Abstract

A method based on fringe reflection is presented to measure the aspheric mirror with higher precise. This method measures the absolute height of the aspheric mirror with dummy paraboloid, while the camera is located beside the optical axis of the test surface. It can be used to measure the aspheric mirror with high deviation. And for locating the camera beside the optical axis, this method doesn’t have occlusion problem and can do the measurement more flexibility. Furthermore, compared with the traditional PMD, this method measures the tested surface with dummy paraboloid instead of the intersection of two straight lines, so it doesn’t need to calibrate the image projection vectors. And the errors of the calibration influence this method less than the traditional method. Therefore, this method can measure the high deviation aspheric mirror with higher precise even if the calibration precise isn’t very high. Computer simulations and preliminary experiment validate the feasibility of this method.

© 2009 OSA

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References

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  1. J. D. Briers, “Optical testing: a review and tutorial for optical engineers,” Opt. Lasers Eng. 32(2), 111–138 (1999).
    [CrossRef]
  2. 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]
  3. M. C. Knauer, J. Kaminski, and G. Hausler, “Phase measuring Deflectometry: a new approach to measuring specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).
    [CrossRef]
  4. M. Petz, and R. Tutsch, “ Reflection grating photogrammetry: a technique for absolute shape measurement of specular free-form surfaces,”Proc. SPIE 5869, 58691D–58691D.12 (2005)
  5. Y. Tang, X. Y. Su, Y. K. Liu, and H. L. Jing, “3D shape measurement of the aspheric mirror by advanced phase measuring deflectometry,” Opt. Express 16(19), 15090–15096 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-19-15090 .
    [CrossRef] [PubMed]
  6. W. S. Li, T. Bothe, C. von Kopylow, and W. Juptner, “Evaluation methods for gradient measurements techniques,” Proc. SPIE 5457, 300–311 (2004).
    [CrossRef]
  7. Y Tang, X., Su, Y., and Liu “A Novel Method Based on Fringe Reflection for Testing Aspheric Precisely and Flexibly,” manuscript in preparation.

2008 (1)

2004 (3)

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]

M. C. Knauer, J. Kaminski, and G. Hausler, “Phase measuring Deflectometry: a new approach to measuring specular free-form surfaces,” Proc. SPIE 5457, 366–376 (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]

1999 (1)

J. D. Briers, “Optical testing: a review and tutorial for optical engineers,” Opt. Lasers Eng. 32(2), 111–138 (1999).
[CrossRef]

Bothe, T.

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]

Briers, J. D.

J. D. Briers, “Optical testing: a review and tutorial for optical engineers,” Opt. Lasers Eng. 32(2), 111–138 (1999).
[CrossRef]

Hausler, G.

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

Jing, H. L.

Juptner, W.

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]

Kaminski, J.

M. C. Knauer, J. Kaminski, and G. Hausler, “Phase measuring Deflectometry: a new approach to measuring 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 measuring 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]

Liu,

Y Tang, X., Su, Y., and Liu “A Novel Method Based on Fringe Reflection for Testing Aspheric Precisely and Flexibly,” manuscript in preparation.

Liu, Y. K.

Su,

Y Tang, X., Su, Y., and Liu “A Novel Method Based on Fringe Reflection for Testing Aspheric Precisely and Flexibly,” manuscript in preparation.

Su, X. Y.

Tang, Y

Y Tang, X., Su, Y., and Liu “A Novel Method Based on Fringe Reflection for Testing Aspheric Precisely and Flexibly,” manuscript in preparation.

Tang, Y.

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]

X.,

Y Tang, X., Su, Y., and Liu “A Novel Method Based on Fringe Reflection for Testing Aspheric Precisely and Flexibly,” manuscript in preparation.

Y.,

Y Tang, X., Su, Y., and Liu “A Novel Method Based on Fringe Reflection for Testing Aspheric Precisely and Flexibly,” manuscript in preparation.

Opt. Express (1)

Opt. Lasers Eng. (1)

J. D. Briers, “Optical testing: a review and tutorial for optical engineers,” Opt. Lasers Eng. 32(2), 111–138 (1999).
[CrossRef]

Proc. SPIE (3)

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]

M. C. Knauer, J. Kaminski, and G. Hausler, “Phase measuring Deflectometry: a new approach to measuring specular free-form surfaces,” Proc. SPIE 5457, 366–376 (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]

Other (2)

Y Tang, X., Su, Y., and Liu “A Novel Method Based on Fringe Reflection for Testing Aspheric Precisely and Flexibly,” manuscript in preparation.

M. Petz, and R. Tutsch, “ Reflection grating photogrammetry: a technique for absolute shape measurement of specular free-form surfaces,”Proc. SPIE 5869, 58691D–58691D.12 (2005)

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Figures (11)

Fig. 1
Fig. 1

the structure of measurement setup

Fig. 2
Fig. 2

the schematic of measurement principle

Fig. 3
Fig. 3

simulated tested surface

Fig. 4
Fig. 4

error of our method without error in the calibration

Fig. 5
Fig. 5

error of our method with error in the calibration

Fig. 6
Fig. 6

error of the traditional method without error in the calibration

Fig. 7
Fig. 7

error of the traditional method with error in the calibration

Fig. 8
Fig. 8

recorded fringe patterns

Fig. 9
Fig. 9

reconstruction surface using three coordinate machine

Fig. 10
Fig. 10

difference between the results of our method and three coordinate machine

Fig. 11
Fig. 11

difference between the results of the traditional method and three coordinate machine

Equations (8)

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

T=T1+MK;
z=(x2+y2)/4R+h0;
w=R'+h0';
S'=T1+[(Sz'T1z)/Kz]K;
R'=[(Sz'w)(Sz'w)2+(Sx'2+Sy'2)]/2;h0'=wR';
nx'=Sx'/2R';ny'=Sy'/2R';nz'=1;
K'=2{[(CS')/(||CS'||)](n'/||n'||)}(n'/||n'||)(CS')/(||CS'||);
f=||KK'||;

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