Abstract

Absolute testing methods are commonly employed in surface metrology to calibrate the reference surface deviation and obtain the absolute deviation of the surface under test. A simple and reliable data-reduction method of absolute shift-rotation method with rotational and translational measurements is presented here, which relies on the decomposition of the surface deviation into rotationally asymmetric and symmetric components. The rotationally asymmetric surface deviation can be simply obtained by classical N-position averaging method. After that, the two-dimensional problem of estimating the other rotationally symmetric surface deviation can be simplified to a one-dimensional problem, and it can be directly calculated out with pixel-level spatial frequency based on several measurements of different translations in one same direction. Since that no orthogonal polynomials fitting, such as Zernike polynomials, is required in the calculation, the data reduction of the method is simple and rapid. Experimental absolute results of spherical surfaces are given.

© 2013 Optical Society of America

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References

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2012 (4)

2011 (1)

X. Hou, P. Yang, F. Wu, and Y. Wan, “Comparative experimental study on absolute measurement of spherical surface with two-sphere method,” Opt. Lasers Eng. 49, 833–840 (2011).
[CrossRef]

2010 (2)

2006 (1)

2005 (1)

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibrations,” Proc. SPIE, 5869, 58690S (2005).
[CrossRef]

2002 (1)

K. Otaki, T. Yamamoto, and Y. Fukuda, “Accuracy evaluation of the point diffraction interferometer for extreme ultraviolet lithography aspheric mirror,” J. Vac. Sci. Technol. B 20, 295–300 (2002).
[CrossRef]

1996 (1)

1993 (1)

1992 (1)

1967 (1)

Ai, C.

Bloemhof, E. E.

Burke, J.

Carakos, R.

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibrations,” Proc. SPIE, 5869, 58690S (2005).
[CrossRef]

Creath, K.

Evans, C. J.

C. J. Evans and R. N. Kestner, “Test optics error removal,” Appl. Opt. 35, 1015–1021 (1996).
[CrossRef]

R. E. Parks, C. J. Evans, and L. Shao, “Calibration of interferometer transmission spheres,” Optical Fabrication and Testing Workshop, OSA Technical Digest Series (Optical Society of America, 1998), Vol. 12, pp. 80–83.

Fujimoto, I.

Fukuda, Y.

K. Otaki, T. Yamamoto, and Y. Fukuda, “Accuracy evaluation of the point diffraction interferometer for extreme ultraviolet lithography aspheric mirror,” J. Vac. Sci. Technol. B 20, 295–300 (2002).
[CrossRef]

Griesmann, U.

U. Griesmann, “Three-flat test solution based on simple mirror symmetry,” Appl. Opt. 45, 5856–5865 (2006).
[CrossRef]

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibrations,” Proc. SPIE, 5869, 58690S (2005).
[CrossRef]

Griesmann, Ul.

J. A. Soons and Ul. Griesmann, “Absolute interferometric tests of spherical surfaces based on rotational and translational shears,” Proc. SPIE 8493, 84930G (2012).
[CrossRef]

Hou, X.

W. Song, F. Wu, and X. Hou, “Method to test rotationally asymmetric surface deviation with high accuracy,” Appl. Opt. 51, 5567–5572 (2012).
[CrossRef]

X. Hou, P. Yang, F. Wu, and Y. Wan, “Comparative experimental study on absolute measurement of spherical surface with two-sphere method,” Opt. Lasers Eng. 49, 833–840 (2011).
[CrossRef]

Ichikawa, H.

H. Ichikawa and T. Yamamoto, “Apparatus and method for wavefront absolute calibration and method of synthesizing wavefronts,” U.S. patent5,982,490 (November9, 1999).

Kestner, R. N.

Kim, M.-Y.

Miao, E.

Nishimura, K.

Otaki, K.

K. Otaki, T. Yamamoto, and Y. Fukuda, “Accuracy evaluation of the point diffraction interferometer for extreme ultraviolet lithography aspheric mirror,” J. Vac. Sci. Technol. B 20, 295–300 (2002).
[CrossRef]

Parks, R. E.

R. E. Parks, C. J. Evans, and L. Shao, “Calibration of interferometer transmission spheres,” Optical Fabrication and Testing Workshop, OSA Technical Digest Series (Optical Society of America, 1998), Vol. 12, pp. 80–83.

Schulz, G.

Schwider, J.

Shao, L.

R. E. Parks, C. J. Evans, and L. Shao, “Calibration of interferometer transmission spheres,” Optical Fabrication and Testing Workshop, OSA Technical Digest Series (Optical Society of America, 1998), Vol. 12, pp. 80–83.

Song, W.

Soons, J.

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibrations,” Proc. SPIE, 5869, 58690S (2005).
[CrossRef]

Soons, J. A.

J. A. Soons and Ul. Griesmann, “Absolute interferometric tests of spherical surfaces based on rotational and translational shears,” Proc. SPIE 8493, 84930G (2012).
[CrossRef]

Su, D.

Sui, Y.

Takatsuji, T.

Wan, Y.

X. Hou, P. Yang, F. Wu, and Y. Wan, “Comparative experimental study on absolute measurement of spherical surface with two-sphere method,” Opt. Lasers Eng. 49, 833–840 (2011).
[CrossRef]

Wang, Q.

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibrations,” Proc. SPIE, 5869, 58690S (2005).
[CrossRef]

Wu, D. S.

Wu, F.

W. Song, F. Wu, and X. Hou, “Method to test rotationally asymmetric surface deviation with high accuracy,” Appl. Opt. 51, 5567–5572 (2012).
[CrossRef]

X. Hou, P. Yang, F. Wu, and Y. Wan, “Comparative experimental study on absolute measurement of spherical surface with two-sphere method,” Opt. Lasers Eng. 49, 833–840 (2011).
[CrossRef]

Wyant, J.

Wyant, J. C.

Yamamoto, T.

K. Otaki, T. Yamamoto, and Y. Fukuda, “Accuracy evaluation of the point diffraction interferometer for extreme ultraviolet lithography aspheric mirror,” J. Vac. Sci. Technol. B 20, 295–300 (2002).
[CrossRef]

H. Ichikawa and T. Yamamoto, “Apparatus and method for wavefront absolute calibration and method of synthesizing wavefronts,” U.S. patent5,982,490 (November9, 1999).

Yang, H.

Yang, P.

X. Hou, P. Yang, F. Wu, and Y. Wan, “Comparative experimental study on absolute measurement of spherical surface with two-sphere method,” Opt. Lasers Eng. 49, 833–840 (2011).
[CrossRef]

Appl. Opt. (8)

J. Vac. Sci. Technol. B (1)

K. Otaki, T. Yamamoto, and Y. Fukuda, “Accuracy evaluation of the point diffraction interferometer for extreme ultraviolet lithography aspheric mirror,” J. Vac. Sci. Technol. B 20, 295–300 (2002).
[CrossRef]

Opt. Lasers Eng. (1)

X. Hou, P. Yang, F. Wu, and Y. Wan, “Comparative experimental study on absolute measurement of spherical surface with two-sphere method,” Opt. Lasers Eng. 49, 833–840 (2011).
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (2)

J. A. Soons and Ul. Griesmann, “Absolute interferometric tests of spherical surfaces based on rotational and translational shears,” Proc. SPIE 8493, 84930G (2012).
[CrossRef]

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibrations,” Proc. SPIE, 5869, 58690S (2005).
[CrossRef]

Other (2)

R. E. Parks, C. J. Evans, and L. Shao, “Calibration of interferometer transmission spheres,” Optical Fabrication and Testing Workshop, OSA Technical Digest Series (Optical Society of America, 1998), Vol. 12, pp. 80–83.

H. Ichikawa and T. Yamamoto, “Apparatus and method for wavefront absolute calibration and method of synthesizing wavefronts,” U.S. patent5,982,490 (November9, 1999).

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Figures (6)

Fig. 1.
Fig. 1.

Scheme of the shift-rotation method.

Fig. 2.
Fig. 2.

Simplified 1D rotationally symmetric surface deviation with translations.

Fig. 3.
Fig. 3.

Spherical reference surface deviation obtained with the method described in this paper.

Fig. 4.
Fig. 4.

Spherical reference surface deviation obtained with the Zernike polynomials fitting method.

Fig. 5.
Fig. 5.

Zernike polynomials decompositions of the results obtained with two different methods, which are shown in Figs. 3 and 4, respectively.

Fig. 6.
Fig. 6.

PSD plots of the spherical reference surface deviation shown in Figs. 3 and 4, respectively.

Tables (1)

Tables Icon

Table 1. Comparison of Several Shift-Rotation Methods

Equations (9)

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Wasy(x,y)=T1(x,y)1Ni=1NTi(x,y),
Tsj(x+sj,y)=W(x+sj,y)+R(x,y),
T1(x,y)Tsj(x+sj,y)=W(x,y)W(x+sj,y).
ansan=b1,ans1an1=b2,,a0as=bns+1,a1as1=bns+2,,asa0=bn+1,anans=b2ns+1.
AX=B,
A(i,ns+2i)=1,A(i,n+2i)=1,fori=1,,ns+1;A(i,in+s1)=1,A(i,ni+1)=1,fori=ns+2,,ns+1+fix(s/2)X=[a0a1an]T,B=[b1b2bns+1+fix(s/2)]T.
AjX=Bj.
X=[jAjT·Aj]1·jAjTBj.
B(1:ns+2)=12{[b1b2bns+2]T[b2ns+1b2nsbn]T}.

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