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Applied Optics

Applied Optics


  • Vol. 37, Iss. 34 — Dec. 1, 1998
  • pp: 8057–8066

Influence of fabrication errors on Wölter mirror imaging performance

Katsumi Sugisaki, Shin-ich Takahashi, Yasuji Yoshidomi, Kuninori Shinada, Osamu Mitomi, Eishiro Uchishiba, Ryuji Hamada, Tokio Kato, and Sadao Aoki  »View Author Affiliations

Applied Optics, Vol. 37, Issue 34, pp. 8057-8066 (1998)

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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

OCIS Codes
(110.7440) Imaging systems : X-ray imaging
(220.0220) Optical design and fabrication : Optical design and fabrication
(290.5880) Scattering : Scattering, rough surfaces
(340.0340) X-ray optics : X-ray optics
(340.7460) X-ray optics : X-ray microscopy
(340.7470) X-ray optics : X-ray mirrors

Original Manuscript: February 5, 1998
Revised Manuscript: July 27, 1998
Published: December 1, 1998

Katsumi Sugisaki, Shin-ich Takahashi, Yasuji Yoshidomi, Kuninori Shinada, Osamu Mitomi, Eishiro Uchishiba, Ryuji Hamada, Tokio Kato, and Sadao Aoki, "Influence of fabrication errors on Wölter mirror imaging performance," Appl. Opt. 37, 8057-8066 (1998)

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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]
  10. R. H. Price, “X-ray microscopy using grazing incidence reflection optics,” AIP Conf. Proc. 75, 189–199 (1981). [CrossRef]
  11. K. Lindsey, “The attainable limits in x-ray mirror fabrication,” Nucl. Instrum. Methods Phys. Res. 221, 14–19 (1984). [CrossRef]
  12. 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]
  13. 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]
  14. 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]
  15. Y. Sakayanagi, S. Aoki, “Soft x-ray imaging with toroidal mirrors,” Appl. Opt. 17, 601–603 (1978). [CrossRef] [PubMed]
  16. M. Born, E. Wolf, “9.3 tolerance conditions for primary aberrations,” in Principles in Optics, 4th ed. (Pergamon, Oxford, 1970).
  17. 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]
  18. 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]
  19. 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]
  20. 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]
  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). [CrossRef] [PubMed]
  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).

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