Abstract

In order to eliminate zeroth order effect and to make the phase shifting algorithm insensitive to phase shifting error, an 11-frame phase shifting algorithm is proposed in this paper. The analytical expression of phase-restoration error function is derived. The principle of phase shifting error compensation and the capability of suppressing zeroth order effect are explained, in comparison of existing algorithm. The analytical results show that this algorithm’s phase-restoration error is proportional to sine of double shearing phase and to biquadratic of phase shifting error. Finally, we generate the interference patterns of 11-frame algorithm and existing algorithm, restore the shearing phases and calculate the phase-restoration errors by simulations. The simulation results verify the theoretical analyses.

© 2013 Optical Society of America

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2007

2004

M. Hasegawa, C. Ouchi, T. Hasegawa, S. Kato, A. Ohkubo, A. Suzuki, K. Sugisaki, M. Okada, K. Otaki, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Recent progress of EUV wave-front metrology in EUVA,” Proc. SPIE5533, 27–36 (2004).
[CrossRef]

T. Hasegawa, C. Ouchi, M. Hasegawa, S. Kato, A. Suzuki, K. Sugisaki, K. Murakami, J. Saito, and M. Niibe, “EUV wavefront metrology system in EUVA,” Proc. SPIE5374, 797–807 (2004).
[CrossRef]

Y. Zhu, K. Sugisakia, C. Ouchia, K. Ohtaki, Z. Liu, M. Ishii, J. Kawakami, J. Saito, K. Murakami, C. Ouchi, M. Hasegawa, S. Kato, T. Hasegawa, A. Suzuki, and M. Niibe, “Lateral shearing interferometer for EUVL: theoretical analysis and experiment,” Proc. SPIE5374, 824–832 (2004).
[CrossRef]

2000

1997

1996

1995

1987

1984

1974

1973

Brangaccio, D. J.

Bruning, J. H.

Creath, K.

Eiju, T.

Gallagher, J. E.

Groot, P.

Harbers, G.

Hariharan, P.

Hasegawa, M.

Y. Zhu, K. Sugisaki, M. Okada, K. Otaki, Z. Liu, J. Kawakami, M. Ishii, J. Saito, K. Murakami, M. Hasegawa, C. Ouchi, S. Kato, T. Hasegawa, A. Suzuki, H. Yokota, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt.46(27), 6783–6792 (2007).
[CrossRef] [PubMed]

M. Hasegawa, C. Ouchi, T. Hasegawa, S. Kato, A. Ohkubo, A. Suzuki, K. Sugisaki, M. Okada, K. Otaki, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Recent progress of EUV wave-front metrology in EUVA,” Proc. SPIE5533, 27–36 (2004).
[CrossRef]

T. Hasegawa, C. Ouchi, M. Hasegawa, S. Kato, A. Suzuki, K. Sugisaki, K. Murakami, J. Saito, and M. Niibe, “EUV wavefront metrology system in EUVA,” Proc. SPIE5374, 797–807 (2004).
[CrossRef]

Y. Zhu, K. Sugisakia, C. Ouchia, K. Ohtaki, Z. Liu, M. Ishii, J. Kawakami, J. Saito, K. Murakami, C. Ouchi, M. Hasegawa, S. Kato, T. Hasegawa, A. Suzuki, and M. Niibe, “Lateral shearing interferometer for EUVL: theoretical analysis and experiment,” Proc. SPIE5374, 824–832 (2004).
[CrossRef]

Hasegawa, T.

Y. Zhu, K. Sugisaki, M. Okada, K. Otaki, Z. Liu, J. Kawakami, M. Ishii, J. Saito, K. Murakami, M. Hasegawa, C. Ouchi, S. Kato, T. Hasegawa, A. Suzuki, H. Yokota, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt.46(27), 6783–6792 (2007).
[CrossRef] [PubMed]

M. Hasegawa, C. Ouchi, T. Hasegawa, S. Kato, A. Ohkubo, A. Suzuki, K. Sugisaki, M. Okada, K. Otaki, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Recent progress of EUV wave-front metrology in EUVA,” Proc. SPIE5533, 27–36 (2004).
[CrossRef]

Y. Zhu, K. Sugisakia, C. Ouchia, K. Ohtaki, Z. Liu, M. Ishii, J. Kawakami, J. Saito, K. Murakami, C. Ouchi, M. Hasegawa, S. Kato, T. Hasegawa, A. Suzuki, and M. Niibe, “Lateral shearing interferometer for EUVL: theoretical analysis and experiment,” Proc. SPIE5374, 824–832 (2004).
[CrossRef]

T. Hasegawa, C. Ouchi, M. Hasegawa, S. Kato, A. Suzuki, K. Sugisaki, K. Murakami, J. Saito, and M. Niibe, “EUV wavefront metrology system in EUVA,” Proc. SPIE5374, 797–807 (2004).
[CrossRef]

Herriott, D. R.

Ishii, M.

Y. Zhu, K. Sugisaki, M. Okada, K. Otaki, Z. Liu, J. Kawakami, M. Ishii, J. Saito, K. Murakami, M. Hasegawa, C. Ouchi, S. Kato, T. Hasegawa, A. Suzuki, H. Yokota, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt.46(27), 6783–6792 (2007).
[CrossRef] [PubMed]

Y. Zhu, K. Sugisakia, C. Ouchia, K. Ohtaki, Z. Liu, M. Ishii, J. Kawakami, J. Saito, K. Murakami, C. Ouchi, M. Hasegawa, S. Kato, T. Hasegawa, A. Suzuki, and M. Niibe, “Lateral shearing interferometer for EUVL: theoretical analysis and experiment,” Proc. SPIE5374, 824–832 (2004).
[CrossRef]

Kamiya, K.

Kato, S.

Y. Zhu, K. Sugisaki, M. Okada, K. Otaki, Z. Liu, J. Kawakami, M. Ishii, J. Saito, K. Murakami, M. Hasegawa, C. Ouchi, S. Kato, T. Hasegawa, A. Suzuki, H. Yokota, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt.46(27), 6783–6792 (2007).
[CrossRef] [PubMed]

M. Hasegawa, C. Ouchi, T. Hasegawa, S. Kato, A. Ohkubo, A. Suzuki, K. Sugisaki, M. Okada, K. Otaki, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Recent progress of EUV wave-front metrology in EUVA,” Proc. SPIE5533, 27–36 (2004).
[CrossRef]

Y. Zhu, K. Sugisakia, C. Ouchia, K. Ohtaki, Z. Liu, M. Ishii, J. Kawakami, J. Saito, K. Murakami, C. Ouchi, M. Hasegawa, S. Kato, T. Hasegawa, A. Suzuki, and M. Niibe, “Lateral shearing interferometer for EUVL: theoretical analysis and experiment,” Proc. SPIE5374, 824–832 (2004).
[CrossRef]

T. Hasegawa, C. Ouchi, M. Hasegawa, S. Kato, A. Suzuki, K. Sugisaki, K. Murakami, J. Saito, and M. Niibe, “EUV wavefront metrology system in EUVA,” Proc. SPIE5374, 797–807 (2004).
[CrossRef]

Kawakami, J.

Y. Zhu, K. Sugisaki, M. Okada, K. Otaki, Z. Liu, J. Kawakami, M. Ishii, J. Saito, K. Murakami, M. Hasegawa, C. Ouchi, S. Kato, T. Hasegawa, A. Suzuki, H. Yokota, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt.46(27), 6783–6792 (2007).
[CrossRef] [PubMed]

Y. Zhu, K. Sugisakia, C. Ouchia, K. Ohtaki, Z. Liu, M. Ishii, J. Kawakami, J. Saito, K. Murakami, C. Ouchi, M. Hasegawa, S. Kato, T. Hasegawa, A. Suzuki, and M. Niibe, “Lateral shearing interferometer for EUVL: theoretical analysis and experiment,” Proc. SPIE5374, 824–832 (2004).
[CrossRef]

Kobayashi, S.

Kunst, P. J.

Leibbrandt, G. W.

Liu, Z.

Y. Zhu, K. Sugisaki, M. Okada, K. Otaki, Z. Liu, J. Kawakami, M. Ishii, J. Saito, K. Murakami, M. Hasegawa, C. Ouchi, S. Kato, T. Hasegawa, A. Suzuki, H. Yokota, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt.46(27), 6783–6792 (2007).
[CrossRef] [PubMed]

Y. Zhu, K. Sugisakia, C. Ouchia, K. Ohtaki, Z. Liu, M. Ishii, J. Kawakami, J. Saito, K. Murakami, C. Ouchi, M. Hasegawa, S. Kato, T. Hasegawa, A. Suzuki, and M. Niibe, “Lateral shearing interferometer for EUVL: theoretical analysis and experiment,” Proc. SPIE5374, 824–832 (2004).
[CrossRef]

Miyashiro, H.

Murakami, K.

Y. Zhu, K. Sugisaki, M. Okada, K. Otaki, Z. Liu, J. Kawakami, M. Ishii, J. Saito, K. Murakami, M. Hasegawa, C. Ouchi, S. Kato, T. Hasegawa, A. Suzuki, H. Yokota, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt.46(27), 6783–6792 (2007).
[CrossRef] [PubMed]

M. Hasegawa, C. Ouchi, T. Hasegawa, S. Kato, A. Ohkubo, A. Suzuki, K. Sugisaki, M. Okada, K. Otaki, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Recent progress of EUV wave-front metrology in EUVA,” Proc. SPIE5533, 27–36 (2004).
[CrossRef]

Y. Zhu, K. Sugisakia, C. Ouchia, K. Ohtaki, Z. Liu, M. Ishii, J. Kawakami, J. Saito, K. Murakami, C. Ouchi, M. Hasegawa, S. Kato, T. Hasegawa, A. Suzuki, and M. Niibe, “Lateral shearing interferometer for EUVL: theoretical analysis and experiment,” Proc. SPIE5374, 824–832 (2004).
[CrossRef]

T. Hasegawa, C. Ouchi, M. Hasegawa, S. Kato, A. Suzuki, K. Sugisaki, K. Murakami, J. Saito, and M. Niibe, “EUV wavefront metrology system in EUVA,” Proc. SPIE5374, 797–807 (2004).
[CrossRef]

Niibe, M.

Y. Zhu, K. Sugisaki, M. Okada, K. Otaki, Z. Liu, J. Kawakami, M. Ishii, J. Saito, K. Murakami, M. Hasegawa, C. Ouchi, S. Kato, T. Hasegawa, A. Suzuki, H. Yokota, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt.46(27), 6783–6792 (2007).
[CrossRef] [PubMed]

M. Hasegawa, C. Ouchi, T. Hasegawa, S. Kato, A. Ohkubo, A. Suzuki, K. Sugisaki, M. Okada, K. Otaki, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Recent progress of EUV wave-front metrology in EUVA,” Proc. SPIE5533, 27–36 (2004).
[CrossRef]

T. Hasegawa, C. Ouchi, M. Hasegawa, S. Kato, A. Suzuki, K. Sugisaki, K. Murakami, J. Saito, and M. Niibe, “EUV wavefront metrology system in EUVA,” Proc. SPIE5374, 797–807 (2004).
[CrossRef]

Y. Zhu, K. Sugisakia, C. Ouchia, K. Ohtaki, Z. Liu, M. Ishii, J. Kawakami, J. Saito, K. Murakami, C. Ouchi, M. Hasegawa, S. Kato, T. Hasegawa, A. Suzuki, and M. Niibe, “Lateral shearing interferometer for EUVL: theoretical analysis and experiment,” Proc. SPIE5374, 824–832 (2004).
[CrossRef]

Nomura, T.

Ohkubo, A.

M. Hasegawa, C. Ouchi, T. Hasegawa, S. Kato, A. Ohkubo, A. Suzuki, K. Sugisaki, M. Okada, K. Otaki, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Recent progress of EUV wave-front metrology in EUVA,” Proc. SPIE5533, 27–36 (2004).
[CrossRef]

Ohtaki, K.

Y. Zhu, K. Sugisakia, C. Ouchia, K. Ohtaki, Z. Liu, M. Ishii, J. Kawakami, J. Saito, K. Murakami, C. Ouchi, M. Hasegawa, S. Kato, T. Hasegawa, A. Suzuki, and M. Niibe, “Lateral shearing interferometer for EUVL: theoretical analysis and experiment,” Proc. SPIE5374, 824–832 (2004).
[CrossRef]

Okada, M.

Y. Zhu, K. Sugisaki, M. Okada, K. Otaki, Z. Liu, J. Kawakami, M. Ishii, J. Saito, K. Murakami, M. Hasegawa, C. Ouchi, S. Kato, T. Hasegawa, A. Suzuki, H. Yokota, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt.46(27), 6783–6792 (2007).
[CrossRef] [PubMed]

M. Hasegawa, C. Ouchi, T. Hasegawa, S. Kato, A. Ohkubo, A. Suzuki, K. Sugisaki, M. Okada, K. Otaki, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Recent progress of EUV wave-front metrology in EUVA,” Proc. SPIE5533, 27–36 (2004).
[CrossRef]

Okuda, S.

Oreb, B. F.

Otaki, K.

Y. Zhu, K. Sugisaki, M. Okada, K. Otaki, Z. Liu, J. Kawakami, M. Ishii, J. Saito, K. Murakami, M. Hasegawa, C. Ouchi, S. Kato, T. Hasegawa, A. Suzuki, H. Yokota, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt.46(27), 6783–6792 (2007).
[CrossRef] [PubMed]

M. Hasegawa, C. Ouchi, T. Hasegawa, S. Kato, A. Ohkubo, A. Suzuki, K. Sugisaki, M. Okada, K. Otaki, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Recent progress of EUV wave-front metrology in EUVA,” Proc. SPIE5533, 27–36 (2004).
[CrossRef]

Ouchi, C.

Y. Zhu, K. Sugisaki, M. Okada, K. Otaki, Z. Liu, J. Kawakami, M. Ishii, J. Saito, K. Murakami, M. Hasegawa, C. Ouchi, S. Kato, T. Hasegawa, A. Suzuki, H. Yokota, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt.46(27), 6783–6792 (2007).
[CrossRef] [PubMed]

M. Hasegawa, C. Ouchi, T. Hasegawa, S. Kato, A. Ohkubo, A. Suzuki, K. Sugisaki, M. Okada, K. Otaki, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Recent progress of EUV wave-front metrology in EUVA,” Proc. SPIE5533, 27–36 (2004).
[CrossRef]

Y. Zhu, K. Sugisakia, C. Ouchia, K. Ohtaki, Z. Liu, M. Ishii, J. Kawakami, J. Saito, K. Murakami, C. Ouchi, M. Hasegawa, S. Kato, T. Hasegawa, A. Suzuki, and M. Niibe, “Lateral shearing interferometer for EUVL: theoretical analysis and experiment,” Proc. SPIE5374, 824–832 (2004).
[CrossRef]

T. Hasegawa, C. Ouchi, M. Hasegawa, S. Kato, A. Suzuki, K. Sugisaki, K. Murakami, J. Saito, and M. Niibe, “EUV wavefront metrology system in EUVA,” Proc. SPIE5374, 797–807 (2004).
[CrossRef]

Ouchia, C.

Y. Zhu, K. Sugisakia, C. Ouchia, K. Ohtaki, Z. Liu, M. Ishii, J. Kawakami, J. Saito, K. Murakami, C. Ouchi, M. Hasegawa, S. Kato, T. Hasegawa, A. Suzuki, and M. Niibe, “Lateral shearing interferometer for EUVL: theoretical analysis and experiment,” Proc. SPIE5374, 824–832 (2004).
[CrossRef]

Rosenfeld, D. P.

Saito, J.

Y. Zhu, K. Sugisaki, M. Okada, K. Otaki, Z. Liu, J. Kawakami, M. Ishii, J. Saito, K. Murakami, M. Hasegawa, C. Ouchi, S. Kato, T. Hasegawa, A. Suzuki, H. Yokota, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt.46(27), 6783–6792 (2007).
[CrossRef] [PubMed]

M. Hasegawa, C. Ouchi, T. Hasegawa, S. Kato, A. Ohkubo, A. Suzuki, K. Sugisaki, M. Okada, K. Otaki, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Recent progress of EUV wave-front metrology in EUVA,” Proc. SPIE5533, 27–36 (2004).
[CrossRef]

T. Hasegawa, C. Ouchi, M. Hasegawa, S. Kato, A. Suzuki, K. Sugisaki, K. Murakami, J. Saito, and M. Niibe, “EUV wavefront metrology system in EUVA,” Proc. SPIE5374, 797–807 (2004).
[CrossRef]

Y. Zhu, K. Sugisakia, C. Ouchia, K. Ohtaki, Z. Liu, M. Ishii, J. Kawakami, J. Saito, K. Murakami, C. Ouchi, M. Hasegawa, S. Kato, T. Hasegawa, A. Suzuki, and M. Niibe, “Lateral shearing interferometer for EUVL: theoretical analysis and experiment,” Proc. SPIE5374, 824–832 (2004).
[CrossRef]

Schmit, J.

Schreiber, H.

Schwider, J.

Sugisaki, K.

Y. Zhu, K. Sugisaki, M. Okada, K. Otaki, Z. Liu, J. Kawakami, M. Ishii, J. Saito, K. Murakami, M. Hasegawa, C. Ouchi, S. Kato, T. Hasegawa, A. Suzuki, H. Yokota, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt.46(27), 6783–6792 (2007).
[CrossRef] [PubMed]

M. Hasegawa, C. Ouchi, T. Hasegawa, S. Kato, A. Ohkubo, A. Suzuki, K. Sugisaki, M. Okada, K. Otaki, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Recent progress of EUV wave-front metrology in EUVA,” Proc. SPIE5533, 27–36 (2004).
[CrossRef]

T. Hasegawa, C. Ouchi, M. Hasegawa, S. Kato, A. Suzuki, K. Sugisaki, K. Murakami, J. Saito, and M. Niibe, “EUV wavefront metrology system in EUVA,” Proc. SPIE5374, 797–807 (2004).
[CrossRef]

Sugisakia, K.

Y. Zhu, K. Sugisakia, C. Ouchia, K. Ohtaki, Z. Liu, M. Ishii, J. Kawakami, J. Saito, K. Murakami, C. Ouchi, M. Hasegawa, S. Kato, T. Hasegawa, A. Suzuki, and M. Niibe, “Lateral shearing interferometer for EUVL: theoretical analysis and experiment,” Proc. SPIE5374, 824–832 (2004).
[CrossRef]

Suzuki, A.

Y. Zhu, K. Sugisaki, M. Okada, K. Otaki, Z. Liu, J. Kawakami, M. Ishii, J. Saito, K. Murakami, M. Hasegawa, C. Ouchi, S. Kato, T. Hasegawa, A. Suzuki, H. Yokota, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt.46(27), 6783–6792 (2007).
[CrossRef] [PubMed]

M. Hasegawa, C. Ouchi, T. Hasegawa, S. Kato, A. Ohkubo, A. Suzuki, K. Sugisaki, M. Okada, K. Otaki, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Recent progress of EUV wave-front metrology in EUVA,” Proc. SPIE5533, 27–36 (2004).
[CrossRef]

Y. Zhu, K. Sugisakia, C. Ouchia, K. Ohtaki, Z. Liu, M. Ishii, J. Kawakami, J. Saito, K. Murakami, C. Ouchi, M. Hasegawa, S. Kato, T. Hasegawa, A. Suzuki, and M. Niibe, “Lateral shearing interferometer for EUVL: theoretical analysis and experiment,” Proc. SPIE5374, 824–832 (2004).
[CrossRef]

T. Hasegawa, C. Ouchi, M. Hasegawa, S. Kato, A. Suzuki, K. Sugisaki, K. Murakami, J. Saito, and M. Niibe, “EUV wavefront metrology system in EUVA,” Proc. SPIE5374, 797–807 (2004).
[CrossRef]

Takeda, M.

M. Hasegawa, C. Ouchi, T. Hasegawa, S. Kato, A. Ohkubo, A. Suzuki, K. Sugisaki, M. Okada, K. Otaki, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Recent progress of EUV wave-front metrology in EUVA,” Proc. SPIE5533, 27–36 (2004).
[CrossRef]

M. Takeda and S. Kobayashi, “Lateral aberration measurements with a digital Talbot interferometer,” Appl. Opt.23(11), 1760–1764 (1984).
[CrossRef] [PubMed]

Tashiro, H.

White, A. D.

Wyant, J. C.

Yokota, H.

Yoshikawa, K.

Zhu, Y.

Y. Zhu, K. Sugisaki, M. Okada, K. Otaki, Z. Liu, J. Kawakami, M. Ishii, J. Saito, K. Murakami, M. Hasegawa, C. Ouchi, S. Kato, T. Hasegawa, A. Suzuki, H. Yokota, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt.46(27), 6783–6792 (2007).
[CrossRef] [PubMed]

Y. Zhu, K. Sugisakia, C. Ouchia, K. Ohtaki, Z. Liu, M. Ishii, J. Kawakami, J. Saito, K. Murakami, C. Ouchi, M. Hasegawa, S. Kato, T. Hasegawa, A. Suzuki, and M. Niibe, “Lateral shearing interferometer for EUVL: theoretical analysis and experiment,” Proc. SPIE5374, 824–832 (2004).
[CrossRef]

Appl. Opt.

J. C. Wyant, “Double frequency grating lateral shear interferometer,” Appl. Opt.12(9), 2057–2060 (1973).
[CrossRef] [PubMed]

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Proc. SPIE

M. Hasegawa, C. Ouchi, T. Hasegawa, S. Kato, A. Ohkubo, A. Suzuki, K. Sugisaki, M. Okada, K. Otaki, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Recent progress of EUV wave-front metrology in EUVA,” Proc. SPIE5533, 27–36 (2004).
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Other

ITRS Organization, “International technology roadmap for semiconductors” (2013), http://www.itrs.net/ .

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Figures (11)

Fig. 1
Fig. 1

Block diagram of double grating lateral shearing interferometer.

Fig. 2
Fig. 2

The relationship between phase-restoration error and shearing phase.

Fig. 3
Fig. 3

The relationship between phase-restoration error and phase shearing error.

Fig. 4
Fig. 4

The wavefront of 0.5λ spherical aberration.

Fig. 5
Fig. 5

The shearing phase (a) and interference pattern (b) when shearing ratio is 0.1, V2 = V3 = 0.02V1 and phase shearing amount is 0.

Fig. 6
Fig. 6

The shearing phase (a) and phase-restoration error (b) restored with 11-frame algorithm.

Fig. 7
Fig. 7

The shearing phase (a) and phase-restoration error (b) restored with 4-frame algorithm.

Fig. 8
Fig. 8

The shearing phase (a) and phase-restoration error (b) restored with 9-frame algorithm.

Fig. 9
Fig. 9

The relationship between phase-restoration error and phase shearing error given by simulation with 11-frame and 9-frame algorithms under the condition of V2 = V3 = 2%V1.

Fig. 10
Fig. 10

The relationship between phase-restoration error and phase shearing error given by simulation with 11-frame and 9-frame algorithms under the condition of V2 = V3 = 0.5%V1.

Fig. 11
Fig. 11

The relationship between phase-restoration error and phase shearing error given by simulation with 11-frame and 9-frame algorithms under the condition of V2 = V3 = 1%V1.

Equations (19)

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ϕ= 2πmx p ,
ϕ j =j 4πx p =j π 2 .
E 1 = a 1 exp(k W 1 ),
E 1 = a 1 exp(k W 1 ),
E 0 = a 0 exp(k W 0 ),
I j = a 0 2 + a 1 2 + a 1 2 +2 a 0 a 1 cos[k( W 1 W 0 )+ϕ ' j ] +2 a 0 a 1 cos[k( W 0 W 1 )+ϕ " j ]+2 a 1 a 1 cos[k( W 1 W 1 )+ ϕ j ],
I j =Q+ V 1 cos( θ 1 + ϕ j )+ V 2 cos( θ 2 + ϕ j /2 )+ V 3 cos( θ 3 + ϕ j /2 ).
( I 5 I 5 )7( I 3 I 3 )+8( I 1 I 1 )=32 V 1 sin θ 1 ,
4( I 4 + I 4 )+8( I 2 + I 2 )8 I 0 =32 V 1 cos θ 1 .
θ 1 = tan 1 [ ( I 5 I 5 )7( I 3 I 3 )+8( I 1 I 1 ) 4( I 4 + I 4 )+8( I 2 + I 2 )8 I 0 ].
ϕ j =j π 2 +jε,
A 1 =[16cos( ε )16cos ( ε ) 3 32cos ( ε ) 5 ]sin θ 1 .
A 1 =(32+96 ε 2 100 ε 4 )sin θ 1 .
A 2 =[ 12 2 ε+O( ε 2 ) ] V 2 V 1 cos θ 2 .
B 1 =[ 32cos ( ε ) 2 64cos ( ε ) 4 ]cos θ 1 .
B 1 =(32+96 ε 2 96 ε 4 )cos θ 1 .
tan β 1 =( 1+ ε 4 824 ε 2 +24 ε 4 )tan θ 1 ( 1+ ε 4 8 )tan θ 1 .
θ ' 1 = tan 1 [ 2( I 3 I 3 )2( I 1 I 1 ) ( I 4 + I 4 )2( I 2 + I 2 )+2 I 0 ].
tanβ ' 1 =( 1+ ε 2 26 ε 2 )tanθ ' 1 ( 1+ ε 2 2 )tanθ ' 1 .

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