Abstract

This research presents a novel method to calibrate a microscopic structured light system using a camera with a telecentric lens. The pin-hole projector calibration follows the standard pin-hole camera calibration procedures. With the calibrated projector, the 3D coordinates of those feature points used for projector calibration are then estimated through iterative Levenberg-Marquardt optimization. Those 3D feature points are further used to calibrate the camera with a telecentric lens. We will describe the mathematical model of a telecentric lens, and demonstrate that the proposed calibration framework can achieve very high accuracy: approximately 10 μm with a volume of approximately 10(H) mm × 8(W) mm × 5(D) mm.

© 2015 Optical Society of America

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References

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  1. S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng 48, 133–140 (2010).
    [Crossref]
  2. R. Windecker, M. Fleischer, and H. J. Tiziani, “Three-dimensional topometry with stereo microscopes,” Opt. Eng. 36, 3372–3377 (1997).
    [Crossref]
  3. C. Zhang, P. S. Huang, and F.-P. Chiang, “Microscopic phase-shifting profilometry based on digital micromirror device technology,” Appl. Opt. 41, 5896–5904 (2002).
    [Crossref] [PubMed]
  4. K.-P. Proll, J.-M. Nivet, K. Körner, and H. J. Tiziani, “Microscopic three-dimensional topometry with ferroelectric liquid-crystal-on-silicon displays,” Appl. Opt. 42, 1773–1778 (2003).
    [Crossref] [PubMed]
  5. R. Rodriguez-Vera, K. Genovese, J. Rayas, and F. Mendoza-Santoyo, “Vibration analysis at microscale by talbot fringe projection method,” Strain 45, 249–258 (2009).
    [Crossref]
  6. A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3d microscopy,” Optik 124, 5052–5056 (2013).
    [Crossref]
  7. C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, “Shape measurement of small objects using lcd fringe projection with phase shifting,” Opt. Commun. 189, 21–29 (2001).
    [Crossref]
  8. C. Quan, C. J. Tay, X. Y. He, X. Kang, and H. M. Shang, “Microscopic surface contouring by fringe projection method,” Opt. Laser Technol. 34, 547–552 (2002).
    [Crossref]
  9. J. Chen, T. Guo, L. Wang, Z. Wu, X. Fu, and X. Hu, “Microscopic fringe projection system and measuring method,” in “Proc. SPIE,” (Chengdu, China, 2013), pp. 87594U.
    [Crossref]
  10. D. S. Mehta, M. Inam, J. Prakash, and A. Biradar, “Liquid-crystal phase-shifting lateral shearing interferometer with improved fringe contrast for 3d surface profilometry,” Appl. Opt. 52, 6119–6125 (2013).
    [Crossref]
  11. Y. Yin, M. Wang, B. Z. Gao, X. Liu, and X. Peng, “Fringe projection 3d microscopy with the general imaging model,” Opt. Express 23, 6846–6857 (2015).
    [Crossref] [PubMed]
  12. D. Li and J. Tian, “An accurate calibration method for a camera with telecentric lenses,” Opt. Lasers Eng. 51, 538–541 (2013).
    [Crossref]
  13. F. Zhu, W. Liu, H. Shi, and X. He, “Accurate 3d measurement system and calibration for speckle projection method,” Opt. Lasers Eng. 48, 1132–1139 (2010).
    [Crossref]
  14. D. Li, C. Liu, and J. Tian, “Telecentric 3d profilometry based on phase-shifting fringe projection,” Opt. Express 22, 31826–31835 (2014).
    [Crossref]
  15. S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 083601 (2006).
    [Crossref]
  16. Y. Wang and S. Zhang, “Superfast multifrequency phase-shifting technique with optimal pulse width modulation,” Opt. Lett. 19, 5149–5155 (2011).

2015 (1)

2014 (1)

2013 (3)

D. S. Mehta, M. Inam, J. Prakash, and A. Biradar, “Liquid-crystal phase-shifting lateral shearing interferometer with improved fringe contrast for 3d surface profilometry,” Appl. Opt. 52, 6119–6125 (2013).
[Crossref]

A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3d microscopy,” Optik 124, 5052–5056 (2013).
[Crossref]

D. Li and J. Tian, “An accurate calibration method for a camera with telecentric lenses,” Opt. Lasers Eng. 51, 538–541 (2013).
[Crossref]

2011 (1)

Y. Wang and S. Zhang, “Superfast multifrequency phase-shifting technique with optimal pulse width modulation,” Opt. Lett. 19, 5149–5155 (2011).

2010 (2)

F. Zhu, W. Liu, H. Shi, and X. He, “Accurate 3d measurement system and calibration for speckle projection method,” Opt. Lasers Eng. 48, 1132–1139 (2010).
[Crossref]

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

2009 (1)

R. Rodriguez-Vera, K. Genovese, J. Rayas, and F. Mendoza-Santoyo, “Vibration analysis at microscale by talbot fringe projection method,” Strain 45, 249–258 (2009).
[Crossref]

2006 (1)

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 083601 (2006).
[Crossref]

2003 (1)

2002 (2)

C. Zhang, P. S. Huang, and F.-P. Chiang, “Microscopic phase-shifting profilometry based on digital micromirror device technology,” Appl. Opt. 41, 5896–5904 (2002).
[Crossref] [PubMed]

C. Quan, C. J. Tay, X. Y. He, X. Kang, and H. M. Shang, “Microscopic surface contouring by fringe projection method,” Opt. Laser Technol. 34, 547–552 (2002).
[Crossref]

2001 (1)

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, “Shape measurement of small objects using lcd fringe projection with phase shifting,” Opt. Commun. 189, 21–29 (2001).
[Crossref]

1997 (1)

R. Windecker, M. Fleischer, and H. J. Tiziani, “Three-dimensional topometry with stereo microscopes,” Opt. Eng. 36, 3372–3377 (1997).
[Crossref]

Biradar, A.

Chen, J.

J. Chen, T. Guo, L. Wang, Z. Wu, X. Fu, and X. Hu, “Microscopic fringe projection system and measuring method,” in “Proc. SPIE,” (Chengdu, China, 2013), pp. 87594U.
[Crossref]

Chiang, F.-P.

Fleischer, M.

R. Windecker, M. Fleischer, and H. J. Tiziani, “Three-dimensional topometry with stereo microscopes,” Opt. Eng. 36, 3372–3377 (1997).
[Crossref]

Fu, X.

J. Chen, T. Guo, L. Wang, Z. Wu, X. Fu, and X. Hu, “Microscopic fringe projection system and measuring method,” in “Proc. SPIE,” (Chengdu, China, 2013), pp. 87594U.
[Crossref]

Gao, B. Z.

Genovese, K.

R. Rodriguez-Vera, K. Genovese, J. Rayas, and F. Mendoza-Santoyo, “Vibration analysis at microscale by talbot fringe projection method,” Strain 45, 249–258 (2009).
[Crossref]

Gorthi, S. S.

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

Guo, T.

J. Chen, T. Guo, L. Wang, Z. Wu, X. Fu, and X. Hu, “Microscopic fringe projection system and measuring method,” in “Proc. SPIE,” (Chengdu, China, 2013), pp. 87594U.
[Crossref]

He, X.

F. Zhu, W. Liu, H. Shi, and X. He, “Accurate 3d measurement system and calibration for speckle projection method,” Opt. Lasers Eng. 48, 1132–1139 (2010).
[Crossref]

He, X. Y.

C. Quan, C. J. Tay, X. Y. He, X. Kang, and H. M. Shang, “Microscopic surface contouring by fringe projection method,” Opt. Laser Technol. 34, 547–552 (2002).
[Crossref]

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, “Shape measurement of small objects using lcd fringe projection with phase shifting,” Opt. Commun. 189, 21–29 (2001).
[Crossref]

Hu, X.

J. Chen, T. Guo, L. Wang, Z. Wu, X. Fu, and X. Hu, “Microscopic fringe projection system and measuring method,” in “Proc. SPIE,” (Chengdu, China, 2013), pp. 87594U.
[Crossref]

Huang, P. S.

Inam, M.

Kang, X.

C. Quan, C. J. Tay, X. Y. He, X. Kang, and H. M. Shang, “Microscopic surface contouring by fringe projection method,” Opt. Laser Technol. 34, 547–552 (2002).
[Crossref]

Körner, K.

A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3d microscopy,” Optik 124, 5052–5056 (2013).
[Crossref]

K.-P. Proll, J.-M. Nivet, K. Körner, and H. J. Tiziani, “Microscopic three-dimensional topometry with ferroelectric liquid-crystal-on-silicon displays,” Appl. Opt. 42, 1773–1778 (2003).
[Crossref] [PubMed]

Li, A.

A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3d microscopy,” Optik 124, 5052–5056 (2013).
[Crossref]

Li, D.

D. Li, C. Liu, and J. Tian, “Telecentric 3d profilometry based on phase-shifting fringe projection,” Opt. Express 22, 31826–31835 (2014).
[Crossref]

D. Li and J. Tian, “An accurate calibration method for a camera with telecentric lenses,” Opt. Lasers Eng. 51, 538–541 (2013).
[Crossref]

Liu, C.

Liu, W.

F. Zhu, W. Liu, H. Shi, and X. He, “Accurate 3d measurement system and calibration for speckle projection method,” Opt. Lasers Eng. 48, 1132–1139 (2010).
[Crossref]

Liu, X.

Y. Yin, M. Wang, B. Z. Gao, X. Liu, and X. Peng, “Fringe projection 3d microscopy with the general imaging model,” Opt. Express 23, 6846–6857 (2015).
[Crossref] [PubMed]

A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3d microscopy,” Optik 124, 5052–5056 (2013).
[Crossref]

Mehta, D. S.

Mendoza-Santoyo, F.

R. Rodriguez-Vera, K. Genovese, J. Rayas, and F. Mendoza-Santoyo, “Vibration analysis at microscale by talbot fringe projection method,” Strain 45, 249–258 (2009).
[Crossref]

Nivet, J.-M.

Osten, W.

A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3d microscopy,” Optik 124, 5052–5056 (2013).
[Crossref]

Peng, X.

Y. Yin, M. Wang, B. Z. Gao, X. Liu, and X. Peng, “Fringe projection 3d microscopy with the general imaging model,” Opt. Express 23, 6846–6857 (2015).
[Crossref] [PubMed]

A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3d microscopy,” Optik 124, 5052–5056 (2013).
[Crossref]

Prakash, J.

Proll, K.-P.

Quan, C.

C. Quan, C. J. Tay, X. Y. He, X. Kang, and H. M. Shang, “Microscopic surface contouring by fringe projection method,” Opt. Laser Technol. 34, 547–552 (2002).
[Crossref]

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, “Shape measurement of small objects using lcd fringe projection with phase shifting,” Opt. Commun. 189, 21–29 (2001).
[Crossref]

Rastogi, P.

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

Rayas, J.

R. Rodriguez-Vera, K. Genovese, J. Rayas, and F. Mendoza-Santoyo, “Vibration analysis at microscale by talbot fringe projection method,” Strain 45, 249–258 (2009).
[Crossref]

Rodriguez-Vera, R.

R. Rodriguez-Vera, K. Genovese, J. Rayas, and F. Mendoza-Santoyo, “Vibration analysis at microscale by talbot fringe projection method,” Strain 45, 249–258 (2009).
[Crossref]

Shang, H. M.

C. Quan, C. J. Tay, X. Y. He, X. Kang, and H. M. Shang, “Microscopic surface contouring by fringe projection method,” Opt. Laser Technol. 34, 547–552 (2002).
[Crossref]

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, “Shape measurement of small objects using lcd fringe projection with phase shifting,” Opt. Commun. 189, 21–29 (2001).
[Crossref]

Shi, H.

F. Zhu, W. Liu, H. Shi, and X. He, “Accurate 3d measurement system and calibration for speckle projection method,” Opt. Lasers Eng. 48, 1132–1139 (2010).
[Crossref]

Tay, C. J.

C. Quan, C. J. Tay, X. Y. He, X. Kang, and H. M. Shang, “Microscopic surface contouring by fringe projection method,” Opt. Laser Technol. 34, 547–552 (2002).
[Crossref]

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, “Shape measurement of small objects using lcd fringe projection with phase shifting,” Opt. Commun. 189, 21–29 (2001).
[Crossref]

Tian, J.

D. Li, C. Liu, and J. Tian, “Telecentric 3d profilometry based on phase-shifting fringe projection,” Opt. Express 22, 31826–31835 (2014).
[Crossref]

D. Li and J. Tian, “An accurate calibration method for a camera with telecentric lenses,” Opt. Lasers Eng. 51, 538–541 (2013).
[Crossref]

Tiziani, H. J.

Wang, C. F.

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, “Shape measurement of small objects using lcd fringe projection with phase shifting,” Opt. Commun. 189, 21–29 (2001).
[Crossref]

Wang, L.

J. Chen, T. Guo, L. Wang, Z. Wu, X. Fu, and X. Hu, “Microscopic fringe projection system and measuring method,” in “Proc. SPIE,” (Chengdu, China, 2013), pp. 87594U.
[Crossref]

Wang, M.

Wang, Y.

Y. Wang and S. Zhang, “Superfast multifrequency phase-shifting technique with optimal pulse width modulation,” Opt. Lett. 19, 5149–5155 (2011).

Windecker, R.

R. Windecker, M. Fleischer, and H. J. Tiziani, “Three-dimensional topometry with stereo microscopes,” Opt. Eng. 36, 3372–3377 (1997).
[Crossref]

Wu, Z.

J. Chen, T. Guo, L. Wang, Z. Wu, X. Fu, and X. Hu, “Microscopic fringe projection system and measuring method,” in “Proc. SPIE,” (Chengdu, China, 2013), pp. 87594U.
[Crossref]

Yin, Y.

Y. Yin, M. Wang, B. Z. Gao, X. Liu, and X. Peng, “Fringe projection 3d microscopy with the general imaging model,” Opt. Express 23, 6846–6857 (2015).
[Crossref] [PubMed]

A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3d microscopy,” Optik 124, 5052–5056 (2013).
[Crossref]

Zhang, C.

Zhang, S.

Y. Wang and S. Zhang, “Superfast multifrequency phase-shifting technique with optimal pulse width modulation,” Opt. Lett. 19, 5149–5155 (2011).

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 083601 (2006).
[Crossref]

Zhao, Q.

A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3d microscopy,” Optik 124, 5052–5056 (2013).
[Crossref]

Zhu, F.

F. Zhu, W. Liu, H. Shi, and X. He, “Accurate 3d measurement system and calibration for speckle projection method,” Opt. Lasers Eng. 48, 1132–1139 (2010).
[Crossref]

Appl. Opt. (3)

Opt. Commun. (1)

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, “Shape measurement of small objects using lcd fringe projection with phase shifting,” Opt. Commun. 189, 21–29 (2001).
[Crossref]

Opt. Eng. (2)

R. Windecker, M. Fleischer, and H. J. Tiziani, “Three-dimensional topometry with stereo microscopes,” Opt. Eng. 36, 3372–3377 (1997).
[Crossref]

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 083601 (2006).
[Crossref]

Opt. Express (2)

Opt. Laser Technol. (1)

C. Quan, C. J. Tay, X. Y. He, X. Kang, and H. M. Shang, “Microscopic surface contouring by fringe projection method,” Opt. Laser Technol. 34, 547–552 (2002).
[Crossref]

Opt. Lasers Eng (1)

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

Opt. Lasers Eng. (2)

D. Li and J. Tian, “An accurate calibration method for a camera with telecentric lenses,” Opt. Lasers Eng. 51, 538–541 (2013).
[Crossref]

F. Zhu, W. Liu, H. Shi, and X. He, “Accurate 3d measurement system and calibration for speckle projection method,” Opt. Lasers Eng. 48, 1132–1139 (2010).
[Crossref]

Opt. Lett. (1)

Y. Wang and S. Zhang, “Superfast multifrequency phase-shifting technique with optimal pulse width modulation,” Opt. Lett. 19, 5149–5155 (2011).

Optik (1)

A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3d microscopy,” Optik 124, 5052–5056 (2013).
[Crossref]

Strain (1)

R. Rodriguez-Vera, K. Genovese, J. Rayas, and F. Mendoza-Santoyo, “Vibration analysis at microscale by talbot fringe projection method,” Strain 45, 249–258 (2009).
[Crossref]

Other (1)

J. Chen, T. Guo, L. Wang, Z. Wu, X. Fu, and X. Hu, “Microscopic fringe projection system and measuring method,” in “Proc. SPIE,” (Chengdu, China, 2013), pp. 87594U.
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 Model of telecentric camera imaging.
Fig. 2
Fig. 2 Model of pinhole projector imaging.
Fig. 3
Fig. 3 Illustration of calibration process. (a) Calibration target; (b) camera image with circle centers; (c) capture image with horizontal pattern projection; (d) capture image with vertical pattern projection; (e) mapped circle center image for projector; (f) estimated 3D position of target points.
Fig. 4
Fig. 4 Reprojection error of the calibration approach. (a) Reprojection error for the camera (RMS: 1.8 μm); (b) reprojection error for the projector (RMS: 1.2 μm)
Fig. 5
Fig. 5 Experimental result of measuring a flat plane. (a) 2D error map, with an RMS error of 4.5 μm; (b) a cross section of (a).
Fig. 6
Fig. 6 Experimental result of measuring complex surface geometry. (a) Picture of a ball grid array; (b) reconstructed 3D geometry; (c) a cross section of (b); (d)–(f) corresponding figures for a flat surface with octagon grooves

Tables (2)

Tables Icon

Table 1 Measurement result of two diagonals on calibration board (in mm).

Tables Icon

Table 2 Measurement result of a linearly translated calibration target point in mm.

Equations (9)

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

[ u c v c 1 ] = [ s x c 0 0 0 0 s y c 0 0 0 0 0 1 ] [ x c y c z c 1 ] ,
[ x c y c z c 1 ] = [ r 11 c r 12 c r 13 c t 1 c r 21 c r 22 c r 23 c t 2 c r 31 c r 32 c r 33 c t 3 c 0 0 0 1 ] [ x w y w z w 1 ] ,
[ u c v c 1 ] = [ m 11 c m 12 c m 13 c m 14 c m 21 c m 22 c m 23 c m 24 c 0 0 0 1 ] [ x w y w z w 1 ]
s p [ u p v p 1 ] = [ α γ u 0 c 0 β v 0 c 0 0 1 ] [ R 3 × 3 p t 3 × 1 p ] [ x w y w z w 1 ] .
I k ( x , y ) = I ( x , y ) + I ( x , y ) cos ( ϕ + 2 k π / N ) ,
ϕ ( x , y ) = tan 1 [ k = 1 N I k sin ( 2 k π / N ) k = 1 N I k cos ( 2 k π / N ) ] .
u p = ϕ h a c ( u c , v c ) × P 1 / 2 π ,
v p = ϕ v a c ( u c , v c ) × P 2 / 2 π ,
min R i , t i [ u p v p 1 ] M p [ R t , t t ] [ x t y t 0 1 ] ,

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