Abstract

A method based on fringe reflection is proposed to measure the optical axis of an aspheric mirror precisely and flexibly. In the measurement, a screen displaying a fringe pattern is moved along its normal direction, and a camera is located beside and observes the fringe pattern reflected via a tested surface. This method can test the optical axis of an aspheric mirror quantitatively before measuring the absolute height of the tested surface. And it can be combined with some presented methods that need to fit the aspheric mirror according to the optical axis to measure the surface. To validate the ability of this method, it is combined with one of the presented methods to measure absolute height of an aspheric mirror precisely and flexibly. Computer simulations and preliminary experiment validate the feasibility of this method.

© 2011 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2010 (1)

2009 (1)

2008 (3)

2005 (1)

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

2004 (1)

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]

1999 (1)

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

Angel, R. P.

Bolado-Gomez, R.

Briers, J. D.

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

Burge, J. H.

Campos-Garcia, M.

Diaz-Uribe, R.

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.

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]

Liu, Y. K.

Moreno-Oliva, V. I.

Parks, R. E.

Petz, M.

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

Su, P.

Su, X. Y.

Tang, Y.

Tutsch, R.

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

Wang, L.

Wu, F.

Appl. Opt. (3)

Opt. Express (2)

Opt. Lasers Eng. (1)

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

Proc. SPIE (2)

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]

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

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Figures (9)

Fig. 1
Fig. 1

The structure of measurement setup.

Fig. 2
Fig. 2

The schematic of measurement principle.

Fig. 3
Fig. 3

Coordinate system transformation.

Fig. 4
Fig. 4

Simulated tested surface.

Fig. 5
Fig. 5

Error of the recovered surface using our method to test the optical axis.

Fig. 6
Fig. 6

Error of the recovered surface using the exact value of the optical axis.

Fig. 7
Fig. 7

Recorded fringe patterns.

Fig. 8
Fig. 8

Reconstruction surface using three-coordinate machine.

Fig. 9
Fig. 9

Difference between the results of our method and three-coordinate machine.

Equations (5)

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

y = a x + b ; z = 0.
[ ( 1 , a , 0 ) × ( C x , C y b , C z ) ] ( x C x , y C y , z C z ) = 0.
a m x + b m y + c m z + d m = 0.
a m x + b m y + c m ( d ) + d m = 0 ; z = d .
f = i = 1 n a m ( S i ) x + b m ( S i ) y + c m ( d ) + d m a m 2 + b m 2 ,

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