Fringe projection systems can be used for the measurement of complex workpiece geometries. Virtual fringe projection systems can be used for the calculation of optimal measurement strategies with respect to criteria like a minimal measurement uncertainty. This is the main field of research of the subproject B5 of the collaborative research centre 489 (CRC 489), funded by the German Research Foundation (DFG). The main task of the subproject is to develop a virtual multisensor assistance system for the calculation of workpiece adapted measurement strategies. This paper focuses on the model and calibration of the used fringe projection sensor.The sensor has to be modelled and the system parameters have to be identified by an accurate calibration procedure. The used fringe projection system has a camera lens with an object-sided telecentricity. Usually, the components projector and camera were described using a pinhole model, which does not reflect the telecentricity. This means, that the existing physical formulations and calibration procedures cannot be used, here.In this paper, the model and calibration strategy for the calculation of the system parameters are described in detail. In order to get a precise simulation model, each intrinsic and extrinsic parameter is considered. To verify the virtual model and the calibration strategy, the calibration was repeated and the standard deviation of the parameters was calculated. Furthermore an optical flat and a groove artefact will be measured and the planarity of the optical flat and the depth of the groove artefact will be determined and compared to the calibrated values.

One of the main tasks of the quality test is the inspection of all relevant geometric parts related to the predefined tolerance range, whereas the uncertainty of measurement has to be less than the tolerance range. The reachable uncertainty of measurement can be determined using method A of the ISO Guide to the Expression of Uncertainty in Measurement (GUM), which is expensive and time consuming and has to be carried out for each individual metrologic case. Furthermore, it is possible to check the suitability of the measurement system for the planned inspection using virtual measurement techniques and therewith to reduce the time and money spent. This means that the uncertainty of measurement is estimated using method B of the GUM. In this paper, a virtual fringe projection system is used for the estimation of the uncertainty of measurement, which is compared with the uncertainty of measurement determined with a real measurement system using method A of the GUM. With the presented method, it is possible to calculate an optimal measurement position within the measurement volume, based on a minimum uncertainty of measurement. Thereby, the influence of the operator related to the uncertainty can be significantly reduced.

Zusammenfassung Virtuelle Sensorsysteme können parallel zur Bauteilkonstruktion zur Messbarkeitsprüfung und für Messunsicherheitsuntersuchungen verwendet werden. Beispielsweise ist es möglich, zu entscheiden, ob die funktionsrelevanten Bauteilflächen mit der geforderten Messunsicherheit erfasst werden können. In diesem Beitrag wird ein Verfahren vorgestellt, mit dem es möglich ist, reale Messunsicherheiten mit Hilfe einer numerischen Computersimulation abzuschätzen. Weiterhin wird die abgeschätzte Unsicherheit mit empirisch abgeschätzten Unsicherheiten verglichen, um die Güte des virtuellen Messsystems zu verifizieren.Summary Virtual sensor systems can be applied to verify the measurability and for measurement uncertainty inspections. This can be done parallel to the component construction. It is possible, for example, to decide if all relevant workpiece surfaces can be measured with the required measurement uncertainty. In this article a method for the estimation of real measurement uncertainties is presented using a numerical computer simulation. To verify the quality of the virtual measurement system, the estimated uncertainties are in addition compared to uncertainties estimated using empirical methods.Schlagwörter Virtuelle Streifenprojektion, virtueller Messablauf, Abschätzung von Messabweichungen, Unsicherheitsanalyse Keywords Virtual fringe projection, virtual measurement, estimation of measurement uncertainty, uncertainty analysis 1 Einleitung

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