Abstract

The resolution of the Wölter mirror, which is utilized as an objective in soft-x-ray microscopes, is limited by fabrication errors. We studied the relation between fabrication errors and imaging performance of the Wölter mirror to determine how this performance could be improved. Figure errors, which are characterized by low spatial frequency, were analyzed by ray tracing, and surface roughness, characterized by high spatial frequency, was analyzed by modified ray tracing. Modified ray tracing was based on ray tracing but took scattering into account. The results of these analyses were compared with experimental data. As a result, we obtained a simple and practical fabricating tolerance criterion that may be employed to obtain higher Wölter mirror resolution. Additionally, we discuss problems in current Wölter mirror fabrication techniques and the changes that might be made in both the design and the fabrication process to improve imaging performance.

© 1998 Optical Society of America

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  1. H. Wölter, “Spiegelsysteme streifenden Einfalls als abbildende Optiken für Röntgenstrahlen,” Ann. Phys. 10, 94–114 (1952).
    [CrossRef]
  2. H. Wölter, “Verallgemeinerte Schwarzschildsche Spiegelsysteme streifender Reflexion als Optiken für Röntgenstrahlen,” Ann. Phys. 10, 286–295 (1952).
    [CrossRef]
  3. A. Franks, B. Gale, “Grazing incidence optics for x-ray microscopy,” in X-ray Microscopy, G. Schmahl, D. Rudolph, eds. (Springer-Verlag, Berlin, 1984), pp. 129–138.
    [CrossRef]
  4. S. Aoki, M. Shiozawa, K. Kamigaki, H. Hashimoto, M. Kokaji, Y. Setsuhara, H. Azechi, M. Yamanaka, T. Yamanaka, Y. Izawa, C. Yamanaka, “Imaging characteristics of a replicated Wolter type I x-ray mirror designed for laser plasma diagnostics,” Jpn. J. Appl. Phys. 26, 952–954 (1987).
    [CrossRef]
  5. K. Ninomiya, K. Honda, S. Aoki, S. Nishimatsu, K. Suzuki, “Fabrication of an axisymmetric Wolter type I mirror with a gold deposited reflecting surface,” Jpn. J. Appl. Phys. 28, 2303–2308 (1989).
    [CrossRef]
  6. S. Inoue, Y. Ogawa, K. Ueda, M. Sumiya, T. Takigawa, S. Aoki, “A soft x-ray microscope using an imaging detector,” Jpn. J. Appl. Phys. 29, L176–L178 (1990).
    [CrossRef]
  7. T. Onuki, K. Sugisaki, S. Aoki, “Fabrication of Wolter type I mirror for soft x-ray,” in International Symposium on Optical Fabrication, Testing, and Surface Evaluation, J. Tsujiuchi, ed., Proc. SPIE1720, 258–263 (1992).
    [CrossRef]
  8. S. Aoki, T. Ogata, S. Sudo, T. Onuki, “Sub-100 nm-resolution grazing incidence soft x-ray microscope with a laser-produced plasma source,” Jpn. J. Appl. Phys. 31, 3477–3480 (1992).
    [CrossRef]
  9. A. Franks, B. Gale, K. Lindsey, D. J. Pugh, C. J. Robbie, M. Stedman, “Optical components for x-ray microscopy,” Ann. N.Y. Acad. Sci. 347, 167–187 (1980).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  21. Y. Uda, T. Onuki, K. Kamigaki, T. Kato, H. Hashimoto, “Ultra-precision CNC machine for grinding, turning and measuring aspheric components,” Precis. Eng. 17, 225–229 (1985).
    [CrossRef]
  22. Y. Tsusaka, H. Suzuki, K. Yamashita, H. Kunieda, Y. Tawara, Y. Ogasaka, Y. Uchibori, H. Honda, M. Itoh, H. Awaki, H. Tsunemi, K. Hayashida, S. Nomoto, M. Wada, E. Miyata, P. J. Serlemitsos, L. Jalota, Y. Soong, “Characterization of the advanced satellite for cosmology and astrophysics x-ray telescope: preflight calibration and ray tracing,” Appl. Opt. 34, 4848–4856 (1995).
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  23. J. E. Harvey, E. C. Moran, W. P. Zmek, “Transfer function characterization of grazing incidence optical systems,” Appl. Opt. 27, 1527–1533 (1988).
    [CrossRef] [PubMed]
  24. J. E. Harvey, “Chapter 11: x-ray optics,” in Handbook of Optics Volume II: Devices, Measurements and Properties, M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, New York, 1996).

1995 (1)

1993 (1)

Y. Iketaki, Y. Horikawa, K. Nagai, S. Mochimaru, Y. Ohta, H. Kamijou, M. Shibuya, “Measurement of knife-edge responses of a Schwarzschild x-ray objective,” Jpn. J. Appl. Phys. 32, 1837–1841 (1993).
[CrossRef]

1992 (1)

S. Aoki, T. Ogata, S. Sudo, T. Onuki, “Sub-100 nm-resolution grazing incidence soft x-ray microscope with a laser-produced plasma source,” Jpn. J. Appl. Phys. 31, 3477–3480 (1992).
[CrossRef]

1990 (1)

S. Inoue, Y. Ogawa, K. Ueda, M. Sumiya, T. Takigawa, S. Aoki, “A soft x-ray microscope using an imaging detector,” Jpn. J. Appl. Phys. 29, L176–L178 (1990).
[CrossRef]

1989 (2)

K. Ninomiya, K. Honda, S. Aoki, S. Nishimatsu, K. Suzuki, “Fabrication of an axisymmetric Wolter type I mirror with a gold deposited reflecting surface,” Jpn. J. Appl. Phys. 28, 2303–2308 (1989).
[CrossRef]

J. A. Trail, R. L. Byer, “Compact scanning soft-x-ray microscope using a laser-produced plasma source and normal-incidence multilayer mirrors,” Opt. Lett. 14, 539–541 (1989).
[CrossRef] [PubMed]

1988 (1)

1987 (1)

S. Aoki, M. Shiozawa, K. Kamigaki, H. Hashimoto, M. Kokaji, Y. Setsuhara, H. Azechi, M. Yamanaka, T. Yamanaka, Y. Izawa, C. Yamanaka, “Imaging characteristics of a replicated Wolter type I x-ray mirror designed for laser plasma diagnostics,” Jpn. J. Appl. Phys. 26, 952–954 (1987).
[CrossRef]

1986 (1)

H. Kunieda, S. Hayakawa, T. Hirano, T. Kii, F. Nagase, N. Sato, Y. Tawara, F. Makino, K. Yamashita, “Roughness measurement of x-ray mirror surfaces,” Jpn. J. Appl. Phys. 25, 1292–1299 (1986).
[CrossRef]

1985 (1)

Y. Uda, T. Onuki, K. Kamigaki, T. Kato, H. Hashimoto, “Ultra-precision CNC machine for grinding, turning and measuring aspheric components,” Precis. Eng. 17, 225–229 (1985).
[CrossRef]

1984 (1)

K. Lindsey, “The attainable limits in x-ray mirror fabrication,” Nucl. Instrum. Methods Phys. Res. 221, 14–19 (1984).
[CrossRef]

1981 (1)

R. H. Price, “X-ray microscopy using grazing incidence reflection optics,” AIP Conf. Proc. 75, 189–199 (1981).
[CrossRef]

1980 (1)

A. Franks, B. Gale, K. Lindsey, D. J. Pugh, C. J. Robbie, M. Stedman, “Optical components for x-ray microscopy,” Ann. N.Y. Acad. Sci. 347, 167–187 (1980).
[CrossRef]

1978 (1)

1977 (1)

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Measurement of the finish of diamond-turned metal surfaces,” Opt. Eng. 16, 360–374 (1977).
[CrossRef]

1952 (2)

H. Wölter, “Spiegelsysteme streifenden Einfalls als abbildende Optiken für Röntgenstrahlen,” Ann. Phys. 10, 94–114 (1952).
[CrossRef]

H. Wölter, “Verallgemeinerte Schwarzschildsche Spiegelsysteme streifender Reflexion als Optiken für Röntgenstrahlen,” Ann. Phys. 10, 286–295 (1952).
[CrossRef]

Aoki, S.

S. Aoki, T. Ogata, S. Sudo, T. Onuki, “Sub-100 nm-resolution grazing incidence soft x-ray microscope with a laser-produced plasma source,” Jpn. J. Appl. Phys. 31, 3477–3480 (1992).
[CrossRef]

S. Inoue, Y. Ogawa, K. Ueda, M. Sumiya, T. Takigawa, S. Aoki, “A soft x-ray microscope using an imaging detector,” Jpn. J. Appl. Phys. 29, L176–L178 (1990).
[CrossRef]

K. Ninomiya, K. Honda, S. Aoki, S. Nishimatsu, K. Suzuki, “Fabrication of an axisymmetric Wolter type I mirror with a gold deposited reflecting surface,” Jpn. J. Appl. Phys. 28, 2303–2308 (1989).
[CrossRef]

S. Aoki, M. Shiozawa, K. Kamigaki, H. Hashimoto, M. Kokaji, Y. Setsuhara, H. Azechi, M. Yamanaka, T. Yamanaka, Y. Izawa, C. Yamanaka, “Imaging characteristics of a replicated Wolter type I x-ray mirror designed for laser plasma diagnostics,” Jpn. J. Appl. Phys. 26, 952–954 (1987).
[CrossRef]

Y. Sakayanagi, S. Aoki, “Soft x-ray imaging with toroidal mirrors,” Appl. Opt. 17, 601–603 (1978).
[CrossRef] [PubMed]

T. Onuki, K. Sugisaki, S. Aoki, “Fabrication of Wolter type I mirror for soft x-ray,” in International Symposium on Optical Fabrication, Testing, and Surface Evaluation, J. Tsujiuchi, ed., Proc. SPIE1720, 258–263 (1992).
[CrossRef]

Awaki, H.

Azechi, H.

S. Aoki, M. Shiozawa, K. Kamigaki, H. Hashimoto, M. Kokaji, Y. Setsuhara, H. Azechi, M. Yamanaka, T. Yamanaka, Y. Izawa, C. Yamanaka, “Imaging characteristics of a replicated Wolter type I x-ray mirror designed for laser plasma diagnostics,” Jpn. J. Appl. Phys. 26, 952–954 (1987).
[CrossRef]

Born, M.

M. Born, E. Wolf, “9.3 tolerance conditions for primary aberrations,” in Principles in Optics, 4th ed. (Pergamon, Oxford, 1970).

Byer, R. L.

Church, E. L.

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Measurement of the finish of diamond-turned metal surfaces,” Opt. Eng. 16, 360–374 (1977).
[CrossRef]

Franks, A.

A. Franks, B. Gale, K. Lindsey, D. J. Pugh, C. J. Robbie, M. Stedman, “Optical components for x-ray microscopy,” Ann. N.Y. Acad. Sci. 347, 167–187 (1980).
[CrossRef]

A. Franks, B. Gale, “Grazing incidence optics for x-ray microscopy,” in X-ray Microscopy, G. Schmahl, D. Rudolph, eds. (Springer-Verlag, Berlin, 1984), pp. 129–138.
[CrossRef]

Gale, B.

A. Franks, B. Gale, K. Lindsey, D. J. Pugh, C. J. Robbie, M. Stedman, “Optical components for x-ray microscopy,” Ann. N.Y. Acad. Sci. 347, 167–187 (1980).
[CrossRef]

A. Franks, B. Gale, “Grazing incidence optics for x-ray microscopy,” in X-ray Microscopy, G. Schmahl, D. Rudolph, eds. (Springer-Verlag, Berlin, 1984), pp. 129–138.
[CrossRef]

Harvey, J. E.

J. E. Harvey, E. C. Moran, W. P. Zmek, “Transfer function characterization of grazing incidence optical systems,” Appl. Opt. 27, 1527–1533 (1988).
[CrossRef] [PubMed]

J. E. Harvey, “Chapter 11: x-ray optics,” in Handbook of Optics Volume II: Devices, Measurements and Properties, M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, New York, 1996).

Hashimoto, H.

S. Aoki, M. Shiozawa, K. Kamigaki, H. Hashimoto, M. Kokaji, Y. Setsuhara, H. Azechi, M. Yamanaka, T. Yamanaka, Y. Izawa, C. Yamanaka, “Imaging characteristics of a replicated Wolter type I x-ray mirror designed for laser plasma diagnostics,” Jpn. J. Appl. Phys. 26, 952–954 (1987).
[CrossRef]

Y. Uda, T. Onuki, K. Kamigaki, T. Kato, H. Hashimoto, “Ultra-precision CNC machine for grinding, turning and measuring aspheric components,” Precis. Eng. 17, 225–229 (1985).
[CrossRef]

Hayakawa, S.

H. Kunieda, S. Hayakawa, T. Hirano, T. Kii, F. Nagase, N. Sato, Y. Tawara, F. Makino, K. Yamashita, “Roughness measurement of x-ray mirror surfaces,” Jpn. J. Appl. Phys. 25, 1292–1299 (1986).
[CrossRef]

Hayashida, K.

Hirai, N.

K. Kinoshita, T. Matsumura, Y. Inagaki, N. Hirai, M. Sugiyama, H. Kihara, N. Watanabe, Y. Shimanuki, “Electronic zooming TV readout system for an x-ray microscope,” in Soft X-Ray Microscopy, C. J. Jacobsen, J. E. Trebes, eds., Proc. SPIE1741, 287–293 (1992).
[CrossRef]

Hirano, T.

H. Kunieda, S. Hayakawa, T. Hirano, T. Kii, F. Nagase, N. Sato, Y. Tawara, F. Makino, K. Yamashita, “Roughness measurement of x-ray mirror surfaces,” Jpn. J. Appl. Phys. 25, 1292–1299 (1986).
[CrossRef]

Honda, H.

Honda, K.

K. Ninomiya, K. Honda, S. Aoki, S. Nishimatsu, K. Suzuki, “Fabrication of an axisymmetric Wolter type I mirror with a gold deposited reflecting surface,” Jpn. J. Appl. Phys. 28, 2303–2308 (1989).
[CrossRef]

Horikawa, Y.

Y. Iketaki, Y. Horikawa, K. Nagai, S. Mochimaru, Y. Ohta, H. Kamijou, M. Shibuya, “Measurement of knife-edge responses of a Schwarzschild x-ray objective,” Jpn. J. Appl. Phys. 32, 1837–1841 (1993).
[CrossRef]

Iketaki, Y.

Y. Iketaki, Y. Horikawa, K. Nagai, S. Mochimaru, Y. Ohta, H. Kamijou, M. Shibuya, “Measurement of knife-edge responses of a Schwarzschild x-ray objective,” Jpn. J. Appl. Phys. 32, 1837–1841 (1993).
[CrossRef]

Inagaki, Y.

K. Kinoshita, T. Matsumura, Y. Inagaki, N. Hirai, M. Sugiyama, H. Kihara, N. Watanabe, Y. Shimanuki, “Electronic zooming TV readout system for an x-ray microscope,” in Soft X-Ray Microscopy, C. J. Jacobsen, J. E. Trebes, eds., Proc. SPIE1741, 287–293 (1992).
[CrossRef]

Inoue, S.

S. Inoue, Y. Ogawa, K. Ueda, M. Sumiya, T. Takigawa, S. Aoki, “A soft x-ray microscope using an imaging detector,” Jpn. J. Appl. Phys. 29, L176–L178 (1990).
[CrossRef]

Itoh, M.

Izawa, Y.

S. Aoki, M. Shiozawa, K. Kamigaki, H. Hashimoto, M. Kokaji, Y. Setsuhara, H. Azechi, M. Yamanaka, T. Yamanaka, Y. Izawa, C. Yamanaka, “Imaging characteristics of a replicated Wolter type I x-ray mirror designed for laser plasma diagnostics,” Jpn. J. Appl. Phys. 26, 952–954 (1987).
[CrossRef]

Jalota, L.

Jenkinson, H. A.

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Measurement of the finish of diamond-turned metal surfaces,” Opt. Eng. 16, 360–374 (1977).
[CrossRef]

Kamigaki, K.

S. Aoki, M. Shiozawa, K. Kamigaki, H. Hashimoto, M. Kokaji, Y. Setsuhara, H. Azechi, M. Yamanaka, T. Yamanaka, Y. Izawa, C. Yamanaka, “Imaging characteristics of a replicated Wolter type I x-ray mirror designed for laser plasma diagnostics,” Jpn. J. Appl. Phys. 26, 952–954 (1987).
[CrossRef]

Y. Uda, T. Onuki, K. Kamigaki, T. Kato, H. Hashimoto, “Ultra-precision CNC machine for grinding, turning and measuring aspheric components,” Precis. Eng. 17, 225–229 (1985).
[CrossRef]

Kamijou, H.

Y. Iketaki, Y. Horikawa, K. Nagai, S. Mochimaru, Y. Ohta, H. Kamijou, M. Shibuya, “Measurement of knife-edge responses of a Schwarzschild x-ray objective,” Jpn. J. Appl. Phys. 32, 1837–1841 (1993).
[CrossRef]

Kato, T.

Y. Uda, T. Onuki, K. Kamigaki, T. Kato, H. Hashimoto, “Ultra-precision CNC machine for grinding, turning and measuring aspheric components,” Precis. Eng. 17, 225–229 (1985).
[CrossRef]

Kihara, H.

K. Kinoshita, T. Matsumura, Y. Inagaki, N. Hirai, M. Sugiyama, H. Kihara, N. Watanabe, Y. Shimanuki, “Electronic zooming TV readout system for an x-ray microscope,” in Soft X-Ray Microscopy, C. J. Jacobsen, J. E. Trebes, eds., Proc. SPIE1741, 287–293 (1992).
[CrossRef]

Kii, T.

H. Kunieda, S. Hayakawa, T. Hirano, T. Kii, F. Nagase, N. Sato, Y. Tawara, F. Makino, K. Yamashita, “Roughness measurement of x-ray mirror surfaces,” Jpn. J. Appl. Phys. 25, 1292–1299 (1986).
[CrossRef]

Kinoshita, K.

K. Kinoshita, T. Matsumura, Y. Inagaki, N. Hirai, M. Sugiyama, H. Kihara, N. Watanabe, Y. Shimanuki, “Electronic zooming TV readout system for an x-ray microscope,” in Soft X-Ray Microscopy, C. J. Jacobsen, J. E. Trebes, eds., Proc. SPIE1741, 287–293 (1992).
[CrossRef]

Kokaji, M.

S. Aoki, M. Shiozawa, K. Kamigaki, H. Hashimoto, M. Kokaji, Y. Setsuhara, H. Azechi, M. Yamanaka, T. Yamanaka, Y. Izawa, C. Yamanaka, “Imaging characteristics of a replicated Wolter type I x-ray mirror designed for laser plasma diagnostics,” Jpn. J. Appl. Phys. 26, 952–954 (1987).
[CrossRef]

Kunieda, H.

Lindsey, K.

K. Lindsey, “The attainable limits in x-ray mirror fabrication,” Nucl. Instrum. Methods Phys. Res. 221, 14–19 (1984).
[CrossRef]

A. Franks, B. Gale, K. Lindsey, D. J. Pugh, C. J. Robbie, M. Stedman, “Optical components for x-ray microscopy,” Ann. N.Y. Acad. Sci. 347, 167–187 (1980).
[CrossRef]

Makino, F.

H. Kunieda, S. Hayakawa, T. Hirano, T. Kii, F. Nagase, N. Sato, Y. Tawara, F. Makino, K. Yamashita, “Roughness measurement of x-ray mirror surfaces,” Jpn. J. Appl. Phys. 25, 1292–1299 (1986).
[CrossRef]

Matsumura, T.

K. Kinoshita, T. Matsumura, Y. Inagaki, N. Hirai, M. Sugiyama, H. Kihara, N. Watanabe, Y. Shimanuki, “Electronic zooming TV readout system for an x-ray microscope,” in Soft X-Ray Microscopy, C. J. Jacobsen, J. E. Trebes, eds., Proc. SPIE1741, 287–293 (1992).
[CrossRef]

Miyata, E.

Mochimaru, S.

Y. Iketaki, Y. Horikawa, K. Nagai, S. Mochimaru, Y. Ohta, H. Kamijou, M. Shibuya, “Measurement of knife-edge responses of a Schwarzschild x-ray objective,” Jpn. J. Appl. Phys. 32, 1837–1841 (1993).
[CrossRef]

Moran, E. C.

Nagai, K.

Y. Iketaki, Y. Horikawa, K. Nagai, S. Mochimaru, Y. Ohta, H. Kamijou, M. Shibuya, “Measurement of knife-edge responses of a Schwarzschild x-ray objective,” Jpn. J. Appl. Phys. 32, 1837–1841 (1993).
[CrossRef]

Nagase, F.

H. Kunieda, S. Hayakawa, T. Hirano, T. Kii, F. Nagase, N. Sato, Y. Tawara, F. Makino, K. Yamashita, “Roughness measurement of x-ray mirror surfaces,” Jpn. J. Appl. Phys. 25, 1292–1299 (1986).
[CrossRef]

Ninomiya, K.

K. Ninomiya, K. Honda, S. Aoki, S. Nishimatsu, K. Suzuki, “Fabrication of an axisymmetric Wolter type I mirror with a gold deposited reflecting surface,” Jpn. J. Appl. Phys. 28, 2303–2308 (1989).
[CrossRef]

Nishimatsu, S.

K. Ninomiya, K. Honda, S. Aoki, S. Nishimatsu, K. Suzuki, “Fabrication of an axisymmetric Wolter type I mirror with a gold deposited reflecting surface,” Jpn. J. Appl. Phys. 28, 2303–2308 (1989).
[CrossRef]

Nomoto, S.

Ogasaka, Y.

Ogata, T.

S. Aoki, T. Ogata, S. Sudo, T. Onuki, “Sub-100 nm-resolution grazing incidence soft x-ray microscope with a laser-produced plasma source,” Jpn. J. Appl. Phys. 31, 3477–3480 (1992).
[CrossRef]

Ogawa, Y.

S. Inoue, Y. Ogawa, K. Ueda, M. Sumiya, T. Takigawa, S. Aoki, “A soft x-ray microscope using an imaging detector,” Jpn. J. Appl. Phys. 29, L176–L178 (1990).
[CrossRef]

Ohta, Y.

Y. Iketaki, Y. Horikawa, K. Nagai, S. Mochimaru, Y. Ohta, H. Kamijou, M. Shibuya, “Measurement of knife-edge responses of a Schwarzschild x-ray objective,” Jpn. J. Appl. Phys. 32, 1837–1841 (1993).
[CrossRef]

Onuki, T.

S. Aoki, T. Ogata, S. Sudo, T. Onuki, “Sub-100 nm-resolution grazing incidence soft x-ray microscope with a laser-produced plasma source,” Jpn. J. Appl. Phys. 31, 3477–3480 (1992).
[CrossRef]

Y. Uda, T. Onuki, K. Kamigaki, T. Kato, H. Hashimoto, “Ultra-precision CNC machine for grinding, turning and measuring aspheric components,” Precis. Eng. 17, 225–229 (1985).
[CrossRef]

T. Onuki, K. Sugisaki, S. Aoki, “Fabrication of Wolter type I mirror for soft x-ray,” in International Symposium on Optical Fabrication, Testing, and Surface Evaluation, J. Tsujiuchi, ed., Proc. SPIE1720, 258–263 (1992).
[CrossRef]

Price, R. H.

R. H. Price, “X-ray microscopy using grazing incidence reflection optics,” AIP Conf. Proc. 75, 189–199 (1981).
[CrossRef]

Pugh, D. J.

A. Franks, B. Gale, K. Lindsey, D. J. Pugh, C. J. Robbie, M. Stedman, “Optical components for x-ray microscopy,” Ann. N.Y. Acad. Sci. 347, 167–187 (1980).
[CrossRef]

Robbie, C. J.

A. Franks, B. Gale, K. Lindsey, D. J. Pugh, C. J. Robbie, M. Stedman, “Optical components for x-ray microscopy,” Ann. N.Y. Acad. Sci. 347, 167–187 (1980).
[CrossRef]

Sakayanagi, Y.

Sato, N.

H. Kunieda, S. Hayakawa, T. Hirano, T. Kii, F. Nagase, N. Sato, Y. Tawara, F. Makino, K. Yamashita, “Roughness measurement of x-ray mirror surfaces,” Jpn. J. Appl. Phys. 25, 1292–1299 (1986).
[CrossRef]

Serlemitsos, P. J.

Setsuhara, Y.

S. Aoki, M. Shiozawa, K. Kamigaki, H. Hashimoto, M. Kokaji, Y. Setsuhara, H. Azechi, M. Yamanaka, T. Yamanaka, Y. Izawa, C. Yamanaka, “Imaging characteristics of a replicated Wolter type I x-ray mirror designed for laser plasma diagnostics,” Jpn. J. Appl. Phys. 26, 952–954 (1987).
[CrossRef]

Shibuya, M.

Y. Iketaki, Y. Horikawa, K. Nagai, S. Mochimaru, Y. Ohta, H. Kamijou, M. Shibuya, “Measurement of knife-edge responses of a Schwarzschild x-ray objective,” Jpn. J. Appl. Phys. 32, 1837–1841 (1993).
[CrossRef]

Shimanuki, Y.

K. Kinoshita, T. Matsumura, Y. Inagaki, N. Hirai, M. Sugiyama, H. Kihara, N. Watanabe, Y. Shimanuki, “Electronic zooming TV readout system for an x-ray microscope,” in Soft X-Ray Microscopy, C. J. Jacobsen, J. E. Trebes, eds., Proc. SPIE1741, 287–293 (1992).
[CrossRef]

Shiozawa, M.

S. Aoki, M. Shiozawa, K. Kamigaki, H. Hashimoto, M. Kokaji, Y. Setsuhara, H. Azechi, M. Yamanaka, T. Yamanaka, Y. Izawa, C. Yamanaka, “Imaging characteristics of a replicated Wolter type I x-ray mirror designed for laser plasma diagnostics,” Jpn. J. Appl. Phys. 26, 952–954 (1987).
[CrossRef]

Soong, Y.

Stedman, M.

A. Franks, B. Gale, K. Lindsey, D. J. Pugh, C. J. Robbie, M. Stedman, “Optical components for x-ray microscopy,” Ann. N.Y. Acad. Sci. 347, 167–187 (1980).
[CrossRef]

Sudo, S.

S. Aoki, T. Ogata, S. Sudo, T. Onuki, “Sub-100 nm-resolution grazing incidence soft x-ray microscope with a laser-produced plasma source,” Jpn. J. Appl. Phys. 31, 3477–3480 (1992).
[CrossRef]

Sugisaki, K.

T. Onuki, K. Sugisaki, S. Aoki, “Fabrication of Wolter type I mirror for soft x-ray,” in International Symposium on Optical Fabrication, Testing, and Surface Evaluation, J. Tsujiuchi, ed., Proc. SPIE1720, 258–263 (1992).
[CrossRef]

Sugiyama, M.

K. Kinoshita, T. Matsumura, Y. Inagaki, N. Hirai, M. Sugiyama, H. Kihara, N. Watanabe, Y. Shimanuki, “Electronic zooming TV readout system for an x-ray microscope,” in Soft X-Ray Microscopy, C. J. Jacobsen, J. E. Trebes, eds., Proc. SPIE1741, 287–293 (1992).
[CrossRef]

Sumiya, M.

S. Inoue, Y. Ogawa, K. Ueda, M. Sumiya, T. Takigawa, S. Aoki, “A soft x-ray microscope using an imaging detector,” Jpn. J. Appl. Phys. 29, L176–L178 (1990).
[CrossRef]

Suzuki, H.

Suzuki, K.

K. Ninomiya, K. Honda, S. Aoki, S. Nishimatsu, K. Suzuki, “Fabrication of an axisymmetric Wolter type I mirror with a gold deposited reflecting surface,” Jpn. J. Appl. Phys. 28, 2303–2308 (1989).
[CrossRef]

Suzuki, Y.

F. Uchida, Y. Suzuki, “Fabrication and testing of grazing incidence mirrors for hard x-rays,” in International Symposium on Optical Fabrication, Testing, and Surface Evaluation, J. Tsujiuchi, ed., Proc. SPIE1720, 264–271 (1992).
[CrossRef]

Takigawa, T.

S. Inoue, Y. Ogawa, K. Ueda, M. Sumiya, T. Takigawa, S. Aoki, “A soft x-ray microscope using an imaging detector,” Jpn. J. Appl. Phys. 29, L176–L178 (1990).
[CrossRef]

Tawara, Y.

Trail, J. A.

Tsunemi, H.

Tsusaka, Y.

Uchibori, Y.

Uchida, F.

F. Uchida, Y. Suzuki, “Fabrication and testing of grazing incidence mirrors for hard x-rays,” in International Symposium on Optical Fabrication, Testing, and Surface Evaluation, J. Tsujiuchi, ed., Proc. SPIE1720, 264–271 (1992).
[CrossRef]

Uda, Y.

Y. Uda, T. Onuki, K. Kamigaki, T. Kato, H. Hashimoto, “Ultra-precision CNC machine for grinding, turning and measuring aspheric components,” Precis. Eng. 17, 225–229 (1985).
[CrossRef]

Ueda, K.

S. Inoue, Y. Ogawa, K. Ueda, M. Sumiya, T. Takigawa, S. Aoki, “A soft x-ray microscope using an imaging detector,” Jpn. J. Appl. Phys. 29, L176–L178 (1990).
[CrossRef]

Wada, M.

Watanabe, N.

K. Kinoshita, T. Matsumura, Y. Inagaki, N. Hirai, M. Sugiyama, H. Kihara, N. Watanabe, Y. Shimanuki, “Electronic zooming TV readout system for an x-ray microscope,” in Soft X-Ray Microscopy, C. J. Jacobsen, J. E. Trebes, eds., Proc. SPIE1741, 287–293 (1992).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, “9.3 tolerance conditions for primary aberrations,” in Principles in Optics, 4th ed. (Pergamon, Oxford, 1970).

Wölter, H.

H. Wölter, “Spiegelsysteme streifenden Einfalls als abbildende Optiken für Röntgenstrahlen,” Ann. Phys. 10, 94–114 (1952).
[CrossRef]

H. Wölter, “Verallgemeinerte Schwarzschildsche Spiegelsysteme streifender Reflexion als Optiken für Röntgenstrahlen,” Ann. Phys. 10, 286–295 (1952).
[CrossRef]

Yamanaka, C.

S. Aoki, M. Shiozawa, K. Kamigaki, H. Hashimoto, M. Kokaji, Y. Setsuhara, H. Azechi, M. Yamanaka, T. Yamanaka, Y. Izawa, C. Yamanaka, “Imaging characteristics of a replicated Wolter type I x-ray mirror designed for laser plasma diagnostics,” Jpn. J. Appl. Phys. 26, 952–954 (1987).
[CrossRef]

Yamanaka, M.

S. Aoki, M. Shiozawa, K. Kamigaki, H. Hashimoto, M. Kokaji, Y. Setsuhara, H. Azechi, M. Yamanaka, T. Yamanaka, Y. Izawa, C. Yamanaka, “Imaging characteristics of a replicated Wolter type I x-ray mirror designed for laser plasma diagnostics,” Jpn. J. Appl. Phys. 26, 952–954 (1987).
[CrossRef]

Yamanaka, T.

S. Aoki, M. Shiozawa, K. Kamigaki, H. Hashimoto, M. Kokaji, Y. Setsuhara, H. Azechi, M. Yamanaka, T. Yamanaka, Y. Izawa, C. Yamanaka, “Imaging characteristics of a replicated Wolter type I x-ray mirror designed for laser plasma diagnostics,” Jpn. J. Appl. Phys. 26, 952–954 (1987).
[CrossRef]

Yamashita, K.

Zavada, J. M.

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Measurement of the finish of diamond-turned metal surfaces,” Opt. Eng. 16, 360–374 (1977).
[CrossRef]

Zehnpfennig, T. F.

T. F. Zehnpfennig, “Figure tolerancing study of an axisymmetric x-ray microscope,” in Applications of Thin Film Multilayered Structures to Figured X-Ray Optics, G. F. Marshall, ed., Proc. SPIE563, 72–80 (1985).
[CrossRef]

Zmek, W. P.

AIP Conf. Proc. (1)

R. H. Price, “X-ray microscopy using grazing incidence reflection optics,” AIP Conf. Proc. 75, 189–199 (1981).
[CrossRef]

Ann. N.Y. Acad. Sci. (1)

A. Franks, B. Gale, K. Lindsey, D. J. Pugh, C. J. Robbie, M. Stedman, “Optical components for x-ray microscopy,” Ann. N.Y. Acad. Sci. 347, 167–187 (1980).
[CrossRef]

Ann. Phys. (2)

H. Wölter, “Spiegelsysteme streifenden Einfalls als abbildende Optiken für Röntgenstrahlen,” Ann. Phys. 10, 94–114 (1952).
[CrossRef]

H. Wölter, “Verallgemeinerte Schwarzschildsche Spiegelsysteme streifender Reflexion als Optiken für Röntgenstrahlen,” Ann. Phys. 10, 286–295 (1952).
[CrossRef]

Appl. Opt. (3)

Jpn. J. Appl. Phys. (6)

Y. Iketaki, Y. Horikawa, K. Nagai, S. Mochimaru, Y. Ohta, H. Kamijou, M. Shibuya, “Measurement of knife-edge responses of a Schwarzschild x-ray objective,” Jpn. J. Appl. Phys. 32, 1837–1841 (1993).
[CrossRef]

H. Kunieda, S. Hayakawa, T. Hirano, T. Kii, F. Nagase, N. Sato, Y. Tawara, F. Makino, K. Yamashita, “Roughness measurement of x-ray mirror surfaces,” Jpn. J. Appl. Phys. 25, 1292–1299 (1986).
[CrossRef]

S. Aoki, T. Ogata, S. Sudo, T. Onuki, “Sub-100 nm-resolution grazing incidence soft x-ray microscope with a laser-produced plasma source,” Jpn. J. Appl. Phys. 31, 3477–3480 (1992).
[CrossRef]

S. Aoki, M. Shiozawa, K. Kamigaki, H. Hashimoto, M. Kokaji, Y. Setsuhara, H. Azechi, M. Yamanaka, T. Yamanaka, Y. Izawa, C. Yamanaka, “Imaging characteristics of a replicated Wolter type I x-ray mirror designed for laser plasma diagnostics,” Jpn. J. Appl. Phys. 26, 952–954 (1987).
[CrossRef]

K. Ninomiya, K. Honda, S. Aoki, S. Nishimatsu, K. Suzuki, “Fabrication of an axisymmetric Wolter type I mirror with a gold deposited reflecting surface,” Jpn. J. Appl. Phys. 28, 2303–2308 (1989).
[CrossRef]

S. Inoue, Y. Ogawa, K. Ueda, M. Sumiya, T. Takigawa, S. Aoki, “A soft x-ray microscope using an imaging detector,” Jpn. J. Appl. Phys. 29, L176–L178 (1990).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. (1)

K. Lindsey, “The attainable limits in x-ray mirror fabrication,” Nucl. Instrum. Methods Phys. Res. 221, 14–19 (1984).
[CrossRef]

Opt. Eng. (1)

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Measurement of the finish of diamond-turned metal surfaces,” Opt. Eng. 16, 360–374 (1977).
[CrossRef]

Opt. Lett. (1)

Precis. Eng. (1)

Y. Uda, T. Onuki, K. Kamigaki, T. Kato, H. Hashimoto, “Ultra-precision CNC machine for grinding, turning and measuring aspheric components,” Precis. Eng. 17, 225–229 (1985).
[CrossRef]

Other (7)

K. Kinoshita, T. Matsumura, Y. Inagaki, N. Hirai, M. Sugiyama, H. Kihara, N. Watanabe, Y. Shimanuki, “Electronic zooming TV readout system for an x-ray microscope,” in Soft X-Ray Microscopy, C. J. Jacobsen, J. E. Trebes, eds., Proc. SPIE1741, 287–293 (1992).
[CrossRef]

J. E. Harvey, “Chapter 11: x-ray optics,” in Handbook of Optics Volume II: Devices, Measurements and Properties, M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, New York, 1996).

M. Born, E. Wolf, “9.3 tolerance conditions for primary aberrations,” in Principles in Optics, 4th ed. (Pergamon, Oxford, 1970).

F. Uchida, Y. Suzuki, “Fabrication and testing of grazing incidence mirrors for hard x-rays,” in International Symposium on Optical Fabrication, Testing, and Surface Evaluation, J. Tsujiuchi, ed., Proc. SPIE1720, 264–271 (1992).
[CrossRef]

T. F. Zehnpfennig, “Figure tolerancing study of an axisymmetric x-ray microscope,” in Applications of Thin Film Multilayered Structures to Figured X-Ray Optics, G. F. Marshall, ed., Proc. SPIE563, 72–80 (1985).
[CrossRef]

T. Onuki, K. Sugisaki, S. Aoki, “Fabrication of Wolter type I mirror for soft x-ray,” in International Symposium on Optical Fabrication, Testing, and Surface Evaluation, J. Tsujiuchi, ed., Proc. SPIE1720, 258–263 (1992).
[CrossRef]

A. Franks, B. Gale, “Grazing incidence optics for x-ray microscopy,” in X-ray Microscopy, G. Schmahl, D. Rudolph, eds. (Springer-Verlag, Berlin, 1984), pp. 129–138.
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Schematic diagram of our Wölter mirror. The magnification and grazing-incidence angles are M = 32 and θ = 40 mrad, respectively. This mirror was designed for 4.5-nm x rays.

Fig. 2
Fig. 2

Configuration and symbol expressions for figure error analysis.

Fig. 3
Fig. 3

Configuration and symbol expressions for the surface roughness analysis.

Fig. 4
Fig. 4

Schematic diagram of the evaluation system for x-ray imaging performance.

Fig. 5
Fig. 5

Resolution contour map for various amplitudes and frequencies of sine-wave errors obtained by ray-tracing analyses.

Fig. 6
Fig. 6

Figure error profile measured for our Wölter mirror.

Fig. 7
Fig. 7

Comparison of calculated and experimental results: (a) LSF obtained by ray tracing, (b) knife-edge profile obtained by ray tracing, (c) LSF obtained experimentally, and (d) knife-edge profile obtained experimentally.

Fig. 8
Fig. 8

Images of a line and space pattern obtained (a) by ray-tracing calculation, and (b) by experimental x-ray imaging. Both the line and the space widths equal 0.45 μm.

Fig. 9
Fig. 9

Schematic diagram of the reflectometer used in the scattering measurements.

Fig. 10
Fig. 10

Example of scattered and incident beam profiles experimentally obtained. (a) shows the complete profiles. (b) shows a magnification of the high angle region in which scattering measurements reached the detector noise level. These profiles were measured with a polished Pyrex glass sample at a grazing-incidence angle of 1.0°.

Fig. 11
Fig. 11

PSD functions derived from the scattering profiles. The curves correspond to the grazing-incidence angles of (I) 0.4°, (II) 1.0°, and (III) 2.4°, respectively. The rms values of the surface roughness calculated from the PSD function are also indicated.

Fig. 12
Fig. 12

Results obtained by modified ray tracing: (a) LSF, and (b) knife-edge profile.

Fig. 13
Fig. 13

Influence of scattering as seen in simulated images based on modified ray tracing: (a) perfect image uninfluenced by scattering, (b) image influenced by region III scattering, (c) image influenced by region II scattering, and (d) image influenced by region I scattering.

Fig. 14
Fig. 14

Relation between results derived from theoretical analyses (lines AB and CD) and the measured spectra of residual manufacturing errors.

Tables (1)

Tables Icon

Table 1 Summary of Our Theoretical and Experimental Analyses of the Effect of Scattering

Equations (17)

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ε z = n = 1 a n   sin n π z L + b n   cos n π z L = n = 1   a ν sin 2 π vz + ϕ ,
ν = 1 l = n 2 L .
Δ x = 2 Δ θ x f M ,
Δ θ x = d ε d z = 2 π ν a ν cos 2 π ν z .
Δ x = 2 π ν × a ν f M cos 2 π ν z .
- 62.8   μ rad     Δ θ     62.8   μ rad .
| Δ x | 2 × 2 Δ θ   f M 11   μ m .
σ < λ 14 1 2   sin   θ 1 2 = λ 28 2   sin   θ .
n λ = d cos   θ s - cos   θ i ,
θ s = θ i + Δ θ .
n λ = cos θ i + Δ θ s - cos   θ i ν .
Δ θ s = - λ ν sin   θ i .
Δ x = Δ θ s f M .
d I d θ s = 2 k 3 π   I R   sin   θ i sin 2   θ s   W p = 16 π 2 λ 3   I R   sin   θ i sin 2 θ i + Δ θ s W - 2 π   sin   θ λ   Δ θ s , k = 2 π / λ .
d I d θ s 16 π 2 λ 3   I R sin 3   θ i + 2   sin 2   θ i   cos   θ i Δ θ s W p .
δ = κ   ν a ν f M ,
a ν < δ M 9.3 ν f .

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