Abstract

A newly developed flexible calibration algorithm for telecentric 3D measurement systems is presented in this paper. We theoretically analyzed the similarities and differences between the telecentric and entocentric system. The telecentric system can be calibrated with the aid of the traditional 2D planar calibration method. An additional two-step refining process is proposed to improve the calibration accuracy effectively. With the calibration and refining algorithm, an affine camera can be calibrated with a reprojection error of 0.07 pixel. A projector with small field of view (FOV) is applied to achieve a full 3D reconstruction in our profilometry system. Experiments with a prototype demonstrate the validation and accuracy of the proposed calibration algorithm and system configuration. The reconstruction accuracy can achieve 5 µm with a measurement FOV of 28.43 mm×21.33 mm and a working distance of 110 mm.

© 2016 Optical Society of America

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References

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  1. Opto Engineering, “Telecentric lenses tutorial: basic information and working principles,” http://www.opto-engineering.com/resources/telecentric-lenses-tutorial .
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    [Crossref]
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    [Crossref]
  6. D. S. Gorpas, K. Politopouslos, and D. Yova, “Development of a computer vision binocular system for non-contact small animal model skin cancer tumor imaging,” in Proceedings of European Conference on Biomedical Optics (International Society for Optics and Photonics, 2007), pp. 66291J.
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    [Crossref]
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    [Crossref]
  10. K. Haskamp, M. Kästner, and E. Reithmeier, “Accurate calibration of a fringe projection system by considering telecentricity,” Proc. SPIE 8082, 80821B (2011).
    [Crossref]
  11. D. Li and J. Tian, “An accurate calibration method for a camera with telecentric lenses,” Opt. Lasers Eng. 51(5), 538–541 (2013).
    [Crossref]
  12. D. Lanman, D. C. Hauagge, and G. Taubin, “Shape from depth discontinuities under orthographic projection,” in Proceedings of IEEE International Conference on Computer Vision Workshop (IEEE, 2009), pp. 1550–1557.
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    [Crossref] [PubMed]
  14. B. Pan, L. Yu, and D. Wu, “High-accuracy 2d digital image correlation measurements with bilateral telecentric lenses: Error analysis and experimental verification,” Exp. Mech. 53(9), 1719–1733 (2013).
    [Crossref]
  15. C. Steger, M. Ulrich, and C. Wiedemann, Machine Vision Algorithms and Applications (Qinghua University, 2008).
  16. R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge University, 2003).
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    [Crossref]
  18. S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
    [Crossref]
  19. J. Heikkila, “Moment and curvature preserving technique for accurate ellipse boundary detection,” in Proceedings of IEEE International Conference on Pattern Recognition (IEEE, 1998), pp. 734–737.
  20. D. Krishnan, T. Tay, and R. Fergus, “Blind deconvolution using a normalized sparsity measure,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 233–240.
  21. A. Datta, J. S. Kim, and T. Kanade, “Accurate camera calibration using iterative refinement of control points,” in Proceedings of IEEE International Conference on Computer Vision Workshop (IEEE, 2009), pp. 1201–1208.
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    [Crossref] [PubMed]
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    [Crossref]
  24. M. Vo, Z. Wang, B. Pan, and T. Pan, “Hyper-accurate flexible calibration technique for fringe-projection-based three-dimensional imaging,” Opt. Express 20(15), 16926–16941 (2012).
    [Crossref]

2015 (2)

2014 (2)

W. Li, Z. Wei, and G. Zhang, “Affine calibration based on invariable extrinsic parameters for stereo light microscope,” Opt. Eng. 53(10), 102105 (2014).
[Crossref]

Z. Chen, H. Liao, and X. Zhang, “Telecentric stereo micro-vision system: Calibration method and experiments,” Opt. Lasers Eng. 57, 82–92 (2014).
[Crossref]

2013 (2)

D. Li and J. Tian, “An accurate calibration method for a camera with telecentric lenses,” Opt. Lasers Eng. 51(5), 538–541 (2013).
[Crossref]

B. Pan, L. Yu, and D. Wu, “High-accuracy 2d digital image correlation measurements with bilateral telecentric lenses: Error analysis and experimental verification,” Exp. Mech. 53(9), 1719–1733 (2013).
[Crossref]

2012 (1)

2011 (1)

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)

2006 (1)

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
[Crossref]

2000 (1)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
[Crossref]

1996 (1)

L. Quan, “Self-calibration of an affine camera from multiple views,” Int. J. Comput. Vis. 19(1), 93–105 (1996).
[Crossref]

1994 (1)

N. Hollinghurst and R. Cipolla, “Uncalibrated stereo hand-eye coordination,” Image Vis. Comput. 12(3), 187–192 (1994).
[Crossref]

1978 (1)

J. J. Moré, “The Levenberg-Marquardt algorithm: implementation and theory,” Lecture Notes in Mathematics 630, 105–116 (1978).
[Crossref]

Amintabar, A.

A. Habed, A. Amintabar, and B. Boufama, “Affine camera calibration from homographies of parallel planes,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2010), pp. 4249–4252.

Boufama, B.

A. Habed, A. Amintabar, and B. Boufama, “Affine camera calibration from homographies of parallel planes,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2010), pp. 4249–4252.

Chen, Z.

Z. Chen, H. Liao, and X. Zhang, “Telecentric stereo micro-vision system: Calibration method and experiments,” Opt. Lasers Eng. 57, 82–92 (2014).
[Crossref]

Cipolla, R.

N. Hollinghurst and R. Cipolla, “Uncalibrated stereo hand-eye coordination,” Image Vis. Comput. 12(3), 187–192 (1994).
[Crossref]

Datta, A.

A. Datta, J. S. Kim, and T. Kanade, “Accurate camera calibration using iterative refinement of control points,” in Proceedings of IEEE International Conference on Computer Vision Workshop (IEEE, 2009), pp. 1201–1208.

Dyer, C. R.

R. Manning and C. R. Dyer, “Affine camera calibration from moving objects,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2001), pp. 494–500.

Fergus, R.

D. Krishnan, T. Tay, and R. Fergus, “Blind deconvolution using a normalized sparsity measure,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 233–240.

Gao, B. Z.

Gorpas, D. S.

D. S. Gorpas, K. Politopouslos, and D. Yova, “Development of a computer vision binocular system for non-contact small animal model skin cancer tumor imaging,” in Proceedings of European Conference on Biomedical Optics (International Society for Optics and Photonics, 2007), pp. 66291J.

Habed, A.

A. Habed, A. Amintabar, and B. Boufama, “Affine camera calibration from homographies of parallel planes,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2010), pp. 4249–4252.

Hartley, R.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge University, 2003).

Haskamp, K.

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

Hauagge, D. C.

D. Lanman, D. C. Hauagge, and G. Taubin, “Shape from depth discontinuities under orthographic projection,” in Proceedings of IEEE International Conference on Computer Vision Workshop (IEEE, 2009), pp. 1550–1557.

Heikkila, J.

J. Heikkila, “Moment and curvature preserving technique for accurate ellipse boundary detection,” in Proceedings of IEEE International Conference on Pattern Recognition (IEEE, 1998), pp. 734–737.

Hoang, T.

Hollinghurst, N.

N. Hollinghurst and R. Cipolla, “Uncalibrated stereo hand-eye coordination,” Image Vis. Comput. 12(3), 187–192 (1994).
[Crossref]

Huang, P. S.

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
[Crossref]

Kanade, T.

A. Datta, J. S. Kim, and T. Kanade, “Accurate camera calibration using iterative refinement of control points,” in Proceedings of IEEE International Conference on Computer Vision Workshop (IEEE, 2009), pp. 1201–1208.

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]

Kim, J. S.

A. Datta, J. S. Kim, and T. Kanade, “Accurate camera calibration using iterative refinement of control points,” in Proceedings of IEEE International Conference on Computer Vision Workshop (IEEE, 2009), pp. 1201–1208.

Krishnan, D.

D. Krishnan, T. Tay, and R. Fergus, “Blind deconvolution using a normalized sparsity measure,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 233–240.

Lanman, D.

D. Lanman, D. C. Hauagge, and G. Taubin, “Shape from depth discontinuities under orthographic projection,” in Proceedings of IEEE International Conference on Computer Vision Workshop (IEEE, 2009), pp. 1550–1557.

Li, B.

Li, D.

D. Li and J. Tian, “An accurate calibration method for a camera with telecentric lenses,” Opt. Lasers Eng. 51(5), 538–541 (2013).
[Crossref]

Li, W.

W. Li, Z. Wei, and G. Zhang, “Affine calibration based on invariable extrinsic parameters for stereo light microscope,” Opt. Eng. 53(10), 102105 (2014).
[Crossref]

Liao, H.

Z. Chen, H. Liao, and X. Zhang, “Telecentric stereo micro-vision system: Calibration method and experiments,” Opt. Lasers Eng. 57, 82–92 (2014).
[Crossref]

Liu, X.

Manning, R.

R. Manning and C. R. Dyer, “Affine camera calibration from moving objects,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2001), pp. 494–500.

Moré, J. J.

J. J. Moré, “The Levenberg-Marquardt algorithm: implementation and theory,” Lecture Notes in Mathematics 630, 105–116 (1978).
[Crossref]

Nguyen, D.

Pan, B.

Pan, T.

Peng, X.

Politopouslos, K.

D. S. Gorpas, K. Politopouslos, and D. Yova, “Development of a computer vision binocular system for non-contact small animal model skin cancer tumor imaging,” in Proceedings of European Conference on Biomedical Optics (International Society for Optics and Photonics, 2007), pp. 66291J.

Quan, L.

L. Quan, “Self-calibration of an affine camera from multiple views,” Int. J. Comput. Vis. 19(1), 93–105 (1996).
[Crossref]

Reithmeier, E.

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

Steger, C.

C. Steger, M. Ulrich, and C. Wiedemann, Machine Vision Algorithms and Applications (Qinghua University, 2008).

Taubin, G.

D. Lanman, D. C. Hauagge, and G. Taubin, “Shape from depth discontinuities under orthographic projection,” in Proceedings of IEEE International Conference on Computer Vision Workshop (IEEE, 2009), pp. 1550–1557.

Tay, T.

D. Krishnan, T. Tay, and R. Fergus, “Blind deconvolution using a normalized sparsity measure,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 233–240.

Tian, J.

D. Li and J. Tian, “An accurate calibration method for a camera with telecentric lenses,” Opt. Lasers Eng. 51(5), 538–541 (2013).
[Crossref]

Ulrich, M.

C. Steger, M. Ulrich, and C. Wiedemann, Machine Vision Algorithms and Applications (Qinghua University, 2008).

Vo, M.

Wang, M.

Wang, Z.

Wei, Z.

W. Li, Z. Wei, and G. Zhang, “Affine calibration based on invariable extrinsic parameters for stereo light microscope,” Opt. Eng. 53(10), 102105 (2014).
[Crossref]

Wiedemann, C.

C. Steger, M. Ulrich, and C. Wiedemann, Machine Vision Algorithms and Applications (Qinghua University, 2008).

Wu, D.

B. Pan, L. Yu, and D. Wu, “High-accuracy 2d digital image correlation measurements with bilateral telecentric lenses: Error analysis and experimental verification,” Exp. Mech. 53(9), 1719–1733 (2013).
[Crossref]

Yin, Y.

Yova, D.

D. S. Gorpas, K. Politopouslos, and D. Yova, “Development of a computer vision binocular system for non-contact small animal model skin cancer tumor imaging,” in Proceedings of European Conference on Biomedical Optics (International Society for Optics and Photonics, 2007), pp. 66291J.

Yu, L.

B. Pan, L. Yu, and D. Wu, “High-accuracy 2d digital image correlation measurements with bilateral telecentric lenses: Error analysis and experimental verification,” Exp. Mech. 53(9), 1719–1733 (2013).
[Crossref]

Zhang, G.

W. Li, Z. Wei, and G. Zhang, “Affine calibration based on invariable extrinsic parameters for stereo light microscope,” Opt. Eng. 53(10), 102105 (2014).
[Crossref]

Zhang, S.

Zhang, X.

Z. Chen, H. Liao, and X. Zhang, “Telecentric stereo micro-vision system: Calibration method and experiments,” Opt. Lasers Eng. 57, 82–92 (2014).
[Crossref]

Zhang, Z.

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
[Crossref]

Zisserman, A.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge University, 2003).

Exp. Mech. (1)

B. Pan, L. Yu, and D. Wu, “High-accuracy 2d digital image correlation measurements with bilateral telecentric lenses: Error analysis and experimental verification,” Exp. Mech. 53(9), 1719–1733 (2013).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
[Crossref]

Image Vis. Comput. (1)

N. Hollinghurst and R. Cipolla, “Uncalibrated stereo hand-eye coordination,” Image Vis. Comput. 12(3), 187–192 (1994).
[Crossref]

Int. J. Comput. Vis. (1)

L. Quan, “Self-calibration of an affine camera from multiple views,” Int. J. Comput. Vis. 19(1), 93–105 (1996).
[Crossref]

Lecture Notes in Mathematics (1)

J. J. Moré, “The Levenberg-Marquardt algorithm: implementation and theory,” Lecture Notes in Mathematics 630, 105–116 (1978).
[Crossref]

Opt. Eng. (2)

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
[Crossref]

W. Li, Z. Wei, and G. Zhang, “Affine calibration based on invariable extrinsic parameters for stereo light microscope,” Opt. Eng. 53(10), 102105 (2014).
[Crossref]

Opt. Express (3)

Opt. Lasers Eng. (2)

Z. Chen, H. Liao, and X. Zhang, “Telecentric stereo micro-vision system: Calibration method and experiments,” Opt. Lasers Eng. 57, 82–92 (2014).
[Crossref]

D. Li and J. Tian, “An accurate calibration method for a camera with telecentric lenses,” Opt. Lasers Eng. 51(5), 538–541 (2013).
[Crossref]

Opt. Lett. (1)

Proc. SPIE (1)

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

Other (10)

D. S. Gorpas, K. Politopouslos, and D. Yova, “Development of a computer vision binocular system for non-contact small animal model skin cancer tumor imaging,” in Proceedings of European Conference on Biomedical Optics (International Society for Optics and Photonics, 2007), pp. 66291J.

A. Habed, A. Amintabar, and B. Boufama, “Affine camera calibration from homographies of parallel planes,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2010), pp. 4249–4252.

R. Manning and C. R. Dyer, “Affine camera calibration from moving objects,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2001), pp. 494–500.

D. Lanman, D. C. Hauagge, and G. Taubin, “Shape from depth discontinuities under orthographic projection,” in Proceedings of IEEE International Conference on Computer Vision Workshop (IEEE, 2009), pp. 1550–1557.

Opto Engineering, “Telecentric lenses tutorial: basic information and working principles,” http://www.opto-engineering.com/resources/telecentric-lenses-tutorial .

J. Heikkila, “Moment and curvature preserving technique for accurate ellipse boundary detection,” in Proceedings of IEEE International Conference on Pattern Recognition (IEEE, 1998), pp. 734–737.

D. Krishnan, T. Tay, and R. Fergus, “Blind deconvolution using a normalized sparsity measure,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 233–240.

A. Datta, J. S. Kim, and T. Kanade, “Accurate camera calibration using iterative refinement of control points,” in Proceedings of IEEE International Conference on Computer Vision Workshop (IEEE, 2009), pp. 1201–1208.

C. Steger, M. Ulrich, and C. Wiedemann, Machine Vision Algorithms and Applications (Qinghua University, 2008).

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge University, 2003).

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Figures (9)

Fig. 1
Fig. 1 Pinhole camera geometry.
Fig. 2
Fig. 2 The object-side telecentric imaging process.
Fig. 3
Fig. 3 Using the self convolution method, the image (a) Before and (b) after being deblurred.
Fig. 4
Fig. 4 Top row: The images of calibration board in five different positions. Bottom row: Images have been undistorted and unprojected to canonical fronto-parallel images.
Fig. 5
Fig. 5 Prototype of telecentric fringe projection profilometry system (all the cables were removed for better demonstration).
Fig. 6
Fig. 6 Reprojection errors of the camera under the four different circumstance
Fig. 7
Fig. 7 Common focus area demonstration of the fringe projection profilometry system.
Fig. 8
Fig. 8 3D images of the control points in 3 different positions.
Fig. 9
Fig. 9 Reconstruction results of two small objects with complex surface geometry.

Tables (2)

Tables Icon

Table 1 Calibration results of the affine camera and projector

Tables Icon

Table 2 Measurement results of the displacements ΔZ

Equations (16)

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

Z c [ u v 1 ] = [ f m x s u o 0 f m y v o 0 0 1 ] [ r 11 r 12 r 13 t x r 21 r 22 r 23 t y r 31 r 32 r 33 t z ] [ X w Y w Z w 1 ] .
[ u v 1 ] = [ ( f / Z c ) X c ( f / Z c ) Y c 1 ] ,
Z c [ u v 1 ] = [ f X c f Y c Z c ] = [ f 0 0 0 0 f 0 0 0 0 1 0 ] [ X c Y c Z c 1 ] ,
[ u v 1 ] = [ m X c m Y c 1 ] = [ m 0 0 0 0 m 0 0 0 0 0 1 ] [ X c Y c Z c 1 ] ,
[ u v 1 ] = [ m m x s u o 0 m m y v o 0 0 1 ] [ r 11 r 12 r 13 t x r 21 r 22 r 23 t y 0 0 0 1 ] [ X w Y w Z w 1 ] ,
[ u v 1 ] = H [ X w Y w Z w 1 ] , H = A [ R t ] ,
A i = H i [ R t ] i 1 , i = [ 1 , N p ] ,
[ u v 1 ] = [ m m x s 0 0 m m y 0 0 0 1 ] [ r 11 r 12 r 13 t x r 21 r 22 r 23 t y 0 0 0 1 ] [ X w Y w Z w 1 ] ,
[ t x t y ] = [ t x t y ] + [ m m x s 0 m m y ] 1 [ u 0 v 0 ] .
x c n = ( 1 + k 1 r 2 + k 2 r 4 ) x c n y c n = ( 1 + k 1 r 2 + k 2 r 4 ) y c n ,
i = 1 N p j = 1 N c p i j p ^ ( A , R i , t i , k 1 , k 2 , M j ) 2 ,
u i p = φ v ( O i c ) 2 π N v W , v i p = φ h ( O i c ) 2 π N h H ,
i n t r i n = [ 3.64 × 10 5 0.01 810.35 0 3.72 × 10 5 621.51 0 0 1 ] ,
e x t r i n = [ 0.91 0.03 0.12 9.95 0.01 0.95 0.005 11.52 0.21 0.03 0.99 5.77 × 10 3 ] ,
i n t r i n a f f i n e = [ 63.46 0.006 0 0 65.75 0 0 0 1 ] ,
e x t r i n a f f i n e = [ 0.98 0.008 0.16 0.98 0.001 0.99 0.04 1.12 0 0 0 1 ] .

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