Abstract

By using the least-squares fitting approach, the calibration procedure for fringe projection profilometry becomes more flexible and easier, since neither the measurement of system geometric parameters nor precise control of plane moving is required. With consideration of camera lens distortion, we propose a modified least-squares calibration method for fringe projection profilometry. In this method, camera lens distortion is involved in the mathematical description of the system for least-squares fitting to reduce its influence. Both simulation and experimental results are shown to verify the validity and ease of use of this modified calibration method.

© 2010 Optical Society of America

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References

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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] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. A. Maurel, P. Cobelli, V. Pagneux, and P. Petitjeans, “Experimental and theoretical inspection of the phase-to-height relation in Fourier transform profilometry,” Appl. Opt. 48, 380-392 (2009).
    [CrossRef] [PubMed]
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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]

2009 (3)

2008 (2)

2007 (1)

2006 (2)

S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 123601-123608 (2006).
[CrossRef]

Z. Wang and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng. 45, 045601 (2006).
[CrossRef]

2005 (3)

Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3-D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44, 113601-113607 (2005).
[CrossRef]

L.-C. Chen and C.-C. Liao, “Calibration of 3D surface profilometry using digital fringe projection,” Meas. Sci. Technol. 16, 1554-1566 (2005).
[CrossRef]

H. Guo, H. He, Y. Yu, and M. Chen, “Least-squares calibration method for fringe projection profilometry,” Opt. Eng. 44, 033603-033609 (2005).
[CrossRef]

2004 (2)

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245-261 (2004).
[CrossRef]

X. Su, W. Song, Y. Cao, and L. Xiang, “Phase-height mapping and coordinate calibration simultaneously in phase-measuring profilometry,” Opt. Eng. 43, 708-712 (2004).
[CrossRef]

2003 (2)

H. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216, 65-80 (2003).
[CrossRef]

Q. Hu, P. S. Huang, Q. Fu, and F.-P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42, 487-493 (2003).
[CrossRef]

2001 (1)

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263-284 (2001).
[CrossRef]

2000 (1)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Machine Intell. 22, 1330-1334(2000).
[CrossRef]

1986 (1)

1984 (1)

1983 (1)

Asundi, A.

Bachor, H. A.

Bone, D. J.

Bouguet, J. Y.

J. Y. Bouguet, “Camera calibration toolbox for MATLAB,” http://www.vision.caltech.edu/bouguetj/calib_doc.

Cao, Y.

Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3-D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44, 113601-113607 (2005).
[CrossRef]

X. Su, W. Song, Y. Cao, and L. Xiang, “Phase-height mapping and coordinate calibration simultaneously in phase-measuring profilometry,” Opt. Eng. 43, 708-712 (2004).
[CrossRef]

Chen, L.-C.

L.-C. Chen and C.-C. Liao, “Calibration of 3D surface profilometry using digital fringe projection,” Meas. Sci. Technol. 16, 1554-1566 (2005).
[CrossRef]

Chen, M.

H. Guo, H. He, Y. Yu, and M. Chen, “Least-squares calibration method for fringe projection profilometry,” Opt. Eng. 44, 033603-033609 (2005).
[CrossRef]

Chen, W.

Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3-D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44, 113601-113607 (2005).
[CrossRef]

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245-261 (2004).
[CrossRef]

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263-284 (2001).
[CrossRef]

Chiang, F.-P.

Q. Hu, P. S. Huang, Q. Fu, and F.-P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42, 487-493 (2003).
[CrossRef]

Cobelli, P.

Du, H.

Fu, Q.

Q. Hu, P. S. Huang, Q. Fu, and F.-P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42, 487-493 (2003).
[CrossRef]

Fujigaki, M.

M. Fujigaki, A. Takagishi, T. Matui, and Y. Morimoto, “Development of real-time shape measurement system using whole-space tabulation method,” in Two- and Three-Dimensional Methods for Inspection and Metrology VI (SPIE, 2008), pp. 706606-706608.

Gao, W.

Guo, H.

H. Guo, H. He, Y. Yu, and M. Chen, “Least-squares calibration method for fringe projection profilometry,” Opt. Eng. 44, 033603-033609 (2005).
[CrossRef]

Halioua, M.

Harding, K.

K. Harding, “Industrial metrology: engineering precision,” Nat. Photon. 2, 667-669 (2008).
[CrossRef]

He, H.

H. Guo, H. He, Y. Yu, and M. Chen, “Least-squares calibration method for fringe projection profilometry,” Opt. Eng. 44, 033603-033609 (2005).
[CrossRef]

Heikkila, J.

J. Heikkila and O. Silven, “A four-step camera calibration procedure with implicit image correction,” in 1997 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 1997), pp. 1106-1112.
[CrossRef]

Hu, Q.

Q. Hu, P. S. Huang, Q. Fu, and F.-P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42, 487-493 (2003).
[CrossRef]

Huang, L.

Huang, P. S.

S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 123601-123608 (2006).
[CrossRef]

Q. Hu, P. S. Huang, Q. Fu, and F.-P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42, 487-493 (2003).
[CrossRef]

Kemao, Q.

Li, Y.

Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3-D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44, 113601-113607 (2005).
[CrossRef]

Liao, C.-C.

L.-C. Chen and C.-C. Liao, “Calibration of 3D surface profilometry using digital fringe projection,” Meas. Sci. Technol. 16, 1554-1566 (2005).
[CrossRef]

Liu, H.

H. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216, 65-80 (2003).
[CrossRef]

Liu, H. C.

Ma, H.

Z. Wang and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng. 45, 045601 (2006).
[CrossRef]

Matui, T.

M. Fujigaki, A. Takagishi, T. Matui, and Y. Morimoto, “Development of real-time shape measurement system using whole-space tabulation method,” in Two- and Three-Dimensional Methods for Inspection and Metrology VI (SPIE, 2008), pp. 706606-706608.

Maurel, A.

Morimoto, Y.

M. Fujigaki, A. Takagishi, T. Matui, and Y. Morimoto, “Development of real-time shape measurement system using whole-space tabulation method,” in Two- and Three-Dimensional Methods for Inspection and Metrology VI (SPIE, 2008), pp. 706606-706608.

Mutoh, K.

Pagneux, V.

Pan, B.

Park, S.

Petitjeans, P.

Reichard, K.

H. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216, 65-80 (2003).
[CrossRef]

Sandeman, R. J.

Silven, O.

J. Heikkila and O. Silven, “A four-step camera calibration procedure with implicit image correction,” in 1997 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 1997), pp. 1106-1112.
[CrossRef]

Song, W.

X. Su, W. Song, Y. Cao, and L. Xiang, “Phase-height mapping and coordinate calibration simultaneously in phase-measuring profilometry,” Opt. Eng. 43, 708-712 (2004).
[CrossRef]

Srinivasan, V.

Su, W. H.

H. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216, 65-80 (2003).
[CrossRef]

Su, X.

Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3-D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44, 113601-113607 (2005).
[CrossRef]

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245-261 (2004).
[CrossRef]

X. Su, W. Song, Y. Cao, and L. Xiang, “Phase-height mapping and coordinate calibration simultaneously in phase-measuring profilometry,” Opt. Eng. 43, 708-712 (2004).
[CrossRef]

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263-284 (2001).
[CrossRef]

Takagishi, A.

M. Fujigaki, A. Takagishi, T. Matui, and Y. Morimoto, “Development of real-time shape measurement system using whole-space tabulation method,” in Two- and Three-Dimensional Methods for Inspection and Metrology VI (SPIE, 2008), pp. 706606-706608.

Takeda, M.

Wang, H.

Wang, Z.

Xiang, L.

Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3-D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44, 113601-113607 (2005).
[CrossRef]

X. Su, W. Song, Y. Cao, and L. Xiang, “Phase-height mapping and coordinate calibration simultaneously in phase-measuring profilometry,” Opt. Eng. 43, 708-712 (2004).
[CrossRef]

Xie, H.

Yin, S.

H. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216, 65-80 (2003).
[CrossRef]

Yu, Y.

H. Guo, H. He, Y. Yu, and M. Chen, “Least-squares calibration method for fringe projection profilometry,” Opt. Eng. 44, 033603-033609 (2005).
[CrossRef]

Zhang, Q.

Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3-D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44, 113601-113607 (2005).
[CrossRef]

Zhang, S.

S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 123601-123608 (2006).
[CrossRef]

Zhang, Z.

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Machine Intell. 22, 1330-1334(2000).
[CrossRef]

Appl. Opt. (6)

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

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Machine Intell. 22, 1330-1334(2000).
[CrossRef]

Meas. Sci. Technol. (1)

L.-C. Chen and C.-C. Liao, “Calibration of 3D surface profilometry using digital fringe projection,” Meas. Sci. Technol. 16, 1554-1566 (2005).
[CrossRef]

Nat. Photon. (1)

K. Harding, “Industrial metrology: engineering precision,” Nat. Photon. 2, 667-669 (2008).
[CrossRef]

Opt. Commun. (1)

H. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216, 65-80 (2003).
[CrossRef]

Opt. Eng. (6)

H. Guo, H. He, Y. Yu, and M. Chen, “Least-squares calibration method for fringe projection profilometry,” Opt. Eng. 44, 033603-033609 (2005).
[CrossRef]

Z. Wang and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng. 45, 045601 (2006).
[CrossRef]

Q. Hu, P. S. Huang, Q. Fu, and F.-P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42, 487-493 (2003).
[CrossRef]

X. Su, W. Song, Y. Cao, and L. Xiang, “Phase-height mapping and coordinate calibration simultaneously in phase-measuring profilometry,” Opt. Eng. 43, 708-712 (2004).
[CrossRef]

S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 123601-123608 (2006).
[CrossRef]

Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3-D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44, 113601-113607 (2005).
[CrossRef]

Opt. Lasers Eng. (2)

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263-284 (2001).
[CrossRef]

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245-261 (2004).
[CrossRef]

Opt. Lett. (2)

Other (3)

M. Fujigaki, A. Takagishi, T. Matui, and Y. Morimoto, “Development of real-time shape measurement system using whole-space tabulation method,” in Two- and Three-Dimensional Methods for Inspection and Metrology VI (SPIE, 2008), pp. 706606-706608.

J. Y. Bouguet, “Camera calibration toolbox for MATLAB,” http://www.vision.caltech.edu/bouguetj/calib_doc.

J. Heikkila and O. Silven, “A four-step camera calibration procedure with implicit image correction,” in 1997 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 1997), pp. 1106-1112.
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Schematic diagram of the FPP system.

Fig. 2
Fig. 2

Camera coordinates.

Fig. 3
Fig. 3

Calibration gauge blocks in simulation: (a) 3D height distribution of calibration gauge blocks, (b) a representative simulated fringe pattern, and (c) its unwrapped phase map.

Fig. 4
Fig. 4

Target in simulation: (a) 3D true height distribution of target, (b) representative simulated fringe pattern, and (c) its unwrapped phase map.

Fig. 5
Fig. 5

Simulation results under the no-distortion condition: (a) reconstructed result by the existing method, (b) reconstructed result by the proposed method, (c) reconstruction error from fringe patterns with no noise by the existing method, (d) reconstruction error from fringe patterns with no noise by the proposed method, (e) reconstruction error from fringe patterns with noise by the existing method, and (f) reconstruction error from fringe patterns with noise by the proposed method.

Fig. 6
Fig. 6

Coefficients determined with existing method, c 1 c 5 and d 0 d 5 , as well as coefficients determined with the proposed method, C 1 C 13 and D 0 D 13 .

Fig. 7
Fig. 7

Simulation results under the camera lens distortion condition: (a) reconstructed result by the existing method, (b) reconstructed result by the proposed method, (c) reconstruction error from fringe patterns with noise by the existing method, and (d) reconstruction error from fringe patterns with noise by the proposed method.

Fig. 8
Fig. 8

Simulation results under both the camera lens and projector lens distortion condition: (a) reconstructed result by the existing method, (b) reconstructed result by the proposed method, (c) reconstruction error from fringe patterns with noise by the existing method, and (d) reconstruction error from fringe patterns with noise by the proposed method.

Fig. 9
Fig. 9

Calibration experiment: (a) representative fringe patterns in three separate measurements and (b) their unwrapped phase data used for least-squares calibration.

Fig. 10
Fig. 10

Reconstruction of the calibration reference plane: (a) with the existing method, (b) with the proposed method, and (c) histogram of the measured height results.

Fig. 11
Fig. 11

Testing measurement: (a) representative fringe pattern and (b) unwrapped phase map.

Fig. 12
Fig. 12

Measurement result: (a) point clouds with the existing method (b)–(c) measured height distribution on the target block with the existing method; (d) point clouds with the proposed method (e)–(f) measured height distribution on the target block with the proposed method.

Fig. 13
Fig. 13

Error distribution: (a) with the existing method and (b) with the proposed method.

Equations (18)

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

z = 1 + c 1 ϕ + ( c 2 + c 3 ϕ ) x n + ( c 4 + c 5 ϕ ) y n d 0 + d 1 ϕ + ( d 2 + d 3 ϕ ) x n + ( d 4 + d 5 ϕ ) y n ,
x d = [ 1 + k c 1 r n 2 + k c 2 r n 4 + k c 5 r n 6 ] x n + d x ,
y d = [ 1 + k c 1 r n 2 + k c 2 r n 4 + k c 5 r n 6 ] y n + d y ,
d x = 2 k c 3 x n y n + k c 4 ( r n 2 + 2 x n 2 ) ,
d y = k c 3 ( r n 2 + 2 y n 2 ) + 2 k c 4 x n y n ,
x d = [ 1 + k c 1 r n 2 + k c 2 r n 4 ] x n ,
y d = [ 1 + k c 1 r n 2 + k c 2 r n 4 ] y n ,
x n = x d 1 + k c 1 r n 2 + k c 2 r n 4 ( 1 k c 1 r n 2 k c 2 r n 4 ) x d ,
y n = y d 1 + k c 1 r n 2 + k c 2 r n 4 ( 1 k c 1 r n 2 k c 2 r n 4 ) y d .
z = { [ 1 + c 1 ϕ + ( c 2 + c 3 ϕ ) x d + ( c 4 + c 5 ϕ ) y d + ( c 6 + c 7 ϕ ) r d 2 x d + ( c 8 + c 9 ϕ ) r d 2 y d + ( c 10 + c 11 ϕ ) r d 4 x d + ( c 12 + c 13 ϕ ) r d 4 y d ] } / { [ d 0 + d 1 ϕ + ( d 2 + d 3 ϕ ) x d + ( d 4 + d 5 ϕ ) y d + ( d 6 + d 7 ϕ ) r d 2 x d + ( d 8 + d 9 ϕ ) r d 2 y d + ( d 10 + d 11 ϕ ) r d 4 x d + ( d 12 + d 13 ϕ ) r d 4 y d ] } ,
x p = f c 1 x d + α c y d + c c 1 ,
y p = f c 2 y d + c c 2 ,
X = f c 1 x d = x p c c 1 ,
Y = f c 1 y d = y p c c 2 .
z = { [ 1 + C 1 ϕ + ( C 2 + C 3 ϕ ) X + ( C 4 + C 5 ϕ ) Y + ( C 6 + C 7 ϕ ) R 2 X + ( C 8 + C 9 ϕ ) R 2 Y + ( C 10 + C 11 ϕ ) R 4 X + ( C 12 + C 13 ϕ ) R 4 Y ] } / { [ D 0 + D 1 ϕ + ( D 2 + D 3 ϕ ) X + ( D 4 + D 5 ϕ ) Y + ( D 6 + D 7 ϕ ) R 2 X + ( D 8 + D 9 ϕ ) R 2 Y + ( D 10 + D 11 ϕ ) R 4 X + ( D 12 + D 13 ϕ ) R 4 Y ] } ,
R 2 = X 2 + Y 2 .
S = n = 1 N { [ 1 + C 1 ϕ n + ( C 2 + C 3 ϕ n ) X n + ( C 4 + C 5 ϕ n ) Y n + ( C 6 + C 7 ϕ n ) R n 2 X n + ( C 8 + C 9 ϕ n ) R n 2 Y n + ( C 10 + C 11 ϕ n ) R n 4 X n + ( C 12 + C 13 ϕ n ) R n 4 Y n ] [ D 0 + D 1 ϕ n + ( D 2 + D 3 ϕ n ) X n + ( D 4 + D 5 ϕ n ) Y n + ( D 6 + D 7 ϕ n ) R n 2 X n + ( D 8 + D 9 ϕ n ) R n 2 Y n + ( D 10 + D 11 ϕ n ) R n 4 X n + ( D 12 + D 13 ϕ n ) R n 4 Y n ] z n g } 2 ,
{ S C i = 0 , i = 1 , 2 , , 13 S D j = 0 , j = 0 , 1 , , 13 .

Metrics