Abstract

Geometric properties and construction of the spiral collimator are discussed. The expression for the efficiency of power conversion of a divergent soft x-ray point source into a parallel beam is obtained. The efficiency of the spiral collimator is shown to be up to 30–90% in the whole soft x-ray spectral range. This efficiency is limited only by the fundamental reason: x-ray radiation absorption in the mirror coating of the spiral collimator. In this sense, the spiral collimator is more effective than any known x-ray optical collimation system with one or manifold reflections.

© 1991 Optical Society of America

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  1. A. V. Vinogradov, “XUV cavity and pumping optics,” J. Phys. 47, 286–297 (1986).
  2. J. E. Young, J. J. Macklin, S. E. Harris, “Grazing-incidence ellipsoidal reflector for longitudinally pumping short-wavelength lasers,” Opt. Lett. 12, 90–92 (1987).
    [CrossRef] [PubMed]
  3. R. Tatchyn, P. Csonka, H. Kilic, H. Watanabe, A. Fuller, M. Beck, A. Toor, J. Underwood, R. Catura, “Focusing of undulator light at SPEAR with a lacquer-coated mirror to power densities of 109 W/cm2,” in Soft X-Ray Optics and Technology, E.-E. Koch, F. Haber, G. Schmahl, eds., Proc. Soc. Photo-Opt. Instrum. Eng.733, 368–378 (1986).
    [CrossRef]
  4. A. V. Vinogradov, O. I. Tolstikhin, “Soft x-ray concentrators,” Tr. Fiz. Inst. Akad. Nauk SSSR 196, 168–181 (1989).
  5. A. V. Vinogradov, N. N. Zorev, I. V. Kozhevnikov, “On the limitations and possibilities of soft x-ray optics,” Tr. Fiz. Inst. Akad. Nauk SSSR 176, 195–210 (1986).
  6. R. Benattar, ed., X-Ray Instrumentation in Medicine and Biology, Plasma Physics, Astrophysics, and Synchrotron Radiation, Proc. Soc. Photo-Opt. Instrum. Eng.1140 (1989).
  7. V. K. Baranov, “Properties of parabolic focons,” Opt. Mekh. Prom. 6, 1–5 (1965).
  8. I. V. Kozhevnikov, “X-ray optical systems with manifold reflections,” Tr. Fiz. Inst. Akad. Nauk SSSR 196, 143–167 (1989).
  9. A. V. Vinogradov, I. V. Kozhevnikov, “Properties of x-ray waveguides,” Sov. Phys. Tech. Phys. 29, 1023–1026 (1984).
  10. M. Watanabe, I. H. Suzuki, T. Hidaka, M. Nishi, Y. Mitsuhashi, “Soft x-ray transmission characteristics of hollow-core fused-quartz fibers,” Appl. Opt. 24, 4206–4209 (1985).
    [CrossRef] [PubMed]
  11. V. A. Arkadev, A. I. Kolomiytsev, M. A. Kumakhov, I. Y. Ponomazov, I. A. Khodeev, Yu. P. Chertov, I. M. Shakhparanov, “Broadband x-ray optics with large angle aperture,” Sov. Phys. Usp. 157, 529–537 (1989).
    [CrossRef]
  12. W. D. Welford, L. Winston, The Optics of Nonimaging Concentrators (Academic, New York, 1978).
  13. A. V. Vinogradov, O. I. Tolstikhin, “Properties of an ideal optical x-ray concentrator,” Sov. Phys. Lebedev Inst. Rep. 9, 28–33 (1985).
  14. A. V. Vinogradov, V. F. Kovalev, I. V. Kozhevnikov, V. V. Pustovalov, “Concave mirrors for turning of x-ray beams,” Sov. Phys. Tech. Phys. 30, 144–150 (1986).
  15. A. V. Vinogradov, V. F. Kovalev, I. V. Kozhevnikov, V. V. Pustovalov, “The diffraction theory of grazing modes for x-ray mirrors and x-ray cavity,” Sov. Phys. Tech. Phys. 30, 335–344 (1986).
  16. B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B.K. Fujikawa, “Low-energy x-ray interaction coefficients: Photoabsorption, scattering and reflection,” At. Data Nucl. Data Tables 27, 1–144 (1982).
    [CrossRef]
  17. R. E. Burge, J. H. Beswetterick, M. T. Brown, P. S. Charalambous, P. J. Duke, G. F. Foster, A. R. Hare, A. G. Michette, D. Morris, G. R. Morrison, A. W. Potts, T. Taguchi, “Scanning x-ray microscopy,” in Proceedings on X-Ray Instrumentation in Medicine and Biology, Plasma Physics, Astrophysics, and Synchrotron Radiation, R. Benattar, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.1140, 528–529 (1989).
  18. A. V. Vinogradov, A. V. Popov, “On x-ray reflection at grazing incidence,” Opt. Spectrosc. 65, 1109–1111 (1988).
  19. A. V. Vinogradov, N. N. Zorev, I. V. Kozhevnikov, I. I. Yakushkin, “On the effect of total x-ray reflection,” Sov. Phys. JETP 62, 1225–1230 (1985).

1989 (3)

A. V. Vinogradov, O. I. Tolstikhin, “Soft x-ray concentrators,” Tr. Fiz. Inst. Akad. Nauk SSSR 196, 168–181 (1989).

I. V. Kozhevnikov, “X-ray optical systems with manifold reflections,” Tr. Fiz. Inst. Akad. Nauk SSSR 196, 143–167 (1989).

V. A. Arkadev, A. I. Kolomiytsev, M. A. Kumakhov, I. Y. Ponomazov, I. A. Khodeev, Yu. P. Chertov, I. M. Shakhparanov, “Broadband x-ray optics with large angle aperture,” Sov. Phys. Usp. 157, 529–537 (1989).
[CrossRef]

1988 (1)

A. V. Vinogradov, A. V. Popov, “On x-ray reflection at grazing incidence,” Opt. Spectrosc. 65, 1109–1111 (1988).

1987 (1)

1986 (4)

A. V. Vinogradov, “XUV cavity and pumping optics,” J. Phys. 47, 286–297 (1986).

A. V. Vinogradov, V. F. Kovalev, I. V. Kozhevnikov, V. V. Pustovalov, “Concave mirrors for turning of x-ray beams,” Sov. Phys. Tech. Phys. 30, 144–150 (1986).

A. V. Vinogradov, V. F. Kovalev, I. V. Kozhevnikov, V. V. Pustovalov, “The diffraction theory of grazing modes for x-ray mirrors and x-ray cavity,” Sov. Phys. Tech. Phys. 30, 335–344 (1986).

A. V. Vinogradov, N. N. Zorev, I. V. Kozhevnikov, “On the limitations and possibilities of soft x-ray optics,” Tr. Fiz. Inst. Akad. Nauk SSSR 176, 195–210 (1986).

1985 (3)

A. V. Vinogradov, O. I. Tolstikhin, “Properties of an ideal optical x-ray concentrator,” Sov. Phys. Lebedev Inst. Rep. 9, 28–33 (1985).

M. Watanabe, I. H. Suzuki, T. Hidaka, M. Nishi, Y. Mitsuhashi, “Soft x-ray transmission characteristics of hollow-core fused-quartz fibers,” Appl. Opt. 24, 4206–4209 (1985).
[CrossRef] [PubMed]

A. V. Vinogradov, N. N. Zorev, I. V. Kozhevnikov, I. I. Yakushkin, “On the effect of total x-ray reflection,” Sov. Phys. JETP 62, 1225–1230 (1985).

1984 (1)

A. V. Vinogradov, I. V. Kozhevnikov, “Properties of x-ray waveguides,” Sov. Phys. Tech. Phys. 29, 1023–1026 (1984).

1982 (1)

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B.K. Fujikawa, “Low-energy x-ray interaction coefficients: Photoabsorption, scattering and reflection,” At. Data Nucl. Data Tables 27, 1–144 (1982).
[CrossRef]

1965 (1)

V. K. Baranov, “Properties of parabolic focons,” Opt. Mekh. Prom. 6, 1–5 (1965).

Arkadev, V. A.

V. A. Arkadev, A. I. Kolomiytsev, M. A. Kumakhov, I. Y. Ponomazov, I. A. Khodeev, Yu. P. Chertov, I. M. Shakhparanov, “Broadband x-ray optics with large angle aperture,” Sov. Phys. Usp. 157, 529–537 (1989).
[CrossRef]

Baranov, V. K.

V. K. Baranov, “Properties of parabolic focons,” Opt. Mekh. Prom. 6, 1–5 (1965).

Beck, M.

R. Tatchyn, P. Csonka, H. Kilic, H. Watanabe, A. Fuller, M. Beck, A. Toor, J. Underwood, R. Catura, “Focusing of undulator light at SPEAR with a lacquer-coated mirror to power densities of 109 W/cm2,” in Soft X-Ray Optics and Technology, E.-E. Koch, F. Haber, G. Schmahl, eds., Proc. Soc. Photo-Opt. Instrum. Eng.733, 368–378 (1986).
[CrossRef]

Beswetterick, J. H.

R. E. Burge, J. H. Beswetterick, M. T. Brown, P. S. Charalambous, P. J. Duke, G. F. Foster, A. R. Hare, A. G. Michette, D. Morris, G. R. Morrison, A. W. Potts, T. Taguchi, “Scanning x-ray microscopy,” in Proceedings on X-Ray Instrumentation in Medicine and Biology, Plasma Physics, Astrophysics, and Synchrotron Radiation, R. Benattar, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.1140, 528–529 (1989).

Brown, M. T.

R. E. Burge, J. H. Beswetterick, M. T. Brown, P. S. Charalambous, P. J. Duke, G. F. Foster, A. R. Hare, A. G. Michette, D. Morris, G. R. Morrison, A. W. Potts, T. Taguchi, “Scanning x-ray microscopy,” in Proceedings on X-Ray Instrumentation in Medicine and Biology, Plasma Physics, Astrophysics, and Synchrotron Radiation, R. Benattar, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.1140, 528–529 (1989).

Burge, R. E.

R. E. Burge, J. H. Beswetterick, M. T. Brown, P. S. Charalambous, P. J. Duke, G. F. Foster, A. R. Hare, A. G. Michette, D. Morris, G. R. Morrison, A. W. Potts, T. Taguchi, “Scanning x-ray microscopy,” in Proceedings on X-Ray Instrumentation in Medicine and Biology, Plasma Physics, Astrophysics, and Synchrotron Radiation, R. Benattar, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.1140, 528–529 (1989).

Catura, R.

R. Tatchyn, P. Csonka, H. Kilic, H. Watanabe, A. Fuller, M. Beck, A. Toor, J. Underwood, R. Catura, “Focusing of undulator light at SPEAR with a lacquer-coated mirror to power densities of 109 W/cm2,” in Soft X-Ray Optics and Technology, E.-E. Koch, F. Haber, G. Schmahl, eds., Proc. Soc. Photo-Opt. Instrum. Eng.733, 368–378 (1986).
[CrossRef]

Charalambous, P. S.

R. E. Burge, J. H. Beswetterick, M. T. Brown, P. S. Charalambous, P. J. Duke, G. F. Foster, A. R. Hare, A. G. Michette, D. Morris, G. R. Morrison, A. W. Potts, T. Taguchi, “Scanning x-ray microscopy,” in Proceedings on X-Ray Instrumentation in Medicine and Biology, Plasma Physics, Astrophysics, and Synchrotron Radiation, R. Benattar, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.1140, 528–529 (1989).

Chertov, Yu. P.

V. A. Arkadev, A. I. Kolomiytsev, M. A. Kumakhov, I. Y. Ponomazov, I. A. Khodeev, Yu. P. Chertov, I. M. Shakhparanov, “Broadband x-ray optics with large angle aperture,” Sov. Phys. Usp. 157, 529–537 (1989).
[CrossRef]

Csonka, P.

R. Tatchyn, P. Csonka, H. Kilic, H. Watanabe, A. Fuller, M. Beck, A. Toor, J. Underwood, R. Catura, “Focusing of undulator light at SPEAR with a lacquer-coated mirror to power densities of 109 W/cm2,” in Soft X-Ray Optics and Technology, E.-E. Koch, F. Haber, G. Schmahl, eds., Proc. Soc. Photo-Opt. Instrum. Eng.733, 368–378 (1986).
[CrossRef]

Duke, P. J.

R. E. Burge, J. H. Beswetterick, M. T. Brown, P. S. Charalambous, P. J. Duke, G. F. Foster, A. R. Hare, A. G. Michette, D. Morris, G. R. Morrison, A. W. Potts, T. Taguchi, “Scanning x-ray microscopy,” in Proceedings on X-Ray Instrumentation in Medicine and Biology, Plasma Physics, Astrophysics, and Synchrotron Radiation, R. Benattar, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.1140, 528–529 (1989).

Foster, G. F.

R. E. Burge, J. H. Beswetterick, M. T. Brown, P. S. Charalambous, P. J. Duke, G. F. Foster, A. R. Hare, A. G. Michette, D. Morris, G. R. Morrison, A. W. Potts, T. Taguchi, “Scanning x-ray microscopy,” in Proceedings on X-Ray Instrumentation in Medicine and Biology, Plasma Physics, Astrophysics, and Synchrotron Radiation, R. Benattar, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.1140, 528–529 (1989).

Fujikawa, B.K.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B.K. Fujikawa, “Low-energy x-ray interaction coefficients: Photoabsorption, scattering and reflection,” At. Data Nucl. Data Tables 27, 1–144 (1982).
[CrossRef]

Fuller, A.

R. Tatchyn, P. Csonka, H. Kilic, H. Watanabe, A. Fuller, M. Beck, A. Toor, J. Underwood, R. Catura, “Focusing of undulator light at SPEAR with a lacquer-coated mirror to power densities of 109 W/cm2,” in Soft X-Ray Optics and Technology, E.-E. Koch, F. Haber, G. Schmahl, eds., Proc. Soc. Photo-Opt. Instrum. Eng.733, 368–378 (1986).
[CrossRef]

Hare, A. R.

R. E. Burge, J. H. Beswetterick, M. T. Brown, P. S. Charalambous, P. J. Duke, G. F. Foster, A. R. Hare, A. G. Michette, D. Morris, G. R. Morrison, A. W. Potts, T. Taguchi, “Scanning x-ray microscopy,” in Proceedings on X-Ray Instrumentation in Medicine and Biology, Plasma Physics, Astrophysics, and Synchrotron Radiation, R. Benattar, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.1140, 528–529 (1989).

Harris, S. E.

Henke, B. L.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B.K. Fujikawa, “Low-energy x-ray interaction coefficients: Photoabsorption, scattering and reflection,” At. Data Nucl. Data Tables 27, 1–144 (1982).
[CrossRef]

Hidaka, T.

Khodeev, I. A.

V. A. Arkadev, A. I. Kolomiytsev, M. A. Kumakhov, I. Y. Ponomazov, I. A. Khodeev, Yu. P. Chertov, I. M. Shakhparanov, “Broadband x-ray optics with large angle aperture,” Sov. Phys. Usp. 157, 529–537 (1989).
[CrossRef]

Kilic, H.

R. Tatchyn, P. Csonka, H. Kilic, H. Watanabe, A. Fuller, M. Beck, A. Toor, J. Underwood, R. Catura, “Focusing of undulator light at SPEAR with a lacquer-coated mirror to power densities of 109 W/cm2,” in Soft X-Ray Optics and Technology, E.-E. Koch, F. Haber, G. Schmahl, eds., Proc. Soc. Photo-Opt. Instrum. Eng.733, 368–378 (1986).
[CrossRef]

Kolomiytsev, A. I.

V. A. Arkadev, A. I. Kolomiytsev, M. A. Kumakhov, I. Y. Ponomazov, I. A. Khodeev, Yu. P. Chertov, I. M. Shakhparanov, “Broadband x-ray optics with large angle aperture,” Sov. Phys. Usp. 157, 529–537 (1989).
[CrossRef]

Kovalev, V. F.

A. V. Vinogradov, V. F. Kovalev, I. V. Kozhevnikov, V. V. Pustovalov, “The diffraction theory of grazing modes for x-ray mirrors and x-ray cavity,” Sov. Phys. Tech. Phys. 30, 335–344 (1986).

A. V. Vinogradov, V. F. Kovalev, I. V. Kozhevnikov, V. V. Pustovalov, “Concave mirrors for turning of x-ray beams,” Sov. Phys. Tech. Phys. 30, 144–150 (1986).

Kozhevnikov, I. V.

I. V. Kozhevnikov, “X-ray optical systems with manifold reflections,” Tr. Fiz. Inst. Akad. Nauk SSSR 196, 143–167 (1989).

A. V. Vinogradov, V. F. Kovalev, I. V. Kozhevnikov, V. V. Pustovalov, “Concave mirrors for turning of x-ray beams,” Sov. Phys. Tech. Phys. 30, 144–150 (1986).

A. V. Vinogradov, V. F. Kovalev, I. V. Kozhevnikov, V. V. Pustovalov, “The diffraction theory of grazing modes for x-ray mirrors and x-ray cavity,” Sov. Phys. Tech. Phys. 30, 335–344 (1986).

A. V. Vinogradov, N. N. Zorev, I. V. Kozhevnikov, “On the limitations and possibilities of soft x-ray optics,” Tr. Fiz. Inst. Akad. Nauk SSSR 176, 195–210 (1986).

A. V. Vinogradov, N. N. Zorev, I. V. Kozhevnikov, I. I. Yakushkin, “On the effect of total x-ray reflection,” Sov. Phys. JETP 62, 1225–1230 (1985).

A. V. Vinogradov, I. V. Kozhevnikov, “Properties of x-ray waveguides,” Sov. Phys. Tech. Phys. 29, 1023–1026 (1984).

Kumakhov, M. A.

V. A. Arkadev, A. I. Kolomiytsev, M. A. Kumakhov, I. Y. Ponomazov, I. A. Khodeev, Yu. P. Chertov, I. M. Shakhparanov, “Broadband x-ray optics with large angle aperture,” Sov. Phys. Usp. 157, 529–537 (1989).
[CrossRef]

Lee, P.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B.K. Fujikawa, “Low-energy x-ray interaction coefficients: Photoabsorption, scattering and reflection,” At. Data Nucl. Data Tables 27, 1–144 (1982).
[CrossRef]

Macklin, J. J.

Michette, A. G.

R. E. Burge, J. H. Beswetterick, M. T. Brown, P. S. Charalambous, P. J. Duke, G. F. Foster, A. R. Hare, A. G. Michette, D. Morris, G. R. Morrison, A. W. Potts, T. Taguchi, “Scanning x-ray microscopy,” in Proceedings on X-Ray Instrumentation in Medicine and Biology, Plasma Physics, Astrophysics, and Synchrotron Radiation, R. Benattar, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.1140, 528–529 (1989).

Mitsuhashi, Y.

Morris, D.

R. E. Burge, J. H. Beswetterick, M. T. Brown, P. S. Charalambous, P. J. Duke, G. F. Foster, A. R. Hare, A. G. Michette, D. Morris, G. R. Morrison, A. W. Potts, T. Taguchi, “Scanning x-ray microscopy,” in Proceedings on X-Ray Instrumentation in Medicine and Biology, Plasma Physics, Astrophysics, and Synchrotron Radiation, R. Benattar, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.1140, 528–529 (1989).

Morrison, G. R.

R. E. Burge, J. H. Beswetterick, M. T. Brown, P. S. Charalambous, P. J. Duke, G. F. Foster, A. R. Hare, A. G. Michette, D. Morris, G. R. Morrison, A. W. Potts, T. Taguchi, “Scanning x-ray microscopy,” in Proceedings on X-Ray Instrumentation in Medicine and Biology, Plasma Physics, Astrophysics, and Synchrotron Radiation, R. Benattar, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.1140, 528–529 (1989).

Nishi, M.

Ponomazov, I. Y.

V. A. Arkadev, A. I. Kolomiytsev, M. A. Kumakhov, I. Y. Ponomazov, I. A. Khodeev, Yu. P. Chertov, I. M. Shakhparanov, “Broadband x-ray optics with large angle aperture,” Sov. Phys. Usp. 157, 529–537 (1989).
[CrossRef]

Popov, A. V.

A. V. Vinogradov, A. V. Popov, “On x-ray reflection at grazing incidence,” Opt. Spectrosc. 65, 1109–1111 (1988).

Potts, A. W.

R. E. Burge, J. H. Beswetterick, M. T. Brown, P. S. Charalambous, P. J. Duke, G. F. Foster, A. R. Hare, A. G. Michette, D. Morris, G. R. Morrison, A. W. Potts, T. Taguchi, “Scanning x-ray microscopy,” in Proceedings on X-Ray Instrumentation in Medicine and Biology, Plasma Physics, Astrophysics, and Synchrotron Radiation, R. Benattar, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.1140, 528–529 (1989).

Pustovalov, V. V.

A. V. Vinogradov, V. F. Kovalev, I. V. Kozhevnikov, V. V. Pustovalov, “The diffraction theory of grazing modes for x-ray mirrors and x-ray cavity,” Sov. Phys. Tech. Phys. 30, 335–344 (1986).

A. V. Vinogradov, V. F. Kovalev, I. V. Kozhevnikov, V. V. Pustovalov, “Concave mirrors for turning of x-ray beams,” Sov. Phys. Tech. Phys. 30, 144–150 (1986).

Shakhparanov, I. M.

V. A. Arkadev, A. I. Kolomiytsev, M. A. Kumakhov, I. Y. Ponomazov, I. A. Khodeev, Yu. P. Chertov, I. M. Shakhparanov, “Broadband x-ray optics with large angle aperture,” Sov. Phys. Usp. 157, 529–537 (1989).
[CrossRef]

Shimabukuro, R. L.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B.K. Fujikawa, “Low-energy x-ray interaction coefficients: Photoabsorption, scattering and reflection,” At. Data Nucl. Data Tables 27, 1–144 (1982).
[CrossRef]

Suzuki, I. H.

Taguchi, T.

R. E. Burge, J. H. Beswetterick, M. T. Brown, P. S. Charalambous, P. J. Duke, G. F. Foster, A. R. Hare, A. G. Michette, D. Morris, G. R. Morrison, A. W. Potts, T. Taguchi, “Scanning x-ray microscopy,” in Proceedings on X-Ray Instrumentation in Medicine and Biology, Plasma Physics, Astrophysics, and Synchrotron Radiation, R. Benattar, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.1140, 528–529 (1989).

Tanaka, T. J.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B.K. Fujikawa, “Low-energy x-ray interaction coefficients: Photoabsorption, scattering and reflection,” At. Data Nucl. Data Tables 27, 1–144 (1982).
[CrossRef]

Tatchyn, R.

R. Tatchyn, P. Csonka, H. Kilic, H. Watanabe, A. Fuller, M. Beck, A. Toor, J. Underwood, R. Catura, “Focusing of undulator light at SPEAR with a lacquer-coated mirror to power densities of 109 W/cm2,” in Soft X-Ray Optics and Technology, E.-E. Koch, F. Haber, G. Schmahl, eds., Proc. Soc. Photo-Opt. Instrum. Eng.733, 368–378 (1986).
[CrossRef]

Tolstikhin, O. I.

A. V. Vinogradov, O. I. Tolstikhin, “Soft x-ray concentrators,” Tr. Fiz. Inst. Akad. Nauk SSSR 196, 168–181 (1989).

A. V. Vinogradov, O. I. Tolstikhin, “Properties of an ideal optical x-ray concentrator,” Sov. Phys. Lebedev Inst. Rep. 9, 28–33 (1985).

Toor, A.

R. Tatchyn, P. Csonka, H. Kilic, H. Watanabe, A. Fuller, M. Beck, A. Toor, J. Underwood, R. Catura, “Focusing of undulator light at SPEAR with a lacquer-coated mirror to power densities of 109 W/cm2,” in Soft X-Ray Optics and Technology, E.-E. Koch, F. Haber, G. Schmahl, eds., Proc. Soc. Photo-Opt. Instrum. Eng.733, 368–378 (1986).
[CrossRef]

Underwood, J.

R. Tatchyn, P. Csonka, H. Kilic, H. Watanabe, A. Fuller, M. Beck, A. Toor, J. Underwood, R. Catura, “Focusing of undulator light at SPEAR with a lacquer-coated mirror to power densities of 109 W/cm2,” in Soft X-Ray Optics and Technology, E.-E. Koch, F. Haber, G. Schmahl, eds., Proc. Soc. Photo-Opt. Instrum. Eng.733, 368–378 (1986).
[CrossRef]

Vinogradov, A. V.

A. V. Vinogradov, O. I. Tolstikhin, “Soft x-ray concentrators,” Tr. Fiz. Inst. Akad. Nauk SSSR 196, 168–181 (1989).

A. V. Vinogradov, A. V. Popov, “On x-ray reflection at grazing incidence,” Opt. Spectrosc. 65, 1109–1111 (1988).

A. V. Vinogradov, “XUV cavity and pumping optics,” J. Phys. 47, 286–297 (1986).

A. V. Vinogradov, V. F. Kovalev, I. V. Kozhevnikov, V. V. Pustovalov, “Concave mirrors for turning of x-ray beams,” Sov. Phys. Tech. Phys. 30, 144–150 (1986).

A. V. Vinogradov, V. F. Kovalev, I. V. Kozhevnikov, V. V. Pustovalov, “The diffraction theory of grazing modes for x-ray mirrors and x-ray cavity,” Sov. Phys. Tech. Phys. 30, 335–344 (1986).

A. V. Vinogradov, N. N. Zorev, I. V. Kozhevnikov, “On the limitations and possibilities of soft x-ray optics,” Tr. Fiz. Inst. Akad. Nauk SSSR 176, 195–210 (1986).

A. V. Vinogradov, N. N. Zorev, I. V. Kozhevnikov, I. I. Yakushkin, “On the effect of total x-ray reflection,” Sov. Phys. JETP 62, 1225–1230 (1985).

A. V. Vinogradov, O. I. Tolstikhin, “Properties of an ideal optical x-ray concentrator,” Sov. Phys. Lebedev Inst. Rep. 9, 28–33 (1985).

A. V. Vinogradov, I. V. Kozhevnikov, “Properties of x-ray waveguides,” Sov. Phys. Tech. Phys. 29, 1023–1026 (1984).

Watanabe, H.

R. Tatchyn, P. Csonka, H. Kilic, H. Watanabe, A. Fuller, M. Beck, A. Toor, J. Underwood, R. Catura, “Focusing of undulator light at SPEAR with a lacquer-coated mirror to power densities of 109 W/cm2,” in Soft X-Ray Optics and Technology, E.-E. Koch, F. Haber, G. Schmahl, eds., Proc. Soc. Photo-Opt. Instrum. Eng.733, 368–378 (1986).
[CrossRef]

Watanabe, M.

Welford, W. D.

W. D. Welford, L. Winston, The Optics of Nonimaging Concentrators (Academic, New York, 1978).

Winston, L.

W. D. Welford, L. Winston, The Optics of Nonimaging Concentrators (Academic, New York, 1978).

Yakushkin, I. I.

A. V. Vinogradov, N. N. Zorev, I. V. Kozhevnikov, I. I. Yakushkin, “On the effect of total x-ray reflection,” Sov. Phys. JETP 62, 1225–1230 (1985).

Young, J. E.

Zorev, N. N.

A. V. Vinogradov, N. N. Zorev, I. V. Kozhevnikov, “On the limitations and possibilities of soft x-ray optics,” Tr. Fiz. Inst. Akad. Nauk SSSR 176, 195–210 (1986).

A. V. Vinogradov, N. N. Zorev, I. V. Kozhevnikov, I. I. Yakushkin, “On the effect of total x-ray reflection,” Sov. Phys. JETP 62, 1225–1230 (1985).

Appl. Opt. (1)

At. Data Nucl. Data Tables (1)

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B.K. Fujikawa, “Low-energy x-ray interaction coefficients: Photoabsorption, scattering and reflection,” At. Data Nucl. Data Tables 27, 1–144 (1982).
[CrossRef]

J. Phys. (1)

A. V. Vinogradov, “XUV cavity and pumping optics,” J. Phys. 47, 286–297 (1986).

Opt. Lett. (1)

Opt. Mekh. Prom. (1)

V. K. Baranov, “Properties of parabolic focons,” Opt. Mekh. Prom. 6, 1–5 (1965).

Opt. Spectrosc. (1)

A. V. Vinogradov, A. V. Popov, “On x-ray reflection at grazing incidence,” Opt. Spectrosc. 65, 1109–1111 (1988).

Sov. Phys. JETP (1)

A. V. Vinogradov, N. N. Zorev, I. V. Kozhevnikov, I. I. Yakushkin, “On the effect of total x-ray reflection,” Sov. Phys. JETP 62, 1225–1230 (1985).

Sov. Phys. Lebedev Inst. Rep. (1)

A. V. Vinogradov, O. I. Tolstikhin, “Properties of an ideal optical x-ray concentrator,” Sov. Phys. Lebedev Inst. Rep. 9, 28–33 (1985).

Sov. Phys. Tech. Phys. (3)

A. V. Vinogradov, V. F. Kovalev, I. V. Kozhevnikov, V. V. Pustovalov, “Concave mirrors for turning of x-ray beams,” Sov. Phys. Tech. Phys. 30, 144–150 (1986).

A. V. Vinogradov, V. F. Kovalev, I. V. Kozhevnikov, V. V. Pustovalov, “The diffraction theory of grazing modes for x-ray mirrors and x-ray cavity,” Sov. Phys. Tech. Phys. 30, 335–344 (1986).

A. V. Vinogradov, I. V. Kozhevnikov, “Properties of x-ray waveguides,” Sov. Phys. Tech. Phys. 29, 1023–1026 (1984).

Sov. Phys. Usp. (1)

V. A. Arkadev, A. I. Kolomiytsev, M. A. Kumakhov, I. Y. Ponomazov, I. A. Khodeev, Yu. P. Chertov, I. M. Shakhparanov, “Broadband x-ray optics with large angle aperture,” Sov. Phys. Usp. 157, 529–537 (1989).
[CrossRef]

Tr. Fiz. Inst. Akad. Nauk SSSR (3)

I. V. Kozhevnikov, “X-ray optical systems with manifold reflections,” Tr. Fiz. Inst. Akad. Nauk SSSR 196, 143–167 (1989).

A. V. Vinogradov, O. I. Tolstikhin, “Soft x-ray concentrators,” Tr. Fiz. Inst. Akad. Nauk SSSR 196, 168–181 (1989).

A. V. Vinogradov, N. N. Zorev, I. V. Kozhevnikov, “On the limitations and possibilities of soft x-ray optics,” Tr. Fiz. Inst. Akad. Nauk SSSR 176, 195–210 (1986).

Other (4)

R. Benattar, ed., X-Ray Instrumentation in Medicine and Biology, Plasma Physics, Astrophysics, and Synchrotron Radiation, Proc. Soc. Photo-Opt. Instrum. Eng.1140 (1989).

W. D. Welford, L. Winston, The Optics of Nonimaging Concentrators (Academic, New York, 1978).

R. E. Burge, J. H. Beswetterick, M. T. Brown, P. S. Charalambous, P. J. Duke, G. F. Foster, A. R. Hare, A. G. Michette, D. Morris, G. R. Morrison, A. W. Potts, T. Taguchi, “Scanning x-ray microscopy,” in Proceedings on X-Ray Instrumentation in Medicine and Biology, Plasma Physics, Astrophysics, and Synchrotron Radiation, R. Benattar, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.1140, 528–529 (1989).

R. Tatchyn, P. Csonka, H. Kilic, H. Watanabe, A. Fuller, M. Beck, A. Toor, J. Underwood, R. Catura, “Focusing of undulator light at SPEAR with a lacquer-coated mirror to power densities of 109 W/cm2,” in Soft X-Ray Optics and Technology, E.-E. Koch, F. Haber, G. Schmahl, eds., Proc. Soc. Photo-Opt. Instrum. Eng.733, 368–378 (1986).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Efficiency of paraboloid and spiral x-ray collimators with different coating materials: ∗, paraboloid, formulas for efficiency ν(λ) in terms of Re and Im are from Ref. 13; ⟐, spiral collimator, calculations were made according to Eq. (5).

Fig. 2
Fig. 2

Spiral collimator.

Equations (6)

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ρ ( φ ) = ρ 0 exp π φ tan φ 0 , φ 0 π 2 ,
φ 0 φ π , ρ 0 ρ ρ 0 exp π φ 0 tan φ 0 .
ν = sin 2 φ 0 2 + 1 2 φ 0 π sin φ j = 1 n ( φ ) R [ θ j ( φ ) ] d φ ,
j = 1 n ( φ ) R [ θ j ( φ ) ] φ 0 0 θ j = π 2 exp ( ξ φ ) ξ = 2 Im 1 1 .
ν max ( λ ) = 1 2 1 + exp ( ξ π ) 1 + ξ 2 , ξ = 2 Im 1 1 .
r ( θ ) = 1 + A θ , θ 0 ,

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