Abstract

This paper proposes a mathematical measurement model of a highly reflected, specular surface with structured light method. In the measurement, an auxiliary fringe pattern named amplitude perturbation is adopted to be projected onto the measured surface. The amplitude perturbation can ease the procedure of searching the corresponding points between the phase map of the measured surface and that of the reference plane by locking up the most reliable point as the starting unwrapping point whose true phase can be calculated accurately. The proposed method is also suitable for measuring the step surfaces such as gauge blocks with different heights. Furthermore, the image segmentation technology is introduced in the phase unwrapping procedure to increase the speed. Based on the unwrapped phase map, zonal wave-front reconstruction algorithm is implemented to realize three-dimensional, highly reflected, specular surface reconstruction. Experimental studies show that the developed methodology displays accuracy and high stability for highly reflected, specular surface measurement.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263–284 (2001).
    [CrossRef]
  2. W. Chen, P. Bu, S. Zheng, and X. Su, “Study on Fourier transforms profilometry based on bi-color projecting,” Opt. Laser Technol. 39, 821–827 (2007).
    [CrossRef]
  3. R. Zheng, Y. Wang, X. Zhang, and Y. Song, “Two-dimensional phase-measuring profilometry,” Appl. Opt. 44, 954–958 (2005).
    [CrossRef]
  4. M. Halioua and H.-C. Liu, “Optical three-dimensional sensing by phase measuring profilometry,” Opt Lasers Eng. 11, 185–215 (1989).
    [CrossRef]
  5. M. Chang and C.-S. Ho, “Phase-measuring profilometry using sinusoidal grating,” Exp. Mech. 33, 117–122 (1993).
    [CrossRef]
  6. G. Häusler, C. Richter, K.-H. Leitz, and M. C. Knauer, “Microdeflectometry—a novel tool to acquire three-dimensional microtopography with nanometer height resolution,” Opt. Lett. 33, 396–398 (2008).
    [CrossRef]
  7. Y.-L. Xiao, X. Su, W. Chen, and Y. Liu, “Three-dimensional shape measurement of aspheric mirrors with fringe reflection photogrammetry,” Appl. Opt. 51, 457–464 (2012).
    [CrossRef]
  8. W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. 70, 998–1006 (1980).
    [CrossRef]
  9. F. Chen and X. Su, “Phase-unwrapping algorithm for the measurement of 3D object,” Optik 123, 2272–2275 (2012).
    [CrossRef]
  10. F. W. Y. Chan, “A novel optical method without phase unwrapping for subsurface flaw detection,” Opt Lasers Eng. 47, 186–193 (2009).
    [CrossRef]
  11. S. Li, S. Liu, and H. Zhang, “3D shape measurement of optical free-form surface based on fringe projection,” Proc. SPIE 8082, 80822Z (2011).
    [CrossRef]
  12. X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt Lasers Eng. 42, 245–261 (2004).
    [CrossRef]
  13. H. Jing, X. Su, and Y. Liu, “Specular surface measurement based on fringe reflection and analysis of 3D shape reconstruction technique,” Optoelectron. Eng. 35, 37–42 (2008).
  14. Y. He and Y. Cao, “A composite-structured-light 3D measurement method based on fringe parameter calibration,” Opt. Lasers Eng. 49, 773–779 (2011).
    [CrossRef]
  15. Y. He and Y. Cao, “Shifted-phase calibration for a 3-D profilometry system based on orthogonal composite grating projection,” Optik 122, 1730–1734 (2011).
  16. W. Zou and J. P Rolland, “Iterative zonal wave-front estimation algorithm for optical testing with general-shaped pupils,” J. Opt. Soc. Am. A 22, 938–951 (2005).
    [CrossRef]

2012 (2)

2011 (3)

S. Li, S. Liu, and H. Zhang, “3D shape measurement of optical free-form surface based on fringe projection,” Proc. SPIE 8082, 80822Z (2011).
[CrossRef]

Y. He and Y. Cao, “A composite-structured-light 3D measurement method based on fringe parameter calibration,” Opt. Lasers Eng. 49, 773–779 (2011).
[CrossRef]

Y. He and Y. Cao, “Shifted-phase calibration for a 3-D profilometry system based on orthogonal composite grating projection,” Optik 122, 1730–1734 (2011).

2009 (1)

F. W. Y. Chan, “A novel optical method without phase unwrapping for subsurface flaw detection,” Opt Lasers Eng. 47, 186–193 (2009).
[CrossRef]

2008 (2)

G. Häusler, C. Richter, K.-H. Leitz, and M. C. Knauer, “Microdeflectometry—a novel tool to acquire three-dimensional microtopography with nanometer height resolution,” Opt. Lett. 33, 396–398 (2008).
[CrossRef]

H. Jing, X. Su, and Y. Liu, “Specular surface measurement based on fringe reflection and analysis of 3D shape reconstruction technique,” Optoelectron. Eng. 35, 37–42 (2008).

2007 (1)

W. Chen, P. Bu, S. Zheng, and X. Su, “Study on Fourier transforms profilometry based on bi-color projecting,” Opt. Laser Technol. 39, 821–827 (2007).
[CrossRef]

2005 (2)

2004 (1)

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

2001 (1)

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

1993 (1)

M. Chang and C.-S. Ho, “Phase-measuring profilometry using sinusoidal grating,” Exp. Mech. 33, 117–122 (1993).
[CrossRef]

1989 (1)

M. Halioua and H.-C. Liu, “Optical three-dimensional sensing by phase measuring profilometry,” Opt Lasers Eng. 11, 185–215 (1989).
[CrossRef]

1980 (1)

Bu, P.

W. Chen, P. Bu, S. Zheng, and X. Su, “Study on Fourier transforms profilometry based on bi-color projecting,” Opt. Laser Technol. 39, 821–827 (2007).
[CrossRef]

Cao, Y.

Y. He and Y. Cao, “A composite-structured-light 3D measurement method based on fringe parameter calibration,” Opt. Lasers Eng. 49, 773–779 (2011).
[CrossRef]

Y. He and Y. Cao, “Shifted-phase calibration for a 3-D profilometry system based on orthogonal composite grating projection,” Optik 122, 1730–1734 (2011).

Chan, F. W. Y.

F. W. Y. Chan, “A novel optical method without phase unwrapping for subsurface flaw detection,” Opt Lasers Eng. 47, 186–193 (2009).
[CrossRef]

Chang, M.

M. Chang and C.-S. Ho, “Phase-measuring profilometry using sinusoidal grating,” Exp. Mech. 33, 117–122 (1993).
[CrossRef]

Chen, F.

F. Chen and X. Su, “Phase-unwrapping algorithm for the measurement of 3D object,” Optik 123, 2272–2275 (2012).
[CrossRef]

Chen, W.

Y.-L. Xiao, X. Su, W. Chen, and Y. Liu, “Three-dimensional shape measurement of aspheric mirrors with fringe reflection photogrammetry,” Appl. Opt. 51, 457–464 (2012).
[CrossRef]

W. Chen, P. Bu, S. Zheng, and X. Su, “Study on Fourier transforms profilometry based on bi-color projecting,” Opt. Laser Technol. 39, 821–827 (2007).
[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]

Halioua, M.

M. Halioua and H.-C. Liu, “Optical three-dimensional sensing by phase measuring profilometry,” Opt Lasers Eng. 11, 185–215 (1989).
[CrossRef]

Häusler, G.

He, Y.

Y. He and Y. Cao, “Shifted-phase calibration for a 3-D profilometry system based on orthogonal composite grating projection,” Optik 122, 1730–1734 (2011).

Y. He and Y. Cao, “A composite-structured-light 3D measurement method based on fringe parameter calibration,” Opt. Lasers Eng. 49, 773–779 (2011).
[CrossRef]

Ho, C.-S.

M. Chang and C.-S. Ho, “Phase-measuring profilometry using sinusoidal grating,” Exp. Mech. 33, 117–122 (1993).
[CrossRef]

Jing, H.

H. Jing, X. Su, and Y. Liu, “Specular surface measurement based on fringe reflection and analysis of 3D shape reconstruction technique,” Optoelectron. Eng. 35, 37–42 (2008).

Knauer, M. C.

Leitz, K.-H.

Li, S.

S. Li, S. Liu, and H. Zhang, “3D shape measurement of optical free-form surface based on fringe projection,” Proc. SPIE 8082, 80822Z (2011).
[CrossRef]

Liu, H.-C.

M. Halioua and H.-C. Liu, “Optical three-dimensional sensing by phase measuring profilometry,” Opt Lasers Eng. 11, 185–215 (1989).
[CrossRef]

Liu, S.

S. Li, S. Liu, and H. Zhang, “3D shape measurement of optical free-form surface based on fringe projection,” Proc. SPIE 8082, 80822Z (2011).
[CrossRef]

Liu, Y.

Y.-L. Xiao, X. Su, W. Chen, and Y. Liu, “Three-dimensional shape measurement of aspheric mirrors with fringe reflection photogrammetry,” Appl. Opt. 51, 457–464 (2012).
[CrossRef]

H. Jing, X. Su, and Y. Liu, “Specular surface measurement based on fringe reflection and analysis of 3D shape reconstruction technique,” Optoelectron. Eng. 35, 37–42 (2008).

Richter, C.

Rolland, J. P

Song, Y.

Southwell, W. H.

Su, X.

F. Chen and X. Su, “Phase-unwrapping algorithm for the measurement of 3D object,” Optik 123, 2272–2275 (2012).
[CrossRef]

Y.-L. Xiao, X. Su, W. Chen, and Y. Liu, “Three-dimensional shape measurement of aspheric mirrors with fringe reflection photogrammetry,” Appl. Opt. 51, 457–464 (2012).
[CrossRef]

H. Jing, X. Su, and Y. Liu, “Specular surface measurement based on fringe reflection and analysis of 3D shape reconstruction technique,” Optoelectron. Eng. 35, 37–42 (2008).

W. Chen, P. Bu, S. Zheng, and X. Su, “Study on Fourier transforms profilometry based on bi-color projecting,” Opt. Laser Technol. 39, 821–827 (2007).
[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]

Wang, Y.

Xiao, Y.-L.

Zhang, H.

S. Li, S. Liu, and H. Zhang, “3D shape measurement of optical free-form surface based on fringe projection,” Proc. SPIE 8082, 80822Z (2011).
[CrossRef]

Zhang, X.

Zheng, R.

Zheng, S.

W. Chen, P. Bu, S. Zheng, and X. Su, “Study on Fourier transforms profilometry based on bi-color projecting,” Opt. Laser Technol. 39, 821–827 (2007).
[CrossRef]

Zou, W.

Appl. Opt. (2)

Exp. Mech. (1)

M. Chang and C.-S. Ho, “Phase-measuring profilometry using sinusoidal grating,” Exp. Mech. 33, 117–122 (1993).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt Lasers Eng. (3)

F. W. Y. Chan, “A novel optical method without phase unwrapping for subsurface flaw detection,” Opt Lasers Eng. 47, 186–193 (2009).
[CrossRef]

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

M. Halioua and H.-C. Liu, “Optical three-dimensional sensing by phase measuring profilometry,” Opt Lasers Eng. 11, 185–215 (1989).
[CrossRef]

Opt. Laser Technol. (1)

W. Chen, P. Bu, S. Zheng, and X. Su, “Study on Fourier transforms profilometry based on bi-color projecting,” Opt. Laser Technol. 39, 821–827 (2007).
[CrossRef]

Opt. Lasers Eng. (2)

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

Y. He and Y. Cao, “A composite-structured-light 3D measurement method based on fringe parameter calibration,” Opt. Lasers Eng. 49, 773–779 (2011).
[CrossRef]

Opt. Lett. (1)

Optik (2)

Y. He and Y. Cao, “Shifted-phase calibration for a 3-D profilometry system based on orthogonal composite grating projection,” Optik 122, 1730–1734 (2011).

F. Chen and X. Su, “Phase-unwrapping algorithm for the measurement of 3D object,” Optik 123, 2272–2275 (2012).
[CrossRef]

Optoelectron. Eng. (1)

H. Jing, X. Su, and Y. Liu, “Specular surface measurement based on fringe reflection and analysis of 3D shape reconstruction technique,” Optoelectron. Eng. 35, 37–42 (2008).

Proc. SPIE (1)

S. Li, S. Liu, and H. Zhang, “3D shape measurement of optical free-form surface based on fringe projection,” Proc. SPIE 8082, 80822Z (2011).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (16)

Fig. 1.
Fig. 1.

Schematic diagram of PMD.

Fig. 2.
Fig. 2.

Principle of amplitude perturbation. (a) Fringe pattern with perturbed stripe in horizontal direction. (b) Vertical cross section of the perturbed sinusoidal fringe.

Fig. 3.
Fig. 3.

Flow chart of phase unwrapping.

Fig. 4.
Fig. 4.

2D plot for perturbation function.

Fig. 5.
Fig. 5.

One-dimensional plot for perturbation function. (a) Before filtering and (b) after filtering.

Fig. 6.
Fig. 6.

Histogram of phase difference between nominal value and calculated one in simulation experiment with noise.

Fig. 7.
Fig. 7.

Measurement setup. (a) Schematic diagram and (b) photo.

Fig. 8.
Fig. 8.

Ultraprecision machined mirror used as the reference plane.

Fig. 9.
Fig. 9.

CCD captured images of projected fringe pattern on reference mirror. (a) Horizontal fringe pattern and (b) vertical fringe pattern.

Fig. 10.
Fig. 10.

Unwrapped phase map of mere reference mirror in selected region. (a) Horizontal direction and (b) vertical direction.

Fig. 11.
Fig. 11.

Two gauge blocks on the reference plane.

Fig. 12.
Fig. 12.

CCD captured images of projected fringe pattern on measured blocks. (a) Horizontal fringe pattern and (b) vertical fringe pattern.

Fig. 13.
Fig. 13.

Validation template used for measurement of gauge blocks.

Fig. 14.
Fig. 14.

Unwrapped phase. (a) Horizontal fringe patterns and (b) vertical fringe patterns.

Fig. 15.
Fig. 15.

Reconstructed gauge blocks.

Fig. 16.
Fig. 16.

Map of surface height deviation. (a) Gauge block with height of 7 mm and (b) gauge block with height of 4 mm.

Tables (2)

Tables Icon

Table 1. Comparison between Calculated True Phase and Nominal Phase

Tables Icon

Table 2. Error of Surface Height Measurement

Equations (11)

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

In(x,y)=A+Bcos(2π·yT+2π(n1)N)n=1,2,N,
Isn(x,y)=Aγ+Bγcos(2π·yT+Δϕ(x,y)+2π(n1)N)=Aγ+Bγcos(ϕ(x,y)+2π(n1)N)n=1,2,N,
φ(x,y)=arctan[n=1NIsn(x,y)sin(2πn/N)n=1NIsn(x,y)cos(2πn/N)],
ϕ(x,y)=φ(x,y)+2πk(x,y),
{2htanθΔlhtanθ+htan(θ+2α)Δl=dhdΔl=TΔϕ2π.
I5(x,y)=A+η(x,y)·Bcos[2π·yTy+2π(N1)N],
η(x,y)={λ,2πyTy[2Qπ,(2Q+1)π]1,2πyTy[2Qπ,(2Q+1)π],
η(x,y)=I1(x,y)I3(x,y)+2I5(x,y)I1(x,y)2I2(x,y)+I3(x,y).
ϕ(x,y)=φ(x,y)+2Qπ=arctanI4(x,y)I2(x,y)I1(x,y)I3(x,y)+2Qπ.
M(x,y)=Bγ(x,y)=2[n=1NIsn(x,y)sin(2πn/N)]2+[n=1NIsn(x,y)cos(2πn/N)]/N.
ϕ(Sn)=φ(Sn)2π·Round(φ(Sn)ϕ(Sn1)2π).

Metrics