Abstract

This paper presents the outcome of research into the effects of ambient temperature changes on structured-light three-dimensional (3D) scanners. The tests were conducted in a thermal chamber and consisted of a comparison of the 3D measurement of a special reference unit (made of a carbon composite) performed at different temperatures, with measurements performed at the calibration temperature. A contact measuring arm with temperature compensation was used as a reference. Based on the results of these experiments, we propose a method that allows us to extend the existing scanner calibration method by using a temperature-correction procedure that is based on linear and nonlinear mathematical models. An exemplary application of this procedure has shown that the range of temperatures in which scanner accuracy is within declared limits can be increased 11-fold.

© 2014 Optical Society of America

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2014 (2)

M. Trusiak, M. Wielgus, and K. Patorski, “Advanced processing of optical fringe patterns by automated selective reconstruction and enhanced fast empirical mode decomposition,” Opt. Lasers Eng. 52, 230–240 (2014).
[CrossRef]

J. Huang and Q. Wu, “A new reconstruction method based on fringe projection of three-dimensional measuring system,” Opt. Lasers Eng. 52, 115–122 (2014).
[CrossRef]

2013 (3)

M. Wengierow, L. Salbut, Z. Ramatowski, R. Szumski, and K. Szykiedans, “Measurement system based on multi-wavelength interferometry for long gauge block calibration,” Metrol. Meas. Syst. 20, 479–490 (2013).

M. Karaszewski, M. Adamczyk, R. Sitnik, J. Michoński, W. Załuski, E. Bunsch, and P. Bolewicki, “Automated full-3D digitization system for documentation of paintings,” Proc. SPIE 8790, 87900X (2013).

J. Lenar, M. Witkowski, V. Carbone, S. Kolk, M. Adamczyk, R. Sitnik, M. van der Krogt, and N. Verdonschot, “Lower body kinematics based on a multidirectional four-dimensional structured light measurement,” J. Biomed. Opt. 18, 56014 (2013).
[CrossRef]

2012 (1)

Z. H. Zhang, “Review of single-shot 3D shape measurement by phase calculation-based fringe projection techniques,” Opt. Lasers Eng. 50, 1097–1106 (2012).
[CrossRef]

2011 (1)

J. Sładek, P. Błaszczyk, M. Kupiec, and R. Sitnik, “The hybrid contact-optical coordinate measuring system,” Measurement 44, 502–510 (2011).

2010 (2)

S. Zhang, “Recent progress on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48, 149–158 (2010).
[CrossRef]

S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng. 48, 133–140 (2010).
[CrossRef]

2009 (2)

G. Sansoni, M. Trebeschi, and F. Docchio, “State-of-the-art and applications of 3D imaging sensors in industry, cultural heritage, medicine, and criminal investigation,” Sensors 9, 568–601 (2009).
[CrossRef]

D. Rieke-Zapp, W. Tecklenburg, J. Peipe, H. Hastedt, and C. Haig, “Evaluation of the geometric stability and the accuracy potential of digital cameras—comparing mechanical stabilization versus parameterization,” ISPRS J. Photogramm. Remote Sens. 64, 248–258 (2009).

2008 (1)

X. Chen, J. Xi, T. Jiang, and Y. Jin, “Research and development of an accurate 3D shape measurement system based on fringe projection: model analysis and performance evaluation,” Precis. Eng. 32, 215–221 (2008).
[CrossRef]

2003 (3)

G. H. Notni and G. Notni, “Digital fringe projection in 3D shape measurement—an error analysis,” Proc. SPIE 5144, 372–380 (2003).

J.-P. Kruth, L. Zhou, and P. Vanherck, “Thermal error analysis and compensation of an LED-CMOS camera 3D measuring system,” Meas. Sci. Rev. 3, 5–8 (2003).

P. S. Huang, Q. Hu, and F. Chiang, “Error compensation for a three-dimensional shape measurement system,” Opt. Express 42, 482–486 (2003).

2002 (1)

R. Sitnik and M. Kujawińska, “From cloud of point co-ordinates to 3D virtual environment: the data conversion system,” Opt. Eng. 41, 416–427 (2002).
[CrossRef]

2000 (1)

F. Chen, G. M. Brown, and M. Song, “Overview of 3-D shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

1997 (1)

C. S. Fraser, “Digital camera self-calibration,” ISPRS J. 52, 149–159 (1997).

Adamczyk, M.

J. Lenar, M. Witkowski, V. Carbone, S. Kolk, M. Adamczyk, R. Sitnik, M. van der Krogt, and N. Verdonschot, “Lower body kinematics based on a multidirectional four-dimensional structured light measurement,” J. Biomed. Opt. 18, 56014 (2013).
[CrossRef]

M. Karaszewski, M. Adamczyk, R. Sitnik, J. Michoński, W. Załuski, E. Bunsch, and P. Bolewicki, “Automated full-3D digitization system for documentation of paintings,” Proc. SPIE 8790, 87900X (2013).

Blaszczyk, P.

J. Sładek, P. Błaszczyk, M. Kupiec, and R. Sitnik, “The hybrid contact-optical coordinate measuring system,” Measurement 44, 502–510 (2011).

Bolewicki, P.

M. Karaszewski, M. Adamczyk, R. Sitnik, J. Michoński, W. Załuski, E. Bunsch, and P. Bolewicki, “Automated full-3D digitization system for documentation of paintings,” Proc. SPIE 8790, 87900X (2013).

Bräuer-Burchardt, C.

C. Bräuer-Burchardt, A. Breitbarth, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, “Calibration evaluation and calibration stability monitoring of fringe projection based 3D scanners,” in International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol. XXXVIII-3/W22, ISPRS Conference PIA 2011, Munich, Germany, 5–7 October, 2011.

Breitbarth, A.

C. Bräuer-Burchardt, A. Breitbarth, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, “Calibration evaluation and calibration stability monitoring of fringe projection based 3D scanners,” in International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol. XXXVIII-3/W22, ISPRS Conference PIA 2011, Munich, Germany, 5–7 October, 2011.

Brown, G. M.

F. Chen, G. M. Brown, and M. Song, “Overview of 3-D shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Bunsch, E.

M. Karaszewski, M. Adamczyk, R. Sitnik, J. Michoński, W. Załuski, E. Bunsch, and P. Bolewicki, “Automated full-3D digitization system for documentation of paintings,” Proc. SPIE 8790, 87900X (2013).

Carbone, V.

J. Lenar, M. Witkowski, V. Carbone, S. Kolk, M. Adamczyk, R. Sitnik, M. van der Krogt, and N. Verdonschot, “Lower body kinematics based on a multidirectional four-dimensional structured light measurement,” J. Biomed. Opt. 18, 56014 (2013).
[CrossRef]

Chen, F.

F. Chen, G. M. Brown, and M. Song, “Overview of 3-D shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Chen, X.

X. Chen, J. Xi, T. Jiang, and Y. Jin, “Research and development of an accurate 3D shape measurement system based on fringe projection: model analysis and performance evaluation,” Precis. Eng. 32, 215–221 (2008).
[CrossRef]

Chiang, F.

P. S. Huang, Q. Hu, and F. Chiang, “Error compensation for a three-dimensional shape measurement system,” Opt. Express 42, 482–486 (2003).

Cyganek, B.

B. Cyganek and J. P. Siebert, An Introduction to 3D Computer Vision Techniques and Algorithms (Wiley, 2009).

Docchio, F.

G. Sansoni, M. Trebeschi, and F. Docchio, “State-of-the-art and applications of 3D imaging sensors in industry, cultural heritage, medicine, and criminal investigation,” Sensors 9, 568–601 (2009).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd ed. (Cambridge University, 2007).

Fraser, C. S.

C. S. Fraser, “Digital camera self-calibration,” ISPRS J. 52, 149–159 (1997).

Gorthi, S.

S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng. 48, 133–140 (2010).
[CrossRef]

Haig, C.

D. Rieke-Zapp, W. Tecklenburg, J. Peipe, H. Hastedt, and C. Haig, “Evaluation of the geometric stability and the accuracy potential of digital cameras—comparing mechanical stabilization versus parameterization,” ISPRS J. Photogramm. Remote Sens. 64, 248–258 (2009).

Handel, H.

H. Handel, “Compensation of thermal errors in vision based measurement systems using a system identification approach,” in 9th International Conference on Signal Processing (ICSP) (IEEE, 2008), pp. 1329–1333.

H. Handel, “Analyzing the influences of camera warm-up effects on image acquisition,” in 8th Asian Conference on Computer Vision (ACCV) (Springer, 2007), Vol. 4844, pp. 258–268.

Hastedt, H.

D. Rieke-Zapp, W. Tecklenburg, J. Peipe, H. Hastedt, and C. Haig, “Evaluation of the geometric stability and the accuracy potential of digital cameras—comparing mechanical stabilization versus parameterization,” ISPRS J. Photogramm. Remote Sens. 64, 248–258 (2009).

Heinze, M.

C. Bräuer-Burchardt, A. Breitbarth, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, “Calibration evaluation and calibration stability monitoring of fringe projection based 3D scanners,” in International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol. XXXVIII-3/W22, ISPRS Conference PIA 2011, Munich, Germany, 5–7 October, 2011.

Hu, Q.

P. S. Huang, Q. Hu, and F. Chiang, “Error compensation for a three-dimensional shape measurement system,” Opt. Express 42, 482–486 (2003).

Huang, J.

J. Huang and Q. Wu, “A new reconstruction method based on fringe projection of three-dimensional measuring system,” Opt. Lasers Eng. 52, 115–122 (2014).
[CrossRef]

Huang, P. S.

P. S. Huang, Q. Hu, and F. Chiang, “Error compensation for a three-dimensional shape measurement system,” Opt. Express 42, 482–486 (2003).

Jiang, T.

X. Chen, J. Xi, T. Jiang, and Y. Jin, “Research and development of an accurate 3D shape measurement system based on fringe projection: model analysis and performance evaluation,” Precis. Eng. 32, 215–221 (2008).
[CrossRef]

Jin, Y.

X. Chen, J. Xi, T. Jiang, and Y. Jin, “Research and development of an accurate 3D shape measurement system based on fringe projection: model analysis and performance evaluation,” Precis. Eng. 32, 215–221 (2008).
[CrossRef]

Karaszewski, M.

M. Karaszewski, M. Adamczyk, R. Sitnik, J. Michoński, W. Załuski, E. Bunsch, and P. Bolewicki, “Automated full-3D digitization system for documentation of paintings,” Proc. SPIE 8790, 87900X (2013).

Kolk, S.

J. Lenar, M. Witkowski, V. Carbone, S. Kolk, M. Adamczyk, R. Sitnik, M. van der Krogt, and N. Verdonschot, “Lower body kinematics based on a multidirectional four-dimensional structured light measurement,” J. Biomed. Opt. 18, 56014 (2013).
[CrossRef]

Kruth, J.-P.

J.-P. Kruth, L. Zhou, and P. Vanherck, “Thermal error analysis and compensation of an LED-CMOS camera 3D measuring system,” Meas. Sci. Rev. 3, 5–8 (2003).

Kühmstedt, P.

C. Bräuer-Burchardt, A. Breitbarth, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, “Calibration evaluation and calibration stability monitoring of fringe projection based 3D scanners,” in International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol. XXXVIII-3/W22, ISPRS Conference PIA 2011, Munich, Germany, 5–7 October, 2011.

Kujawinska, M.

R. Sitnik and M. Kujawińska, “From cloud of point co-ordinates to 3D virtual environment: the data conversion system,” Opt. Eng. 41, 416–427 (2002).
[CrossRef]

Kupiec, M.

J. Sładek, P. Błaszczyk, M. Kupiec, and R. Sitnik, “The hybrid contact-optical coordinate measuring system,” Measurement 44, 502–510 (2011).

Lenar, J.

J. Lenar, M. Witkowski, V. Carbone, S. Kolk, M. Adamczyk, R. Sitnik, M. van der Krogt, and N. Verdonschot, “Lower body kinematics based on a multidirectional four-dimensional structured light measurement,” J. Biomed. Opt. 18, 56014 (2013).
[CrossRef]

Michonski, J.

M. Karaszewski, M. Adamczyk, R. Sitnik, J. Michoński, W. Załuski, E. Bunsch, and P. Bolewicki, “Automated full-3D digitization system for documentation of paintings,” Proc. SPIE 8790, 87900X (2013).

Munkelt, C.

C. Bräuer-Burchardt, A. Breitbarth, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, “Calibration evaluation and calibration stability monitoring of fringe projection based 3D scanners,” in International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol. XXXVIII-3/W22, ISPRS Conference PIA 2011, Munich, Germany, 5–7 October, 2011.

Notni, G.

G. H. Notni and G. Notni, “Digital fringe projection in 3D shape measurement—an error analysis,” Proc. SPIE 5144, 372–380 (2003).

C. Bräuer-Burchardt, A. Breitbarth, C. Munkelt, M. Heinze, P. Kühmstedt, and G. Notni, “Calibration evaluation and calibration stability monitoring of fringe projection based 3D scanners,” in International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol. XXXVIII-3/W22, ISPRS Conference PIA 2011, Munich, Germany, 5–7 October, 2011.

Notni, G. H.

G. H. Notni and G. Notni, “Digital fringe projection in 3D shape measurement—an error analysis,” Proc. SPIE 5144, 372–380 (2003).

Patorski, K.

M. Trusiak, M. Wielgus, and K. Patorski, “Advanced processing of optical fringe patterns by automated selective reconstruction and enhanced fast empirical mode decomposition,” Opt. Lasers Eng. 52, 230–240 (2014).
[CrossRef]

Peipe, J.

D. Rieke-Zapp, W. Tecklenburg, J. Peipe, H. Hastedt, and C. Haig, “Evaluation of the geometric stability and the accuracy potential of digital cameras—comparing mechanical stabilization versus parameterization,” ISPRS J. Photogramm. Remote Sens. 64, 248–258 (2009).

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd ed. (Cambridge University, 2007).

Ramatowski, Z.

M. Wengierow, L. Salbut, Z. Ramatowski, R. Szumski, and K. Szykiedans, “Measurement system based on multi-wavelength interferometry for long gauge block calibration,” Metrol. Meas. Syst. 20, 479–490 (2013).

Rastogi, P.

S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng. 48, 133–140 (2010).
[CrossRef]

Rieke-Zapp, D.

D. Rieke-Zapp, W. Tecklenburg, J. Peipe, H. Hastedt, and C. Haig, “Evaluation of the geometric stability and the accuracy potential of digital cameras—comparing mechanical stabilization versus parameterization,” ISPRS J. Photogramm. Remote Sens. 64, 248–258 (2009).

Salbut, L.

M. Wengierow, L. Salbut, Z. Ramatowski, R. Szumski, and K. Szykiedans, “Measurement system based on multi-wavelength interferometry for long gauge block calibration,” Metrol. Meas. Syst. 20, 479–490 (2013).

Sansoni, G.

G. Sansoni, M. Trebeschi, and F. Docchio, “State-of-the-art and applications of 3D imaging sensors in industry, cultural heritage, medicine, and criminal investigation,” Sensors 9, 568–601 (2009).
[CrossRef]

Siebert, J. P.

B. Cyganek and J. P. Siebert, An Introduction to 3D Computer Vision Techniques and Algorithms (Wiley, 2009).

Sitnik, R.

J. Lenar, M. Witkowski, V. Carbone, S. Kolk, M. Adamczyk, R. Sitnik, M. van der Krogt, and N. Verdonschot, “Lower body kinematics based on a multidirectional four-dimensional structured light measurement,” J. Biomed. Opt. 18, 56014 (2013).
[CrossRef]

M. Karaszewski, M. Adamczyk, R. Sitnik, J. Michoński, W. Załuski, E. Bunsch, and P. Bolewicki, “Automated full-3D digitization system for documentation of paintings,” Proc. SPIE 8790, 87900X (2013).

J. Sładek, P. Błaszczyk, M. Kupiec, and R. Sitnik, “The hybrid contact-optical coordinate measuring system,” Measurement 44, 502–510 (2011).

R. Sitnik and M. Kujawińska, “From cloud of point co-ordinates to 3D virtual environment: the data conversion system,” Opt. Eng. 41, 416–427 (2002).
[CrossRef]

Sladek, J.

J. Sładek, P. Błaszczyk, M. Kupiec, and R. Sitnik, “The hybrid contact-optical coordinate measuring system,” Measurement 44, 502–510 (2011).

Song, M.

F. Chen, G. M. Brown, and M. Song, “Overview of 3-D shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Szumski, R.

M. Wengierow, L. Salbut, Z. Ramatowski, R. Szumski, and K. Szykiedans, “Measurement system based on multi-wavelength interferometry for long gauge block calibration,” Metrol. Meas. Syst. 20, 479–490 (2013).

Szykiedans, K.

M. Wengierow, L. Salbut, Z. Ramatowski, R. Szumski, and K. Szykiedans, “Measurement system based on multi-wavelength interferometry for long gauge block calibration,” Metrol. Meas. Syst. 20, 479–490 (2013).

Tecklenburg, W.

D. Rieke-Zapp, W. Tecklenburg, J. Peipe, H. Hastedt, and C. Haig, “Evaluation of the geometric stability and the accuracy potential of digital cameras—comparing mechanical stabilization versus parameterization,” ISPRS J. Photogramm. Remote Sens. 64, 248–258 (2009).

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd ed. (Cambridge University, 2007).

Trebeschi, M.

G. Sansoni, M. Trebeschi, and F. Docchio, “State-of-the-art and applications of 3D imaging sensors in industry, cultural heritage, medicine, and criminal investigation,” Sensors 9, 568–601 (2009).
[CrossRef]

Trusiak, M.

M. Trusiak, M. Wielgus, and K. Patorski, “Advanced processing of optical fringe patterns by automated selective reconstruction and enhanced fast empirical mode decomposition,” Opt. Lasers Eng. 52, 230–240 (2014).
[CrossRef]

van der Krogt, M.

J. Lenar, M. Witkowski, V. Carbone, S. Kolk, M. Adamczyk, R. Sitnik, M. van der Krogt, and N. Verdonschot, “Lower body kinematics based on a multidirectional four-dimensional structured light measurement,” J. Biomed. Opt. 18, 56014 (2013).
[CrossRef]

Vanherck, P.

J.-P. Kruth, L. Zhou, and P. Vanherck, “Thermal error analysis and compensation of an LED-CMOS camera 3D measuring system,” Meas. Sci. Rev. 3, 5–8 (2003).

Verdonschot, N.

J. Lenar, M. Witkowski, V. Carbone, S. Kolk, M. Adamczyk, R. Sitnik, M. van der Krogt, and N. Verdonschot, “Lower body kinematics based on a multidirectional four-dimensional structured light measurement,” J. Biomed. Opt. 18, 56014 (2013).
[CrossRef]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd ed. (Cambridge University, 2007).

Wengierow, M.

M. Wengierow, L. Salbut, Z. Ramatowski, R. Szumski, and K. Szykiedans, “Measurement system based on multi-wavelength interferometry for long gauge block calibration,” Metrol. Meas. Syst. 20, 479–490 (2013).

Wielgus, M.

M. Trusiak, M. Wielgus, and K. Patorski, “Advanced processing of optical fringe patterns by automated selective reconstruction and enhanced fast empirical mode decomposition,” Opt. Lasers Eng. 52, 230–240 (2014).
[CrossRef]

Witkowski, M.

J. Lenar, M. Witkowski, V. Carbone, S. Kolk, M. Adamczyk, R. Sitnik, M. van der Krogt, and N. Verdonschot, “Lower body kinematics based on a multidirectional four-dimensional structured light measurement,” J. Biomed. Opt. 18, 56014 (2013).
[CrossRef]

Wu, Q.

J. Huang and Q. Wu, “A new reconstruction method based on fringe projection of three-dimensional measuring system,” Opt. Lasers Eng. 52, 115–122 (2014).
[CrossRef]

Xi, J.

X. Chen, J. Xi, T. Jiang, and Y. Jin, “Research and development of an accurate 3D shape measurement system based on fringe projection: model analysis and performance evaluation,” Precis. Eng. 32, 215–221 (2008).
[CrossRef]

Zaluski, W.

M. Karaszewski, M. Adamczyk, R. Sitnik, J. Michoński, W. Załuski, E. Bunsch, and P. Bolewicki, “Automated full-3D digitization system for documentation of paintings,” Proc. SPIE 8790, 87900X (2013).

Zhang, S.

S. Zhang, “Recent progress on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48, 149–158 (2010).
[CrossRef]

Zhang, Z. H.

Z. H. Zhang, “Review of single-shot 3D shape measurement by phase calculation-based fringe projection techniques,” Opt. Lasers Eng. 50, 1097–1106 (2012).
[CrossRef]

Zhou, L.

J.-P. Kruth, L. Zhou, and P. Vanherck, “Thermal error analysis and compensation of an LED-CMOS camera 3D measuring system,” Meas. Sci. Rev. 3, 5–8 (2003).

ISPRS J. (1)

C. S. Fraser, “Digital camera self-calibration,” ISPRS J. 52, 149–159 (1997).

ISPRS J. Photogramm. Remote Sens. (1)

D. Rieke-Zapp, W. Tecklenburg, J. Peipe, H. Hastedt, and C. Haig, “Evaluation of the geometric stability and the accuracy potential of digital cameras—comparing mechanical stabilization versus parameterization,” ISPRS J. Photogramm. Remote Sens. 64, 248–258 (2009).

J. Biomed. Opt. (1)

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Figures (12)

Fig. 1.
Fig. 1.

Geometric model of a scanner: (3) a projector and (2) a detector are attached to (1) a base beam that is fixed in the middle. The optical axes of the detector and projector lenses intersect at an angle of γ at point P ( x 0 , y 0 , z 0 ) , when the base length is L .

Fig. 2.
Fig. 2.

Ruled surfaces in the temperature and base angle domains representing Δ x and Δ z deviations. The area defining the uncertainty of scanners with a design similar to the tested model is marked in gray [12].

Fig. 3.
Fig. 3.

Increasing the base angle γ will result in a greater area not being covered by the measurement (lighter colored areas).

Fig. 4.
Fig. 4.

Construction of a group of three planes, and an overall view of the reference unit.

Fig. 5.
Fig. 5.

View of the test stand in the thermal chamber.

Fig. 6.
Fig. 6.

Left: reference unit measurement with a 3D scanner. Right: reference unit measurement with a measuring arm.

Fig. 7.
Fig. 7.

Graph showing the relationship between coordinates x of point P 1 and temperature; coordinates are marked in red and average values are marked in blue. (Red, P 1 coordinates value; blue, mean coordinates value.)

Fig. 8.
Fig. 8.

Top: visualization of a single 3D scanner measurement. Bottom: processed data prepared for calculations.

Fig. 9.
Fig. 9.

Top left and right, bottom left: relationship between coordinate deviations for points P 1 P 8 . Bottom right: some distance deviations.

Fig. 10.
Fig. 10.

Visualization of the deformation of the measurement volume caused by changes in temperature.

Fig. 11.
Fig. 11.

Results of applying the proposed methods to the P 1 P 8 point coordinates (coordinates shown separately).

Fig. 12.
Fig. 12.

3D scanner’s range of accurate operation.

Tables (1)

Tables Icon

Table 1. RMS Error Calculated for Each Compensation Model

Equations (10)

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

X T · X · α = X T · Y .
X = [ x 0 y 0 x 1 y 1 z 0 T 0 z 1 T 1 x k y k z k T k ] .
Y x = [ Δ x 0 Δ x 1 Δ x k ] , Y y = [ Δ y 0 Δ y 1 Δ y k ] , Y z = [ Δ z 0 Δ z 1 Δ z k ] ,
α x = [ A x B x C x D x E x ] , α y = [ A y B y C y D y E y ] , α z = [ A z B z C z D z E z ] .
Δ x = A x · x + B x · y + C x · z + D x · T + E x ,
Δ y = A y · x + B y · y + C y · z + D y · T + E y ,
Δ z = A z · x + B z · y + C z · z + D z · T + E z .
Δ x = P x 3 ( t , x , y , z ) ,
Δ y = P y 3 ( t , x , y , z ) ,
Δ z = P z 3 ( t , x , y , z ) .

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