Abstract

A mathematical description of the absolute surface height distribution in generalized fringe projection profilometry under large measuring depth range is presented. Based on least-squares polynomial fitting, a nonlinear calibration to determine the mapping between phase change and surface height is proposed by considering the unequal height arrangement of the projector and the camera. To solve surface height from phase change, an iteration method is brought forward. Experiments are implemented to demonstrate the validity of the proposed calibration and an accuracy of 0.3 mm for surface profile under 300 mm measuring depth can be achieved.

© 2013 Optical Society of America

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References

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2013 (1)

F. Zhu, D. Lei, and X. He, “Measurement system of dynamic microscopic deformation for membrane based on fringe projection,” Opt. Eng. 52, 033604 (2013).
[CrossRef]

2012 (1)

2011 (1)

2010 (3)

2009 (1)

X. Chen, J. Xi, Y. Jin, and J. Sun, “Accurate calibration for a camera-projector measurement system based on structured light projection,” Opt. Lasers Eng. 47, 310–319 (2009).
[CrossRef]

2007 (2)

C. Quan, C. J. Tay, and L. J. Chen, “A study on carrier-removal techniques in fringe projection profilometry,” Opt. Laser Technol. 39, 1155–1161 (2007).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng. 46, 043601 (2007).
[CrossRef]

2006 (1)

2004 (1)

S. Pavageau, R. Dallier, N. Servagent, and T. Bosch, “A new algorithm for large surfaces profiling by fringe projection,” Sens. Actuators A 115, 178–184 (2004).
[CrossRef]

2003 (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]

2001 (2)

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

1994 (1)

1982 (1)

Asundi, A.

Bai, P.

Bi, H. B.

Bosch, T.

S. Pavageau, R. Dallier, N. Servagent, and T. Bosch, “A new algorithm for large surfaces profiling by fringe projection,” Sens. Actuators A 115, 178–184 (2004).
[CrossRef]

Chen, L. J.

C. Quan, C. J. Tay, and L. J. Chen, “A study on carrier-removal techniques in fringe projection profilometry,” Opt. Laser Technol. 39, 1155–1161 (2007).
[CrossRef]

Chen, W.

Chen, X.

X. Chen, J. Xi, Y. Jin, and J. Sun, “Accurate calibration for a camera-projector measurement system based on structured light projection,” Opt. Lasers Eng. 47, 310–319 (2009).
[CrossRef]

Chua, P. S. K.

Dallier, R.

S. Pavageau, R. Dallier, N. Servagent, and T. Bosch, “A new algorithm for large surfaces profiling by fringe projection,” Sens. Actuators A 115, 178–184 (2004).
[CrossRef]

Du, H.

English, C.

P. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng. 46, 043601 (2007).
[CrossRef]

Gao, B. Z.

He, X.

F. Zhu, D. Lei, and X. He, “Measurement system of dynamic microscopic deformation for membrane based on fringe projection,” Opt. Eng. 52, 033604 (2013).
[CrossRef]

F. Zhu, H. Shi, P. Bai, and X. He, “Three-dimensional shape measurement and calibration for fringe projection by considering unequal height of the projector and the camera,” Appl. Opt. 50, 1575–1583 (2011).
[CrossRef]

He, X. Y.

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]

Hoang, T.

Huang, L.

Ina, H.

Jia, P.

P. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng. 46, 043601 (2007).
[CrossRef]

Jin, Y.

X. Chen, J. Xi, Y. Jin, and J. Sun, “Accurate calibration for a camera-projector measurement system based on structured light projection,” Opt. Lasers Eng. 47, 310–319 (2009).
[CrossRef]

Kobayashi, S.

Kofman, J.

P. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng. 46, 043601 (2007).
[CrossRef]

Lei, D.

F. Zhu, D. Lei, and X. He, “Measurement system of dynamic microscopic deformation for membrane based on fringe projection,” Opt. Eng. 52, 033604 (2013).
[CrossRef]

Li, A.

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, X.

Nguyen, D.

Oliver, J.

Pan, B.

Pavageau, S.

S. Pavageau, R. Dallier, N. Servagent, and T. Bosch, “A new algorithm for large surfaces profiling by fringe projection,” Sens. Actuators A 115, 178–184 (2004).
[CrossRef]

Peng, X.

Quan, C.

C. Quan, C. J. Tay, and L. J. Chen, “A study on carrier-removal techniques in fringe projection profilometry,” Opt. Laser Technol. 39, 1155–1161 (2007).
[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]

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]

Servagent, N.

S. Pavageau, R. Dallier, N. Servagent, and T. Bosch, “A new algorithm for large surfaces profiling by fringe projection,” Sens. Actuators A 115, 178–184 (2004).
[CrossRef]

Shang, H. M.

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.

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.

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

Sun, J.

X. Chen, J. Xi, Y. Jin, and J. Sun, “Accurate calibration for a camera-projector measurement system based on structured light projection,” Opt. Lasers Eng. 47, 310–319 (2009).
[CrossRef]

Takeda, M.

Tan, Y.

Tay, C. J.

C. Quan, C. J. Tay, and L. J. Chen, “A study on carrier-removal techniques in fringe projection profilometry,” Opt. Laser Technol. 39, 1155–1161 (2007).
[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]

Van Der Weide, D.

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, Z.

Wang, Z. Y.

Xi, J.

X. Chen, J. Xi, Y. Jin, and J. Sun, “Accurate calibration for a camera-projector measurement system based on structured light projection,” Opt. Lasers Eng. 47, 310–319 (2009).
[CrossRef]

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]

Yin, Y.

Zhang, S.

Zhao, H.

Zhu, F.

F. Zhu, D. Lei, and X. He, “Measurement system of dynamic microscopic deformation for membrane based on fringe projection,” Opt. Eng. 52, 033604 (2013).
[CrossRef]

F. Zhu, H. Shi, P. Bai, and X. He, “Three-dimensional shape measurement and calibration for fringe projection by considering unequal height of the projector and the camera,” Appl. Opt. 50, 1575–1583 (2011).
[CrossRef]

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

Opt. Commun. (2)

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]

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. (2)

P. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng. 46, 043601 (2007).
[CrossRef]

F. Zhu, D. Lei, and X. He, “Measurement system of dynamic microscopic deformation for membrane based on fringe projection,” Opt. Eng. 52, 033604 (2013).
[CrossRef]

Opt. Express (2)

Opt. Laser Technol. (1)

C. Quan, C. J. Tay, and L. J. Chen, “A study on carrier-removal techniques in fringe projection profilometry,” Opt. Laser Technol. 39, 1155–1161 (2007).
[CrossRef]

Opt. Lasers Eng. (2)

X. Chen, J. Xi, Y. Jin, and J. Sun, “Accurate calibration for a camera-projector measurement system based on structured light projection,” Opt. Lasers Eng. 47, 310–319 (2009).
[CrossRef]

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

Opt. Lett. (2)

Sens. Actuators A (1)

S. Pavageau, R. Dallier, N. Servagent, and T. Bosch, “A new algorithm for large surfaces profiling by fringe projection,” Sens. Actuators A 115, 178–184 (2004).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Schematic experimental setup of fringe projection profilometry.

Fig. 2.
Fig. 2.

3D profiles of measurement results of different standard step heights: (a) 0.5 mm, (b) 2 mm, (c) 10 mm, and (d) 50 mm.

Fig. 3.
Fig. 3.

Experimental results of a tilted plate: (a) 3D plot of plate tilt and (b) slice of (a) along y axis.

Fig. 4.
Fig. 4.

Experimental results: (a) mask, (b) reconstructed 3D profile, and (c) height distribution along line A–B with different calibrations.

Equations (9)

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

Δφ=φBφA=2π[0y+Δyf(u)du0yf(u)du].
Δφ=2πf·Δy,
Δy=h/tanα+h/tanβ,
Δy=h(ay+b)/(1h/H1),
Δyh(ay+b)(1+h/H1+h2/H12).
Δφ(cy+d)(h+ph2+qh3)=C(h)y+D(h),
h+ph2+qh3=Δφcy+d=t,
ph2+ht=0.
hi+1=2qhi3+phi2+t3qhi2+2phi+1

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