Abstract

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.

© 2012 Optical Society of America

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References

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  1. R. Schmitt, F. Koerfer, O. Sawodny, J. Zimmermann, R. Krüger-Sehm, M. Xu, T. Dziomba, L. Koenders, G. Goch, A. Tausendfreund, S. Patzelt, S. Simon, L. Rockstroh, C. Bellon, A. Staude, P. Woias, F. Goldschmidtböing, and M. Rabold, “Virtuelle Messgeräte: Definition und Stand der Entwicklung,” Tech. Mess. 75, 298–310 (2008).
    [CrossRef]
  2. Y. Hu, Q. Yang, and P. Wei, “Development of a novel virtual coordinate measuring machine,” in I2MTC—International Instrumentation and Measurement Technology Conference (IEEE, 2009), pp. 230–233.
  3. M. Trenk, M. Franke, and H. Schwenke, “The ‘Virtual CMM’ a software tool for uncertainty evaluation—practical application in an accredited calibration lab,” in ASPE Proceedings on Uncertainty Analysis in Measurement and Design (ASPE, 2004), pp. 1–6.
  4. C. L. Giusca, A. B. Forbes, and R. K. Leach, “A virtual machine-based uncertainty evaluation for a traceable areal surface texture measuring instrument,” Measurement 44, 988–993 (2011).
    [CrossRef]
  5. C. L. Giusca, A. B. Forbes, and R. K. Leach, “Comparison between GUM, Monte Carlo and Bayesian uncertainty evaluation approaches for an areal surface texture measuring instrument,” in Proceedings of the International Congress of Metrology (Dutch Metrology Institute, 2009), Vol. 14, pp. 988–993.
  6. T. Böttner, “Untersuchungen zur Messunsicherheit mit Hilfe eines virtuellen Streifenprojektionssystems,” Ph.D. thesis (Leibniz Universität Hannover, 2008).
  7. A. Weckenmann, W. Hartmann, and J. Weickmann, “Model and simulation of fringe projection measurements as part of an assistance system for multi component fringe projection sensors,” Proc. SPIE 7102, 71020N (2008).
    [CrossRef]
  8. A. Weckenmann, W. Hartmann, and J. Weickmann, “Multi-component fringe projection sensors: Assistance system for short and robust inspection processes,” in Proceedings of the 2008 NCSL International Workshop and Symposium (NCSL, 2008), pp. 43–49.
  9. J. Weickmann, A. Weckenmann, and P. F. Brenner, “Automatic, task-sensitive and simulation-based optimization of fringe projection measurements,” Key Eng. Mater. 437, 439–443 (2010).
    [CrossRef]
  10. International Organization for Standardization, GUM—Guide to the Expression of Uncertainty in Measurement (DIN/Beuth-Verlag, 1995).
  11. K. Haskamp, M. Kästner, R. Gillhaus, and E. Reithmeier, “Messunsicherheitsanalyse mittels virtueller Streifen-projektionstechnik auf Grundlage von Polygonmodellen,” Tech. Mess. 78, 60–68 (2011).
    [CrossRef]
  12. K. Haskamp, M. Kästner, and E. Reithmeier, “Accurate calibration of a fringe projection system by considering telecentricity,” Proc. SPIE 8082, 80821B (2011).
    [CrossRef]
  13. S. Kammel, “Deflektometrische Untersuchung spiegelnd reflektierender Freiformflächen,” Ph.D. thesis (Universität Karlsruhe, 2004).

2011 (3)

C. L. Giusca, A. B. Forbes, and R. K. Leach, “A virtual machine-based uncertainty evaluation for a traceable areal surface texture measuring instrument,” Measurement 44, 988–993 (2011).
[CrossRef]

K. Haskamp, M. Kästner, R. Gillhaus, and E. Reithmeier, “Messunsicherheitsanalyse mittels virtueller Streifen-projektionstechnik auf Grundlage von Polygonmodellen,” Tech. Mess. 78, 60–68 (2011).
[CrossRef]

K. Haskamp, M. Kästner, and E. Reithmeier, “Accurate calibration of a fringe projection system by considering telecentricity,” Proc. SPIE 8082, 80821B (2011).
[CrossRef]

2010 (1)

J. Weickmann, A. Weckenmann, and P. F. Brenner, “Automatic, task-sensitive and simulation-based optimization of fringe projection measurements,” Key Eng. Mater. 437, 439–443 (2010).
[CrossRef]

2008 (2)

R. Schmitt, F. Koerfer, O. Sawodny, J. Zimmermann, R. Krüger-Sehm, M. Xu, T. Dziomba, L. Koenders, G. Goch, A. Tausendfreund, S. Patzelt, S. Simon, L. Rockstroh, C. Bellon, A. Staude, P. Woias, F. Goldschmidtböing, and M. Rabold, “Virtuelle Messgeräte: Definition und Stand der Entwicklung,” Tech. Mess. 75, 298–310 (2008).
[CrossRef]

A. Weckenmann, W. Hartmann, and J. Weickmann, “Model and simulation of fringe projection measurements as part of an assistance system for multi component fringe projection sensors,” Proc. SPIE 7102, 71020N (2008).
[CrossRef]

Bellon, C.

R. Schmitt, F. Koerfer, O. Sawodny, J. Zimmermann, R. Krüger-Sehm, M. Xu, T. Dziomba, L. Koenders, G. Goch, A. Tausendfreund, S. Patzelt, S. Simon, L. Rockstroh, C. Bellon, A. Staude, P. Woias, F. Goldschmidtböing, and M. Rabold, “Virtuelle Messgeräte: Definition und Stand der Entwicklung,” Tech. Mess. 75, 298–310 (2008).
[CrossRef]

Böttner, T.

T. Böttner, “Untersuchungen zur Messunsicherheit mit Hilfe eines virtuellen Streifenprojektionssystems,” Ph.D. thesis (Leibniz Universität Hannover, 2008).

Brenner, P. F.

J. Weickmann, A. Weckenmann, and P. F. Brenner, “Automatic, task-sensitive and simulation-based optimization of fringe projection measurements,” Key Eng. Mater. 437, 439–443 (2010).
[CrossRef]

Dziomba, T.

R. Schmitt, F. Koerfer, O. Sawodny, J. Zimmermann, R. Krüger-Sehm, M. Xu, T. Dziomba, L. Koenders, G. Goch, A. Tausendfreund, S. Patzelt, S. Simon, L. Rockstroh, C. Bellon, A. Staude, P. Woias, F. Goldschmidtböing, and M. Rabold, “Virtuelle Messgeräte: Definition und Stand der Entwicklung,” Tech. Mess. 75, 298–310 (2008).
[CrossRef]

Forbes, A. B.

C. L. Giusca, A. B. Forbes, and R. K. Leach, “A virtual machine-based uncertainty evaluation for a traceable areal surface texture measuring instrument,” Measurement 44, 988–993 (2011).
[CrossRef]

C. L. Giusca, A. B. Forbes, and R. K. Leach, “Comparison between GUM, Monte Carlo and Bayesian uncertainty evaluation approaches for an areal surface texture measuring instrument,” in Proceedings of the International Congress of Metrology (Dutch Metrology Institute, 2009), Vol. 14, pp. 988–993.

Franke, M.

M. Trenk, M. Franke, and H. Schwenke, “The ‘Virtual CMM’ a software tool for uncertainty evaluation—practical application in an accredited calibration lab,” in ASPE Proceedings on Uncertainty Analysis in Measurement and Design (ASPE, 2004), pp. 1–6.

Gillhaus, R.

K. Haskamp, M. Kästner, R. Gillhaus, and E. Reithmeier, “Messunsicherheitsanalyse mittels virtueller Streifen-projektionstechnik auf Grundlage von Polygonmodellen,” Tech. Mess. 78, 60–68 (2011).
[CrossRef]

Giusca, C. L.

C. L. Giusca, A. B. Forbes, and R. K. Leach, “A virtual machine-based uncertainty evaluation for a traceable areal surface texture measuring instrument,” Measurement 44, 988–993 (2011).
[CrossRef]

C. L. Giusca, A. B. Forbes, and R. K. Leach, “Comparison between GUM, Monte Carlo and Bayesian uncertainty evaluation approaches for an areal surface texture measuring instrument,” in Proceedings of the International Congress of Metrology (Dutch Metrology Institute, 2009), Vol. 14, pp. 988–993.

Goch, G.

R. Schmitt, F. Koerfer, O. Sawodny, J. Zimmermann, R. Krüger-Sehm, M. Xu, T. Dziomba, L. Koenders, G. Goch, A. Tausendfreund, S. Patzelt, S. Simon, L. Rockstroh, C. Bellon, A. Staude, P. Woias, F. Goldschmidtböing, and M. Rabold, “Virtuelle Messgeräte: Definition und Stand der Entwicklung,” Tech. Mess. 75, 298–310 (2008).
[CrossRef]

Goldschmidtböing, F.

R. Schmitt, F. Koerfer, O. Sawodny, J. Zimmermann, R. Krüger-Sehm, M. Xu, T. Dziomba, L. Koenders, G. Goch, A. Tausendfreund, S. Patzelt, S. Simon, L. Rockstroh, C. Bellon, A. Staude, P. Woias, F. Goldschmidtböing, and M. Rabold, “Virtuelle Messgeräte: Definition und Stand der Entwicklung,” Tech. Mess. 75, 298–310 (2008).
[CrossRef]

Hartmann, W.

A. Weckenmann, W. Hartmann, and J. Weickmann, “Model and simulation of fringe projection measurements as part of an assistance system for multi component fringe projection sensors,” Proc. SPIE 7102, 71020N (2008).
[CrossRef]

A. Weckenmann, W. Hartmann, and J. Weickmann, “Multi-component fringe projection sensors: Assistance system for short and robust inspection processes,” in Proceedings of the 2008 NCSL International Workshop and Symposium (NCSL, 2008), pp. 43–49.

Haskamp, K.

K. Haskamp, M. Kästner, R. Gillhaus, and E. Reithmeier, “Messunsicherheitsanalyse mittels virtueller Streifen-projektionstechnik auf Grundlage von Polygonmodellen,” Tech. Mess. 78, 60–68 (2011).
[CrossRef]

K. Haskamp, M. Kästner, and E. Reithmeier, “Accurate calibration of a fringe projection system by considering telecentricity,” Proc. SPIE 8082, 80821B (2011).
[CrossRef]

Hu, Y.

Y. Hu, Q. Yang, and P. Wei, “Development of a novel virtual coordinate measuring machine,” in I2MTC—International Instrumentation and Measurement Technology Conference (IEEE, 2009), pp. 230–233.

Kammel, S.

S. Kammel, “Deflektometrische Untersuchung spiegelnd reflektierender Freiformflächen,” Ph.D. thesis (Universität Karlsruhe, 2004).

Kästner, M.

K. Haskamp, M. Kästner, and E. Reithmeier, “Accurate calibration of a fringe projection system by considering telecentricity,” Proc. SPIE 8082, 80821B (2011).
[CrossRef]

K. Haskamp, M. Kästner, R. Gillhaus, and E. Reithmeier, “Messunsicherheitsanalyse mittels virtueller Streifen-projektionstechnik auf Grundlage von Polygonmodellen,” Tech. Mess. 78, 60–68 (2011).
[CrossRef]

Koenders, L.

R. Schmitt, F. Koerfer, O. Sawodny, J. Zimmermann, R. Krüger-Sehm, M. Xu, T. Dziomba, L. Koenders, G. Goch, A. Tausendfreund, S. Patzelt, S. Simon, L. Rockstroh, C. Bellon, A. Staude, P. Woias, F. Goldschmidtböing, and M. Rabold, “Virtuelle Messgeräte: Definition und Stand der Entwicklung,” Tech. Mess. 75, 298–310 (2008).
[CrossRef]

Koerfer, F.

R. Schmitt, F. Koerfer, O. Sawodny, J. Zimmermann, R. Krüger-Sehm, M. Xu, T. Dziomba, L. Koenders, G. Goch, A. Tausendfreund, S. Patzelt, S. Simon, L. Rockstroh, C. Bellon, A. Staude, P. Woias, F. Goldschmidtböing, and M. Rabold, “Virtuelle Messgeräte: Definition und Stand der Entwicklung,” Tech. Mess. 75, 298–310 (2008).
[CrossRef]

Krüger-Sehm, R.

R. Schmitt, F. Koerfer, O. Sawodny, J. Zimmermann, R. Krüger-Sehm, M. Xu, T. Dziomba, L. Koenders, G. Goch, A. Tausendfreund, S. Patzelt, S. Simon, L. Rockstroh, C. Bellon, A. Staude, P. Woias, F. Goldschmidtböing, and M. Rabold, “Virtuelle Messgeräte: Definition und Stand der Entwicklung,” Tech. Mess. 75, 298–310 (2008).
[CrossRef]

Leach, R. K.

C. L. Giusca, A. B. Forbes, and R. K. Leach, “A virtual machine-based uncertainty evaluation for a traceable areal surface texture measuring instrument,” Measurement 44, 988–993 (2011).
[CrossRef]

C. L. Giusca, A. B. Forbes, and R. K. Leach, “Comparison between GUM, Monte Carlo and Bayesian uncertainty evaluation approaches for an areal surface texture measuring instrument,” in Proceedings of the International Congress of Metrology (Dutch Metrology Institute, 2009), Vol. 14, pp. 988–993.

Patzelt, S.

R. Schmitt, F. Koerfer, O. Sawodny, J. Zimmermann, R. Krüger-Sehm, M. Xu, T. Dziomba, L. Koenders, G. Goch, A. Tausendfreund, S. Patzelt, S. Simon, L. Rockstroh, C. Bellon, A. Staude, P. Woias, F. Goldschmidtböing, and M. Rabold, “Virtuelle Messgeräte: Definition und Stand der Entwicklung,” Tech. Mess. 75, 298–310 (2008).
[CrossRef]

Rabold, M.

R. Schmitt, F. Koerfer, O. Sawodny, J. Zimmermann, R. Krüger-Sehm, M. Xu, T. Dziomba, L. Koenders, G. Goch, A. Tausendfreund, S. Patzelt, S. Simon, L. Rockstroh, C. Bellon, A. Staude, P. Woias, F. Goldschmidtböing, and M. Rabold, “Virtuelle Messgeräte: Definition und Stand der Entwicklung,” Tech. Mess. 75, 298–310 (2008).
[CrossRef]

Reithmeier, E.

K. Haskamp, M. Kästner, R. Gillhaus, and E. Reithmeier, “Messunsicherheitsanalyse mittels virtueller Streifen-projektionstechnik auf Grundlage von Polygonmodellen,” Tech. Mess. 78, 60–68 (2011).
[CrossRef]

K. Haskamp, M. Kästner, and E. Reithmeier, “Accurate calibration of a fringe projection system by considering telecentricity,” Proc. SPIE 8082, 80821B (2011).
[CrossRef]

Rockstroh, L.

R. Schmitt, F. Koerfer, O. Sawodny, J. Zimmermann, R. Krüger-Sehm, M. Xu, T. Dziomba, L. Koenders, G. Goch, A. Tausendfreund, S. Patzelt, S. Simon, L. Rockstroh, C. Bellon, A. Staude, P. Woias, F. Goldschmidtböing, and M. Rabold, “Virtuelle Messgeräte: Definition und Stand der Entwicklung,” Tech. Mess. 75, 298–310 (2008).
[CrossRef]

Sawodny, O.

R. Schmitt, F. Koerfer, O. Sawodny, J. Zimmermann, R. Krüger-Sehm, M. Xu, T. Dziomba, L. Koenders, G. Goch, A. Tausendfreund, S. Patzelt, S. Simon, L. Rockstroh, C. Bellon, A. Staude, P. Woias, F. Goldschmidtböing, and M. Rabold, “Virtuelle Messgeräte: Definition und Stand der Entwicklung,” Tech. Mess. 75, 298–310 (2008).
[CrossRef]

Schmitt, R.

R. Schmitt, F. Koerfer, O. Sawodny, J. Zimmermann, R. Krüger-Sehm, M. Xu, T. Dziomba, L. Koenders, G. Goch, A. Tausendfreund, S. Patzelt, S. Simon, L. Rockstroh, C. Bellon, A. Staude, P. Woias, F. Goldschmidtböing, and M. Rabold, “Virtuelle Messgeräte: Definition und Stand der Entwicklung,” Tech. Mess. 75, 298–310 (2008).
[CrossRef]

Schwenke, H.

M. Trenk, M. Franke, and H. Schwenke, “The ‘Virtual CMM’ a software tool for uncertainty evaluation—practical application in an accredited calibration lab,” in ASPE Proceedings on Uncertainty Analysis in Measurement and Design (ASPE, 2004), pp. 1–6.

Simon, S.

R. Schmitt, F. Koerfer, O. Sawodny, J. Zimmermann, R. Krüger-Sehm, M. Xu, T. Dziomba, L. Koenders, G. Goch, A. Tausendfreund, S. Patzelt, S. Simon, L. Rockstroh, C. Bellon, A. Staude, P. Woias, F. Goldschmidtböing, and M. Rabold, “Virtuelle Messgeräte: Definition und Stand der Entwicklung,” Tech. Mess. 75, 298–310 (2008).
[CrossRef]

Staude, A.

R. Schmitt, F. Koerfer, O. Sawodny, J. Zimmermann, R. Krüger-Sehm, M. Xu, T. Dziomba, L. Koenders, G. Goch, A. Tausendfreund, S. Patzelt, S. Simon, L. Rockstroh, C. Bellon, A. Staude, P. Woias, F. Goldschmidtböing, and M. Rabold, “Virtuelle Messgeräte: Definition und Stand der Entwicklung,” Tech. Mess. 75, 298–310 (2008).
[CrossRef]

Tausendfreund, A.

R. Schmitt, F. Koerfer, O. Sawodny, J. Zimmermann, R. Krüger-Sehm, M. Xu, T. Dziomba, L. Koenders, G. Goch, A. Tausendfreund, S. Patzelt, S. Simon, L. Rockstroh, C. Bellon, A. Staude, P. Woias, F. Goldschmidtböing, and M. Rabold, “Virtuelle Messgeräte: Definition und Stand der Entwicklung,” Tech. Mess. 75, 298–310 (2008).
[CrossRef]

Trenk, M.

M. Trenk, M. Franke, and H. Schwenke, “The ‘Virtual CMM’ a software tool for uncertainty evaluation—practical application in an accredited calibration lab,” in ASPE Proceedings on Uncertainty Analysis in Measurement and Design (ASPE, 2004), pp. 1–6.

Weckenmann, A.

J. Weickmann, A. Weckenmann, and P. F. Brenner, “Automatic, task-sensitive and simulation-based optimization of fringe projection measurements,” Key Eng. Mater. 437, 439–443 (2010).
[CrossRef]

A. Weckenmann, W. Hartmann, and J. Weickmann, “Model and simulation of fringe projection measurements as part of an assistance system for multi component fringe projection sensors,” Proc. SPIE 7102, 71020N (2008).
[CrossRef]

A. Weckenmann, W. Hartmann, and J. Weickmann, “Multi-component fringe projection sensors: Assistance system for short and robust inspection processes,” in Proceedings of the 2008 NCSL International Workshop and Symposium (NCSL, 2008), pp. 43–49.

Wei, P.

Y. Hu, Q. Yang, and P. Wei, “Development of a novel virtual coordinate measuring machine,” in I2MTC—International Instrumentation and Measurement Technology Conference (IEEE, 2009), pp. 230–233.

Weickmann, J.

J. Weickmann, A. Weckenmann, and P. F. Brenner, “Automatic, task-sensitive and simulation-based optimization of fringe projection measurements,” Key Eng. Mater. 437, 439–443 (2010).
[CrossRef]

A. Weckenmann, W. Hartmann, and J. Weickmann, “Model and simulation of fringe projection measurements as part of an assistance system for multi component fringe projection sensors,” Proc. SPIE 7102, 71020N (2008).
[CrossRef]

A. Weckenmann, W. Hartmann, and J. Weickmann, “Multi-component fringe projection sensors: Assistance system for short and robust inspection processes,” in Proceedings of the 2008 NCSL International Workshop and Symposium (NCSL, 2008), pp. 43–49.

Woias, P.

R. Schmitt, F. Koerfer, O. Sawodny, J. Zimmermann, R. Krüger-Sehm, M. Xu, T. Dziomba, L. Koenders, G. Goch, A. Tausendfreund, S. Patzelt, S. Simon, L. Rockstroh, C. Bellon, A. Staude, P. Woias, F. Goldschmidtböing, and M. Rabold, “Virtuelle Messgeräte: Definition und Stand der Entwicklung,” Tech. Mess. 75, 298–310 (2008).
[CrossRef]

Xu, M.

R. Schmitt, F. Koerfer, O. Sawodny, J. Zimmermann, R. Krüger-Sehm, M. Xu, T. Dziomba, L. Koenders, G. Goch, A. Tausendfreund, S. Patzelt, S. Simon, L. Rockstroh, C. Bellon, A. Staude, P. Woias, F. Goldschmidtböing, and M. Rabold, “Virtuelle Messgeräte: Definition und Stand der Entwicklung,” Tech. Mess. 75, 298–310 (2008).
[CrossRef]

Yang, Q.

Y. Hu, Q. Yang, and P. Wei, “Development of a novel virtual coordinate measuring machine,” in I2MTC—International Instrumentation and Measurement Technology Conference (IEEE, 2009), pp. 230–233.

Zimmermann, J.

R. Schmitt, F. Koerfer, O. Sawodny, J. Zimmermann, R. Krüger-Sehm, M. Xu, T. Dziomba, L. Koenders, G. Goch, A. Tausendfreund, S. Patzelt, S. Simon, L. Rockstroh, C. Bellon, A. Staude, P. Woias, F. Goldschmidtböing, and M. Rabold, “Virtuelle Messgeräte: Definition und Stand der Entwicklung,” Tech. Mess. 75, 298–310 (2008).
[CrossRef]

Key Eng. Mater. (1)

J. Weickmann, A. Weckenmann, and P. F. Brenner, “Automatic, task-sensitive and simulation-based optimization of fringe projection measurements,” Key Eng. Mater. 437, 439–443 (2010).
[CrossRef]

Measurement (1)

C. L. Giusca, A. B. Forbes, and R. K. Leach, “A virtual machine-based uncertainty evaluation for a traceable areal surface texture measuring instrument,” Measurement 44, 988–993 (2011).
[CrossRef]

Proc. SPIE (2)

A. Weckenmann, W. Hartmann, and J. Weickmann, “Model and simulation of fringe projection measurements as part of an assistance system for multi component fringe projection sensors,” Proc. SPIE 7102, 71020N (2008).
[CrossRef]

K. Haskamp, M. Kästner, and E. Reithmeier, “Accurate calibration of a fringe projection system by considering telecentricity,” Proc. SPIE 8082, 80821B (2011).
[CrossRef]

Tech. Mess. (2)

K. Haskamp, M. Kästner, R. Gillhaus, and E. Reithmeier, “Messunsicherheitsanalyse mittels virtueller Streifen-projektionstechnik auf Grundlage von Polygonmodellen,” Tech. Mess. 78, 60–68 (2011).
[CrossRef]

R. Schmitt, F. Koerfer, O. Sawodny, J. Zimmermann, R. Krüger-Sehm, M. Xu, T. Dziomba, L. Koenders, G. Goch, A. Tausendfreund, S. Patzelt, S. Simon, L. Rockstroh, C. Bellon, A. Staude, P. Woias, F. Goldschmidtböing, and M. Rabold, “Virtuelle Messgeräte: Definition und Stand der Entwicklung,” Tech. Mess. 75, 298–310 (2008).
[CrossRef]

Other (7)

Y. Hu, Q. Yang, and P. Wei, “Development of a novel virtual coordinate measuring machine,” in I2MTC—International Instrumentation and Measurement Technology Conference (IEEE, 2009), pp. 230–233.

M. Trenk, M. Franke, and H. Schwenke, “The ‘Virtual CMM’ a software tool for uncertainty evaluation—practical application in an accredited calibration lab,” in ASPE Proceedings on Uncertainty Analysis in Measurement and Design (ASPE, 2004), pp. 1–6.

C. L. Giusca, A. B. Forbes, and R. K. Leach, “Comparison between GUM, Monte Carlo and Bayesian uncertainty evaluation approaches for an areal surface texture measuring instrument,” in Proceedings of the International Congress of Metrology (Dutch Metrology Institute, 2009), Vol. 14, pp. 988–993.

T. Böttner, “Untersuchungen zur Messunsicherheit mit Hilfe eines virtuellen Streifenprojektionssystems,” Ph.D. thesis (Leibniz Universität Hannover, 2008).

A. Weckenmann, W. Hartmann, and J. Weickmann, “Multi-component fringe projection sensors: Assistance system for short and robust inspection processes,” in Proceedings of the 2008 NCSL International Workshop and Symposium (NCSL, 2008), pp. 43–49.

International Organization for Standardization, GUM—Guide to the Expression of Uncertainty in Measurement (DIN/Beuth-Verlag, 1995).

S. Kammel, “Deflektometrische Untersuchung spiegelnd reflektierender Freiformflächen,” Ph.D. thesis (Universität Karlsruhe, 2004).

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Figures (3)

Fig. 1.
Fig. 1.

Virtual concept of the fringe projection system.

Fig. 2.
Fig. 2.

Principle for the estimation of the areal uncertainty of measurement.

Fig. 3.
Fig. 3.

Areal uncertainty of measurement of a planar calibration artifact.

Tables (2)

Tables Icon

Table 1. Main Influence Quantities and the Associated Uncertainty of Measurement

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Table 2. Uncertainty of Measurement of the Geometric Attributes of a Sphere

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

i,j,Ii,j*,ϕcalc,i,j,ψcalc,i,j,pcalc,i,j,di,j.
s(dRes,I)=1N1k=1N(dRes,I,kd¯Res,I)2,
uC(dRes,I)=s(d¯Res,I)=s(dRes,I)N+|d¯Res,I|,
R2=(xMx)2+(yMy)2+(zMz)2,
s(R)=1N1k=1N(RR¯)2,
uC(R)=s(R)N+usys,

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