Abstract

We propose a design method of phase-analysis algorithms based on two-dimensional grating phase shifting for Talbot interferometry, Talbot-Lau imaging, or the Ronchi test. These algorithms are designed to separate the two orthogonal shearing wavefronts and eliminate error effects of unwanted diffraction orders, simultaneously. Taking the effect of multidiffraction into account, moving the two-dimensional grating along a certain pass leads to a series of phase-shifted interfrograms, from which two orthogonal shearing wavefronts are derived, for the tested wavefront to be retrieved. The designing process is demonstrated, and the residual errors are analyzed via simulation works and experimental comparison.

© 2011 Optical Society of America

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References

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2010 (1)

W. Zhao, X. Su, Q. Zhang, and L. Xiang, “Wavefront reconstruction method using the intensity image of phase-shift grating,” Opt. Lasers Eng. 48, 600–604 (2010).
[CrossRef]

2009 (2)

M. L. Cruz, A. Castro, and V. Arrizon, “Phase shifting digital holography implemented with a twisted-nematic liquid-crystal display,” Appl. Opt. 48, 6907–6912 (2009).
[CrossRef] [PubMed]

W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805(2009).
[CrossRef]

2007 (2)

2006 (1)

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45, 5254–5262(2006).
[CrossRef]

2004 (1)

K. A. Goldberg, P. Naulleau, S. Rekawa, P. Denham, J. A. Liddle, E. Anderson, K. Jackson, J. Bokor, and D. Attwood, “At-wavelength interferometry of high-NA diffraction-limited EUV Optics,” AIP Conf. Proc. 705, 855–860 (2004).
[CrossRef]

2003 (1)

2001 (1)

2000 (1)

S. Lai, B. King, and M. A. Nerfeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
[CrossRef]

1999 (2)

J. Braat and A. J. E. M. Janssen, “Improved Ronchi test with extended source,” J. Opt. Soc. Am. A 16, 131–140 (1999).
[CrossRef]

M. Visser, M. Dekker, P. Hegeman, and J. Braat, “Extended-source interferometry for at-wavelength testing of EUV optics,” Proc. SPIE 3676, 253–263 (1999).
[CrossRef]

1996 (1)

1984 (1)

1982 (1)

1974 (2)

Absil, E.

Anderson, E.

K. A. Goldberg, P. Naulleau, S. Rekawa, P. Denham, J. A. Liddle, E. Anderson, K. Jackson, J. Bokor, and D. Attwood, “At-wavelength interferometry of high-NA diffraction-limited EUV Optics,” AIP Conf. Proc. 705, 855–860 (2004).
[CrossRef]

Arrizon, V.

Atlan, M.

Attwood, D.

K. A. Goldberg, P. Naulleau, S. Rekawa, P. Denham, J. A. Liddle, E. Anderson, K. Jackson, J. Bokor, and D. Attwood, “At-wavelength interferometry of high-NA diffraction-limited EUV Optics,” AIP Conf. Proc. 705, 855–860 (2004).
[CrossRef]

Boker, J.

Bokor, J.

K. A. Goldberg, P. Naulleau, S. Rekawa, P. Denham, J. A. Liddle, E. Anderson, K. Jackson, J. Bokor, and D. Attwood, “At-wavelength interferometry of high-NA diffraction-limited EUV Optics,” AIP Conf. Proc. 705, 855–860 (2004).
[CrossRef]

Braat, J.

M. Visser, M. Dekker, P. Hegeman, and J. Braat, “Extended-source interferometry for at-wavelength testing of EUV optics,” Proc. SPIE 3676, 253–263 (1999).
[CrossRef]

J. Braat and A. J. E. M. Janssen, “Improved Ronchi test with extended source,” J. Opt. Soc. Am. A 16, 131–140 (1999).
[CrossRef]

Brangaccio, D. J.

Bruning, J. H.

Castro, A.

Chen, W.

W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805(2009).
[CrossRef]

Cruz, M. L.

Dekker, M.

M. Visser, M. Dekker, P. Hegeman, and J. Braat, “Extended-source interferometry for at-wavelength testing of EUV optics,” Proc. SPIE 3676, 253–263 (1999).
[CrossRef]

Denham, P.

K. A. Goldberg, P. Naulleau, S. Rekawa, P. Denham, J. A. Liddle, E. Anderson, K. Jackson, J. Bokor, and D. Attwood, “At-wavelength interferometry of high-NA diffraction-limited EUV Optics,” AIP Conf. Proc. 705, 855–860 (2004).
[CrossRef]

Fu, Y.

W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805(2009).
[CrossRef]

Gallagher, J. E.

Goldberg, K. A.

K. A. Goldberg, P. Naulleau, S. Rekawa, P. Denham, J. A. Liddle, E. Anderson, K. Jackson, J. Bokor, and D. Attwood, “At-wavelength interferometry of high-NA diffraction-limited EUV Optics,” AIP Conf. Proc. 705, 855–860 (2004).
[CrossRef]

K. A. Goldberg and J. Boker, “Fourier-transform method of phase-shift determination,” Appl. Opt. 40, 2886–2894 (2001).
[CrossRef]

Gross, M.

Harbers, G.

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. Yokoda, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt. 46, 6783–6792 (2007).
[CrossRef] [PubMed]

K. Sugisaki, M. Hasegawa, M. Okada, Y. Zhu, K. Otaki, Z. Liu, M. Ishii, J. Kawakami, K. Murakami, J. Saito, S. Kato, C. Ouchi, A. Ohkubo, Y. Sekine, T. Hasegawa, A. Suzuki, M. Niibe, and M. Takeda, “EUVA’s challenges toward 0.1 nm accuracy in EUV at-wavelength interferometry,” in Fringe 2005: The 5th International Workshop on Automatic Processing of Fringe Patterns, OstenW., ed. (Springer, 2005) pp. 252–266.
[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. Yokoda, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt. 46, 6783–6792 (2007).
[CrossRef] [PubMed]

K. Sugisaki, M. Hasegawa, M. Okada, Y. Zhu, K. Otaki, Z. Liu, M. Ishii, J. Kawakami, K. Murakami, J. Saito, S. Kato, C. Ouchi, A. Ohkubo, Y. Sekine, T. Hasegawa, A. Suzuki, M. Niibe, and M. Takeda, “EUVA’s challenges toward 0.1 nm accuracy in EUV at-wavelength interferometry,” in Fringe 2005: The 5th International Workshop on Automatic Processing of Fringe Patterns, OstenW., ed. (Springer, 2005) pp. 252–266.
[CrossRef]

Hattori, T.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45, 5254–5262(2006).
[CrossRef]

Hegeman, P.

M. Visser, M. Dekker, P. Hegeman, and J. Braat, “Extended-source interferometry for at-wavelength testing of EUV optics,” Proc. SPIE 3676, 253–263 (1999).
[CrossRef]

Herriott, D. R.

Ina, H.

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. Yokoda, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt. 46, 6783–6792 (2007).
[CrossRef] [PubMed]

K. Sugisaki, M. Hasegawa, M. Okada, Y. Zhu, K. Otaki, Z. Liu, M. Ishii, J. Kawakami, K. Murakami, J. Saito, S. Kato, C. Ouchi, A. Ohkubo, Y. Sekine, T. Hasegawa, A. Suzuki, M. Niibe, and M. Takeda, “EUVA’s challenges toward 0.1 nm accuracy in EUV at-wavelength interferometry,” in Fringe 2005: The 5th International Workshop on Automatic Processing of Fringe Patterns, OstenW., ed. (Springer, 2005) pp. 252–266.
[CrossRef]

Jackson, K.

K. A. Goldberg, P. Naulleau, S. Rekawa, P. Denham, J. A. Liddle, E. Anderson, K. Jackson, J. Bokor, and D. Attwood, “At-wavelength interferometry of high-NA diffraction-limited EUV Optics,” AIP Conf. Proc. 705, 855–860 (2004).
[CrossRef]

Janssen, A. J. E. M.

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. Yokoda, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt. 46, 6783–6792 (2007).
[CrossRef] [PubMed]

K. Sugisaki, M. Hasegawa, M. Okada, Y. Zhu, K. Otaki, Z. Liu, M. Ishii, J. Kawakami, K. Murakami, J. Saito, S. Kato, C. Ouchi, A. Ohkubo, Y. Sekine, T. Hasegawa, A. Suzuki, M. Niibe, and M. Takeda, “EUVA’s challenges toward 0.1 nm accuracy in EUV at-wavelength interferometry,” in Fringe 2005: The 5th International Workshop on Automatic Processing of Fringe Patterns, OstenW., ed. (Springer, 2005) pp. 252–266.
[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. Yokoda, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt. 46, 6783–6792 (2007).
[CrossRef] [PubMed]

K. Sugisaki, M. Hasegawa, M. Okada, Y. Zhu, K. Otaki, Z. Liu, M. Ishii, J. Kawakami, K. Murakami, J. Saito, S. Kato, C. Ouchi, A. Ohkubo, Y. Sekine, T. Hasegawa, A. Suzuki, M. Niibe, and M. Takeda, “EUVA’s challenges toward 0.1 nm accuracy in EUV at-wavelength interferometry,” in Fringe 2005: The 5th International Workshop on Automatic Processing of Fringe Patterns, OstenW., ed. (Springer, 2005) pp. 252–266.
[CrossRef]

King, B.

S. Lai, B. King, and M. A. Nerfeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
[CrossRef]

Kobayashi, S.

Kunst, P. J.

Lai, S.

S. Lai, B. King, and M. A. Nerfeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
[CrossRef]

Leibbrandt, G. W. R.

Liddle, J. A.

K. A. Goldberg, P. Naulleau, S. Rekawa, P. Denham, J. A. Liddle, E. Anderson, K. Jackson, J. Bokor, and D. Attwood, “At-wavelength interferometry of high-NA diffraction-limited EUV Optics,” AIP Conf. Proc. 705, 855–860 (2004).
[CrossRef]

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. Yokoda, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt. 46, 6783–6792 (2007).
[CrossRef] [PubMed]

K. Sugisaki, M. Hasegawa, M. Okada, Y. Zhu, K. Otaki, Z. Liu, M. Ishii, J. Kawakami, K. Murakami, J. Saito, S. Kato, C. Ouchi, A. Ohkubo, Y. Sekine, T. Hasegawa, A. Suzuki, M. Niibe, and M. Takeda, “EUVA’s challenges toward 0.1 nm accuracy in EUV at-wavelength interferometry,” in Fringe 2005: The 5th International Workshop on Automatic Processing of Fringe Patterns, OstenW., ed. (Springer, 2005) pp. 252–266.
[CrossRef]

Malacara, D.

D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007), pp. 568–596.

Momose, A.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45, 5254–5262(2006).
[CrossRef]

A. Momose, “Phase-sensitive imaging and phase tomography using X-ray interferometers,” Opt. Express 11, 2303–2314(2003).
[CrossRef] [PubMed]

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. Yokoda, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt. 46, 6783–6792 (2007).
[CrossRef] [PubMed]

K. Sugisaki, M. Hasegawa, M. Okada, Y. Zhu, K. Otaki, Z. Liu, M. Ishii, J. Kawakami, K. Murakami, J. Saito, S. Kato, C. Ouchi, A. Ohkubo, Y. Sekine, T. Hasegawa, A. Suzuki, M. Niibe, and M. Takeda, “EUVA’s challenges toward 0.1 nm accuracy in EUV at-wavelength interferometry,” in Fringe 2005: The 5th International Workshop on Automatic Processing of Fringe Patterns, OstenW., ed. (Springer, 2005) pp. 252–266.
[CrossRef]

Naulleau, P.

K. A. Goldberg, P. Naulleau, S. Rekawa, P. Denham, J. A. Liddle, E. Anderson, K. Jackson, J. Bokor, and D. Attwood, “At-wavelength interferometry of high-NA diffraction-limited EUV Optics,” AIP Conf. Proc. 705, 855–860 (2004).
[CrossRef]

Nerfeld, M. A.

S. Lai, B. King, and M. A. Nerfeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
[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. Yokoda, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt. 46, 6783–6792 (2007).
[CrossRef] [PubMed]

K. Sugisaki, M. Hasegawa, M. Okada, Y. Zhu, K. Otaki, Z. Liu, M. Ishii, J. Kawakami, K. Murakami, J. Saito, S. Kato, C. Ouchi, A. Ohkubo, Y. Sekine, T. Hasegawa, A. Suzuki, M. Niibe, and M. Takeda, “EUVA’s challenges toward 0.1 nm accuracy in EUV at-wavelength interferometry,” in Fringe 2005: The 5th International Workshop on Automatic Processing of Fringe Patterns, OstenW., ed. (Springer, 2005) pp. 252–266.
[CrossRef]

Ohkubo, A.

K. Sugisaki, M. Hasegawa, M. Okada, Y. Zhu, K. Otaki, Z. Liu, M. Ishii, J. Kawakami, K. Murakami, J. Saito, S. Kato, C. Ouchi, A. Ohkubo, Y. Sekine, T. Hasegawa, A. Suzuki, M. Niibe, and M. Takeda, “EUVA’s challenges toward 0.1 nm accuracy in EUV at-wavelength interferometry,” in Fringe 2005: The 5th International Workshop on Automatic Processing of Fringe Patterns, OstenW., ed. (Springer, 2005) pp. 252–266.
[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. Yokoda, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt. 46, 6783–6792 (2007).
[CrossRef] [PubMed]

K. Sugisaki, M. Hasegawa, M. Okada, Y. Zhu, K. Otaki, Z. Liu, M. Ishii, J. Kawakami, K. Murakami, J. Saito, S. Kato, C. Ouchi, A. Ohkubo, Y. Sekine, T. Hasegawa, A. Suzuki, M. Niibe, and M. Takeda, “EUVA’s challenges toward 0.1 nm accuracy in EUV at-wavelength interferometry,” in Fringe 2005: The 5th International Workshop on Automatic Processing of Fringe Patterns, OstenW., ed. (Springer, 2005) pp. 252–266.
[CrossRef]

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. Yokoda, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt. 46, 6783–6792 (2007).
[CrossRef] [PubMed]

K. Sugisaki, M. Hasegawa, M. Okada, Y. Zhu, K. Otaki, Z. Liu, M. Ishii, J. Kawakami, K. Murakami, J. Saito, S. Kato, C. Ouchi, A. Ohkubo, Y. Sekine, T. Hasegawa, A. Suzuki, M. Niibe, and M. Takeda, “EUVA’s challenges toward 0.1 nm accuracy in EUV at-wavelength interferometry,” in Fringe 2005: The 5th International Workshop on Automatic Processing of Fringe Patterns, OstenW., ed. (Springer, 2005) pp. 252–266.
[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. Yokoda, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt. 46, 6783–6792 (2007).
[CrossRef] [PubMed]

K. Sugisaki, M. Hasegawa, M. Okada, Y. Zhu, K. Otaki, Z. Liu, M. Ishii, J. Kawakami, K. Murakami, J. Saito, S. Kato, C. Ouchi, A. Ohkubo, Y. Sekine, T. Hasegawa, A. Suzuki, M. Niibe, and M. Takeda, “EUVA’s challenges toward 0.1 nm accuracy in EUV at-wavelength interferometry,” in Fringe 2005: The 5th International Workshop on Automatic Processing of Fringe Patterns, OstenW., ed. (Springer, 2005) pp. 252–266.
[CrossRef]

Quan, C.

W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805(2009).
[CrossRef]

Rekawa, S.

K. A. Goldberg, P. Naulleau, S. Rekawa, P. Denham, J. A. Liddle, E. Anderson, K. Jackson, J. Bokor, and D. Attwood, “At-wavelength interferometry of high-NA diffraction-limited EUV Optics,” AIP Conf. Proc. 705, 855–860 (2004).
[CrossRef]

Rimmer, M. P.

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. Yokoda, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt. 46, 6783–6792 (2007).
[CrossRef] [PubMed]

K. Sugisaki, M. Hasegawa, M. Okada, Y. Zhu, K. Otaki, Z. Liu, M. Ishii, J. Kawakami, K. Murakami, J. Saito, S. Kato, C. Ouchi, A. Ohkubo, Y. Sekine, T. Hasegawa, A. Suzuki, M. Niibe, and M. Takeda, “EUVA’s challenges toward 0.1 nm accuracy in EUV at-wavelength interferometry,” in Fringe 2005: The 5th International Workshop on Automatic Processing of Fringe Patterns, OstenW., ed. (Springer, 2005) pp. 252–266.
[CrossRef]

Sekine, Y.

K. Sugisaki, M. Hasegawa, M. Okada, Y. Zhu, K. Otaki, Z. Liu, M. Ishii, J. Kawakami, K. Murakami, J. Saito, S. Kato, C. Ouchi, A. Ohkubo, Y. Sekine, T. Hasegawa, A. Suzuki, M. Niibe, and M. Takeda, “EUVA’s challenges toward 0.1 nm accuracy in EUV at-wavelength interferometry,” in Fringe 2005: The 5th International Workshop on Automatic Processing of Fringe Patterns, OstenW., ed. (Springer, 2005) pp. 252–266.
[CrossRef]

Su, X.

W. Zhao, X. Su, Q. Zhang, and L. Xiang, “Wavefront reconstruction method using the intensity image of phase-shift grating,” Opt. Lasers Eng. 48, 600–604 (2010).
[CrossRef]

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. Yokoda, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt. 46, 6783–6792 (2007).
[CrossRef] [PubMed]

K. Sugisaki, M. Hasegawa, M. Okada, Y. Zhu, K. Otaki, Z. Liu, M. Ishii, J. Kawakami, K. Murakami, J. Saito, S. Kato, C. Ouchi, A. Ohkubo, Y. Sekine, T. Hasegawa, A. Suzuki, M. Niibe, and M. Takeda, “EUVA’s challenges toward 0.1 nm accuracy in EUV at-wavelength interferometry,” in Fringe 2005: The 5th International Workshop on Automatic Processing of Fringe Patterns, OstenW., ed. (Springer, 2005) pp. 252–266.
[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. Yokoda, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt. 46, 6783–6792 (2007).
[CrossRef] [PubMed]

K. Sugisaki, M. Hasegawa, M. Okada, Y. Zhu, K. Otaki, Z. Liu, M. Ishii, J. Kawakami, K. Murakami, J. Saito, S. Kato, C. Ouchi, A. Ohkubo, Y. Sekine, T. Hasegawa, A. Suzuki, M. Niibe, and M. Takeda, “EUVA’s challenges toward 0.1 nm accuracy in EUV at-wavelength interferometry,” in Fringe 2005: The 5th International Workshop on Automatic Processing of Fringe Patterns, OstenW., ed. (Springer, 2005) pp. 252–266.
[CrossRef]

Suzuki, Y.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45, 5254–5262(2006).
[CrossRef]

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[CrossRef]

K. Sugisaki, M. Hasegawa, M. Okada, Y. Zhu, K. Otaki, Z. Liu, M. Ishii, J. Kawakami, K. Murakami, J. Saito, S. Kato, C. Ouchi, A. Ohkubo, Y. Sekine, T. Hasegawa, A. Suzuki, M. Niibe, and M. Takeda, “EUVA’s challenges toward 0.1 nm accuracy in EUV at-wavelength interferometry,” in Fringe 2005: The 5th International Workshop on Automatic Processing of Fringe Patterns, OstenW., ed. (Springer, 2005) pp. 252–266.
[CrossRef]

Takeda, Y.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45, 5254–5262(2006).
[CrossRef]

Tay, C. J.

W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805(2009).
[CrossRef]

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M. Visser, M. Dekker, P. Hegeman, and J. Braat, “Extended-source interferometry for at-wavelength testing of EUV optics,” Proc. SPIE 3676, 253–263 (1999).
[CrossRef]

White, A. D.

Xiang, L.

W. Zhao, X. Su, Q. Zhang, and L. Xiang, “Wavefront reconstruction method using the intensity image of phase-shift grating,” Opt. Lasers Eng. 48, 600–604 (2010).
[CrossRef]

Yashiro, W.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45, 5254–5262(2006).
[CrossRef]

Yokoda, H.

Zhang, Q.

W. Zhao, X. Su, Q. Zhang, and L. Xiang, “Wavefront reconstruction method using the intensity image of phase-shift grating,” Opt. Lasers Eng. 48, 600–604 (2010).
[CrossRef]

Zhao, W.

W. Zhao, X. Su, Q. Zhang, and L. Xiang, “Wavefront reconstruction method using the intensity image of phase-shift grating,” Opt. Lasers Eng. 48, 600–604 (2010).
[CrossRef]

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. Yokoda, and M. Niibe, “Wavefront measurement interferometry at the operational wavelength of extreme-ultraviolet lithography,” Appl. Opt. 46, 6783–6792 (2007).
[CrossRef] [PubMed]

K. Sugisaki, M. Hasegawa, M. Okada, Y. Zhu, K. Otaki, Z. Liu, M. Ishii, J. Kawakami, K. Murakami, J. Saito, S. Kato, C. Ouchi, A. Ohkubo, Y. Sekine, T. Hasegawa, A. Suzuki, M. Niibe, and M. Takeda, “EUVA’s challenges toward 0.1 nm accuracy in EUV at-wavelength interferometry,” in Fringe 2005: The 5th International Workshop on Automatic Processing of Fringe Patterns, OstenW., ed. (Springer, 2005) pp. 252–266.
[CrossRef]

AIP Conf. Proc. (1)

K. A. Goldberg, P. Naulleau, S. Rekawa, P. Denham, J. A. Liddle, E. Anderson, K. Jackson, J. Bokor, and D. Attwood, “At-wavelength interferometry of high-NA diffraction-limited EUV Optics,” AIP Conf. Proc. 705, 855–860 (2004).
[CrossRef]

Appl. Opt. (7)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Jpn. J. Appl. Phys. (1)

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45, 5254–5262(2006).
[CrossRef]

Opt. Commun. (2)

S. Lai, B. King, and M. A. Nerfeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
[CrossRef]

W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805(2009).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (1)

W. Zhao, X. Su, Q. Zhang, and L. Xiang, “Wavefront reconstruction method using the intensity image of phase-shift grating,” Opt. Lasers Eng. 48, 600–604 (2010).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

M. Visser, M. Dekker, P. Hegeman, and J. Braat, “Extended-source interferometry for at-wavelength testing of EUV optics,” Proc. SPIE 3676, 253–263 (1999).
[CrossRef]

Other (3)

K. Sugisaki, M. Hasegawa, M. Okada, Y. Zhu, K. Otaki, Z. Liu, M. Ishii, J. Kawakami, K. Murakami, J. Saito, S. Kato, C. Ouchi, A. Ohkubo, Y. Sekine, T. Hasegawa, A. Suzuki, M. Niibe, and M. Takeda, “EUVA’s challenges toward 0.1 nm accuracy in EUV at-wavelength interferometry,” in Fringe 2005: The 5th International Workshop on Automatic Processing of Fringe Patterns, OstenW., ed. (Springer, 2005) pp. 252–266.
[CrossRef]

CODE V 10.3 Reference Manual, Appendix C Zernike Polynomials, Fringe Zernike Polynomials, C-8.

D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007), pp. 568–596.

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Figures (5)

Fig. 1
Fig. 1

Experimental layout of Talbot interferometer with two-dimensional grating.

Fig. 2
Fig. 2

Talbot interferogram and its spectra. (a) Talbot interferogram, (b) Fourier transform of the Talbot interferogram showing the multiple diffraction orders of the two- dimensional grating.

Fig. 3
Fig. 3

Experimental result of the wavefront measurement with Fig. 1 configuration for comparison of two different phase-analysis methods, i.e. the proposed phase-shift algorithm of Eqs. (3, 4) and the FTM proposed in [11]. (a) Interpreted with fringe Zernike coefficients, (b) phase-contrast map and cross section graph analyzed by the PSI method, (c) phase-contrast map and cross section graph analyzed by the FTM.

Fig. 4
Fig. 4

Difference between our proposed PSI method and the FTM.

Fig. 5
Fig. 5

Simulation results for estimating the error effects of other unwanted higher-order diffractions in a fringe Zernike polynomials expression. The measurement error in the retrieved wavefronts using Eqs. (3, 4) are seen to be dominated by the third and fifth order effects, which can be further eliminated by the algorithms proposed in Eqs. (17, 18).

Tables (1)

Tables Icon

Table 1 Phase Shift Amounts Between Different Diffraction Orders for Each Step

Equations (18)

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I = a 0 + a 1 , 0 cos ( φ 1 , 0 ) + a 0 , 1 cos ( φ 0 , 1 ) + a 1 , 1 cos ( φ 1 , 1 ) + a 1 , 1 cos ( φ 1 , 1 ) ,
I k = a 0 + a 1 , 0 cos ( φ 1 , 0 + δ x ) + a 0 , 1 cos ( φ 0 , 1 + δ y ) + a 1 , 1 cos ( φ 1 , 1 + N 1 , 1 ) + a 1 , 1 cos ( φ 1 , 1 + N 1 , 1 ) ,
φ 1 , 0 = 2 ( I 2 I ) 6 + 2 2 ( I 3 I 7 ) + 2 ( I 4 I 8 ) 2 ( I 2 I ) 6 2 ( I 1 2 I + 5 I 9 ) + 2 ( I 4 I 8 ) ,
φ 0 , 1 = 2 ( I 2 I ) 6 2 2 ( I 3 I 7 ) + 2 ( I 4 I 8 ) 2 ( I 2 I ) 6 2 ( I 1 2 I + 5 I 9 ) 2 ( I 4 I 8 ) .
I = a 0 + m = 2 k 1 2 k + 1 a m 0 cos ( φ m 0 ) + n = 2 l 1 2 l + 1 a 0 n cos ( φ 0 n ) + m = 2 k 1 2 k + 1 n = 2 l 1 2 l + 1 a m n cos ( φ m n ) + m = 2 k 1 2 k + 1 m = 2 k 1 2 k + 1 a m m cos ( φ m m ) + n = 2 l 1 2 l + 1 n = 2 l 1 2 l + 1 a n n cos ( φ n n ) ,
I = a 0 + m = 2 k 1 2 k + 1 a m 0 cos ( φ m 0 + m δ ) x + n = 2 l 1 2 l + 1 a 0 n cos ( φ 0 n + n δ y ) + m = 2 k 1 2 k + 1 n = 2 l 1 2 l + 1 a m n cos ( φ m n + m δ x n δ y ) + m = 2 k 1 2 k + 1 m = 2 k 1 2 k + 1 a m m cos ( φ m m + m δ x m δ x ) + n = 2 l 1 2 l + 1 n = 2 l 1 2 l + 1 a n n cos ( φ n n + n δ y n δ ) y .
I = a 0 + m = 2 k 1 2 k + 1 a m 0 cos ( φ m 0 + m δ ) x + n = 2 l 1 2 l + 1 a 0 n cos ( φ 0 n + n δ + y π ) + m = 2 k 1 2 k + 1 n = 2 l 1 2 l + 1 a m n cos ( φ m n + m δ x n δ y n π ) + m = 2 k 1 2 k + 1 m = 2 k 1 2 k + 1 a m m cos ( φ m m + m δ x m δ ) x + n = 2 l 1 2 l + 1 n = 2 l 1 2 l + 1 a n n cos ( φ n n + n δ y n δ + y n π n π ) ,
I = a 0 + m = 2 k 1 2 k + 1 a m 0 cos ( φ m 0 + m δ ) x n = 2 l 1 2 l + 1 a 0 n cos ( φ 0 n + n δ ) y m = 2 k 1 2 k + 1 n = 2 l 1 2 l + 1 a m n cos ( φ m n + m δ x n δ ) y + m = 2 k 1 2 k + 1 m = 2 k 1 2 k + 1 a m m cos ( φ m m + m δ x m δ ) x + n = 2 l 1 2 l + 1 n = 2 l 1 2 l + 1 a n n cos ( φ n n + n δ y n δ ) y .
I + I = 2 a 0 + 2 m = 2 k 1 2 k + 1 a m 0 cos ( φ m 0 + m δ ) x + 2 m = 2 k 1 2 k + 1 m = 2 k 1 2 k + 1 a m m cos ( φ m m + m δ x m δ ) x + 2 n = 2 l 1 2 l + 1 n = 2 l 1 2 l + 1 a n n cos ( φ n n + n δ y n δ ) y .
I + I = 2 a 0 + 2 m = 2 k 1 2 k + 1 a m 0 cos ( φ m 0 + m δ ) x ,
I = a 0 + m = 2 k 1 2 k + 1 a m 0 cos ( φ m 0 + m δ x + π ) + n = 2 l 1 2 l + 1 a 0 n cos ( φ 0 n + n δ ) y + m = 2 k 1 2 k + 1 n = 2 l 1 2 l + 1 a m n cos ( φ m n + m δ x n δ y + m π ) + m = 2 k 1 2 k + 1 m = 2 k 1 2 k + 1 a m m cos ( φ m m + m δ x m δ x + m π m π ) + n = 2 l 1 2 l + 1 n = 2 l 1 2 l + 1 a n n cos ( φ n n + n δ y n δ y ) ,
I = a 0 m = 2 k 1 2 k + 1 a m 0 cos ( φ m 0 + m δ ) x + n = 2 l 1 2 l + 1 a 0 n cos ( φ 0 n + n δ ) y m = 2 k 1 2 k + 1 n = 2 l 1 2 l + 1 a m n cos ( φ m n + m δ x n δ ) y + m = 2 k 1 2 k + 1 m = 2 k 1 2 k + 1 a m m cos ( φ m m + m δ x m δ ) x + n = 2 l 1 2 l + 1 n = 2 l 1 2 l + 1 a n n cos ( φ n n + n δ y n δ ) y .
I + I = 2 a 0 + 2 n = 2 l 1 2 l + 1 a 0 n cos ( φ 0 n + n δ ) y + 2 m = 2 k 1 2 k + 1 m = 2 k 1 2 k + 1 a m m cos ( φ m m + m δ x m δ ) x + 2 n = 2 l 1 2 l + 1 n = 2 l 1 2 l + 1 a n n cos ( φ n n + n δ y n δ ) y .
I + I = 2 a 0 + 2 n = 2 l 1 2 l + 1 a 0 n cos ( φ 0 n + n δ ) y ,
I 1 X = I 1 + I 10 = I 1 + I 10 , I 2 X = I 2 + I 11 = I 2 + I 11 , I 3 X = I 3 + I 12 = I 3 + I 12 , I 4 X = I 4 + I 13 = I 4 + I 13 , I 5 X = I 5 + I 14 = I 5 + I 14 , I 6 X = I 6 + I 15 = I 6 + I 15 , I 7 X = I 7 + I 16 = I 7 + I 16 , I 8 X = I 8 + I 17 = I 8 + I 17 , I 9 X = I 9 + I 18 = I 9 + I 10 ,
I 1 Y = I 1 + I 19 = I 1 + I 14 , I 2 Y = I 2 + I 20 = I 2 + I 15 , I 3 Y = I 3 + I 21 = I 3 + I 16 , I 4 Y = I 4 + I 22 = I 4 + I 17 , I 5 Y = I 5 + I 23 = I 5 + I 10 , I 6 Y = I 6 + I 24 = I 6 + I 11 , I 7 Y = I 7 + I 25 = I 7 + I 12 , I 8 Y = I 8 + I 26 = I 8 + I 13 , I 9 Y = I 9 + I 27 = I 9 + I 14 .
φ 1 , 0 = 2 ( I 2 I 6 + I 11 I 15 ) + 2 2 ( I 3 I 7 + I 12 I 16 ) + 2 ( I 4 I 8 + I 13 - I 17 ) 2 ( I 2 I 6 + I 11 I 15 ) 2 ( I 1 2 I 5 + I 9 + 2 I 10 2 I 14 ) + 2 ( I 4 I 8 + I 13 I 17 ) ,
φ 0 , 1 = 2 ( I 2 I 6 I 11 + I 15 ) 2 2 ( I 3 I 7 I 12 + I 16 ) + 2 ( I 4 I 8 I 13 + I 17 ) 2 ( I 2 I 6 I 11 + I 15 ) 2 ( I 1 2 I 5 + I 9 2 I 10 + 2 I 14 ) 2 ( I 4 I 8 I 13 + I 17 ) ,

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