Abstract

Digital projectors are used as standard parts at present in fringe projection profilometry systems to project structured-light patterns onto the object surface to be measured, and the distortion of the projector lens must be calibrated and compensated accurately to satisfy the accuracy requirement of industrial applications. A novel method is proposed to determine the projector pixel coordinates of the marker points of a calibration target accurately in terms of projective transform. With the method, the projector can be calibrated with accuracy of sub-pixel level. The method is applicable for the calibration target with a chessboard pattern or a circle pattern, and the calibration result is independent on the results of camera calibration. Experimental results are shown to demonstrate the effectiveness and validity of the proposed method.

© 2017 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2016 (2)

2015 (2)

2014 (3)

2013 (1)

D. He, X. Liu, X. Peng, Y. Ding, and B. Z. Gao, “Eccentricity error identification and compensation for high-accuracy 3D optical measurement,” Meas. Sci. Technol. 24(7), 075402 (2013).
[Crossref] [PubMed]

2012 (1)

H. Anwar, I. Din, and K. Park, “Projector calibration for 3D scanning using virtual target images,” Int. J. Precis. Eng. Manuf. 13(1), 125–131 (2012).
[Crossref]

2010 (2)

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

Z. Y. Wang, D. A. Nguyen, and J. C. Barnes, “Some practical considerations in fringe projection profilometry,” Opt. Lasers Eng. 48(2), 218–225 (2010).
[Crossref]

2008 (2)

Z. W. Li, Y. S. Shi, C. J. Wang, and Y. Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[Crossref]

S. Zhang and R. Chung, “Use of LCD panel for calibrating structured-light-based range sensing system,” IEEE Trans. Instrum. Meas. 57(11), 2623–2630 (2008).
[Crossref]

2006 (1)

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

2000 (2)

F. Chen, G. W. Brown, and M. Song, “Overview of the three-dimentional shape measurement using optical methods,” Opt. Eng. 39(1), 10–22 (2000).
[Crossref]

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

1987 (1)

R. Y. Tsai, “A versatile camera calibration technique for high accuracy 3D machine vision metrology using off-the shelf TV cameras and lenses,” IEEE J. Robot. Autom. 3(4), 323–344 (1987).
[Crossref]

Anwar, H.

H. Anwar, I. Din, and K. Park, “Projector calibration for 3D scanning using virtual target images,” Int. J. Precis. Eng. Manuf. 13(1), 125–131 (2012).
[Crossref]

Barnes, J. C.

Z. Y. Wang, D. A. Nguyen, and J. C. Barnes, “Some practical considerations in fringe projection profilometry,” Opt. Lasers Eng. 48(2), 218–225 (2010).
[Crossref]

Brown, G. W.

F. Chen, G. W. Brown, and M. Song, “Overview of the three-dimentional shape measurement using optical methods,” Opt. Eng. 39(1), 10–22 (2000).
[Crossref]

Cai, Z.

Chang, Z.

Chen, F.

F. Chen, G. W. Brown, and M. Song, “Overview of the three-dimentional shape measurement using optical methods,” Opt. Eng. 39(1), 10–22 (2000).
[Crossref]

Chen, L.

Chung, R.

S. Zhang and R. Chung, “Use of LCD panel for calibrating structured-light-based range sensing system,” IEEE Trans. Instrum. Meas. 57(11), 2623–2630 (2008).
[Crossref]

Deng, D.

Din, I.

H. Anwar, I. Din, and K. Park, “Projector calibration for 3D scanning using virtual target images,” Int. J. Precis. Eng. Manuf. 13(1), 125–131 (2012).
[Crossref]

Ding, Y.

D. He, X. Liu, X. Peng, Y. Ding, and B. Z. Gao, “Eccentricity error identification and compensation for high-accuracy 3D optical measurement,” Meas. Sci. Technol. 24(7), 075402 (2013).
[Crossref] [PubMed]

Gao, B. Z.

D. He, X. Liu, X. Peng, Y. Ding, and B. Z. Gao, “Eccentricity error identification and compensation for high-accuracy 3D optical measurement,” Meas. Sci. Technol. 24(7), 075402 (2013).
[Crossref] [PubMed]

Gao, F.

Gorthi, S. S.

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

Guo, H.

Guo, Q. H.

He, D.

D. He, X. Liu, X. Peng, Y. Ding, and B. Z. Gao, “Eccentricity error identification and compensation for high-accuracy 3D optical measurement,” Meas. Sci. Technol. 24(7), 075402 (2013).
[Crossref] [PubMed]

He, T.

Huang, S.

Huang, Z. R.

Hui, B. W.

D. Li, G. Wen, B. W. Hui, S. Qiu, and W. Wang, “Cross-ratio invariant based line scan camera geometric calibration with static linear data,” Opt. Lasers Eng. 62(6), 119–125 (2014).
[Crossref]

Jiang, X.

Li, D.

D. Li, G. Wen, B. W. Hui, S. Qiu, and W. Wang, “Cross-ratio invariant based line scan camera geometric calibration with static linear data,” Opt. Lasers Eng. 62(6), 119–125 (2014).
[Crossref]

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

Li, X.

Li, Z. W.

Z. W. Li, Y. S. Shi, C. J. Wang, and Y. Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[Crossref]

Liu, C.

Liu, X.

J. Peng, X. Liu, D. Deng, H. Guo, Z. Cai, and X. Peng, “Suppression of projector distortion in phase-measuring profilometry by projecting adaptive fringe patterns,” Opt. Express 24(19), 21846–21860 (2016).
[Crossref] [PubMed]

D. He, X. Liu, X. Peng, Y. Ding, and B. Z. Gao, “Eccentricity error identification and compensation for high-accuracy 3D optical measurement,” Meas. Sci. Technol. 24(7), 075402 (2013).
[Crossref] [PubMed]

Lu, J.

Mo, R.

Nguyen, D. A.

Z. Y. Wang, D. A. Nguyen, and J. C. Barnes, “Some practical considerations in fringe projection profilometry,” Opt. Lasers Eng. 48(2), 218–225 (2010).
[Crossref]

Park, K.

H. Anwar, I. Din, and K. Park, “Projector calibration for 3D scanning using virtual target images,” Int. J. Precis. Eng. Manuf. 13(1), 125–131 (2012).
[Crossref]

Peng, J.

Peng, X.

J. Peng, X. Liu, D. Deng, H. Guo, Z. Cai, and X. Peng, “Suppression of projector distortion in phase-measuring profilometry by projecting adaptive fringe patterns,” Opt. Express 24(19), 21846–21860 (2016).
[Crossref] [PubMed]

D. He, X. Liu, X. Peng, Y. Ding, and B. Z. Gao, “Eccentricity error identification and compensation for high-accuracy 3D optical measurement,” Meas. Sci. Technol. 24(7), 075402 (2013).
[Crossref] [PubMed]

Qiu, S.

D. Li, G. Wen, B. W. Hui, S. Qiu, and W. Wang, “Cross-ratio invariant based line scan camera geometric calibration with static linear data,” Opt. Lasers Eng. 62(6), 119–125 (2014).
[Crossref]

Rastogi, P.

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

Shi, Y. S.

Z. W. Li, Y. S. Shi, C. J. Wang, and Y. Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[Crossref]

Song, M.

F. Chen, G. W. Brown, and M. Song, “Overview of the three-dimentional shape measurement using optical methods,” Opt. Eng. 39(1), 10–22 (2000).
[Crossref]

Sun, H.

Tian, J.

Tsai, R. Y.

R. Y. Tsai, “A versatile camera calibration technique for high accuracy 3D machine vision metrology using off-the shelf TV cameras and lenses,” IEEE J. Robot. Autom. 3(4), 323–344 (1987).
[Crossref]

Wang, C. J.

Z. W. Li, Y. S. Shi, C. J. Wang, and Y. Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[Crossref]

Wang, W.

D. Li, G. Wen, B. W. Hui, S. Qiu, and W. Wang, “Cross-ratio invariant based line scan camera geometric calibration with static linear data,” Opt. Lasers Eng. 62(6), 119–125 (2014).
[Crossref]

Wang, Y. Y.

Z. W. Li, Y. S. Shi, C. J. Wang, and Y. Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[Crossref]

Wang, Z.

Wang, Z. Y.

Z. Y. Wang, D. A. Nguyen, and J. C. Barnes, “Some practical considerations in fringe projection profilometry,” Opt. Lasers Eng. 48(2), 218–225 (2010).
[Crossref]

Wen, G.

D. Li, G. Wen, B. W. Hui, S. Qiu, and W. Wang, “Cross-ratio invariant based line scan camera geometric calibration with static linear data,” Opt. Lasers Eng. 62(6), 119–125 (2014).
[Crossref]

Xi, J. T.

Xie, L.

Xu, L.

Yu, Y. G.

Zhang, S.

S. Zhang and R. Chung, “Use of LCD panel for calibrating structured-light-based range sensing system,” IEEE Trans. Instrum. Meas. 57(11), 2623–2630 (2008).
[Crossref]

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

Zhang, Z.

Appl. Opt. (4)

IEEE J. Robot. Autom. (1)

R. Y. Tsai, “A versatile camera calibration technique for high accuracy 3D machine vision metrology using off-the shelf TV cameras and lenses,” IEEE J. Robot. Autom. 3(4), 323–344 (1987).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

S. Zhang and R. Chung, “Use of LCD panel for calibrating structured-light-based range sensing system,” IEEE Trans. Instrum. Meas. 57(11), 2623–2630 (2008).
[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]

Int. J. Precis. Eng. Manuf. (1)

H. Anwar, I. Din, and K. Park, “Projector calibration for 3D scanning using virtual target images,” Int. J. Precis. Eng. Manuf. 13(1), 125–131 (2012).
[Crossref]

Meas. Sci. Technol. (1)

D. He, X. Liu, X. Peng, Y. Ding, and B. Z. Gao, “Eccentricity error identification and compensation for high-accuracy 3D optical measurement,” Meas. Sci. Technol. 24(7), 075402 (2013).
[Crossref] [PubMed]

Opt. Eng. (3)

Z. W. Li, Y. S. Shi, C. J. Wang, and Y. Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[Crossref]

F. Chen, G. W. Brown, and M. Song, “Overview of the three-dimentional shape measurement using optical methods,” Opt. Eng. 39(1), 10–22 (2000).
[Crossref]

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

Opt. Express (2)

Opt. Lasers Eng. (3)

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

Z. Y. Wang, D. A. Nguyen, and J. C. Barnes, “Some practical considerations in fringe projection profilometry,” Opt. Lasers Eng. 48(2), 218–225 (2010).
[Crossref]

D. Li, G. Wen, B. W. Hui, S. Qiu, and W. Wang, “Cross-ratio invariant based line scan camera geometric calibration with static linear data,” Opt. Lasers Eng. 62(6), 119–125 (2014).
[Crossref]

Other (1)

E. Casas-Alvero, Analytic Projective Geometry (European Mathematical Society, 2014).

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Figures (8)

Fig. 1
Fig. 1

The pinhole model of the camera and the projector.

Fig. 2
Fig. 2

Projective geometry in FPP: (a) projective invariance of the cross ratio, (b) intersection of two lines.

Fig. 3
Fig. 3

Schematic diagram of the sub-pixel mapping: (a) the marker point and auxiliary points in the camera image plane, (b) the mapping points on the projector DMD.

Fig. 4
Fig. 4

Degenerated cases: (a) case 1 in camera image plane, (b) case 2 in camera image plane, (c-d) mapping points on the projector DMD.

Fig. 5
Fig. 5

Camera images and absolute phase maps: (a) the chessboard calibration target, (b-c) the images of the projected fringe patterns in vertical and horizontal directions, respectively, (d-e) marker points and absolute phase maps in two different directions.

Fig. 6
Fig. 6

Re-projection error comparison (with a chessboard pattern): (a) P2P method, (b) our proposed method, (c) partial enlargement of our proposed method.

Fig. 7
Fig. 7

Re-projection error comparison (with a circle pattern): (a) the calibration target, (b-c) circle centers, circle edges and absolute phase maps in two different directions, respectively, (d-f) re-projection errors of P2P method, circle fitting method and our proposed method, respectively.

Fig. 8
Fig. 8

Comparison of phase error compensation: (a) a ceramic plate with white illumination, (b) absolute phase map of the plate, (c) without compensation, (d-g) compensated results by using the P2P method, the circle fitting method, the adaptive fringe pattern method and our proposed method, respectively.

Tables (2)

Tables Icon

Table 1 Calibrated intrinsic parameters with standard error (Unit: pixel)

Tables Icon

Table 2 Calibrated coefficients of lens distortion with standard errors

Equations (9)

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

s [ u p v p 1 ] = [ f u 0 u p 0 0 f v v p 0 0 0 1 ] [ R , T ] [ x y z 1 ]
P d = ( 1 + k 1 r p 2 + k 2 r p 4 ) P p + [ 2 p 1 u p v p + p 2 ( r p 2 + 2 u p 2 ) 2 p 2 u p v p + p 1 ( r p 2 + 2 u p 2 ) ]
I V i ( u c , v c ) = I V + I V cos [ Φ V ( u c , v c ) + δ i ] i = 1 , 2 , , N
I H i ( u c , v c ) = I H + I H cos [ Φ H ( u c , v c ) + δ i ] i = 1 , 2 , , N
Φ V ( u c , v c ) = a r c t a n [ i = 1 N I V i ( u c , v c ) sin ( δ i ) i = 1 N I V i ( u c , v c ) cos ( δ i ) ] , Φ H ( u c , v c ) = a r c t a n [ i = 1 N I H i ( u c , v c ) sin ( δ i ) i = 1 N I H i ( u c , v c ) cos ( δ i ) ]
u p = Φ V 2 π T V , v p = Φ H 2 π T H
( P 1 , P 2 ; P 3 , P 4 ) = P 1 P 3 / P 2 P 3 P 1 P 4 / P 2 P 4
{ A p = a + λ 1 b , E p = a + λ 2 b , F p = a + λ 3 b , C p = a + λ 4 b B p = a ¯ + τ 1 b ¯ , E p = a ¯ + τ 2 b ¯ , G p = a ¯ + τ 3 b ¯ , D p = a ¯ + τ 4 b ¯
( A p ,E p ;F p ,C p ) = ( λ 1 - λ 3 ) ( λ 2 - λ 4 ) ( λ 2 - λ 3 ) ( λ 1 - λ 4 ) , ( B p ,E p ;G p ,D p ) = ( τ 1 - τ 3 ) ( τ 2 - τ 4 ) ( τ 2 - τ 3 ) ( τ 1 - τ 4 )

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