Abstract

By combining a fringe projection setup with a telecentric lens, a fringe pattern could be projected and imaged within a small area, making it possible to measure the three-dimensional (3D) surfaces of micro-components. This paper focuses on the flexible calibration of the fringe projection profilometry (FPP) system using a telecentric lens. An analytical telecentric projector-camera calibration model is introduced, in which the rig structure parameters remain invariant for all views, and the 3D calibration target can be located on the projector image plane with sub-pixel precision. Based on the presented calibration model, a two-step calibration procedure is proposed. First, the initial parameters, e.g., the projector-camera rig, projector intrinsic matrix, and coordinates of the control points of a 3D calibration target, are estimated using the affine camera factorization calibration method. Second, a bundle adjustment algorithm with various simultaneous views is applied to refine the calibrated parameters, especially the rig structure parameters and coordinates of the control points forth 3D target. Because the control points are determined during the calibration, there is no need for an accurate 3D reference target, whose is costly and extremely difficult to fabricate, particularly for tiny objects used to calibrate the telecentric FPP system. Real experiments were performed to validate the performance of the proposed calibration method. The test results showed that the proposed approach is very accurate and reliable.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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2017 (11)

Y. Hu, Q. Chen, T. Tao, H. Li, and C. Zuo, “Absolute three-dimensional micro surface profile measurement based on a Greenough-type stereomicroscope,” Meas. Sci. Technol. 28, 45004 (2017).

B. Li and S. Zhang, “Microscopic structured light 3D profilometry: Binary defocusing technique vs. sinusoidal fringe projection,” Opt. Lasers Eng. 96, 117–123 (2017).

S. Yang, M. Liu, J. Song, S. Yin, Y. Guo, Y. Ren, and J. Zhu, “Flexible digital projector calibration method based on per-pixel distortion measurement and correction,” Opt. Lasers Eng. 92, 29–38 (2017).

T. Collins and A. Bartoli, “Planar Structure-from-Motion with Affine Camera Models: Closed-Form Solutions, Ambiguities and Degeneracy Analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 39(6), 1237–1255 (2017).
[PubMed]

C. Steger, “A Comprehensive and Versatile Camera Model for Cameras with Tilt Lenses,” Int. J. Comput. Vis. 123(2), 1–39 (2017).

X. Liu, Z. Cai, Y. Yin, H. Jiang, D. He, W. He, Z. Zhang, and X. Peng, “Calibration of fringe projection profilometry using an inaccurate 2D reference target,” Opt. Lasers Eng. 89, 131–137 (2017).

R. Chen, J. Xu, S. Zhang, H. Chen, Y. Guan, and K. Chen, “A self-recalibration method based on scale-invariant registration for structured light measurement systems,” Opt. Lasers Eng. 88, 75–81 (2017).

H. Lin, H. Liu, and L. Yao, “3D-shape reconstruction based on a sub-pixel-level mapping relationship between the camera and projector,” Proc. SPIE 10255, 1025504 (2017).

Z. Cai, X. Liu, A. Li, Q. Tang, X. Peng, and B. Z. Gao, “Phase-3D mapping method developed from back-projection stereovision model for fringe projection profilometry,” Opt. Express 25(2), 1262–1277 (2017).
[PubMed]

P. Lu, C. Sun, B. Liu, and P. Wang, “Accurate and robust calibration method based on pattern geometric constraints for fringe projection profilometry,” Appl. Opt. 56(4), 784–794 (2017).
[PubMed]

W. Zhang, W. Li, L. Yu, H. Luo, H. Zhao, and H. Xia, “Sub-pixel projector calibration method for fringe projection profilometry,” Opt. Express 25(16), 19158–19169 (2017).
[PubMed]

2016 (6)

L. Rao, F. Da, W. Kong, and H. Huang, “Flexible calibration method for telecentric fringe projection profilometry systems,” Opt. Express 24(2), 1222–1237 (2016).
[PubMed]

J. Lu, R. Mo, H. Sun, and Z. Chang, “Flexible calibration of phase-to-height conversion in fringe projection profilometry,” Appl. Opt. 55(23), 6381–6388 (2016).
[PubMed]

Y. An, T. Bell, B. Li, J. Xu, and S. Zhang, “Method for large-range structured light system calibration,” Appl. Opt. 55(33), 9563–9572 (2016).
[PubMed]

S. Van der Jeught and J. J. J. Dirckx, “Real-time structured light profilometry: a review,” Opt. Lasers Eng. 87, 18–31 (2016).

Q. Mei, J. Gao, H. Lin, Y. Chen, H. Yunbo, W. Wang, G. Zhang, and X. Chen, “Structure light telecentric stereoscopic vision 3D measurement system based on Scheimpflug condition,” Opt. Lasers Eng. 86, 83–91 (2016).

L. Yao and H. Liu, “A flexible calibration approach for cameras with double-sided telecentric lenses,” Int. J. Adv. Robot. Syst. 13, 82 (2016).

2015 (4)

2014 (5)

J. Zhang, X. Chen, J. Xi, and Z. Wu, “Aberration correction of double-sided telecentric zoom lenses using lens modules,” Appl. Opt. 53(27), 6123–6132 (2014).
[PubMed]

B. Li and S. Zhang, “Structured light system calibration method with optimal fringe angle,” Appl. Opt. 53(33), 7942–7950 (2014).
[PubMed]

D. Li, C. Liu, and J. Tian, “Telecentric 3D profilometry based on phase-shifting fringe projection,” Opt. Express 22(26), 31826–31835 (2014).
[PubMed]

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

H. Luo, J. Xu, N. Hoa Binh, S. Liu, C. Zhang, and K. Chen, “A simple calibration procedure for structured light system,” Opt. Lasers Eng. 57, 6–12 (2014).

2013 (4)

L. Merner, Y. Wang, and S. Zhang, “Accurate calibration for 3D shape measurement system using a binary defocusing technique,” Opt. Lasers Eng. 51, 514–519 (2013).

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

Z. Zhang, S. Huang, S. Meng, F. Gao, and X. Jiang, “A simple, flexible and automatic 3D calibration method for a phase calculation-based fringe projection imaging system,” Opt. Express 21(10), 12218–12227 (2013).
[PubMed]

F. Zhu, H. Shi, P. Bai, D. Lei, and X. He, “Nonlinear calibration for generalized fringe projection profilometry under large measuring depth range,” Appl. Opt. 52(32), 7718–7723 (2013).
[PubMed]

2012 (2)

2011 (1)

2010 (1)

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).

2006 (1)

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 83601 (2006).

1996 (1)

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

1992 (1)

C. Tomasi and T. Kanade, “Shape and motion from image streams under orthography: a factorization method,” Int. J. Comput. Vis. 9, 137–154 (1992).

1987 (1)

An, Y.

Bai, P.

Bartoli, A.

T. Collins and A. Bartoli, “Planar Structure-from-Motion with Affine Camera Models: Closed-Form Solutions, Ambiguities and Degeneracy Analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 39(6), 1237–1255 (2017).
[PubMed]

Bell, T.

Cai, Z.

Z. Cai, X. Liu, A. Li, Q. Tang, X. Peng, and B. Z. Gao, “Phase-3D mapping method developed from back-projection stereovision model for fringe projection profilometry,” Opt. Express 25(2), 1262–1277 (2017).
[PubMed]

X. Liu, Z. Cai, Y. Yin, H. Jiang, D. He, W. He, Z. Zhang, and X. Peng, “Calibration of fringe projection profilometry using an inaccurate 2D reference target,” Opt. Lasers Eng. 89, 131–137 (2017).

Chang, Z.

Chen, H.

R. Chen, J. Xu, S. Zhang, H. Chen, Y. Guan, and K. Chen, “A self-recalibration method based on scale-invariant registration for structured light measurement systems,” Opt. Lasers Eng. 88, 75–81 (2017).

Chen, K.

R. Chen, J. Xu, S. Zhang, H. Chen, Y. Guan, and K. Chen, “A self-recalibration method based on scale-invariant registration for structured light measurement systems,” Opt. Lasers Eng. 88, 75–81 (2017).

H. Luo, J. Xu, N. Hoa Binh, S. Liu, C. Zhang, and K. Chen, “A simple calibration procedure for structured light system,” Opt. Lasers Eng. 57, 6–12 (2014).

Chen, Q.

Y. Hu, Q. Chen, T. Tao, H. Li, and C. Zuo, “Absolute three-dimensional micro surface profile measurement based on a Greenough-type stereomicroscope,” Meas. Sci. Technol. 28, 45004 (2017).

Chen, R.

R. Chen, J. Xu, S. Zhang, H. Chen, Y. Guan, and K. Chen, “A self-recalibration method based on scale-invariant registration for structured light measurement systems,” Opt. Lasers Eng. 88, 75–81 (2017).

Chen, X.

Q. Mei, J. Gao, H. Lin, Y. Chen, H. Yunbo, W. Wang, G. Zhang, and X. Chen, “Structure light telecentric stereoscopic vision 3D measurement system based on Scheimpflug condition,” Opt. Lasers Eng. 86, 83–91 (2016).

J. Zhang, X. Chen, J. Xi, and Z. Wu, “Aberration correction of double-sided telecentric zoom lenses using lens modules,” Appl. Opt. 53(27), 6123–6132 (2014).
[PubMed]

Chen, Y.

Q. Mei, J. Gao, H. Lin, Y. Chen, H. Yunbo, W. Wang, G. Zhang, and X. Chen, “Structure light telecentric stereoscopic vision 3D measurement system based on Scheimpflug condition,” Opt. Lasers Eng. 86, 83–91 (2016).

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).

Collins, T.

T. Collins and A. Bartoli, “Planar Structure-from-Motion with Affine Camera Models: Closed-Form Solutions, Ambiguities and Degeneracy Analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 39(6), 1237–1255 (2017).
[PubMed]

Cordova Esparza, D. M.

J. G. Rico Espino, J. Gonzalez-Barbosa, R. A. Gomez Loenzo, D. M. Cordova Esparza, and R. Gonzalez-Barbosa, “Vision system for 3D reconstruction with telecentric lens,” in Mexican Conference on Pattern Recognition (Springer-Verlag, 2012), pp. 127–136.

Da, F.

Deng, D.

Dirckx, J. J. J.

S. Van der Jeught and J. J. J. Dirckx, “Real-time structured light profilometry: a review,” Opt. Lasers Eng. 87, 18–31 (2016).

Fallavollita, P.

Y. Oyamada, P. Fallavollita, and N. Navab, “Single Camera Calibration using partially visible calibration objects based on Random Dots Marker Tracking Algorithm,” in IEEE and ACM International Symposium on Mixed and Augmented Reality (IEEE, 2012).

Gao, B. Z.

Gao, F.

Gao, J.

Q. Mei, J. Gao, H. Lin, Y. Chen, H. Yunbo, W. Wang, G. Zhang, and X. Chen, “Structure light telecentric stereoscopic vision 3D measurement system based on Scheimpflug condition,” Opt. Lasers Eng. 86, 83–91 (2016).

Gomez Loenzo, R. A.

J. G. Rico Espino, J. Gonzalez-Barbosa, R. A. Gomez Loenzo, D. M. Cordova Esparza, and R. Gonzalez-Barbosa, “Vision system for 3D reconstruction with telecentric lens,” in Mexican Conference on Pattern Recognition (Springer-Verlag, 2012), pp. 127–136.

Gonzalez-Barbosa, J.

J. G. Rico Espino, J. Gonzalez-Barbosa, R. A. Gomez Loenzo, D. M. Cordova Esparza, and R. Gonzalez-Barbosa, “Vision system for 3D reconstruction with telecentric lens,” in Mexican Conference on Pattern Recognition (Springer-Verlag, 2012), pp. 127–136.

Gonzalez-Barbosa, R.

J. G. Rico Espino, J. Gonzalez-Barbosa, R. A. Gomez Loenzo, D. M. Cordova Esparza, and R. Gonzalez-Barbosa, “Vision system for 3D reconstruction with telecentric lens,” in Mexican Conference on Pattern Recognition (Springer-Verlag, 2012), pp. 127–136.

Guan, Y.

R. Chen, J. Xu, S. Zhang, H. Chen, Y. Guan, and K. Chen, “A self-recalibration method based on scale-invariant registration for structured light measurement systems,” Opt. Lasers Eng. 88, 75–81 (2017).

Guo, Q.

Guo, Y.

S. Yang, M. Liu, J. Song, S. Yin, Y. Guo, Y. Ren, and J. Zhu, “Flexible digital projector calibration method based on per-pixel distortion measurement and correction,” Opt. Lasers Eng. 92, 29–38 (2017).

He, D.

X. Liu, Z. Cai, Y. Yin, H. Jiang, D. He, W. He, Z. Zhang, and X. Peng, “Calibration of fringe projection profilometry using an inaccurate 2D reference target,” Opt. Lasers Eng. 89, 131–137 (2017).

He, W.

X. Liu, Z. Cai, Y. Yin, H. Jiang, D. He, W. He, Z. Zhang, and X. Peng, “Calibration of fringe projection profilometry using an inaccurate 2D reference target,” Opt. Lasers Eng. 89, 131–137 (2017).

He, X.

F. Zhu, H. Shi, P. Bai, D. Lei, and X. He, “Nonlinear calibration for generalized fringe projection profilometry under large measuring depth range,” Appl. Opt. 52(32), 7718–7723 (2013).
[PubMed]

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).

Hoa Binh, N.

H. Luo, J. Xu, N. Hoa Binh, S. Liu, C. Zhang, and K. Chen, “A simple calibration procedure for structured light system,” Opt. Lasers Eng. 57, 6–12 (2014).

Horn, B. K. P.

Hu, Y.

Y. Hu, Q. Chen, T. Tao, H. Li, and C. Zuo, “Absolute three-dimensional micro surface profile measurement based on a Greenough-type stereomicroscope,” Meas. Sci. Technol. 28, 45004 (2017).

Huang, H.

Huang, P. S.

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 83601 (2006).

Huang, S.

Huang, Z.

Huiyang, L.

L. Huiyang, C. Zhong, and Z. Xianmin, “Calibration of camera with small FOV and DOF telecentric lens,” in IEEE International Conference on Robotics and Biomimetics (IEEE, 2013), pp. 498–503.

Jiang, H.

X. Liu, Z. Cai, Y. Yin, H. Jiang, D. He, W. He, Z. Zhang, and X. Peng, “Calibration of fringe projection profilometry using an inaccurate 2D reference target,” Opt. Lasers Eng. 89, 131–137 (2017).

Jiang, X.

Kanade, T.

J. S. Kim and T. Kanade, “Multiaperture telecentric lens for 3D reconstruction,” Opt. Lett. 36(7), 1050–1052 (2011).
[PubMed]

C. Tomasi and T. Kanade, “Shape and motion from image streams under orthography: a factorization method,” Int. J. Comput. Vis. 9, 137–154 (1992).

Kim, J. S.

Kong, W.

Lei, D.

Li, A.

Li, B.

Li, D.

D. Li, C. Liu, and J. Tian, “Telecentric 3D profilometry based on phase-shifting fringe projection,” Opt. Express 22(26), 31826–31835 (2014).
[PubMed]

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

Li, H.

Y. Hu, Q. Chen, T. Tao, H. Li, and C. Zuo, “Absolute three-dimensional micro surface profile measurement based on a Greenough-type stereomicroscope,” Meas. Sci. Technol. 28, 45004 (2017).

Li, W.

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).

Lin, H.

H. Lin, H. Liu, and L. Yao, “3D-shape reconstruction based on a sub-pixel-level mapping relationship between the camera and projector,” Proc. SPIE 10255, 1025504 (2017).

Q. Mei, J. Gao, H. Lin, Y. Chen, H. Yunbo, W. Wang, G. Zhang, and X. Chen, “Structure light telecentric stereoscopic vision 3D measurement system based on Scheimpflug condition,” Opt. Lasers Eng. 86, 83–91 (2016).

Liu, B.

Liu, C.

Liu, H.

H. Lin, H. Liu, and L. Yao, “3D-shape reconstruction based on a sub-pixel-level mapping relationship between the camera and projector,” Proc. SPIE 10255, 1025504 (2017).

L. Yao and H. Liu, “A flexible calibration approach for cameras with double-sided telecentric lenses,” Int. J. Adv. Robot. Syst. 13, 82 (2016).

Liu, M.

S. Yang, M. Liu, J. Song, S. Yin, Y. Guo, Y. Ren, and J. Zhu, “Flexible digital projector calibration method based on per-pixel distortion measurement and correction,” Opt. Lasers Eng. 92, 29–38 (2017).

Liu, S.

H. Luo, J. Xu, N. Hoa Binh, S. Liu, C. Zhang, and K. Chen, “A simple calibration procedure for structured light system,” Opt. Lasers Eng. 57, 6–12 (2014).

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).

Liu, X.

Lu, J.

Lu, P.

Luo, H.

W. Zhang, W. Li, L. Yu, H. Luo, H. Zhao, and H. Xia, “Sub-pixel projector calibration method for fringe projection profilometry,” Opt. Express 25(16), 19158–19169 (2017).
[PubMed]

H. Luo, J. Xu, N. Hoa Binh, S. Liu, C. Zhang, and K. Chen, “A simple calibration procedure for structured light system,” Opt. Lasers Eng. 57, 6–12 (2014).

Matsumoto, Y.

H. Tanaka, Y. Sumi, and Y. Matsumoto, “A solution to pose ambiguity of visual markers using Moir patterns,” in IEEE/RSJ International Conference on Intelligent Robots and Systems (IEEE, 2014), pp. 3129–3134.

Mei, Q.

Q. Mei, J. Gao, H. Lin, Y. Chen, H. Yunbo, W. Wang, G. Zhang, and X. Chen, “Structure light telecentric stereoscopic vision 3D measurement system based on Scheimpflug condition,” Opt. Lasers Eng. 86, 83–91 (2016).

Meng, S.

Merner, L.

L. Merner, Y. Wang, and S. Zhang, “Accurate calibration for 3D shape measurement system using a binary defocusing technique,” Opt. Lasers Eng. 51, 514–519 (2013).

Mikš, A.

Mo, R.

Moreno, D.

D. Moreno and G. Taubin, “Simple, Accurate, and Robust Projector-Camera Calibration,” in International Conference on 3D Imaging (IEEE, 2012), pp. 464–471.

Navab, N.

Y. Oyamada, P. Fallavollita, and N. Navab, “Single Camera Calibration using partially visible calibration objects based on Random Dots Marker Tracking Algorithm,” in IEEE and ACM International Symposium on Mixed and Augmented Reality (IEEE, 2012).

Novák, J.

Oyamada, Y.

Y. Oyamada, P. Fallavollita, and N. Navab, “Single Camera Calibration using partially visible calibration objects based on Random Dots Marker Tracking Algorithm,” in IEEE and ACM International Symposium on Mixed and Augmented Reality (IEEE, 2012).

Peng, J.

Peng, X.

Quan, L.

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

Rao, L.

Ren, Y.

S. Yang, M. Liu, J. Song, S. Yin, Y. Guo, Y. Ren, and J. Zhu, “Flexible digital projector calibration method based on per-pixel distortion measurement and correction,” Opt. Lasers Eng. 92, 29–38 (2017).

Rico Espino, J. G.

J. G. Rico Espino, J. Gonzalez-Barbosa, R. A. Gomez Loenzo, D. M. Cordova Esparza, and R. Gonzalez-Barbosa, “Vision system for 3D reconstruction with telecentric lens,” in Mexican Conference on Pattern Recognition (Springer-Verlag, 2012), pp. 127–136.

Shi, H.

F. Zhu, H. Shi, P. Bai, D. Lei, and X. He, “Nonlinear calibration for generalized fringe projection profilometry under large measuring depth range,” Appl. Opt. 52(32), 7718–7723 (2013).
[PubMed]

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).

Song, J.

S. Yang, M. Liu, J. Song, S. Yin, Y. Guo, Y. Ren, and J. Zhu, “Flexible digital projector calibration method based on per-pixel distortion measurement and correction,” Opt. Lasers Eng. 92, 29–38 (2017).

Steger, C.

C. Steger, “A Comprehensive and Versatile Camera Model for Cameras with Tilt Lenses,” Int. J. Comput. Vis. 123(2), 1–39 (2017).

Sumi, Y.

H. Tanaka, Y. Sumi, and Y. Matsumoto, “A solution to pose ambiguity of visual markers using Moir patterns,” in IEEE/RSJ International Conference on Intelligent Robots and Systems (IEEE, 2014), pp. 3129–3134.

Sun, C.

Sun, H.

Tanaka, H.

H. Tanaka, Y. Sumi, and Y. Matsumoto, “A solution to pose ambiguity of visual markers using Moir patterns,” in IEEE/RSJ International Conference on Intelligent Robots and Systems (IEEE, 2014), pp. 3129–3134.

Tang, Q.

Tao, T.

Y. Hu, Q. Chen, T. Tao, H. Li, and C. Zuo, “Absolute three-dimensional micro surface profile measurement based on a Greenough-type stereomicroscope,” Meas. Sci. Technol. 28, 45004 (2017).

Taubin, G.

D. Moreno and G. Taubin, “Simple, Accurate, and Robust Projector-Camera Calibration,” in International Conference on 3D Imaging (IEEE, 2012), pp. 464–471.

Tian, J.

D. Li, C. Liu, and J. Tian, “Telecentric 3D profilometry based on phase-shifting fringe projection,” Opt. Express 22(26), 31826–31835 (2014).
[PubMed]

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

Tomasi, C.

C. Tomasi and T. Kanade, “Shape and motion from image streams under orthography: a factorization method,” Int. J. Comput. Vis. 9, 137–154 (1992).

Van der Jeught, S.

S. Van der Jeught and J. J. J. Dirckx, “Real-time structured light profilometry: a review,” Opt. Lasers Eng. 87, 18–31 (2016).

Wang, M.

Wang, P.

Wang, W.

Q. Mei, J. Gao, H. Lin, Y. Chen, H. Yunbo, W. Wang, G. Zhang, and X. Chen, “Structure light telecentric stereoscopic vision 3D measurement system based on Scheimpflug condition,” Opt. Lasers Eng. 86, 83–91 (2016).

Wang, Y.

L. Merner, Y. Wang, and S. Zhang, “Accurate calibration for 3D shape measurement system using a binary defocusing technique,” Opt. Lasers Eng. 51, 514–519 (2013).

Wu, Z.

Xi, J.

Xia, H.

Xianmin, Z.

L. Huiyang, C. Zhong, and Z. Xianmin, “Calibration of camera with small FOV and DOF telecentric lens,” in IEEE International Conference on Robotics and Biomimetics (IEEE, 2013), pp. 498–503.

Xu, J.

R. Chen, J. Xu, S. Zhang, H. Chen, Y. Guan, and K. Chen, “A self-recalibration method based on scale-invariant registration for structured light measurement systems,” Opt. Lasers Eng. 88, 75–81 (2017).

Y. An, T. Bell, B. Li, J. Xu, and S. Zhang, “Method for large-range structured light system calibration,” Appl. Opt. 55(33), 9563–9572 (2016).
[PubMed]

H. Luo, J. Xu, N. Hoa Binh, S. Liu, C. Zhang, and K. Chen, “A simple calibration procedure for structured light system,” Opt. Lasers Eng. 57, 6–12 (2014).

Yang, S.

S. Yang, M. Liu, J. Song, S. Yin, Y. Guo, Y. Ren, and J. Zhu, “Flexible digital projector calibration method based on per-pixel distortion measurement and correction,” Opt. Lasers Eng. 92, 29–38 (2017).

Yao, L.

H. Lin, H. Liu, and L. Yao, “3D-shape reconstruction based on a sub-pixel-level mapping relationship between the camera and projector,” Proc. SPIE 10255, 1025504 (2017).

L. Yao and H. Liu, “A flexible calibration approach for cameras with double-sided telecentric lenses,” Int. J. Adv. Robot. Syst. 13, 82 (2016).

Yin, S.

S. Yang, M. Liu, J. Song, S. Yin, Y. Guo, Y. Ren, and J. Zhu, “Flexible digital projector calibration method based on per-pixel distortion measurement and correction,” Opt. Lasers Eng. 92, 29–38 (2017).

Yin, Y.

Yu, L.

Yu, Y.

Yunbo, H.

Q. Mei, J. Gao, H. Lin, Y. Chen, H. Yunbo, W. Wang, G. Zhang, and X. Chen, “Structure light telecentric stereoscopic vision 3D measurement system based on Scheimpflug condition,” Opt. Lasers Eng. 86, 83–91 (2016).

Zhang, C.

H. Luo, J. Xu, N. Hoa Binh, S. Liu, C. Zhang, and K. Chen, “A simple calibration procedure for structured light system,” Opt. Lasers Eng. 57, 6–12 (2014).

Zhang, G.

Q. Mei, J. Gao, H. Lin, Y. Chen, H. Yunbo, W. Wang, G. Zhang, and X. Chen, “Structure light telecentric stereoscopic vision 3D measurement system based on Scheimpflug condition,” Opt. Lasers Eng. 86, 83–91 (2016).

Zhang, J.

Zhang, S.

B. Li and S. Zhang, “Microscopic structured light 3D profilometry: Binary defocusing technique vs. sinusoidal fringe projection,” Opt. Lasers Eng. 96, 117–123 (2017).

R. Chen, J. Xu, S. Zhang, H. Chen, Y. Guan, and K. Chen, “A self-recalibration method based on scale-invariant registration for structured light measurement systems,” Opt. Lasers Eng. 88, 75–81 (2017).

Y. An, T. Bell, B. Li, J. Xu, and S. Zhang, “Method for large-range structured light system calibration,” Appl. Opt. 55(33), 9563–9572 (2016).
[PubMed]

B. Li and S. Zhang, “Flexible calibration method for microscopic structured light system using telecentric lens,” Opt. Express 23(20), 25795–25803 (2015).
[PubMed]

B. Li and S. Zhang, “Structured light system calibration method with optimal fringe angle,” Appl. Opt. 53(33), 7942–7950 (2014).
[PubMed]

L. Merner, Y. Wang, and S. Zhang, “Accurate calibration for 3D shape measurement system using a binary defocusing technique,” Opt. Lasers Eng. 51, 514–519 (2013).

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 83601 (2006).

Zhang, W.

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).

Zhang, Z.

X. Liu, Z. Cai, Y. Yin, H. Jiang, D. He, W. He, Z. Zhang, and X. Peng, “Calibration of fringe projection profilometry using an inaccurate 2D reference target,” Opt. Lasers Eng. 89, 131–137 (2017).

Z. Zhang, S. Huang, S. Meng, F. Gao, and X. Jiang, “A simple, flexible and automatic 3D calibration method for a phase calculation-based fringe projection imaging system,” Opt. Express 21(10), 12218–12227 (2013).
[PubMed]

Zhao, H.

Zhong, C.

L. Huiyang, C. Zhong, and Z. Xianmin, “Calibration of camera with small FOV and DOF telecentric lens,” in IEEE International Conference on Robotics and Biomimetics (IEEE, 2013), pp. 498–503.

Zhu, F.

F. Zhu, H. Shi, P. Bai, D. Lei, and X. He, “Nonlinear calibration for generalized fringe projection profilometry under large measuring depth range,” Appl. Opt. 52(32), 7718–7723 (2013).
[PubMed]

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).

Zhu, J.

S. Yang, M. Liu, J. Song, S. Yin, Y. Guo, Y. Ren, and J. Zhu, “Flexible digital projector calibration method based on per-pixel distortion measurement and correction,” Opt. Lasers Eng. 92, 29–38 (2017).

Zuo, C.

Y. Hu, Q. Chen, T. Tao, H. Li, and C. Zuo, “Absolute three-dimensional micro surface profile measurement based on a Greenough-type stereomicroscope,” Meas. Sci. Technol. 28, 45004 (2017).

Appl. Opt. (9)

A. Mikš and J. Novák, “Design of a double-sided telecentric zoom lens,” Appl. Opt. 51(24), 5928–5935 (2012).
[PubMed]

J. Zhang, X. Chen, J. Xi, and Z. Wu, “Aberration correction of double-sided telecentric zoom lenses using lens modules,” Appl. Opt. 53(27), 6123–6132 (2014).
[PubMed]

J. Lu, R. Mo, H. Sun, and Z. Chang, “Flexible calibration of phase-to-height conversion in fringe projection profilometry,” Appl. Opt. 55(23), 6381–6388 (2016).
[PubMed]

F. Zhu, H. Shi, P. Bai, D. Lei, and X. He, “Nonlinear calibration for generalized fringe projection profilometry under large measuring depth range,” Appl. Opt. 52(32), 7718–7723 (2013).
[PubMed]

P. Lu, C. Sun, B. Liu, and P. Wang, “Accurate and robust calibration method based on pattern geometric constraints for fringe projection profilometry,” Appl. Opt. 56(4), 784–794 (2017).
[PubMed]

Y. An, T. Bell, B. Li, J. Xu, and S. Zhang, “Method for large-range structured light system calibration,” Appl. Opt. 55(33), 9563–9572 (2016).
[PubMed]

B. Li and S. Zhang, “Structured light system calibration method with optimal fringe angle,” Appl. Opt. 53(33), 7942–7950 (2014).
[PubMed]

Z. Huang, J. Xi, Y. Yu, and Q. Guo, “Accurate projector calibration based on a new point-to-point mapping relationship between the camera and projector images,” Appl. Opt. 54, 347 (2015).

J. Peng, M. Wang, D. Deng, X. Liu, Y. Yin, and X. Peng, “Distortion correction for microscopic fringe projection system with Scheimpflug telecentric lens,” Appl. Opt. 54(34), 10055–10062 (2015).
[PubMed]

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

T. Collins and A. Bartoli, “Planar Structure-from-Motion with Affine Camera Models: Closed-Form Solutions, Ambiguities and Degeneracy Analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 39(6), 1237–1255 (2017).
[PubMed]

Int. J. Adv. Robot. Syst. (1)

L. Yao and H. Liu, “A flexible calibration approach for cameras with double-sided telecentric lenses,” Int. J. Adv. Robot. Syst. 13, 82 (2016).

Int. J. Comput. Vis. (3)

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

C. Steger, “A Comprehensive and Versatile Camera Model for Cameras with Tilt Lenses,” Int. J. Comput. Vis. 123(2), 1–39 (2017).

C. Tomasi and T. Kanade, “Shape and motion from image streams under orthography: a factorization method,” Int. J. Comput. Vis. 9, 137–154 (1992).

J. Opt. Soc. Am. A (1)

Meas. Sci. Technol. (1)

Y. Hu, Q. Chen, T. Tao, H. Li, and C. Zuo, “Absolute three-dimensional micro surface profile measurement based on a Greenough-type stereomicroscope,” Meas. Sci. Technol. 28, 45004 (2017).

Opt. Eng. (1)

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 83601 (2006).

Opt. Express (7)

Opt. Lasers Eng. (11)

X. Liu, Z. Cai, Y. Yin, H. Jiang, D. He, W. He, Z. Zhang, and X. Peng, “Calibration of fringe projection profilometry using an inaccurate 2D reference target,” Opt. Lasers Eng. 89, 131–137 (2017).

R. Chen, J. Xu, S. Zhang, H. Chen, Y. Guan, and K. Chen, “A self-recalibration method based on scale-invariant registration for structured light measurement systems,” Opt. Lasers Eng. 88, 75–81 (2017).

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

S. Yang, M. Liu, J. Song, S. Yin, Y. Guo, Y. Ren, and J. Zhu, “Flexible digital projector calibration method based on per-pixel distortion measurement and correction,” Opt. Lasers Eng. 92, 29–38 (2017).

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

Q. Mei, J. Gao, H. Lin, Y. Chen, H. Yunbo, W. Wang, G. Zhang, and X. Chen, “Structure light telecentric stereoscopic vision 3D measurement system based on Scheimpflug condition,” Opt. Lasers Eng. 86, 83–91 (2016).

H. Luo, J. Xu, N. Hoa Binh, S. Liu, C. Zhang, and K. Chen, “A simple calibration procedure for structured light system,” Opt. Lasers Eng. 57, 6–12 (2014).

B. Li and S. Zhang, “Microscopic structured light 3D profilometry: Binary defocusing technique vs. sinusoidal fringe projection,” Opt. Lasers Eng. 96, 117–123 (2017).

S. Van der Jeught and J. J. J. Dirckx, “Real-time structured light profilometry: a review,” Opt. Lasers Eng. 87, 18–31 (2016).

L. Merner, Y. Wang, and S. Zhang, “Accurate calibration for 3D shape measurement system using a binary defocusing technique,” Opt. Lasers Eng. 51, 514–519 (2013).

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).

Opt. Lett. (2)

Proc. SPIE (1)

H. Lin, H. Liu, and L. Yao, “3D-shape reconstruction based on a sub-pixel-level mapping relationship between the camera and projector,” Proc. SPIE 10255, 1025504 (2017).

Other (7)

D. Moreno and G. Taubin, “Simple, Accurate, and Robust Projector-Camera Calibration,” in International Conference on 3D Imaging (IEEE, 2012), pp. 464–471.

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

K. Kanatani, Y. Sugaya, and Y. Kanazawa, “Self-calibration of Affine Cameras,” in Guide to 3D Vision Computation (Springer International Publishing, 2016), pp. 163–182.

H. Tanaka, Y. Sumi, and Y. Matsumoto, “A solution to pose ambiguity of visual markers using Moir patterns,” in IEEE/RSJ International Conference on Intelligent Robots and Systems (IEEE, 2014), pp. 3129–3134.

L. Huiyang, C. Zhong, and Z. Xianmin, “Calibration of camera with small FOV and DOF telecentric lens,” in IEEE International Conference on Robotics and Biomimetics (IEEE, 2013), pp. 498–503.

J. G. Rico Espino, J. Gonzalez-Barbosa, R. A. Gomez Loenzo, D. M. Cordova Esparza, and R. Gonzalez-Barbosa, “Vision system for 3D reconstruction with telecentric lens,” in Mexican Conference on Pattern Recognition (Springer-Verlag, 2012), pp. 127–136.

Y. Oyamada, P. Fallavollita, and N. Navab, “Single Camera Calibration using partially visible calibration objects based on Random Dots Marker Tracking Algorithm,” in IEEE and ACM International Symposium on Mixed and Augmented Reality (IEEE, 2012).

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Figures (12)

Fig. 1
Fig. 1 Measurement model of FPP system with bi-telecentric lens.
Fig. 2
Fig. 2 Selected projector-camera coordinates. (a) Rig model when Z C axis is approximately parallel with Z P X P plane (b) Rig model when Z C axis is approximately parallel with Y P Z P plane.
Fig. 3
Fig. 3 Sub-pixels on camera image plane correspond to pixels on projector image plane.
Fig. 4
Fig. 4 3D object target for calibration. (a) Designed calibration object with circular dots (b) Photograph of 3D calibration target.
Fig. 5
Fig. 5 Examples of calibration images. (a) Completely illuminated camera image (b) and (c) Projector images achieved by sub-pixel mapping, where pixels with same color correspond respectively to same camera column (b) and same camera row (c).
Fig. 6
Fig. 6 Estimated 3D control points.
Fig. 7
Fig. 7 Re-projection error after bundle adjustment. (a) Re-projection error of camera images (b) Re-projection error of projector images.
Fig. 8
Fig. 8 Reconstructed errors of calibrated control points.
Fig. 9
Fig. 9 Measured depth map of step master (mm).
Fig. 10
Fig. 10 Reconstruction of calibration target. (a) Reconstructed calibration target (b) Reconstructed calibration target rendered with texture (c) Region on surface of reconstructed calibration target with color depth.
Fig. 11
Fig. 11 Reconstruction of coin. (a) Photo of reconstructed coin; (b) Whole view of reconstructed coin; (c) Region on surface of reconstructed coin rendered with color depth.
Fig. 12
Fig. 12 Reconstruction of BGA solder balls. (a) Photo of reconstructed BGA solder balls; (b) and (c) Views of reconstructed BGA solder balls.

Tables (2)

Tables Icon

Table 1 Estimated intrinsic parameters

Tables Icon

Table 2 Measured results of step master ( μm)

Equations (28)

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

[ m 1 ]=K[ R 2×3 t s 0 1×3 1 ][ P 1 ],
K=[ m 0 u 0 0 m v 0 0 0 1 ].
[ m P 1 ]= K P [ R P2×3 t Ps 0 1×3 1 ][ P 1 ],
[ m C 1 ]= K c [ R c2×3 t cs 0 1×3 1 ][ P 1 ],
[ m p 1 ]= K p [ I 2×3 0 2×1 0 1×3 1 ][ P 1 ],
[ m C 1 ]= K C [ R P2×3 C t Ps C 0 1×3 1 ][ P 1 ].
{ R P C = R C R P 1 t P C = t C R C R P 1 t P .
{ R P C = R C R P 1 t P C = R P C × [ 0 y oC 0 ] T ,
{ R P C = R C R P 1 t P C = R P C × [ x oC 0 0 ] T ,
[ u c v c 1 ]=[ h 11 h 12 h 13 h 21 h 22 h 23 0 0 1 ][ x w y w 1 ]=H[ x w y w 1 ].
H C P = H T P ( H T C ) 1 .
W C = [ u ¯ C11 u ¯ C12 u ¯ C1l v ¯ C11 v ¯ C12 v ¯ C1l u ¯ Cn1 u ¯ Cn2 u ¯ Cnl v ¯ Cn1 v ¯ Cn2 v ¯ Cnl ] 2n×l ,
W P = [ u ¯ P11 u ¯ P12 u ¯ P1l v ¯ P11 v ¯ P12 v ¯ P1l u ¯ Pn1 u ¯ Pn2 u ¯ Pnl v ¯ Pn1 v ¯ Pn2 v ¯ Pnl ] 2n×l .
{ u ¯ Cij = u Cij 1 m j=1 m u Cij v ¯ Cij = v Cij 1 m j=1 m v Cij ,
{ u ¯ Pij = u Pij 1 m j=1 m u Pij v ¯ Pij = v Pij 1 m j=1 m v Pij .
M C = [ r C 1 11 r C 1 12 r C 1 13 r C 1 21 r C 1 22 r C 1 23 r C n 11 r C n 12 r C n 13 r C n 21 r C n 22 r C n 23 ] 2n×3 ,
M P = [ r P 1 11 r P 1 12 r P 1 13 r P 1 21 r P 1 22 r P 1 23 r P n 11 r P n 12 r P n 13 r P n 21 r P n 22 r P n 23 ] 2n×3 ,
M P = [ r P 1 11 r P 1 12 r P 1 13 r P 1 21 r P 1 22 r P 1 23 r P n 11 r P n 12 r P n 13 r P n 21 r P n 22 r P n 23 ] 2n×3 ,
S= [ x 1 x 2 x l y 1 y 2 y l z 1 z 2 z l ] 3×l .
{ W C = M C S W P = M P S .
R Pi = [ r Pxi T r Pyi T r Pzi T ] T ,
t Psi = [ t Pxi t Pyi ] T ,
o C = [ o Cx o Cy o Cz ] T = R P C [ t Cs 0 ]+[ t Ps 0 ].
y oC = o Cy n Cy n Cx × o Cx .
x oC = o Cx n Cx n Cy × o Cy .
e= i=1 n j=1 m [ m P ij p ˜ P ij ( R Pi , t Psi , K P , x j , y j , z j ) 2 + m C ij p ˜ Cij ( R Pi , t Psi , R P C , t P C , x j , y j , z j ) 2 ] ,
P con = R t P con + t t ,
( R t , t t )=argmin j=1 m R t P conj + R t P estj ,

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