Abstract

A Monte Carlo ray-trace model of nonideal microchannel plate (MCP) x-ray optics is described. The model takes into account angular misalignments, both transverse and axial, between the channels and the multifiber bundles; pincushion distortion of the square channels; radiusing of the channel vertices; and scattering from microroughness of the channel walls. The model also takes into account the spectrum and nonisotropic nature of the illuminating radiation. Using optical, scanning electron, and atomic force microscopies, as well as x-ray scattering data obtained with a laser plasma x-ray source, we have determined a partial error budget for the focusing action of a real square-pore MCP, leaving only the interchannel long-axis misalignment to be found by comparison of simulated and measured images. The power of the Monte Carlo model in directing the future development of MCP optics is illustrated.

© 1997 Optical Society of America

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  1. H. N. Chapman, K. A. Nugent, S. W. Wilkins, “X-ray focusing using square channel capillary arrays,” Rev. Sci. Instrum. 62, 1542–1561 (1991).
    [CrossRef]
  2. P. Kaaret, P. Geissbühler, A. Chen, E. Glavinas, “X-ray focusing using microchannel plates,” Appl. Opt. 31, 7339–7343 (1992).
    [CrossRef] [PubMed]
  3. G. W. Fraser, A. N. Brunton, J. E. Lees, J. F. Pearson, W. B. Feller, “X-ray focusing using square-pore microchannel plates: first observation of cruxiform image structure,” Nucl. Instrum. Methods A 324, 404–407 (1993).
    [CrossRef]
  4. G. W. Fraser, A. N. Brunton, J. E. Lees, D. L. Emberson, “Production of quasiparallel X-ray beams using microchannel plate X-ray lenses,” Nucl. Instrum. Methods A 334, 579–588 (1993).
    [CrossRef]
  5. G. W. Fraser, A. N. Brunton, J. E. Lees, J. F. Pearson, R. Willingale, D. L. Emberson, W. B. Feller, M. Stedman, J. Haycocks, “Development of microchannel plate (MCP) X-ray optics,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R. B. Hoover, A. B. C. Walker, eds. Proc. SPIE2011, 215–226 (1993).
    [CrossRef]
  6. W. C. Priedhorsky, A. G. Peele, K. A. Nugent, “X-ray all-sky monitor with extraordinary sensitivity,” Mon. Not. R. Astron. Soc. 279, 733–750 (1996).
    [CrossRef]
  7. A. G. Peele, K. A. Nugent, A. V. Rode, K. Gabel, M. C. Richardson, R. Strack, W. Siegmund, “X-ray focusing using lobster-eye optics: a comparison of theory with experiment,” Appl. Opt. 35, 4420–4425 (1996).
    [CrossRef] [PubMed]
  8. H. N. Chapman, K. A. Nugent, S. W. Wilkins, “X-ray focusing using cylindrical-channel capillary arrays. I. Theory,” Appl. Opt. 32, 6316–6332 (1993).
    [CrossRef] [PubMed]
  9. J. R. P. Angel, “Lobster eyes as x-ray telescopes,” Astrophys. J. 233, 364–373 (1979).
    [CrossRef]
  10. A. N. Brunton, “MCP x-ray optics,” Ph.D. thesis (University of Leicester, UK, 1995).
  11. J. L. Wiza, “Microchannel plate detectors,” Nucl. Instrum. Methods 162, 587–601 (1979).
    [CrossRef]
  12. E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).
    [CrossRef]
  13. B. L. Henke, “Low energy x-ray interactions: photoionization, scattering, specular and Bragg reflection,” in Topical Conference on Low-Energy X-ray Diagnostics, , D. Attwood, B. Henke, eds. (American Institute of Physics, New York, 1981), pp. 146–155.
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    [CrossRef]
  17. P. D. Rockett, C. R. Bird, C. J. Hailey, D. Sullivan, D. B. Brown, P. G. Burkhalter, “X-ray calibration of Kodak direct exposure film,” Appl. Opt. 24, 2536–2542 (1985).
    [CrossRef] [PubMed]
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    [CrossRef]
  19. H. N. Chapman, K. A. Nugent, S. W. Wilkins, “X-ray focusing using cylindrical-channel capillary arrays. II. Experiments,” Appl. Opt. 32, 6333–6340 (1993).
    [CrossRef] [PubMed]
  20. A. N. Brunton, J. E. Lees, G. W. Fraser, A. S. Tremsin, W. B. Feller, P. L. White, “MCP based x-ray collimators for lithography of semiconductor devices,” in Multilayer and Grazing Incidence X-ray and EUV Optics III, R. B. Hoover, A. B. C. Walker, eds., Proc. SPIE Vol. 2805, 212–221 (1996).
    [CrossRef]
  21. National Physical Laboratory, Division of Mechanical and Optical Metrology, Teddington, Middlesex, TW11 0LW, UK.

1996 (2)

W. C. Priedhorsky, A. G. Peele, K. A. Nugent, “X-ray all-sky monitor with extraordinary sensitivity,” Mon. Not. R. Astron. Soc. 279, 733–750 (1996).
[CrossRef]

A. G. Peele, K. A. Nugent, A. V. Rode, K. Gabel, M. C. Richardson, R. Strack, W. Siegmund, “X-ray focusing using lobster-eye optics: a comparison of theory with experiment,” Appl. Opt. 35, 4420–4425 (1996).
[CrossRef] [PubMed]

1993 (4)

H. N. Chapman, K. A. Nugent, S. W. Wilkins, “X-ray focusing using cylindrical-channel capillary arrays. I. Theory,” Appl. Opt. 32, 6316–6332 (1993).
[CrossRef] [PubMed]

G. W. Fraser, A. N. Brunton, J. E. Lees, J. F. Pearson, W. B. Feller, “X-ray focusing using square-pore microchannel plates: first observation of cruxiform image structure,” Nucl. Instrum. Methods A 324, 404–407 (1993).
[CrossRef]

G. W. Fraser, A. N. Brunton, J. E. Lees, D. L. Emberson, “Production of quasiparallel X-ray beams using microchannel plate X-ray lenses,” Nucl. Instrum. Methods A 334, 579–588 (1993).
[CrossRef]

H. N. Chapman, K. A. Nugent, S. W. Wilkins, “X-ray focusing using cylindrical-channel capillary arrays. II. Experiments,” Appl. Opt. 32, 6333–6340 (1993).
[CrossRef] [PubMed]

1992 (1)

1991 (1)

H. N. Chapman, K. A. Nugent, S. W. Wilkins, “X-ray focusing using square channel capillary arrays,” Rev. Sci. Instrum. 62, 1542–1561 (1991).
[CrossRef]

1986 (1)

B. L. Henke, J. Y. Uejio, G. F. Stone, C. H. Dittmore, F. G. Fujiwara, “High-energy x-ray response of photographic films: models and measurement,” J. Opt. Soc. Am. B 3, 1540–1550 (1986).
[CrossRef]

1985 (1)

1979 (3)

J. R. P. Angel, “Lobster eyes as x-ray telescopes,” Astrophys. J. 233, 364–373 (1979).
[CrossRef]

J. L. Wiza, “Microchannel plate detectors,” Nucl. Instrum. Methods 162, 587–601 (1979).
[CrossRef]

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).
[CrossRef]

Angel, J. R. P.

J. R. P. Angel, “Lobster eyes as x-ray telescopes,” Astrophys. J. 233, 364–373 (1979).
[CrossRef]

Batani, D.

I. C. E. Turcu, I. N. Ross, P. Trenda, C. W. Wharton, R. A. Meldrum, H. Daido, M. S. Schulz, P. Fluck, A. G. Michette, A. P. Juna, J. R. Maldonado, H. Shields, G. J. Tallents, L. Dwivedi, J. Krishnan, D. L. Stevens, T. J. Jenner, D. Batani, H. Goodson, “Picosecond excimer laser-plasma x-ray source for microscopy, biochemistry and lithography,” in Applications of Laser Plasma Radiation, M. C. Richardson, ed., Proc. SPIE2015, 243–260 (1994).
[CrossRef]

Bird, C. R.

Brown, D. B.

Brunton, A. N.

G. W. Fraser, A. N. Brunton, J. E. Lees, J. F. Pearson, W. B. Feller, “X-ray focusing using square-pore microchannel plates: first observation of cruxiform image structure,” Nucl. Instrum. Methods A 324, 404–407 (1993).
[CrossRef]

G. W. Fraser, A. N. Brunton, J. E. Lees, D. L. Emberson, “Production of quasiparallel X-ray beams using microchannel plate X-ray lenses,” Nucl. Instrum. Methods A 334, 579–588 (1993).
[CrossRef]

G. W. Fraser, A. N. Brunton, J. E. Lees, J. F. Pearson, R. Willingale, D. L. Emberson, W. B. Feller, M. Stedman, J. Haycocks, “Development of microchannel plate (MCP) X-ray optics,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R. B. Hoover, A. B. C. Walker, eds. Proc. SPIE2011, 215–226 (1993).
[CrossRef]

A. N. Brunton, “MCP x-ray optics,” Ph.D. thesis (University of Leicester, UK, 1995).

A. N. Brunton, J. E. Lees, G. W. Fraser, A. S. Tremsin, W. B. Feller, P. L. White, “MCP based x-ray collimators for lithography of semiconductor devices,” in Multilayer and Grazing Incidence X-ray and EUV Optics III, R. B. Hoover, A. B. C. Walker, eds., Proc. SPIE Vol. 2805, 212–221 (1996).
[CrossRef]

Burkhalter, P. G.

Chapman, H. N.

H. N. Chapman, K. A. Nugent, S. W. Wilkins, “X-ray focusing using cylindrical-channel capillary arrays. I. Theory,” Appl. Opt. 32, 6316–6332 (1993).
[CrossRef] [PubMed]

H. N. Chapman, K. A. Nugent, S. W. Wilkins, “X-ray focusing using cylindrical-channel capillary arrays. II. Experiments,” Appl. Opt. 32, 6333–6340 (1993).
[CrossRef] [PubMed]

H. N. Chapman, K. A. Nugent, S. W. Wilkins, “X-ray focusing using square channel capillary arrays,” Rev. Sci. Instrum. 62, 1542–1561 (1991).
[CrossRef]

Chen, A.

Church, E. L.

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).
[CrossRef]

Cromer, D. T.

D. T. Cromer, D. Liberman, “Relativistic calculation of anomolous scattering factors for x-rays,’ (Los Alamos Laboratory, Los Alamos, N.M., 1970).

Daido, H.

I. C. E. Turcu, I. N. Ross, P. Trenda, C. W. Wharton, R. A. Meldrum, H. Daido, M. S. Schulz, P. Fluck, A. G. Michette, A. P. Juna, J. R. Maldonado, H. Shields, G. J. Tallents, L. Dwivedi, J. Krishnan, D. L. Stevens, T. J. Jenner, D. Batani, H. Goodson, “Picosecond excimer laser-plasma x-ray source for microscopy, biochemistry and lithography,” in Applications of Laser Plasma Radiation, M. C. Richardson, ed., Proc. SPIE2015, 243–260 (1994).
[CrossRef]

Dittmore, C. H.

B. L. Henke, J. Y. Uejio, G. F. Stone, C. H. Dittmore, F. G. Fujiwara, “High-energy x-ray response of photographic films: models and measurement,” J. Opt. Soc. Am. B 3, 1540–1550 (1986).
[CrossRef]

Dwivedi, L.

I. C. E. Turcu, I. N. Ross, P. Trenda, C. W. Wharton, R. A. Meldrum, H. Daido, M. S. Schulz, P. Fluck, A. G. Michette, A. P. Juna, J. R. Maldonado, H. Shields, G. J. Tallents, L. Dwivedi, J. Krishnan, D. L. Stevens, T. J. Jenner, D. Batani, H. Goodson, “Picosecond excimer laser-plasma x-ray source for microscopy, biochemistry and lithography,” in Applications of Laser Plasma Radiation, M. C. Richardson, ed., Proc. SPIE2015, 243–260 (1994).
[CrossRef]

Emberson, D. L.

G. W. Fraser, A. N. Brunton, J. E. Lees, D. L. Emberson, “Production of quasiparallel X-ray beams using microchannel plate X-ray lenses,” Nucl. Instrum. Methods A 334, 579–588 (1993).
[CrossRef]

G. W. Fraser, A. N. Brunton, J. E. Lees, J. F. Pearson, R. Willingale, D. L. Emberson, W. B. Feller, M. Stedman, J. Haycocks, “Development of microchannel plate (MCP) X-ray optics,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R. B. Hoover, A. B. C. Walker, eds. Proc. SPIE2011, 215–226 (1993).
[CrossRef]

Feller, W. B.

G. W. Fraser, A. N. Brunton, J. E. Lees, J. F. Pearson, W. B. Feller, “X-ray focusing using square-pore microchannel plates: first observation of cruxiform image structure,” Nucl. Instrum. Methods A 324, 404–407 (1993).
[CrossRef]

G. W. Fraser, A. N. Brunton, J. E. Lees, J. F. Pearson, R. Willingale, D. L. Emberson, W. B. Feller, M. Stedman, J. Haycocks, “Development of microchannel plate (MCP) X-ray optics,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R. B. Hoover, A. B. C. Walker, eds. Proc. SPIE2011, 215–226 (1993).
[CrossRef]

A. N. Brunton, J. E. Lees, G. W. Fraser, A. S. Tremsin, W. B. Feller, P. L. White, “MCP based x-ray collimators for lithography of semiconductor devices,” in Multilayer and Grazing Incidence X-ray and EUV Optics III, R. B. Hoover, A. B. C. Walker, eds., Proc. SPIE Vol. 2805, 212–221 (1996).
[CrossRef]

Fluck, P.

I. C. E. Turcu, I. N. Ross, P. Trenda, C. W. Wharton, R. A. Meldrum, H. Daido, M. S. Schulz, P. Fluck, A. G. Michette, A. P. Juna, J. R. Maldonado, H. Shields, G. J. Tallents, L. Dwivedi, J. Krishnan, D. L. Stevens, T. J. Jenner, D. Batani, H. Goodson, “Picosecond excimer laser-plasma x-ray source for microscopy, biochemistry and lithography,” in Applications of Laser Plasma Radiation, M. C. Richardson, ed., Proc. SPIE2015, 243–260 (1994).
[CrossRef]

Fraser, G. W.

G. W. Fraser, A. N. Brunton, J. E. Lees, J. F. Pearson, W. B. Feller, “X-ray focusing using square-pore microchannel plates: first observation of cruxiform image structure,” Nucl. Instrum. Methods A 324, 404–407 (1993).
[CrossRef]

G. W. Fraser, A. N. Brunton, J. E. Lees, D. L. Emberson, “Production of quasiparallel X-ray beams using microchannel plate X-ray lenses,” Nucl. Instrum. Methods A 334, 579–588 (1993).
[CrossRef]

G. W. Fraser, A. N. Brunton, J. E. Lees, J. F. Pearson, R. Willingale, D. L. Emberson, W. B. Feller, M. Stedman, J. Haycocks, “Development of microchannel plate (MCP) X-ray optics,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R. B. Hoover, A. B. C. Walker, eds. Proc. SPIE2011, 215–226 (1993).
[CrossRef]

A. N. Brunton, J. E. Lees, G. W. Fraser, A. S. Tremsin, W. B. Feller, P. L. White, “MCP based x-ray collimators for lithography of semiconductor devices,” in Multilayer and Grazing Incidence X-ray and EUV Optics III, R. B. Hoover, A. B. C. Walker, eds., Proc. SPIE Vol. 2805, 212–221 (1996).
[CrossRef]

Fujiwara, F. G.

B. L. Henke, J. Y. Uejio, G. F. Stone, C. H. Dittmore, F. G. Fujiwara, “High-energy x-ray response of photographic films: models and measurement,” J. Opt. Soc. Am. B 3, 1540–1550 (1986).
[CrossRef]

Gabel, K.

A. G. Peele, K. A. Nugent, A. V. Rode, K. Gabel, M. C. Richardson, R. Strack, W. Siegmund, “X-ray focusing using lobster-eye optics: a comparison of theory with experiment,” Appl. Opt. 35, 4420–4425 (1996).
[CrossRef] [PubMed]

Geissbühler, P.

Glavinas, E.

Goodson, H.

I. C. E. Turcu, I. N. Ross, P. Trenda, C. W. Wharton, R. A. Meldrum, H. Daido, M. S. Schulz, P. Fluck, A. G. Michette, A. P. Juna, J. R. Maldonado, H. Shields, G. J. Tallents, L. Dwivedi, J. Krishnan, D. L. Stevens, T. J. Jenner, D. Batani, H. Goodson, “Picosecond excimer laser-plasma x-ray source for microscopy, biochemistry and lithography,” in Applications of Laser Plasma Radiation, M. C. Richardson, ed., Proc. SPIE2015, 243–260 (1994).
[CrossRef]

Hailey, C. J.

Haycocks, J.

G. W. Fraser, A. N. Brunton, J. E. Lees, J. F. Pearson, R. Willingale, D. L. Emberson, W. B. Feller, M. Stedman, J. Haycocks, “Development of microchannel plate (MCP) X-ray optics,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R. B. Hoover, A. B. C. Walker, eds. Proc. SPIE2011, 215–226 (1993).
[CrossRef]

Henke, B. L.

B. L. Henke, J. Y. Uejio, G. F. Stone, C. H. Dittmore, F. G. Fujiwara, “High-energy x-ray response of photographic films: models and measurement,” J. Opt. Soc. Am. B 3, 1540–1550 (1986).
[CrossRef]

B. L. Henke, “Low energy x-ray interactions: photoionization, scattering, specular and Bragg reflection,” in Topical Conference on Low-Energy X-ray Diagnostics, , D. Attwood, B. Henke, eds. (American Institute of Physics, New York, 1981), pp. 146–155.

Jenkinson, H. A.

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).
[CrossRef]

Jenner, T. J.

I. C. E. Turcu, I. N. Ross, P. Trenda, C. W. Wharton, R. A. Meldrum, H. Daido, M. S. Schulz, P. Fluck, A. G. Michette, A. P. Juna, J. R. Maldonado, H. Shields, G. J. Tallents, L. Dwivedi, J. Krishnan, D. L. Stevens, T. J. Jenner, D. Batani, H. Goodson, “Picosecond excimer laser-plasma x-ray source for microscopy, biochemistry and lithography,” in Applications of Laser Plasma Radiation, M. C. Richardson, ed., Proc. SPIE2015, 243–260 (1994).
[CrossRef]

Juna, A. P.

I. C. E. Turcu, I. N. Ross, P. Trenda, C. W. Wharton, R. A. Meldrum, H. Daido, M. S. Schulz, P. Fluck, A. G. Michette, A. P. Juna, J. R. Maldonado, H. Shields, G. J. Tallents, L. Dwivedi, J. Krishnan, D. L. Stevens, T. J. Jenner, D. Batani, H. Goodson, “Picosecond excimer laser-plasma x-ray source for microscopy, biochemistry and lithography,” in Applications of Laser Plasma Radiation, M. C. Richardson, ed., Proc. SPIE2015, 243–260 (1994).
[CrossRef]

Kaaret, P.

Krishnan, J.

I. C. E. Turcu, I. N. Ross, P. Trenda, C. W. Wharton, R. A. Meldrum, H. Daido, M. S. Schulz, P. Fluck, A. G. Michette, A. P. Juna, J. R. Maldonado, H. Shields, G. J. Tallents, L. Dwivedi, J. Krishnan, D. L. Stevens, T. J. Jenner, D. Batani, H. Goodson, “Picosecond excimer laser-plasma x-ray source for microscopy, biochemistry and lithography,” in Applications of Laser Plasma Radiation, M. C. Richardson, ed., Proc. SPIE2015, 243–260 (1994).
[CrossRef]

Lees, J. E.

G. W. Fraser, A. N. Brunton, J. E. Lees, J. F. Pearson, W. B. Feller, “X-ray focusing using square-pore microchannel plates: first observation of cruxiform image structure,” Nucl. Instrum. Methods A 324, 404–407 (1993).
[CrossRef]

G. W. Fraser, A. N. Brunton, J. E. Lees, D. L. Emberson, “Production of quasiparallel X-ray beams using microchannel plate X-ray lenses,” Nucl. Instrum. Methods A 334, 579–588 (1993).
[CrossRef]

G. W. Fraser, A. N. Brunton, J. E. Lees, J. F. Pearson, R. Willingale, D. L. Emberson, W. B. Feller, M. Stedman, J. Haycocks, “Development of microchannel plate (MCP) X-ray optics,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R. B. Hoover, A. B. C. Walker, eds. Proc. SPIE2011, 215–226 (1993).
[CrossRef]

A. N. Brunton, J. E. Lees, G. W. Fraser, A. S. Tremsin, W. B. Feller, P. L. White, “MCP based x-ray collimators for lithography of semiconductor devices,” in Multilayer and Grazing Incidence X-ray and EUV Optics III, R. B. Hoover, A. B. C. Walker, eds., Proc. SPIE Vol. 2805, 212–221 (1996).
[CrossRef]

Liberman, D.

D. T. Cromer, D. Liberman, “Relativistic calculation of anomolous scattering factors for x-rays,’ (Los Alamos Laboratory, Los Alamos, N.M., 1970).

Maldonado, J. R.

I. C. E. Turcu, I. N. Ross, P. Trenda, C. W. Wharton, R. A. Meldrum, H. Daido, M. S. Schulz, P. Fluck, A. G. Michette, A. P. Juna, J. R. Maldonado, H. Shields, G. J. Tallents, L. Dwivedi, J. Krishnan, D. L. Stevens, T. J. Jenner, D. Batani, H. Goodson, “Picosecond excimer laser-plasma x-ray source for microscopy, biochemistry and lithography,” in Applications of Laser Plasma Radiation, M. C. Richardson, ed., Proc. SPIE2015, 243–260 (1994).
[CrossRef]

Meldrum, R. A.

I. C. E. Turcu, I. N. Ross, P. Trenda, C. W. Wharton, R. A. Meldrum, H. Daido, M. S. Schulz, P. Fluck, A. G. Michette, A. P. Juna, J. R. Maldonado, H. Shields, G. J. Tallents, L. Dwivedi, J. Krishnan, D. L. Stevens, T. J. Jenner, D. Batani, H. Goodson, “Picosecond excimer laser-plasma x-ray source for microscopy, biochemistry and lithography,” in Applications of Laser Plasma Radiation, M. C. Richardson, ed., Proc. SPIE2015, 243–260 (1994).
[CrossRef]

Michette, A. G.

I. C. E. Turcu, I. N. Ross, P. Trenda, C. W. Wharton, R. A. Meldrum, H. Daido, M. S. Schulz, P. Fluck, A. G. Michette, A. P. Juna, J. R. Maldonado, H. Shields, G. J. Tallents, L. Dwivedi, J. Krishnan, D. L. Stevens, T. J. Jenner, D. Batani, H. Goodson, “Picosecond excimer laser-plasma x-ray source for microscopy, biochemistry and lithography,” in Applications of Laser Plasma Radiation, M. C. Richardson, ed., Proc. SPIE2015, 243–260 (1994).
[CrossRef]

Nugent, K. A.

W. C. Priedhorsky, A. G. Peele, K. A. Nugent, “X-ray all-sky monitor with extraordinary sensitivity,” Mon. Not. R. Astron. Soc. 279, 733–750 (1996).
[CrossRef]

A. G. Peele, K. A. Nugent, A. V. Rode, K. Gabel, M. C. Richardson, R. Strack, W. Siegmund, “X-ray focusing using lobster-eye optics: a comparison of theory with experiment,” Appl. Opt. 35, 4420–4425 (1996).
[CrossRef] [PubMed]

H. N. Chapman, K. A. Nugent, S. W. Wilkins, “X-ray focusing using cylindrical-channel capillary arrays. I. Theory,” Appl. Opt. 32, 6316–6332 (1993).
[CrossRef] [PubMed]

H. N. Chapman, K. A. Nugent, S. W. Wilkins, “X-ray focusing using cylindrical-channel capillary arrays. II. Experiments,” Appl. Opt. 32, 6333–6340 (1993).
[CrossRef] [PubMed]

H. N. Chapman, K. A. Nugent, S. W. Wilkins, “X-ray focusing using square channel capillary arrays,” Rev. Sci. Instrum. 62, 1542–1561 (1991).
[CrossRef]

Pearson, J. F.

G. W. Fraser, A. N. Brunton, J. E. Lees, J. F. Pearson, W. B. Feller, “X-ray focusing using square-pore microchannel plates: first observation of cruxiform image structure,” Nucl. Instrum. Methods A 324, 404–407 (1993).
[CrossRef]

G. W. Fraser, A. N. Brunton, J. E. Lees, J. F. Pearson, R. Willingale, D. L. Emberson, W. B. Feller, M. Stedman, J. Haycocks, “Development of microchannel plate (MCP) X-ray optics,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R. B. Hoover, A. B. C. Walker, eds. Proc. SPIE2011, 215–226 (1993).
[CrossRef]

Peele, A. G.

A. G. Peele, K. A. Nugent, A. V. Rode, K. Gabel, M. C. Richardson, R. Strack, W. Siegmund, “X-ray focusing using lobster-eye optics: a comparison of theory with experiment,” Appl. Opt. 35, 4420–4425 (1996).
[CrossRef] [PubMed]

W. C. Priedhorsky, A. G. Peele, K. A. Nugent, “X-ray all-sky monitor with extraordinary sensitivity,” Mon. Not. R. Astron. Soc. 279, 733–750 (1996).
[CrossRef]

Priedhorsky, W. C.

W. C. Priedhorsky, A. G. Peele, K. A. Nugent, “X-ray all-sky monitor with extraordinary sensitivity,” Mon. Not. R. Astron. Soc. 279, 733–750 (1996).
[CrossRef]

Richardson, M. C.

A. G. Peele, K. A. Nugent, A. V. Rode, K. Gabel, M. C. Richardson, R. Strack, W. Siegmund, “X-ray focusing using lobster-eye optics: a comparison of theory with experiment,” Appl. Opt. 35, 4420–4425 (1996).
[CrossRef] [PubMed]

Rockett, P. D.

Rode, A. V.

A. G. Peele, K. A. Nugent, A. V. Rode, K. Gabel, M. C. Richardson, R. Strack, W. Siegmund, “X-ray focusing using lobster-eye optics: a comparison of theory with experiment,” Appl. Opt. 35, 4420–4425 (1996).
[CrossRef] [PubMed]

Ross, I. N.

I. C. E. Turcu, I. N. Ross, P. Trenda, C. W. Wharton, R. A. Meldrum, H. Daido, M. S. Schulz, P. Fluck, A. G. Michette, A. P. Juna, J. R. Maldonado, H. Shields, G. J. Tallents, L. Dwivedi, J. Krishnan, D. L. Stevens, T. J. Jenner, D. Batani, H. Goodson, “Picosecond excimer laser-plasma x-ray source for microscopy, biochemistry and lithography,” in Applications of Laser Plasma Radiation, M. C. Richardson, ed., Proc. SPIE2015, 243–260 (1994).
[CrossRef]

Schulz, M. S.

I. C. E. Turcu, I. N. Ross, P. Trenda, C. W. Wharton, R. A. Meldrum, H. Daido, M. S. Schulz, P. Fluck, A. G. Michette, A. P. Juna, J. R. Maldonado, H. Shields, G. J. Tallents, L. Dwivedi, J. Krishnan, D. L. Stevens, T. J. Jenner, D. Batani, H. Goodson, “Picosecond excimer laser-plasma x-ray source for microscopy, biochemistry and lithography,” in Applications of Laser Plasma Radiation, M. C. Richardson, ed., Proc. SPIE2015, 243–260 (1994).
[CrossRef]

Shields, H.

I. C. E. Turcu, I. N. Ross, P. Trenda, C. W. Wharton, R. A. Meldrum, H. Daido, M. S. Schulz, P. Fluck, A. G. Michette, A. P. Juna, J. R. Maldonado, H. Shields, G. J. Tallents, L. Dwivedi, J. Krishnan, D. L. Stevens, T. J. Jenner, D. Batani, H. Goodson, “Picosecond excimer laser-plasma x-ray source for microscopy, biochemistry and lithography,” in Applications of Laser Plasma Radiation, M. C. Richardson, ed., Proc. SPIE2015, 243–260 (1994).
[CrossRef]

Siegmund, W.

A. G. Peele, K. A. Nugent, A. V. Rode, K. Gabel, M. C. Richardson, R. Strack, W. Siegmund, “X-ray focusing using lobster-eye optics: a comparison of theory with experiment,” Appl. Opt. 35, 4420–4425 (1996).
[CrossRef] [PubMed]

Stedman, M.

G. W. Fraser, A. N. Brunton, J. E. Lees, J. F. Pearson, R. Willingale, D. L. Emberson, W. B. Feller, M. Stedman, J. Haycocks, “Development of microchannel plate (MCP) X-ray optics,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R. B. Hoover, A. B. C. Walker, eds. Proc. SPIE2011, 215–226 (1993).
[CrossRef]

Stevens, D. L.

I. C. E. Turcu, I. N. Ross, P. Trenda, C. W. Wharton, R. A. Meldrum, H. Daido, M. S. Schulz, P. Fluck, A. G. Michette, A. P. Juna, J. R. Maldonado, H. Shields, G. J. Tallents, L. Dwivedi, J. Krishnan, D. L. Stevens, T. J. Jenner, D. Batani, H. Goodson, “Picosecond excimer laser-plasma x-ray source for microscopy, biochemistry and lithography,” in Applications of Laser Plasma Radiation, M. C. Richardson, ed., Proc. SPIE2015, 243–260 (1994).
[CrossRef]

Stone, G. F.

B. L. Henke, J. Y. Uejio, G. F. Stone, C. H. Dittmore, F. G. Fujiwara, “High-energy x-ray response of photographic films: models and measurement,” J. Opt. Soc. Am. B 3, 1540–1550 (1986).
[CrossRef]

Strack, R.

A. G. Peele, K. A. Nugent, A. V. Rode, K. Gabel, M. C. Richardson, R. Strack, W. Siegmund, “X-ray focusing using lobster-eye optics: a comparison of theory with experiment,” Appl. Opt. 35, 4420–4425 (1996).
[CrossRef] [PubMed]

Sullivan, D.

Tallents, G. J.

I. C. E. Turcu, I. N. Ross, P. Trenda, C. W. Wharton, R. A. Meldrum, H. Daido, M. S. Schulz, P. Fluck, A. G. Michette, A. P. Juna, J. R. Maldonado, H. Shields, G. J. Tallents, L. Dwivedi, J. Krishnan, D. L. Stevens, T. J. Jenner, D. Batani, H. Goodson, “Picosecond excimer laser-plasma x-ray source for microscopy, biochemistry and lithography,” in Applications of Laser Plasma Radiation, M. C. Richardson, ed., Proc. SPIE2015, 243–260 (1994).
[CrossRef]

Tremsin, A. S.

A. N. Brunton, J. E. Lees, G. W. Fraser, A. S. Tremsin, W. B. Feller, P. L. White, “MCP based x-ray collimators for lithography of semiconductor devices,” in Multilayer and Grazing Incidence X-ray and EUV Optics III, R. B. Hoover, A. B. C. Walker, eds., Proc. SPIE Vol. 2805, 212–221 (1996).
[CrossRef]

Trenda, P.

I. C. E. Turcu, I. N. Ross, P. Trenda, C. W. Wharton, R. A. Meldrum, H. Daido, M. S. Schulz, P. Fluck, A. G. Michette, A. P. Juna, J. R. Maldonado, H. Shields, G. J. Tallents, L. Dwivedi, J. Krishnan, D. L. Stevens, T. J. Jenner, D. Batani, H. Goodson, “Picosecond excimer laser-plasma x-ray source for microscopy, biochemistry and lithography,” in Applications of Laser Plasma Radiation, M. C. Richardson, ed., Proc. SPIE2015, 243–260 (1994).
[CrossRef]

Turcu, I. C. E.

I. C. E. Turcu, I. N. Ross, P. Trenda, C. W. Wharton, R. A. Meldrum, H. Daido, M. S. Schulz, P. Fluck, A. G. Michette, A. P. Juna, J. R. Maldonado, H. Shields, G. J. Tallents, L. Dwivedi, J. Krishnan, D. L. Stevens, T. J. Jenner, D. Batani, H. Goodson, “Picosecond excimer laser-plasma x-ray source for microscopy, biochemistry and lithography,” in Applications of Laser Plasma Radiation, M. C. Richardson, ed., Proc. SPIE2015, 243–260 (1994).
[CrossRef]

Uejio, J. Y.

B. L. Henke, J. Y. Uejio, G. F. Stone, C. H. Dittmore, F. G. Fujiwara, “High-energy x-ray response of photographic films: models and measurement,” J. Opt. Soc. Am. B 3, 1540–1550 (1986).
[CrossRef]

Wharton, C. W.

I. C. E. Turcu, I. N. Ross, P. Trenda, C. W. Wharton, R. A. Meldrum, H. Daido, M. S. Schulz, P. Fluck, A. G. Michette, A. P. Juna, J. R. Maldonado, H. Shields, G. J. Tallents, L. Dwivedi, J. Krishnan, D. L. Stevens, T. J. Jenner, D. Batani, H. Goodson, “Picosecond excimer laser-plasma x-ray source for microscopy, biochemistry and lithography,” in Applications of Laser Plasma Radiation, M. C. Richardson, ed., Proc. SPIE2015, 243–260 (1994).
[CrossRef]

White, P. L.

A. N. Brunton, J. E. Lees, G. W. Fraser, A. S. Tremsin, W. B. Feller, P. L. White, “MCP based x-ray collimators for lithography of semiconductor devices,” in Multilayer and Grazing Incidence X-ray and EUV Optics III, R. B. Hoover, A. B. C. Walker, eds., Proc. SPIE Vol. 2805, 212–221 (1996).
[CrossRef]

Wilkins, S. W.

H. N. Chapman, K. A. Nugent, S. W. Wilkins, “X-ray focusing using cylindrical-channel capillary arrays. II. Experiments,” Appl. Opt. 32, 6333–6340 (1993).
[CrossRef] [PubMed]

H. N. Chapman, K. A. Nugent, S. W. Wilkins, “X-ray focusing using cylindrical-channel capillary arrays. I. Theory,” Appl. Opt. 32, 6316–6332 (1993).
[CrossRef] [PubMed]

H. N. Chapman, K. A. Nugent, S. W. Wilkins, “X-ray focusing using square channel capillary arrays,” Rev. Sci. Instrum. 62, 1542–1561 (1991).
[CrossRef]

Willingale, R.

G. W. Fraser, A. N. Brunton, J. E. Lees, J. F. Pearson, R. Willingale, D. L. Emberson, W. B. Feller, M. Stedman, J. Haycocks, “Development of microchannel plate (MCP) X-ray optics,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R. B. Hoover, A. B. C. Walker, eds. Proc. SPIE2011, 215–226 (1993).
[CrossRef]

Wiza, J. L.

J. L. Wiza, “Microchannel plate detectors,” Nucl. Instrum. Methods 162, 587–601 (1979).
[CrossRef]

Zavada, J. M.

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).
[CrossRef]

Appl. Opt. (2)

A. G. Peele, K. A. Nugent, A. V. Rode, K. Gabel, M. C. Richardson, R. Strack, W. Siegmund, “X-ray focusing using lobster-eye optics: a comparison of theory with experiment,” Appl. Opt. 35, 4420–4425 (1996).
[CrossRef] [PubMed]

H. N. Chapman, K. A. Nugent, S. W. Wilkins, “X-ray focusing using cylindrical-channel capillary arrays. II. Experiments,” Appl. Opt. 32, 6333–6340 (1993).
[CrossRef] [PubMed]

Appl. Opt. (3)

Astrophys. J. (1)

J. R. P. Angel, “Lobster eyes as x-ray telescopes,” Astrophys. J. 233, 364–373 (1979).
[CrossRef]

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

B. L. Henke, J. Y. Uejio, G. F. Stone, C. H. Dittmore, F. G. Fujiwara, “High-energy x-ray response of photographic films: models and measurement,” J. Opt. Soc. Am. B 3, 1540–1550 (1986).
[CrossRef]

Mon. Not. R. Astron. Soc. (1)

W. C. Priedhorsky, A. G. Peele, K. A. Nugent, “X-ray all-sky monitor with extraordinary sensitivity,” Mon. Not. R. Astron. Soc. 279, 733–750 (1996).
[CrossRef]

Nucl. Instrum. Methods A (1)

G. W. Fraser, A. N. Brunton, J. E. Lees, D. L. Emberson, “Production of quasiparallel X-ray beams using microchannel plate X-ray lenses,” Nucl. Instrum. Methods A 334, 579–588 (1993).
[CrossRef]

Nucl. Instrum. Methods (1)

J. L. Wiza, “Microchannel plate detectors,” Nucl. Instrum. Methods 162, 587–601 (1979).
[CrossRef]

Nucl. Instrum. Methods A (1)

G. W. Fraser, A. N. Brunton, J. E. Lees, J. F. Pearson, W. B. Feller, “X-ray focusing using square-pore microchannel plates: first observation of cruxiform image structure,” Nucl. Instrum. Methods A 324, 404–407 (1993).
[CrossRef]

Opt. Eng. (1)

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).
[CrossRef]

Rev. Sci. Instrum. (1)

H. N. Chapman, K. A. Nugent, S. W. Wilkins, “X-ray focusing using square channel capillary arrays,” Rev. Sci. Instrum. 62, 1542–1561 (1991).
[CrossRef]

Other (8)

B. L. Henke, “Low energy x-ray interactions: photoionization, scattering, specular and Bragg reflection,” in Topical Conference on Low-Energy X-ray Diagnostics, , D. Attwood, B. Henke, eds. (American Institute of Physics, New York, 1981), pp. 146–155.

D. T. Cromer, D. Liberman, “Relativistic calculation of anomolous scattering factors for x-rays,’ (Los Alamos Laboratory, Los Alamos, N.M., 1970).

Galileo Electro-Optics Corporation, Galileo Park, Sturbridge, Mass. 01566.

I. C. E. Turcu, I. N. Ross, P. Trenda, C. W. Wharton, R. A. Meldrum, H. Daido, M. S. Schulz, P. Fluck, A. G. Michette, A. P. Juna, J. R. Maldonado, H. Shields, G. J. Tallents, L. Dwivedi, J. Krishnan, D. L. Stevens, T. J. Jenner, D. Batani, H. Goodson, “Picosecond excimer laser-plasma x-ray source for microscopy, biochemistry and lithography,” in Applications of Laser Plasma Radiation, M. C. Richardson, ed., Proc. SPIE2015, 243–260 (1994).
[CrossRef]

G. W. Fraser, A. N. Brunton, J. E. Lees, J. F. Pearson, R. Willingale, D. L. Emberson, W. B. Feller, M. Stedman, J. Haycocks, “Development of microchannel plate (MCP) X-ray optics,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R. B. Hoover, A. B. C. Walker, eds. Proc. SPIE2011, 215–226 (1993).
[CrossRef]

A. N. Brunton, “MCP x-ray optics,” Ph.D. thesis (University of Leicester, UK, 1995).

A. N. Brunton, J. E. Lees, G. W. Fraser, A. S. Tremsin, W. B. Feller, P. L. White, “MCP based x-ray collimators for lithography of semiconductor devices,” in Multilayer and Grazing Incidence X-ray and EUV Optics III, R. B. Hoover, A. B. C. Walker, eds., Proc. SPIE Vol. 2805, 212–221 (1996).
[CrossRef]

National Physical Laboratory, Division of Mechanical and Optical Metrology, Teddington, Middlesex, TW11 0LW, UK.

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Figures (13)

Fig. 1
Fig. 1

Three components of the image produced by an MCP optic. Note that the line-focus 1 and 2 components are essentially periodic in x and y, respectively, actually modified by the reflectivity versus the grazing angle function of the MCP glass (not shown here). The diffuse unreflected component is also periodic in x and y although, for clarity, only its central part in the region - l s D/Lxl s D/L; - l s D/Lyl s D/L is shown in the figure.

Fig. 2
Fig. 2

Pincushion distortion and vertex radiusing of square cross-section channels.

Fig. 3
Fig. 3

SEM micrograph showing four-way multifiber boundaries (A and B) and channel rotation in the xy plane.

Fig. 4
Fig. 4

Comparison of results from the analytical model of Chapman et al.1 with those of our perfect-plate Monte Carlo model. The lines are analytical plots while the individual symbols represent Monte Carlo results. The true focusing efficiency Ω oo is the proportion of rays incident at less than the critical angle on an idealized MCP with unity open area, which are reflected an odd number of times from walls normal to the x axis and an odd number of times from walls parallel to the y axis. Ω ee , similarly, denotes the diffuse image component and Ω oe + Ω eo the focusing efficiency of the line foci. Necessarily Ω oo + Ω ee + Ω oe + Ω eo = 1. The dimensionless parameter α = θ c L/D represents a normalization of the critical reflection angle θ c allowing generalization with respect to channel geometry and (hard) x-ray wavelength.

Fig. 5
Fig. 5

AFM micrograph of microchannel surface. The vertical feature at the right is the remains of a vertical channel wall. Note the striations parallel with the channel axis2 and the debris arising from the diamond saw used to cut the MCP.

Fig. 6
Fig. 6

Microdensitometer scan across film image resulting from illumination of the MCP through a pinhole mask.

Fig. 7
Fig. 7

Image resulting from illumination of a Galileo MCP with silicon K x-rays. Broadening due to multifiber long-axis misalignment angles is indicated. Structure in the diffuse component is not due to the optic, but to the support mesh on a window between the x-ray source and the main vacuum chamber.

Fig. 8
Fig. 8

Cuts along, a, the horizontal cross arm and, b, the vertical cross arm of Fig. 7.

Fig. 9
Fig. 9

a, Illumination uniformity measured by the large-area MCP detector with no focusing MCP present. The circle represents the projection of the optic-active area onto the image plane. b, Illumination used in ray-trace simulation.

Fig. 10
Fig. 10

Deep depletion, cooled CCD spectrum of the Leicester built x-ray source with an electron accelerating voltage of 3.5 kV, multiplied times the transmission of 1 µm of silver. Rectangles indicate spectral bins used in simulation. Note that the vertical scale of the spectrum and the binned approximation are chosen to allow display on the same graph. The bins between 2 and 3 keV appear to lie above the spectrum because of correction for the large bin width around the silicon line.

Fig. 11
Fig. 11

Plot of cumulative frequency of measured interchannel and intermultifiber rotation angles (xy plane misalignments) against integrated Gaussian functions with measured standard deviation s. Note the good straight line fits for both rotation angles between channels within a given multifiber and for angles between multifibers.

Fig. 12
Fig. 12

A 1.74-keV image from simulation of a MCP of Galileo type, with distortions of the magnitudes determined by metrology.

Fig. 13
Fig. 13

Cuts along, a, the horizontal cross arm and, b, the vertical cross arm of Fig. 12. Note the close agreement with their experimental counterparts (Figs. 8a and 8b).

Tables (1)

Tables Icon

Table 1 Various Distortions and Their Contributions to the Width of the Focal Spot

Equations (12)

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x - x 0 2 + y - y 0 2 = ρ 2 ,
ρ = g / 2 + E 2 / 8 g ,
a + t b = r = Gr = G a + t b = Ga + t Gb ,
ϕ i = ϕ i chan + ϕ i multi     i = 1 ,   2 ,   3 .
T = 1 - exp - 4 π σ   sin θ λ 2 ,
ϕ s = λ τ   sin   θ ,
θ t = ϕ t p z + L / 2 / L .
σ 2 = λ 4 π θ 2 I s 1 I 0 ,
τ = 2 π σ m ;     m = 1 4 I s 2 I 0 .
I s 1 = ϕ 1 ϕ 2 I ϕ s d ϕ s ,
I s 1 = ϕ 1 ϕ 2 I ϕ s ϕ s - θ 2 d ϕ s ,
0.67 ϕ 2 multi + ϕ 3 multi / 2 = ϕ 2 chan = ϕ 3 chan ,

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