Abstract

An advanced Phase Measuring Deflectometry(PMD) is proposed to measure the three dimensional (3D) shape of the aspheric mirror. In the measurement process, a liquid crystal display(LCD)screen displaying sinusoidal fringe patterns and a camera observing the fringe patterns reflected via the tested mirror, are moved along the tested mirror optical axis, respectively. At each movement position, the camera records the fringe patterns of the screen located at two different positions. Using these fringe patterns, every camera pixels can find a corresponding point on the tested mirror and gets its coordinate and slope. By integrating, the 3D shape of the tested mirror can be reconstructed. Compared with the traditional PMD, this method doesn’t need complex calibration and can measure the absolute height of the aspheric mirror which has large range of surface geometries unambiguously. Furthermore, this method also has strong anti-noise ability. Computer simulations and preliminary experiment validate the feasibility of this method.

© 2008 Optical Society of America

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References

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  1. T. Bothe, W. S. Li, C. von Kopylow, and W. Juptner, "High-resolution 3D shape measurement on specular surfaces by fringe reflection," Proc. SPIE 5457, 411-422 (2004).
    [CrossRef]
  2. Y. K. Liu, X. Y. Su, and Q. Y. Wu, "Three-Dimensional Shape Measurement for Specular Surface Based on Fringe Reflection," Acta Optical Sinica,  26, 1636-1640 (2006).
  3. W. S. Li, T. Bothe, C. von Kopylow, and W. Juptner, "Evaluation methods for gradient measurements techniques," Proc. SPIE 5457, 300-311 (2004).
    [CrossRef]
  4. M. C. Knauer, J. Kaminski, and G. Hausler, " Phase measuring Deflectometry: a new approach to measure specular free-form surfaces," Proc. SPIE 5457, 366-376 (2004).
    [CrossRef]
  5. M. Petz and R. Tutsch, "Reflection grating photogrammetry: a technique for absolute shape measurement of specular free-form surfaces," Proc. SPIE 5869, (2005),
    [CrossRef]
  6. W. S. Li and X. Y. Su. "Application of improved phase-measuring profilometry in nonconstant environmental light," Opt. Eng,  40, 478-485 (2001).
    [CrossRef]

2006

Y. K. Liu, X. Y. Su, and Q. Y. Wu, "Three-Dimensional Shape Measurement for Specular Surface Based on Fringe Reflection," Acta Optical Sinica,  26, 1636-1640 (2006).

2004

W. S. Li, T. Bothe, C. von Kopylow, and W. Juptner, "Evaluation methods for gradient measurements techniques," Proc. SPIE 5457, 300-311 (2004).
[CrossRef]

M. C. Knauer, J. Kaminski, and G. Hausler, " Phase measuring Deflectometry: a new approach to measure specular free-form surfaces," Proc. SPIE 5457, 366-376 (2004).
[CrossRef]

T. Bothe, W. S. Li, C. von Kopylow, and W. Juptner, "High-resolution 3D shape measurement on specular surfaces by fringe reflection," Proc. SPIE 5457, 411-422 (2004).
[CrossRef]

2001

W. S. Li and X. Y. Su. "Application of improved phase-measuring profilometry in nonconstant environmental light," Opt. Eng,  40, 478-485 (2001).
[CrossRef]

Bothe, T.

T. Bothe, W. S. Li, C. von Kopylow, and W. Juptner, "High-resolution 3D shape measurement on specular surfaces by fringe reflection," Proc. SPIE 5457, 411-422 (2004).
[CrossRef]

W. S. Li, T. Bothe, C. von Kopylow, and W. Juptner, "Evaluation methods for gradient measurements techniques," Proc. SPIE 5457, 300-311 (2004).
[CrossRef]

Hausler, G.

M. C. Knauer, J. Kaminski, and G. Hausler, " Phase measuring Deflectometry: a new approach to measure specular free-form surfaces," Proc. SPIE 5457, 366-376 (2004).
[CrossRef]

Juptner, W.

W. S. Li, T. Bothe, C. von Kopylow, and W. Juptner, "Evaluation methods for gradient measurements techniques," Proc. SPIE 5457, 300-311 (2004).
[CrossRef]

T. Bothe, W. S. Li, C. von Kopylow, and W. Juptner, "High-resolution 3D shape measurement on specular surfaces by fringe reflection," Proc. SPIE 5457, 411-422 (2004).
[CrossRef]

Kaminski, J.

M. C. Knauer, J. Kaminski, and G. Hausler, " Phase measuring Deflectometry: a new approach to measure specular free-form surfaces," Proc. SPIE 5457, 366-376 (2004).
[CrossRef]

Knauer, M. C.

M. C. Knauer, J. Kaminski, and G. Hausler, " Phase measuring Deflectometry: a new approach to measure specular free-form surfaces," Proc. SPIE 5457, 366-376 (2004).
[CrossRef]

Li, W. S.

W. S. Li, T. Bothe, C. von Kopylow, and W. Juptner, "Evaluation methods for gradient measurements techniques," Proc. SPIE 5457, 300-311 (2004).
[CrossRef]

T. Bothe, W. S. Li, C. von Kopylow, and W. Juptner, "High-resolution 3D shape measurement on specular surfaces by fringe reflection," Proc. SPIE 5457, 411-422 (2004).
[CrossRef]

W. S. Li and X. Y. Su. "Application of improved phase-measuring profilometry in nonconstant environmental light," Opt. Eng,  40, 478-485 (2001).
[CrossRef]

Liu, Y. K.

Y. K. Liu, X. Y. Su, and Q. Y. Wu, "Three-Dimensional Shape Measurement for Specular Surface Based on Fringe Reflection," Acta Optical Sinica,  26, 1636-1640 (2006).

Su, X. Y.

Y. K. Liu, X. Y. Su, and Q. Y. Wu, "Three-Dimensional Shape Measurement for Specular Surface Based on Fringe Reflection," Acta Optical Sinica,  26, 1636-1640 (2006).

W. S. Li and X. Y. Su. "Application of improved phase-measuring profilometry in nonconstant environmental light," Opt. Eng,  40, 478-485 (2001).
[CrossRef]

von Kopylow, C.

T. Bothe, W. S. Li, C. von Kopylow, and W. Juptner, "High-resolution 3D shape measurement on specular surfaces by fringe reflection," Proc. SPIE 5457, 411-422 (2004).
[CrossRef]

W. S. Li, T. Bothe, C. von Kopylow, and W. Juptner, "Evaluation methods for gradient measurements techniques," Proc. SPIE 5457, 300-311 (2004).
[CrossRef]

Wu, Q. Y.

Y. K. Liu, X. Y. Su, and Q. Y. Wu, "Three-Dimensional Shape Measurement for Specular Surface Based on Fringe Reflection," Acta Optical Sinica,  26, 1636-1640 (2006).

Acta Optical Sinica

Y. K. Liu, X. Y. Su, and Q. Y. Wu, "Three-Dimensional Shape Measurement for Specular Surface Based on Fringe Reflection," Acta Optical Sinica,  26, 1636-1640 (2006).

Opt. Eng

W. S. Li and X. Y. Su. "Application of improved phase-measuring profilometry in nonconstant environmental light," Opt. Eng,  40, 478-485 (2001).
[CrossRef]

Proc. SPIE

T. Bothe, W. S. Li, C. von Kopylow, and W. Juptner, "High-resolution 3D shape measurement on specular surfaces by fringe reflection," Proc. SPIE 5457, 411-422 (2004).
[CrossRef]

W. S. Li, T. Bothe, C. von Kopylow, and W. Juptner, "Evaluation methods for gradient measurements techniques," Proc. SPIE 5457, 300-311 (2004).
[CrossRef]

M. C. Knauer, J. Kaminski, and G. Hausler, " Phase measuring Deflectometry: a new approach to measure specular free-form surfaces," Proc. SPIE 5457, 366-376 (2004).
[CrossRef]

Other

M. Petz and R. Tutsch, "Reflection grating photogrammetry: a technique for absolute shape measurement of specular free-form surfaces," Proc. SPIE 5869, (2005),
[CrossRef]

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Figures (12)

Fig. 1.
Fig. 1.

the structure of measurement setup.

Fig. 2.
Fig. 2.

the schematic of measurement principle.

Fig. 3.
Fig. 3.

simulated paraboloid surface

Fig. 4.
Fig. 4.

error percentage of the recovered surface within %noise

Fig. 5.
Fig. 5.

error percentage of the recovered surface within 5%noise

Fig. 6.
Fig. 6.

simulated spherical surface

Fig. 7.
Fig. 7.

error percentage of the recovered spherical surface with 1%noise

Fig. 8.
Fig. 8.

recorded fringe patterns

Fig. 9.
Fig. 9.

reconstruction object using our method

Fig. 10.
Fig. 10.

reconstruction object using coordinate machine

Fig. 11.
Fig. 11.

differences of the two results on the x axis

Fig. 12.
Fig. 12.

differences of the two results on the y axis

Equations (10)

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

Δ h = [ 0 p 0 0 p n ] 0 p 0 ;
Δ φ = [ ϕ 0 0 ϕ n 0 ] [ ϕ 0 1 ϕ n 1 ] ;
Δ φ = f ( Δ h )
o p k = Δ h K + o p 0
φ 0 = g ( p )
x k = ϕ k 0 2 π T
R k = p k o y '
R k p k o
y k x k = 1 2 R k x k
y n + 1 = y n + ( y n + 1 x n + 1 + y n x n ) × ( x n + 1 x n ) 2

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