringe projection to be able to provide information on errors caused by the system parameters. This thesis raises questions as to the appropriateness of using sphere-based measurements to represent the performance of a fringe projection system. The flatness measurements made using the estimated system parameters achieved an accuracy of approximately 30 "μm" across a 300 "mm"×140 "mm" flatness artefact, which is similar to measurements made by the commercial system. However, the estimated uncertainty was unable to explain all measurement discrepancy between the fringe projection measurements and the tactile measurements. The result specificity test indicated poor specificity of the mathematical model of fringe projection, namely the camera pinhole model with Brown-Conrady distortion. It is concluded that the level of accuracy of the mathematical model has become a limiting factor in the accuracy of fringe projection measurements, instead of the accuracy of the inputs to the calibration. Therefore, the uncertainty of the system parameters cannot be used to evaluate an uncertainty of a measurement made using a fringe projection system