Abstract

Existing digital fringe projection (DFP) systems mainly use either horizontal or vertical fringe patterns for three-dimensional shape measurement. This paper reveals that these two fringe directions are usually not optimal where the phase change is the largest to a given depth variation. We propose a novel and efficient method to determine the optimal fringe angle by projecting a set of horizontal and vertical fringe patterns onto a step-height object and by further analyzing two resultant phase maps. Experiments demonstrate the existence of the optimal angle and the success of the proposed optimal angle determination method.

© 2013 Optical Society of America

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References

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  1. C. Quan, C. J. Tay, X. Y. He, X. Kang, and H. M. Shang, “Microscopic surface contouring by fringe projection method,” Opt. Laser Technol. 34, 547–552 (2002).
    [CrossRef]
  2. A. Hanafi, T. Gharbi, and J. Cornu, “In vivo measurement of lower back deformations with Fourier-transform profilometry,” Appl. Opt. 44, 2266–2273 (2005).
    [CrossRef]
  3. S. Zhang, ed., Handbook of 3D Machine Vision: Optical Metrology and Imaging, 1st ed. (CRC Press, 2013).
  4. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Laser Eng. 48, 133–140 (2010).
    [CrossRef]
  5. G. Geng, “Structured-light 3D surface imaging: a tutorial,” Adv. Opt. Photon. 3, 128–160 (2011).
    [CrossRef]
  6. X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Laser Eng. 35, 263–284 (2001).
    [CrossRef]
  7. P. Huang and S. Zhang, “Fast three-step phase-shifting algorithm,” Appl. Opt. 45, 5086–5091 (2006).
    [CrossRef]
  8. Q. Zhang and X. Su, “High-speed optical measurement for the drumhead vibration,” Opt. Express 13, 3110–3116 (2005).
    [CrossRef]
  9. D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007).
  10. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).
  11. Y. Wang and S. Zhang, “Superfast multifrequency phase-shifting technique with optimal pulse width modulation,” Opt. Express 19, 5143–5148 (2011).
    [CrossRef]
  12. Y. Xu, L. Ekstrand, J. Dai, and S. Zhang, “Phase error compensation for three-dimensional shape measurement with projector defocusing,” Appl. Opt. 50, 2572–2581 (2011).
    [CrossRef]
  13. W. Chen, X. Su, Y. Cao, L. Xiang, and Q. Zhang, “Fourier transform profilometry based on a fringe pattern with two frequency components,” Optik 119, 57–62 (2008).
    [CrossRef]

2011

2010

S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Laser Eng. 48, 133–140 (2010).
[CrossRef]

2008

W. Chen, X. Su, Y. Cao, L. Xiang, and Q. Zhang, “Fourier transform profilometry based on a fringe pattern with two frequency components,” Optik 119, 57–62 (2008).
[CrossRef]

2006

2005

2002

C. Quan, C. J. Tay, X. Y. He, X. Kang, and H. M. Shang, “Microscopic surface contouring by fringe projection method,” Opt. Laser Technol. 34, 547–552 (2002).
[CrossRef]

2001

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

Cao, Y.

W. Chen, X. Su, Y. Cao, L. Xiang, and Q. Zhang, “Fourier transform profilometry based on a fringe pattern with two frequency components,” Optik 119, 57–62 (2008).
[CrossRef]

Chen, W.

W. Chen, X. Su, Y. Cao, L. Xiang, and Q. Zhang, “Fourier transform profilometry based on a fringe pattern with two frequency components,” Optik 119, 57–62 (2008).
[CrossRef]

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

Cornu, J.

Dai, J.

Ekstrand, L.

Geng, G.

Gharbi, T.

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Gorthi, S.

S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Laser Eng. 48, 133–140 (2010).
[CrossRef]

Hanafi, A.

He, X. Y.

C. Quan, C. J. Tay, X. Y. He, X. Kang, and H. M. Shang, “Microscopic surface contouring by fringe projection method,” Opt. Laser Technol. 34, 547–552 (2002).
[CrossRef]

Huang, P.

Kang, X.

C. Quan, C. J. Tay, X. Y. He, X. Kang, and H. M. Shang, “Microscopic surface contouring by fringe projection method,” Opt. Laser Technol. 34, 547–552 (2002).
[CrossRef]

Malacara, D.

D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007).

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Quan, C.

C. Quan, C. J. Tay, X. Y. He, X. Kang, and H. M. Shang, “Microscopic surface contouring by fringe projection method,” Opt. Laser Technol. 34, 547–552 (2002).
[CrossRef]

Rastogi, P.

S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Laser Eng. 48, 133–140 (2010).
[CrossRef]

Shang, H. M.

C. Quan, C. J. Tay, X. Y. He, X. Kang, and H. M. Shang, “Microscopic surface contouring by fringe projection method,” Opt. Laser Technol. 34, 547–552 (2002).
[CrossRef]

Su, X.

W. Chen, X. Su, Y. Cao, L. Xiang, and Q. Zhang, “Fourier transform profilometry based on a fringe pattern with two frequency components,” Optik 119, 57–62 (2008).
[CrossRef]

Q. Zhang and X. Su, “High-speed optical measurement for the drumhead vibration,” Opt. Express 13, 3110–3116 (2005).
[CrossRef]

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

Tay, C. J.

C. Quan, C. J. Tay, X. Y. He, X. Kang, and H. M. Shang, “Microscopic surface contouring by fringe projection method,” Opt. Laser Technol. 34, 547–552 (2002).
[CrossRef]

Wang, Y.

Xiang, L.

W. Chen, X. Su, Y. Cao, L. Xiang, and Q. Zhang, “Fourier transform profilometry based on a fringe pattern with two frequency components,” Optik 119, 57–62 (2008).
[CrossRef]

Xu, Y.

Zhang, Q.

W. Chen, X. Su, Y. Cao, L. Xiang, and Q. Zhang, “Fourier transform profilometry based on a fringe pattern with two frequency components,” Optik 119, 57–62 (2008).
[CrossRef]

Q. Zhang and X. Su, “High-speed optical measurement for the drumhead vibration,” Opt. Express 13, 3110–3116 (2005).
[CrossRef]

Zhang, S.

Adv. Opt. Photon.

Appl. Opt.

Opt. Express

Opt. Laser Eng.

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

S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Laser Eng. 48, 133–140 (2010).
[CrossRef]

Opt. Laser Technol.

C. Quan, C. J. Tay, X. Y. He, X. Kang, and H. M. Shang, “Microscopic surface contouring by fringe projection method,” Opt. Laser Technol. 34, 547–552 (2002).
[CrossRef]

Optik

W. Chen, X. Su, Y. Cao, L. Xiang, and Q. Zhang, “Fourier transform profilometry based on a fringe pattern with two frequency components,” Optik 119, 57–62 (2008).
[CrossRef]

Other

S. Zhang, ed., Handbook of 3D Machine Vision: Optical Metrology and Imaging, 1st ed. (CRC Press, 2013).

D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007).

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

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Figures (4)

Fig. 1.
Fig. 1.

Calculation of the optimal fringe angle.

Fig. 2.
Fig. 2.

Phase measurements using horizontal and vertical fringe patterns. (a) One of the captured horizontal fringe patterns. (b) Phase difference map ΦHd and (c) 250th row cross section of (b). (d) One of the captured horizontal fringe patterns. (e) Phase difference map ΦVd and (f) 250th row cross section of (e).

Fig. 3.
Fig. 3.

Results for the fringe patterns with the worst and the optimal fringe angles. (a) One of the captured fringe images with θ=0.84rad, the worst fringe angle. (b) Phase difference map of (a) and (c) 250th row cross section of (b). (d) One of the captured fringe images with θo=0.73rad, the optimal fringe angle. (e) Phase difference map of (d) and (f) 250th row cross section of (e).

Fig. 4.
Fig. 4.

Sculpture results under different fringe angles. (a) One of the captured fringe patterns with the worst fringe angle θ=0.84rad. (b) Phase difference map (θ=0.84rad). (c) Recovered 3D shape (θ=0.84rad). (d) One of the captured fringe patterns with the optimal fringe angle θo=0.73rad. (e) Phase difference map (θo=0.73rad). (f) Recovered 3D shape (θo=0.73rad).

Equations (9)

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

I1(x,y)=I(x,y)+I(x,y)cos(ϕ2π/3),
I2(x,y)=I(x,y)+I(x,y)cos(ϕ),
I3(x,y)=I(x,y)+I(x,y)cos(ϕ+2π/3),
ϕ(x,y)=tan1[3(I1I3)/(2I2I1I3)].
ΔΦHd=ΦHoΦHr,
ΔΦVd=ΦVoΦVr.
ΔΦH=ΔΦHdtΔΦHdb,
ΔΦV=ΔΦVdtΔΦVdb.
θo=tan1[ΔΦV/ΔΦH].

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