Abstract
Abstract. For optical 3-D measurement systems, camera noise is the dominant uncertainty factor when optically cooperative surfaces are measured in a stable and controlled environment. In industrial applications repeated measurements are seldom executed for this kind of measurement system. This leads to statistically suboptimal results in subsequent evaluation steps as the important information about the quality of individual measurement points is lost. In this work it will be shown that this information can be recovered for phase measuring optical systems with a model-based noise prediction. The capability of this approach will be demonstrated exemplarily for a fringe projection system and it will be shown that this method is indeed able to generate an individual estimate for the spatial stochastic deviations resulting from image sensor noise for each measurement point. This provides a valuable tool for a statistical characterization and comparison of different evaluation strategies, which is demonstrated exemplarily for two different triangulation procedures.
Highlights
For optical 3-D measurement systems, like fringe projection systems, the achievable accuracy mainly depends on the environmental conditions and the properties of the measurement object
While the deviations are correlated with the micro-topography in the case of noncooperative surfaces, stochastic deviations caused by camera noise come to the fore in the case of cooperative surfaces
This expression is based on the assumption of signal-independent Gaussian noise, where the signal-to-noise ratio (SNR) would increase linearly with the unmodulated intensity I, in Fischer et al (2012) it has been shown that it is valid for a more complex expression of SNR resulting from the advanced linear camera model of the EMVA 1288 guideline (EMVA, 2010)
Summary
For optical 3-D measurement systems, like fringe projection systems, the achievable accuracy mainly depends on the environmental conditions and the properties of the measurement object. The image sensor σI and the phase noise σφ can be found according to Brophy (1990), Rathjen (1995) and Surrel (1997) as σφ = This expression is based on the assumption of signal-independent Gaussian noise (σI = const.), where the signal-to-noise ratio (SNR) would increase linearly with the unmodulated intensity I , in Fischer et al (2012) it has been shown that it is valid for a more complex expression of SNR resulting from the advanced linear camera model of the EMVA 1288 guideline (EMVA, 2010). Plot of a single data column of σz.emp and σz.mod across the pole of the sphere In the following it will be shown how the general phase-noise estimation can be applied to a given measurement system and further developed into a prediction method for the stochastic coordinate deviations of the measured surface points. Relative deviation of the estimated value σz.mod from the empirically determined reference value σz.emp
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