Abstract

The intensity flatness and wavefront shape in a coherent hard-x-ray beam totally reflected by flat mirrors that have surface bumps modeled by Gaussian functions were investigated by use of a wave-optical simulation code. Simulated results revealed the necessity for peak-to-valley height accuracy of better than 1 nm at a lateral resolution near 0.1 mm to remove high-contrast interference fringes and appreciable wavefront phase errors. Three mirrors that had different surface qualities were tested at the 1 km-long beam line at the SPring-8/Japan Synchrotron Radiation Research Institute. Interference fringes faded when the surface figure was corrected below the subnanometer level to a spatial resolution close to 0.1 mm, as indicated by the simulated results.

© 2005 Optical Society of America

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  1. T. Ishikawa, K. Tamasaku, M. Yabashi, S. Goto, Y. Tanaka, H. Yamazaki, K. Takeshita, H. Kimura, H. Ohashi, T. Matsushita, T. Ohata, “1 km beamline at SPring-8,” in Advances in X-Rays, A. K. Freund, T. Ishikawa, A. M. Khounsary, D. C. Mancini, A. G. Michette, S. Oestreich, eds., Proc. SPIE, 4145, 1–10 (2001).
  2. H. Kitamura, “Present status of SPring-8 insertion devices,” J. Synchrotron Radiat. 5, 184–188 (1998).
    [CrossRef]
  3. Y. Mori, K. Yamauchi, K. Yamamura, H. Mimura, A. Saito, H. Kishimoto, Y. Sekito, M. Kanaoka, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, “Development of plasma chemical vaporization machining and elastic emission machining systems for coherent hard x-ray optics,” in X-Ray Mirrors, Crystals, and Multilayers II, A. K. Freund, A. T. Macrander, T. Ishikawa, J. L. Woods, eds., Proc. SPIE4501, 30–42 (2001).
    [CrossRef]
  4. A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, Y. Mori, K. Yamauchi, A. Saito, “Deterministic retrieval of surface waviness by means of topography with coherent x-rays,” J. Synchrotron Radiat. 9, 223–228 (2002).
    [CrossRef] [PubMed]
  5. E. L. Church, P. Z. Takacs, “Prediction of mirror performance from laboratory measurements,” in X-Ray/EUV Optics for Astronomy and Microscopy, R. B. Hoover, ed., Proc. SPIE1160, 323–336 (1989).
    [CrossRef]
  6. E. L. Church, P. Z. Takacs, “Specification of glancing- and normal-incidence x-ray mirrors,” Opt. Eng. 34, 353–360 (1995).
    [CrossRef]
  7. J. Susini, “Design parameter for hard x-ray mirrors: the European Synchrotron Radiation Facility case,” Opt. Eng. 34, 361–376 (1995).
    [CrossRef]
  8. M. Born, E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1997).
  9. Y. Mori, K. Yamamura, Y. Sano, “Development of plasma chemical vaporization machining,” Rev. Sci. Instrum. 71, 4627–4632 (2000).
    [CrossRef]
  10. Y. Mori, K. Yamauchi, K. Yamamura, Y. Sano, “The study of fabrication of the X-ray mirror by numerically controlled plasma chemical vaporization machining: development of the machine for the x-ray mirror fabrication,” Rev. Sci. Instrum. 71, 4620–4626 (2000).
    [CrossRef]
  11. H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Plasma chemical vaporization machining (CVM) for fabrication of optics,” Jpn. J. Appl. Phys. 37, L894–L896 (1998).
    [CrossRef]
  12. H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Computer numerically controlled plasma chemical vaporization machining using a pipe electrode for optical fabrication,” Appl. Opt. 37, 5198–5210 (1998).
    [CrossRef]
  13. Y. Mori, K. Yamauchi, K. Endo, “Elastic emission machining,” Precis. Eng. 9, 123–128 (1987).
    [CrossRef]
  14. Y. Mori, K. Yamauchi, K. Endo, T. Ide, H. Toyota, K. Nishizawa, M. Hasegawa, “Observation of elastic emission machined surfaces by scanning tunneling microscopy,” J. Vac. Sci. Technol. A 8, 621–624 (1990).
    [CrossRef]
  15. Y. Mori, K. Yamauchi, K. Endo, “Mechanism of atomic removal in elastic emission machining,” Precis. Eng. 10, 24–28 (1988).
    [CrossRef]
  16. K. Yamauchi, K. Hirose, H. Goto, K. Sugiyama, K. Inagaki, K. Yamamura, Y. Sano, Y. Mori, “First-principle simulation of removal process in EEM (elastic emission machining),” Comput. Mater. Sci. 14, 232–235 (1999).
    [CrossRef]
  17. Y. Mori, K. Yamauchi, K. Sugiyama, K. Inagaki, S. Shimada, J. Uchikoshi, H. Mimura, T. Imai, K. Kanemura, in Precision Science and Technology for Perfect Surfaces, Y. Furukawa, Y. Mori, T. Kataoka, eds. (Japan Society for Precision Engineering, 1999), pp. 207–212.
  18. P. Z. Takacs, S. K. Feng, E. L. Church, S. Qian, W. Liu, “Long trace profile measurements on cylindrical aspheres,” in Surface Characterization and Testing II, J. E. Greivenkamp, M. Young, eds., Proc. SPIE1164, 203–211 (1989).
    [CrossRef]
  19. M. Bray, “Stitching interferometry and absolute surface shape metrology: similarities,” in Optical Manufacturing and Testing IV, H. P. Stahl, ed., Proc. SPIE4451, 375–383 (2001).
    [CrossRef]

2002

A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, Y. Mori, K. Yamauchi, A. Saito, “Deterministic retrieval of surface waviness by means of topography with coherent x-rays,” J. Synchrotron Radiat. 9, 223–228 (2002).
[CrossRef] [PubMed]

2000

Y. Mori, K. Yamamura, Y. Sano, “Development of plasma chemical vaporization machining,” Rev. Sci. Instrum. 71, 4627–4632 (2000).
[CrossRef]

Y. Mori, K. Yamauchi, K. Yamamura, Y. Sano, “The study of fabrication of the X-ray mirror by numerically controlled plasma chemical vaporization machining: development of the machine for the x-ray mirror fabrication,” Rev. Sci. Instrum. 71, 4620–4626 (2000).
[CrossRef]

1999

K. Yamauchi, K. Hirose, H. Goto, K. Sugiyama, K. Inagaki, K. Yamamura, Y. Sano, Y. Mori, “First-principle simulation of removal process in EEM (elastic emission machining),” Comput. Mater. Sci. 14, 232–235 (1999).
[CrossRef]

1998

H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Computer numerically controlled plasma chemical vaporization machining using a pipe electrode for optical fabrication,” Appl. Opt. 37, 5198–5210 (1998).
[CrossRef]

H. Kitamura, “Present status of SPring-8 insertion devices,” J. Synchrotron Radiat. 5, 184–188 (1998).
[CrossRef]

H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Plasma chemical vaporization machining (CVM) for fabrication of optics,” Jpn. J. Appl. Phys. 37, L894–L896 (1998).
[CrossRef]

1995

E. L. Church, P. Z. Takacs, “Specification of glancing- and normal-incidence x-ray mirrors,” Opt. Eng. 34, 353–360 (1995).
[CrossRef]

J. Susini, “Design parameter for hard x-ray mirrors: the European Synchrotron Radiation Facility case,” Opt. Eng. 34, 361–376 (1995).
[CrossRef]

1990

Y. Mori, K. Yamauchi, K. Endo, T. Ide, H. Toyota, K. Nishizawa, M. Hasegawa, “Observation of elastic emission machined surfaces by scanning tunneling microscopy,” J. Vac. Sci. Technol. A 8, 621–624 (1990).
[CrossRef]

1988

Y. Mori, K. Yamauchi, K. Endo, “Mechanism of atomic removal in elastic emission machining,” Precis. Eng. 10, 24–28 (1988).
[CrossRef]

1987

Y. Mori, K. Yamauchi, K. Endo, “Elastic emission machining,” Precis. Eng. 9, 123–128 (1987).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1997).

Bray, M.

M. Bray, “Stitching interferometry and absolute surface shape metrology: similarities,” in Optical Manufacturing and Testing IV, H. P. Stahl, ed., Proc. SPIE4451, 375–383 (2001).
[CrossRef]

Church, E. L.

E. L. Church, P. Z. Takacs, “Specification of glancing- and normal-incidence x-ray mirrors,” Opt. Eng. 34, 353–360 (1995).
[CrossRef]

E. L. Church, P. Z. Takacs, “Prediction of mirror performance from laboratory measurements,” in X-Ray/EUV Optics for Astronomy and Microscopy, R. B. Hoover, ed., Proc. SPIE1160, 323–336 (1989).
[CrossRef]

P. Z. Takacs, S. K. Feng, E. L. Church, S. Qian, W. Liu, “Long trace profile measurements on cylindrical aspheres,” in Surface Characterization and Testing II, J. E. Greivenkamp, M. Young, eds., Proc. SPIE1164, 203–211 (1989).
[CrossRef]

Ebi, M.

H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Computer numerically controlled plasma chemical vaporization machining using a pipe electrode for optical fabrication,” Appl. Opt. 37, 5198–5210 (1998).
[CrossRef]

H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Plasma chemical vaporization machining (CVM) for fabrication of optics,” Jpn. J. Appl. Phys. 37, L894–L896 (1998).
[CrossRef]

Endo, K.

Y. Mori, K. Yamauchi, K. Endo, T. Ide, H. Toyota, K. Nishizawa, M. Hasegawa, “Observation of elastic emission machined surfaces by scanning tunneling microscopy,” J. Vac. Sci. Technol. A 8, 621–624 (1990).
[CrossRef]

Y. Mori, K. Yamauchi, K. Endo, “Mechanism of atomic removal in elastic emission machining,” Precis. Eng. 10, 24–28 (1988).
[CrossRef]

Y. Mori, K. Yamauchi, K. Endo, “Elastic emission machining,” Precis. Eng. 9, 123–128 (1987).
[CrossRef]

Feng, S. K.

P. Z. Takacs, S. K. Feng, E. L. Church, S. Qian, W. Liu, “Long trace profile measurements on cylindrical aspheres,” in Surface Characterization and Testing II, J. E. Greivenkamp, M. Young, eds., Proc. SPIE1164, 203–211 (1989).
[CrossRef]

Goto, H.

K. Yamauchi, K. Hirose, H. Goto, K. Sugiyama, K. Inagaki, K. Yamamura, Y. Sano, Y. Mori, “First-principle simulation of removal process in EEM (elastic emission machining),” Comput. Mater. Sci. 14, 232–235 (1999).
[CrossRef]

Goto, S.

T. Ishikawa, K. Tamasaku, M. Yabashi, S. Goto, Y. Tanaka, H. Yamazaki, K. Takeshita, H. Kimura, H. Ohashi, T. Matsushita, T. Ohata, “1 km beamline at SPring-8,” in Advances in X-Rays, A. K. Freund, T. Ishikawa, A. M. Khounsary, D. C. Mancini, A. G. Michette, S. Oestreich, eds., Proc. SPIE, 4145, 1–10 (2001).

Hasegawa, M.

Y. Mori, K. Yamauchi, K. Endo, T. Ide, H. Toyota, K. Nishizawa, M. Hasegawa, “Observation of elastic emission machined surfaces by scanning tunneling microscopy,” J. Vac. Sci. Technol. A 8, 621–624 (1990).
[CrossRef]

Hirose, K.

K. Yamauchi, K. Hirose, H. Goto, K. Sugiyama, K. Inagaki, K. Yamamura, Y. Sano, Y. Mori, “First-principle simulation of removal process in EEM (elastic emission machining),” Comput. Mater. Sci. 14, 232–235 (1999).
[CrossRef]

Ide, T.

Y. Mori, K. Yamauchi, K. Endo, T. Ide, H. Toyota, K. Nishizawa, M. Hasegawa, “Observation of elastic emission machined surfaces by scanning tunneling microscopy,” J. Vac. Sci. Technol. A 8, 621–624 (1990).
[CrossRef]

Imai, T.

Y. Mori, K. Yamauchi, K. Sugiyama, K. Inagaki, S. Shimada, J. Uchikoshi, H. Mimura, T. Imai, K. Kanemura, in Precision Science and Technology for Perfect Surfaces, Y. Furukawa, Y. Mori, T. Kataoka, eds. (Japan Society for Precision Engineering, 1999), pp. 207–212.

Inagaki, K.

K. Yamauchi, K. Hirose, H. Goto, K. Sugiyama, K. Inagaki, K. Yamamura, Y. Sano, Y. Mori, “First-principle simulation of removal process in EEM (elastic emission machining),” Comput. Mater. Sci. 14, 232–235 (1999).
[CrossRef]

Y. Mori, K. Yamauchi, K. Sugiyama, K. Inagaki, S. Shimada, J. Uchikoshi, H. Mimura, T. Imai, K. Kanemura, in Precision Science and Technology for Perfect Surfaces, Y. Furukawa, Y. Mori, T. Kataoka, eds. (Japan Society for Precision Engineering, 1999), pp. 207–212.

Ishikawa, T.

A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, Y. Mori, K. Yamauchi, A. Saito, “Deterministic retrieval of surface waviness by means of topography with coherent x-rays,” J. Synchrotron Radiat. 9, 223–228 (2002).
[CrossRef] [PubMed]

Y. Mori, K. Yamauchi, K. Yamamura, H. Mimura, A. Saito, H. Kishimoto, Y. Sekito, M. Kanaoka, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, “Development of plasma chemical vaporization machining and elastic emission machining systems for coherent hard x-ray optics,” in X-Ray Mirrors, Crystals, and Multilayers II, A. K. Freund, A. T. Macrander, T. Ishikawa, J. L. Woods, eds., Proc. SPIE4501, 30–42 (2001).
[CrossRef]

T. Ishikawa, K. Tamasaku, M. Yabashi, S. Goto, Y. Tanaka, H. Yamazaki, K. Takeshita, H. Kimura, H. Ohashi, T. Matsushita, T. Ohata, “1 km beamline at SPring-8,” in Advances in X-Rays, A. K. Freund, T. Ishikawa, A. M. Khounsary, D. C. Mancini, A. G. Michette, S. Oestreich, eds., Proc. SPIE, 4145, 1–10 (2001).

Itoh, H.

H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Plasma chemical vaporization machining (CVM) for fabrication of optics,” Jpn. J. Appl. Phys. 37, L894–L896 (1998).
[CrossRef]

H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Computer numerically controlled plasma chemical vaporization machining using a pipe electrode for optical fabrication,” Appl. Opt. 37, 5198–5210 (1998).
[CrossRef]

Kanaoka, M.

Y. Mori, K. Yamauchi, K. Yamamura, H. Mimura, A. Saito, H. Kishimoto, Y. Sekito, M. Kanaoka, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, “Development of plasma chemical vaporization machining and elastic emission machining systems for coherent hard x-ray optics,” in X-Ray Mirrors, Crystals, and Multilayers II, A. K. Freund, A. T. Macrander, T. Ishikawa, J. L. Woods, eds., Proc. SPIE4501, 30–42 (2001).
[CrossRef]

Kanemura, K.

Y. Mori, K. Yamauchi, K. Sugiyama, K. Inagaki, S. Shimada, J. Uchikoshi, H. Mimura, T. Imai, K. Kanemura, in Precision Science and Technology for Perfect Surfaces, Y. Furukawa, Y. Mori, T. Kataoka, eds. (Japan Society for Precision Engineering, 1999), pp. 207–212.

Kimura, H.

T. Ishikawa, K. Tamasaku, M. Yabashi, S. Goto, Y. Tanaka, H. Yamazaki, K. Takeshita, H. Kimura, H. Ohashi, T. Matsushita, T. Ohata, “1 km beamline at SPring-8,” in Advances in X-Rays, A. K. Freund, T. Ishikawa, A. M. Khounsary, D. C. Mancini, A. G. Michette, S. Oestreich, eds., Proc. SPIE, 4145, 1–10 (2001).

Kishimoto, H.

Y. Mori, K. Yamauchi, K. Yamamura, H. Mimura, A. Saito, H. Kishimoto, Y. Sekito, M. Kanaoka, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, “Development of plasma chemical vaporization machining and elastic emission machining systems for coherent hard x-ray optics,” in X-Ray Mirrors, Crystals, and Multilayers II, A. K. Freund, A. T. Macrander, T. Ishikawa, J. L. Woods, eds., Proc. SPIE4501, 30–42 (2001).
[CrossRef]

Kitamura, H.

H. Kitamura, “Present status of SPring-8 insertion devices,” J. Synchrotron Radiat. 5, 184–188 (1998).
[CrossRef]

Kobayashi, T.

H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Plasma chemical vaporization machining (CVM) for fabrication of optics,” Jpn. J. Appl. Phys. 37, L894–L896 (1998).
[CrossRef]

H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Computer numerically controlled plasma chemical vaporization machining using a pipe electrode for optical fabrication,” Appl. Opt. 37, 5198–5210 (1998).
[CrossRef]

Liu, W.

P. Z. Takacs, S. K. Feng, E. L. Church, S. Qian, W. Liu, “Long trace profile measurements on cylindrical aspheres,” in Surface Characterization and Testing II, J. E. Greivenkamp, M. Young, eds., Proc. SPIE1164, 203–211 (1989).
[CrossRef]

Matsushita, T.

T. Ishikawa, K. Tamasaku, M. Yabashi, S. Goto, Y. Tanaka, H. Yamazaki, K. Takeshita, H. Kimura, H. Ohashi, T. Matsushita, T. Ohata, “1 km beamline at SPring-8,” in Advances in X-Rays, A. K. Freund, T. Ishikawa, A. M. Khounsary, D. C. Mancini, A. G. Michette, S. Oestreich, eds., Proc. SPIE, 4145, 1–10 (2001).

Mimura, H.

Y. Mori, K. Yamauchi, K. Yamamura, H. Mimura, A. Saito, H. Kishimoto, Y. Sekito, M. Kanaoka, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, “Development of plasma chemical vaporization machining and elastic emission machining systems for coherent hard x-ray optics,” in X-Ray Mirrors, Crystals, and Multilayers II, A. K. Freund, A. T. Macrander, T. Ishikawa, J. L. Woods, eds., Proc. SPIE4501, 30–42 (2001).
[CrossRef]

Y. Mori, K. Yamauchi, K. Sugiyama, K. Inagaki, S. Shimada, J. Uchikoshi, H. Mimura, T. Imai, K. Kanemura, in Precision Science and Technology for Perfect Surfaces, Y. Furukawa, Y. Mori, T. Kataoka, eds. (Japan Society for Precision Engineering, 1999), pp. 207–212.

Mori, Y.

A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, Y. Mori, K. Yamauchi, A. Saito, “Deterministic retrieval of surface waviness by means of topography with coherent x-rays,” J. Synchrotron Radiat. 9, 223–228 (2002).
[CrossRef] [PubMed]

Y. Mori, K. Yamamura, Y. Sano, “Development of plasma chemical vaporization machining,” Rev. Sci. Instrum. 71, 4627–4632 (2000).
[CrossRef]

Y. Mori, K. Yamauchi, K. Yamamura, Y. Sano, “The study of fabrication of the X-ray mirror by numerically controlled plasma chemical vaporization machining: development of the machine for the x-ray mirror fabrication,” Rev. Sci. Instrum. 71, 4620–4626 (2000).
[CrossRef]

K. Yamauchi, K. Hirose, H. Goto, K. Sugiyama, K. Inagaki, K. Yamamura, Y. Sano, Y. Mori, “First-principle simulation of removal process in EEM (elastic emission machining),” Comput. Mater. Sci. 14, 232–235 (1999).
[CrossRef]

H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Plasma chemical vaporization machining (CVM) for fabrication of optics,” Jpn. J. Appl. Phys. 37, L894–L896 (1998).
[CrossRef]

H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Computer numerically controlled plasma chemical vaporization machining using a pipe electrode for optical fabrication,” Appl. Opt. 37, 5198–5210 (1998).
[CrossRef]

Y. Mori, K. Yamauchi, K. Endo, T. Ide, H. Toyota, K. Nishizawa, M. Hasegawa, “Observation of elastic emission machined surfaces by scanning tunneling microscopy,” J. Vac. Sci. Technol. A 8, 621–624 (1990).
[CrossRef]

Y. Mori, K. Yamauchi, K. Endo, “Mechanism of atomic removal in elastic emission machining,” Precis. Eng. 10, 24–28 (1988).
[CrossRef]

Y. Mori, K. Yamauchi, K. Endo, “Elastic emission machining,” Precis. Eng. 9, 123–128 (1987).
[CrossRef]

Y. Mori, K. Yamauchi, K. Sugiyama, K. Inagaki, S. Shimada, J. Uchikoshi, H. Mimura, T. Imai, K. Kanemura, in Precision Science and Technology for Perfect Surfaces, Y. Furukawa, Y. Mori, T. Kataoka, eds. (Japan Society for Precision Engineering, 1999), pp. 207–212.

Y. Mori, K. Yamauchi, K. Yamamura, H. Mimura, A. Saito, H. Kishimoto, Y. Sekito, M. Kanaoka, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, “Development of plasma chemical vaporization machining and elastic emission machining systems for coherent hard x-ray optics,” in X-Ray Mirrors, Crystals, and Multilayers II, A. K. Freund, A. T. Macrander, T. Ishikawa, J. L. Woods, eds., Proc. SPIE4501, 30–42 (2001).
[CrossRef]

Nishizawa, K.

Y. Mori, K. Yamauchi, K. Endo, T. Ide, H. Toyota, K. Nishizawa, M. Hasegawa, “Observation of elastic emission machined surfaces by scanning tunneling microscopy,” J. Vac. Sci. Technol. A 8, 621–624 (1990).
[CrossRef]

Ohashi, H.

T. Ishikawa, K. Tamasaku, M. Yabashi, S. Goto, Y. Tanaka, H. Yamazaki, K. Takeshita, H. Kimura, H. Ohashi, T. Matsushita, T. Ohata, “1 km beamline at SPring-8,” in Advances in X-Rays, A. K. Freund, T. Ishikawa, A. M. Khounsary, D. C. Mancini, A. G. Michette, S. Oestreich, eds., Proc. SPIE, 4145, 1–10 (2001).

Ohata, T.

T. Ishikawa, K. Tamasaku, M. Yabashi, S. Goto, Y. Tanaka, H. Yamazaki, K. Takeshita, H. Kimura, H. Ohashi, T. Matsushita, T. Ohata, “1 km beamline at SPring-8,” in Advances in X-Rays, A. K. Freund, T. Ishikawa, A. M. Khounsary, D. C. Mancini, A. G. Michette, S. Oestreich, eds., Proc. SPIE, 4145, 1–10 (2001).

Qian, S.

P. Z. Takacs, S. K. Feng, E. L. Church, S. Qian, W. Liu, “Long trace profile measurements on cylindrical aspheres,” in Surface Characterization and Testing II, J. E. Greivenkamp, M. Young, eds., Proc. SPIE1164, 203–211 (1989).
[CrossRef]

Saito, A.

A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, Y. Mori, K. Yamauchi, A. Saito, “Deterministic retrieval of surface waviness by means of topography with coherent x-rays,” J. Synchrotron Radiat. 9, 223–228 (2002).
[CrossRef] [PubMed]

Y. Mori, K. Yamauchi, K. Yamamura, H. Mimura, A. Saito, H. Kishimoto, Y. Sekito, M. Kanaoka, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, “Development of plasma chemical vaporization machining and elastic emission machining systems for coherent hard x-ray optics,” in X-Ray Mirrors, Crystals, and Multilayers II, A. K. Freund, A. T. Macrander, T. Ishikawa, J. L. Woods, eds., Proc. SPIE4501, 30–42 (2001).
[CrossRef]

Sano, Y.

Y. Mori, K. Yamamura, Y. Sano, “Development of plasma chemical vaporization machining,” Rev. Sci. Instrum. 71, 4627–4632 (2000).
[CrossRef]

Y. Mori, K. Yamauchi, K. Yamamura, Y. Sano, “The study of fabrication of the X-ray mirror by numerically controlled plasma chemical vaporization machining: development of the machine for the x-ray mirror fabrication,” Rev. Sci. Instrum. 71, 4620–4626 (2000).
[CrossRef]

K. Yamauchi, K. Hirose, H. Goto, K. Sugiyama, K. Inagaki, K. Yamamura, Y. Sano, Y. Mori, “First-principle simulation of removal process in EEM (elastic emission machining),” Comput. Mater. Sci. 14, 232–235 (1999).
[CrossRef]

H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Computer numerically controlled plasma chemical vaporization machining using a pipe electrode for optical fabrication,” Appl. Opt. 37, 5198–5210 (1998).
[CrossRef]

H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Plasma chemical vaporization machining (CVM) for fabrication of optics,” Jpn. J. Appl. Phys. 37, L894–L896 (1998).
[CrossRef]

Sekito, Y.

Y. Mori, K. Yamauchi, K. Yamamura, H. Mimura, A. Saito, H. Kishimoto, Y. Sekito, M. Kanaoka, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, “Development of plasma chemical vaporization machining and elastic emission machining systems for coherent hard x-ray optics,” in X-Ray Mirrors, Crystals, and Multilayers II, A. K. Freund, A. T. Macrander, T. Ishikawa, J. L. Woods, eds., Proc. SPIE4501, 30–42 (2001).
[CrossRef]

Shibata, N.

H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Plasma chemical vaporization machining (CVM) for fabrication of optics,” Jpn. J. Appl. Phys. 37, L894–L896 (1998).
[CrossRef]

H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Computer numerically controlled plasma chemical vaporization machining using a pipe electrode for optical fabrication,” Appl. Opt. 37, 5198–5210 (1998).
[CrossRef]

Shimada, S.

Y. Mori, K. Yamauchi, K. Sugiyama, K. Inagaki, S. Shimada, J. Uchikoshi, H. Mimura, T. Imai, K. Kanemura, in Precision Science and Technology for Perfect Surfaces, Y. Furukawa, Y. Mori, T. Kataoka, eds. (Japan Society for Precision Engineering, 1999), pp. 207–212.

Souvorov, A.

A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, Y. Mori, K. Yamauchi, A. Saito, “Deterministic retrieval of surface waviness by means of topography with coherent x-rays,” J. Synchrotron Radiat. 9, 223–228 (2002).
[CrossRef] [PubMed]

Y. Mori, K. Yamauchi, K. Yamamura, H. Mimura, A. Saito, H. Kishimoto, Y. Sekito, M. Kanaoka, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, “Development of plasma chemical vaporization machining and elastic emission machining systems for coherent hard x-ray optics,” in X-Ray Mirrors, Crystals, and Multilayers II, A. K. Freund, A. T. Macrander, T. Ishikawa, J. L. Woods, eds., Proc. SPIE4501, 30–42 (2001).
[CrossRef]

Sugiyama, K.

K. Yamauchi, K. Hirose, H. Goto, K. Sugiyama, K. Inagaki, K. Yamamura, Y. Sano, Y. Mori, “First-principle simulation of removal process in EEM (elastic emission machining),” Comput. Mater. Sci. 14, 232–235 (1999).
[CrossRef]

Y. Mori, K. Yamauchi, K. Sugiyama, K. Inagaki, S. Shimada, J. Uchikoshi, H. Mimura, T. Imai, K. Kanemura, in Precision Science and Technology for Perfect Surfaces, Y. Furukawa, Y. Mori, T. Kataoka, eds. (Japan Society for Precision Engineering, 1999), pp. 207–212.

Susini, J.

J. Susini, “Design parameter for hard x-ray mirrors: the European Synchrotron Radiation Facility case,” Opt. Eng. 34, 361–376 (1995).
[CrossRef]

Takacs, P. Z.

E. L. Church, P. Z. Takacs, “Specification of glancing- and normal-incidence x-ray mirrors,” Opt. Eng. 34, 353–360 (1995).
[CrossRef]

E. L. Church, P. Z. Takacs, “Prediction of mirror performance from laboratory measurements,” in X-Ray/EUV Optics for Astronomy and Microscopy, R. B. Hoover, ed., Proc. SPIE1160, 323–336 (1989).
[CrossRef]

P. Z. Takacs, S. K. Feng, E. L. Church, S. Qian, W. Liu, “Long trace profile measurements on cylindrical aspheres,” in Surface Characterization and Testing II, J. E. Greivenkamp, M. Young, eds., Proc. SPIE1164, 203–211 (1989).
[CrossRef]

Takeshita, K.

T. Ishikawa, K. Tamasaku, M. Yabashi, S. Goto, Y. Tanaka, H. Yamazaki, K. Takeshita, H. Kimura, H. Ohashi, T. Matsushita, T. Ohata, “1 km beamline at SPring-8,” in Advances in X-Rays, A. K. Freund, T. Ishikawa, A. M. Khounsary, D. C. Mancini, A. G. Michette, S. Oestreich, eds., Proc. SPIE, 4145, 1–10 (2001).

Takino, H.

H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Plasma chemical vaporization machining (CVM) for fabrication of optics,” Jpn. J. Appl. Phys. 37, L894–L896 (1998).
[CrossRef]

H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Computer numerically controlled plasma chemical vaporization machining using a pipe electrode for optical fabrication,” Appl. Opt. 37, 5198–5210 (1998).
[CrossRef]

Tamasaku, K.

A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, Y. Mori, K. Yamauchi, A. Saito, “Deterministic retrieval of surface waviness by means of topography with coherent x-rays,” J. Synchrotron Radiat. 9, 223–228 (2002).
[CrossRef] [PubMed]

Y. Mori, K. Yamauchi, K. Yamamura, H. Mimura, A. Saito, H. Kishimoto, Y. Sekito, M. Kanaoka, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, “Development of plasma chemical vaporization machining and elastic emission machining systems for coherent hard x-ray optics,” in X-Ray Mirrors, Crystals, and Multilayers II, A. K. Freund, A. T. Macrander, T. Ishikawa, J. L. Woods, eds., Proc. SPIE4501, 30–42 (2001).
[CrossRef]

T. Ishikawa, K. Tamasaku, M. Yabashi, S. Goto, Y. Tanaka, H. Yamazaki, K. Takeshita, H. Kimura, H. Ohashi, T. Matsushita, T. Ohata, “1 km beamline at SPring-8,” in Advances in X-Rays, A. K. Freund, T. Ishikawa, A. M. Khounsary, D. C. Mancini, A. G. Michette, S. Oestreich, eds., Proc. SPIE, 4145, 1–10 (2001).

Tanaka, H.

H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Plasma chemical vaporization machining (CVM) for fabrication of optics,” Jpn. J. Appl. Phys. 37, L894–L896 (1998).
[CrossRef]

H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Computer numerically controlled plasma chemical vaporization machining using a pipe electrode for optical fabrication,” Appl. Opt. 37, 5198–5210 (1998).
[CrossRef]

Tanaka, Y.

T. Ishikawa, K. Tamasaku, M. Yabashi, S. Goto, Y. Tanaka, H. Yamazaki, K. Takeshita, H. Kimura, H. Ohashi, T. Matsushita, T. Ohata, “1 km beamline at SPring-8,” in Advances in X-Rays, A. K. Freund, T. Ishikawa, A. M. Khounsary, D. C. Mancini, A. G. Michette, S. Oestreich, eds., Proc. SPIE, 4145, 1–10 (2001).

Toyota, H.

Y. Mori, K. Yamauchi, K. Endo, T. Ide, H. Toyota, K. Nishizawa, M. Hasegawa, “Observation of elastic emission machined surfaces by scanning tunneling microscopy,” J. Vac. Sci. Technol. A 8, 621–624 (1990).
[CrossRef]

Uchikoshi, J.

Y. Mori, K. Yamauchi, K. Sugiyama, K. Inagaki, S. Shimada, J. Uchikoshi, H. Mimura, T. Imai, K. Kanemura, in Precision Science and Technology for Perfect Surfaces, Y. Furukawa, Y. Mori, T. Kataoka, eds. (Japan Society for Precision Engineering, 1999), pp. 207–212.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1997).

Yabashi, M.

A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, Y. Mori, K. Yamauchi, A. Saito, “Deterministic retrieval of surface waviness by means of topography with coherent x-rays,” J. Synchrotron Radiat. 9, 223–228 (2002).
[CrossRef] [PubMed]

Y. Mori, K. Yamauchi, K. Yamamura, H. Mimura, A. Saito, H. Kishimoto, Y. Sekito, M. Kanaoka, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, “Development of plasma chemical vaporization machining and elastic emission machining systems for coherent hard x-ray optics,” in X-Ray Mirrors, Crystals, and Multilayers II, A. K. Freund, A. T. Macrander, T. Ishikawa, J. L. Woods, eds., Proc. SPIE4501, 30–42 (2001).
[CrossRef]

T. Ishikawa, K. Tamasaku, M. Yabashi, S. Goto, Y. Tanaka, H. Yamazaki, K. Takeshita, H. Kimura, H. Ohashi, T. Matsushita, T. Ohata, “1 km beamline at SPring-8,” in Advances in X-Rays, A. K. Freund, T. Ishikawa, A. M. Khounsary, D. C. Mancini, A. G. Michette, S. Oestreich, eds., Proc. SPIE, 4145, 1–10 (2001).

Yamamura, K.

Y. Mori, K. Yamauchi, K. Yamamura, Y. Sano, “The study of fabrication of the X-ray mirror by numerically controlled plasma chemical vaporization machining: development of the machine for the x-ray mirror fabrication,” Rev. Sci. Instrum. 71, 4620–4626 (2000).
[CrossRef]

Y. Mori, K. Yamamura, Y. Sano, “Development of plasma chemical vaporization machining,” Rev. Sci. Instrum. 71, 4627–4632 (2000).
[CrossRef]

K. Yamauchi, K. Hirose, H. Goto, K. Sugiyama, K. Inagaki, K. Yamamura, Y. Sano, Y. Mori, “First-principle simulation of removal process in EEM (elastic emission machining),” Comput. Mater. Sci. 14, 232–235 (1999).
[CrossRef]

H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Plasma chemical vaporization machining (CVM) for fabrication of optics,” Jpn. J. Appl. Phys. 37, L894–L896 (1998).
[CrossRef]

H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Computer numerically controlled plasma chemical vaporization machining using a pipe electrode for optical fabrication,” Appl. Opt. 37, 5198–5210 (1998).
[CrossRef]

Y. Mori, K. Yamauchi, K. Yamamura, H. Mimura, A. Saito, H. Kishimoto, Y. Sekito, M. Kanaoka, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, “Development of plasma chemical vaporization machining and elastic emission machining systems for coherent hard x-ray optics,” in X-Ray Mirrors, Crystals, and Multilayers II, A. K. Freund, A. T. Macrander, T. Ishikawa, J. L. Woods, eds., Proc. SPIE4501, 30–42 (2001).
[CrossRef]

Yamauchi, K.

A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, Y. Mori, K. Yamauchi, A. Saito, “Deterministic retrieval of surface waviness by means of topography with coherent x-rays,” J. Synchrotron Radiat. 9, 223–228 (2002).
[CrossRef] [PubMed]

Y. Mori, K. Yamauchi, K. Yamamura, Y. Sano, “The study of fabrication of the X-ray mirror by numerically controlled plasma chemical vaporization machining: development of the machine for the x-ray mirror fabrication,” Rev. Sci. Instrum. 71, 4620–4626 (2000).
[CrossRef]

K. Yamauchi, K. Hirose, H. Goto, K. Sugiyama, K. Inagaki, K. Yamamura, Y. Sano, Y. Mori, “First-principle simulation of removal process in EEM (elastic emission machining),” Comput. Mater. Sci. 14, 232–235 (1999).
[CrossRef]

Y. Mori, K. Yamauchi, K. Endo, T. Ide, H. Toyota, K. Nishizawa, M. Hasegawa, “Observation of elastic emission machined surfaces by scanning tunneling microscopy,” J. Vac. Sci. Technol. A 8, 621–624 (1990).
[CrossRef]

Y. Mori, K. Yamauchi, K. Endo, “Mechanism of atomic removal in elastic emission machining,” Precis. Eng. 10, 24–28 (1988).
[CrossRef]

Y. Mori, K. Yamauchi, K. Endo, “Elastic emission machining,” Precis. Eng. 9, 123–128 (1987).
[CrossRef]

Y. Mori, K. Yamauchi, K. Sugiyama, K. Inagaki, S. Shimada, J. Uchikoshi, H. Mimura, T. Imai, K. Kanemura, in Precision Science and Technology for Perfect Surfaces, Y. Furukawa, Y. Mori, T. Kataoka, eds. (Japan Society for Precision Engineering, 1999), pp. 207–212.

Y. Mori, K. Yamauchi, K. Yamamura, H. Mimura, A. Saito, H. Kishimoto, Y. Sekito, M. Kanaoka, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, “Development of plasma chemical vaporization machining and elastic emission machining systems for coherent hard x-ray optics,” in X-Ray Mirrors, Crystals, and Multilayers II, A. K. Freund, A. T. Macrander, T. Ishikawa, J. L. Woods, eds., Proc. SPIE4501, 30–42 (2001).
[CrossRef]

Yamazaki, H.

T. Ishikawa, K. Tamasaku, M. Yabashi, S. Goto, Y. Tanaka, H. Yamazaki, K. Takeshita, H. Kimura, H. Ohashi, T. Matsushita, T. Ohata, “1 km beamline at SPring-8,” in Advances in X-Rays, A. K. Freund, T. Ishikawa, A. M. Khounsary, D. C. Mancini, A. G. Michette, S. Oestreich, eds., Proc. SPIE, 4145, 1–10 (2001).

Appl. Opt.

Comput. Mater. Sci.

K. Yamauchi, K. Hirose, H. Goto, K. Sugiyama, K. Inagaki, K. Yamamura, Y. Sano, Y. Mori, “First-principle simulation of removal process in EEM (elastic emission machining),” Comput. Mater. Sci. 14, 232–235 (1999).
[CrossRef]

J. Synchrotron Radiat.

H. Kitamura, “Present status of SPring-8 insertion devices,” J. Synchrotron Radiat. 5, 184–188 (1998).
[CrossRef]

A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, Y. Mori, K. Yamauchi, A. Saito, “Deterministic retrieval of surface waviness by means of topography with coherent x-rays,” J. Synchrotron Radiat. 9, 223–228 (2002).
[CrossRef] [PubMed]

J. Vac. Sci. Technol. A

Y. Mori, K. Yamauchi, K. Endo, T. Ide, H. Toyota, K. Nishizawa, M. Hasegawa, “Observation of elastic emission machined surfaces by scanning tunneling microscopy,” J. Vac. Sci. Technol. A 8, 621–624 (1990).
[CrossRef]

Jpn. J. Appl. Phys.

H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Plasma chemical vaporization machining (CVM) for fabrication of optics,” Jpn. J. Appl. Phys. 37, L894–L896 (1998).
[CrossRef]

Opt. Eng.

E. L. Church, P. Z. Takacs, “Specification of glancing- and normal-incidence x-ray mirrors,” Opt. Eng. 34, 353–360 (1995).
[CrossRef]

J. Susini, “Design parameter for hard x-ray mirrors: the European Synchrotron Radiation Facility case,” Opt. Eng. 34, 361–376 (1995).
[CrossRef]

Precis. Eng.

Y. Mori, K. Yamauchi, K. Endo, “Elastic emission machining,” Precis. Eng. 9, 123–128 (1987).
[CrossRef]

Y. Mori, K. Yamauchi, K. Endo, “Mechanism of atomic removal in elastic emission machining,” Precis. Eng. 10, 24–28 (1988).
[CrossRef]

Rev. Sci. Instrum.

Y. Mori, K. Yamamura, Y. Sano, “Development of plasma chemical vaporization machining,” Rev. Sci. Instrum. 71, 4627–4632 (2000).
[CrossRef]

Y. Mori, K. Yamauchi, K. Yamamura, Y. Sano, “The study of fabrication of the X-ray mirror by numerically controlled plasma chemical vaporization machining: development of the machine for the x-ray mirror fabrication,” Rev. Sci. Instrum. 71, 4620–4626 (2000).
[CrossRef]

Other

M. Born, E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1997).

E. L. Church, P. Z. Takacs, “Prediction of mirror performance from laboratory measurements,” in X-Ray/EUV Optics for Astronomy and Microscopy, R. B. Hoover, ed., Proc. SPIE1160, 323–336 (1989).
[CrossRef]

Y. Mori, K. Yamauchi, K. Yamamura, H. Mimura, A. Saito, H. Kishimoto, Y. Sekito, M. Kanaoka, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, “Development of plasma chemical vaporization machining and elastic emission machining systems for coherent hard x-ray optics,” in X-Ray Mirrors, Crystals, and Multilayers II, A. K. Freund, A. T. Macrander, T. Ishikawa, J. L. Woods, eds., Proc. SPIE4501, 30–42 (2001).
[CrossRef]

Y. Mori, K. Yamauchi, K. Sugiyama, K. Inagaki, S. Shimada, J. Uchikoshi, H. Mimura, T. Imai, K. Kanemura, in Precision Science and Technology for Perfect Surfaces, Y. Furukawa, Y. Mori, T. Kataoka, eds. (Japan Society for Precision Engineering, 1999), pp. 207–212.

P. Z. Takacs, S. K. Feng, E. L. Church, S. Qian, W. Liu, “Long trace profile measurements on cylindrical aspheres,” in Surface Characterization and Testing II, J. E. Greivenkamp, M. Young, eds., Proc. SPIE1164, 203–211 (1989).
[CrossRef]

M. Bray, “Stitching interferometry and absolute surface shape metrology: similarities,” in Optical Manufacturing and Testing IV, H. P. Stahl, ed., Proc. SPIE4451, 375–383 (2001).
[CrossRef]

T. Ishikawa, K. Tamasaku, M. Yabashi, S. Goto, Y. Tanaka, H. Yamazaki, K. Takeshita, H. Kimura, H. Ohashi, T. Matsushita, T. Ohata, “1 km beamline at SPring-8,” in Advances in X-Rays, A. K. Freund, T. Ishikawa, A. M. Khounsary, D. C. Mancini, A. G. Michette, S. Oestreich, eds., Proc. SPIE, 4145, 1–10 (2001).

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Figures (9)

Fig. 1
Fig. 1

Schematic of the wave-optical simulator.

Fig. 2
Fig. 2

Surface figure error model with a Gaussian function.

Fig. 3
Fig. 3

Calculated intensity and wavefront phase distributions: (a) Calculated intensity distributions (the intensity fluctuation caused by Fresnel diffraction at the mirror edges was removed) and (b) calculated wavefront phase distributions (the phase fluctuation caused by Fresnel diffraction at the mirror edges was removed).

Fig. 4
Fig. 4

Definitions of the degrees of intensity modulation and wavefront phase error: (a) normalized amplitude of intensity (ΔI/I), (b) definition of phase error (Δϕ).

Fig. 5
Fig. 5

Relationships of bump width to normalized amplitude of intensity modulation and wavefront phase error: (a) normalized amplitude of intensity modulation, (b) wavefront phase error.

Fig. 6
Fig. 6

Measured profiles of the mirror surfaces prepared for the experiment: (a) Conventionally polished mirror surface. (b) PCVM-processed surface. Figure error is corrected in a spatial wavelength range longer than 5 mm. (c) PCVM–EEM-processed surface. Figure error is corrected with a spatial resolution close to 0.1 mm. PV, peak-to-valley

Fig. 7
Fig. 7

Dimensional details of the experimental setup.

Fig. 8
Fig. 8

Reflected beam images observed by use of an x-ray zooming tube and a CCD camera: (a) conventionally polished mirror, (b) PCVM-processed mirror, (c) PCVM–EEM-processed mirror.

Fig. 9
Fig. 9

Calculated and measured intensity profiles of the x-ray beams totally reflected by as-received, PCVM-processed, and PCVM–EEM-processed mirrors with a camera distance of 966 mm: (a) conventionally polished mirror, (b) PCVM processed mirror, (c) PCVM–EEM-processed mirror.

Equations (5)

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

V ( M , t ) = Slit K 1 ( P , M ) V ( P , t s ( P , M ) / c ) d P ,
V ( Q , t ) = Mirror K 2 ( M , Q ) V ( M , t s ( M , Q ) / c ) d M ,
V ( Q , t ) = Mirror Slit K ( P , M , Q ) × V ( P , t s ( M , Q ) / c s ( P , M ) / c ) d P d M ,
K ( P , M , Q ) = K 1 ( M , Q ) K 2 ( P , M ) .
I ( Q ) = V ( Q , t ) V * ( Q , t ) .

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