Abstract

The absolute testing method of shift-rotation that combines the traditional N-position method and Zernike polynomial fitting has been commonly employed in surface metrology. It preserves the high spatial frequency of the surface deviation with the N-position method to obtain the rotationally asymmetric surface deviation, but it suffers the kNθ order angular terms errors missed by the N-position method when it calculates the rotationally symmetric surface deviation with the Zernike rotationally symmetric polynomial fitting method. An optimized absolute testing method of shift-rotation is presented in this paper. It considers the missing kNθ order errors when the equations of the rotationally symmetric surface deviation are solved. As a result, it is more accurate than the traditional method. Experimental absolute results of spherical surfaces are given.

© 2013 Optical Society of America

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References

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2013

W. Song, F. Wu, X. Hou, G. Wu, B. Liu, and Y. Wan, “Absolute calibration of spherical reference surface for a Fizeau interferometer with the shift-rotation method of iterative algorithm,” Opt. Eng. 52, 336011 (2013).

W. Song, X. Hou, F. Wu, and Y. Wan, “Simple and rapid data-reduction method with pixel-level spatial frequency of shift-rotation method,” Appl. Opt. 52, 5974–5978 (2013).
[CrossRef]

2012

2011

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

2002

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]

2001

B. Dörband and G. Seitz, “Interferometric testing of optical surfaces at its current limit,” Optik 112, 392–398 (2001).
[CrossRef]

1996

Bloemhof, E. E.

Dörband, B.

B. Dörband and G. Seitz, “Interferometric testing of optical surfaces at its current limit,” Optik 112, 392–398 (2001).
[CrossRef]

Evans, C. J.

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.

J. A. Soons and U. 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, X. Hou, G. Wu, B. Liu, and Y. Wan, “Absolute calibration of spherical reference surface for a Fizeau interferometer with the shift-rotation method of iterative algorithm,” Opt. Eng. 52, 336011 (2013).

W. Song, X. Hou, F. Wu, and Y. Wan, “Simple and rapid data-reduction method with pixel-level spatial frequency of shift-rotation method,” Appl. Opt. 52, 5974–5978 (2013).
[CrossRef]

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 (9November1999).

Kestner, R. N.

Kim, M. Y.

Liu, B.

W. Song, F. Wu, X. Hou, G. Wu, B. Liu, and Y. Wan, “Absolute calibration of spherical reference surface for a Fizeau interferometer with the shift-rotation method of iterative algorithm,” Opt. Eng. 52, 336011 (2013).

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]

Seitz, G.

B. Dörband and G. Seitz, “Interferometric testing of optical surfaces at its current limit,” Optik 112, 392–398 (2001).
[CrossRef]

Song, W.

Soons, J. A.

J. A. Soons and U. 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.

W. Song, X. Hou, F. Wu, and Y. Wan, “Simple and rapid data-reduction method with pixel-level spatial frequency of shift-rotation method,” Appl. Opt. 52, 5974–5978 (2013).
[CrossRef]

W. Song, F. Wu, X. Hou, G. Wu, B. Liu, and Y. Wan, “Absolute calibration of spherical reference surface for a Fizeau interferometer with the shift-rotation method of iterative algorithm,” Opt. Eng. 52, 336011 (2013).

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]

Wu, F.

W. Song, F. Wu, X. Hou, G. Wu, B. Liu, and Y. Wan, “Absolute calibration of spherical reference surface for a Fizeau interferometer with the shift-rotation method of iterative algorithm,” Opt. Eng. 52, 336011 (2013).

W. Song, X. Hou, F. Wu, and Y. Wan, “Simple and rapid data-reduction method with pixel-level spatial frequency of shift-rotation method,” Appl. Opt. 52, 5974–5978 (2013).
[CrossRef]

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]

Wu, G.

W. Song, F. Wu, X. Hou, G. Wu, B. Liu, and Y. Wan, “Absolute calibration of spherical reference surface for a Fizeau interferometer with the shift-rotation method of iterative algorithm,” Opt. Eng. 52, 336011 (2013).

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 (9November1999).

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.

J. Vac. Sci. Technol. B

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. Eng.

W. Song, F. Wu, X. Hou, G. Wu, B. Liu, and Y. Wan, “Absolute calibration of spherical reference surface for a Fizeau interferometer with the shift-rotation method of iterative algorithm,” Opt. Eng. 52, 336011 (2013).

Opt. Lasers Eng.

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.

Optik

B. Dörband and G. Seitz, “Interferometric testing of optical surfaces at its current limit,” Optik 112, 392–398 (2001).
[CrossRef]

Proc. SPIE

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

Other

H. Ichikawa and T. Yamamoto, “Apparatus and method for wavefront absolute calibration and method of synthesizing wavefronts,” U.S. patent5,982,490 (9November1999).

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Figures (8)

Fig. 1.
Fig. 1.

Scheme of the absolute testing method of shift-rotation. (a) The original measurement (0°), (b) a 180° rotational measurement, and (c) a shifted measurement with a translation in the x direction.

Fig. 2.
Fig. 2.

Reference surface deviation obtained with the traditional shift-rotation method, PV=56.04nm, RMS=3.47nm.

Fig. 3.
Fig. 3.

Reference surface deviation obtained with the optimized shift-rotation method, PV=73.53nm, RMS=4.62nm.

Fig. 4.
Fig. 4.

Reference surface deviation obtained with the absolute method of two-sphere, PV=64.38nm, RMS=4.46nm.

Fig. 5.
Fig. 5.

Residual figure between Figs. 2 and 4, PV=63.27nm, RMS=3.66nm.

Fig. 6.
Fig. 6.

Residual figure between Figs. 3 and 4, PV=60.55nm, RMS=1.34nm.

Fig. 7.
Fig. 7.

Comparison of first 45 terms of the Zernike standard polynomial decompositions results shown in Figs. 2 and 3, respectively.

Fig. 8.
Fig. 8.

Residual figure between Figs. 2 and 3, PV=23.92nm, RMS=3.00nm.

Equations (6)

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

Wasy(x,y)=T1(x,y)1Ni=1NTi(x,y),
TN+1(x+s,y)=W(x+s,y)+R(x,y),
T1(x,y)TN+1(x+s,y)=W(x,y)W(x+s,y).
T1(x,y)TN+1(x+s,y)=Wasy(x,y)Wasy(x+s,y)+Wsym(x,y)Wsym(x+s,y),
T1(x,y)1Ni=1NTi(x,y)=Wasy(x,y)WkNθ(x,y),
T1(x,y)TN+1(x+s,y)=Wasy(x,y)WkNθ(x,y)[Wasy(x+s,y)WkNθ(x+s,y)]+Wsym(x,y)Wsym(x+s,y)+WkNθ(x,y)WkNθ(x+s,y).

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