Abstract

A practical design for upcoming spaceborne x-ray telescopes with ultrahigh angular resolution is proposed. Particular attention is directed to technological simplicity and robust as well as cheap components. Based on dispersion corrected Fresnel lenses, an optimized arrangement will be identified with respect to the instrumental sensitivity for a given focal spot size. We show that this optical Gamow peak essentially depends on the radial transmission profile of a diffractive–refractive aperture. Examples for energies above 4 keV illustrate astronomical capabilities for large-scale compact and segmented objectives as well. The spectral and spatial resolutions of conventional semiconductor detectors are very well matched to imaging characteristics of those achromatic lenses. The constraints to fabrication techniques using most promising materials like Li, Be, and plastics are discussed.

© 2007 Optical Society of America

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References

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  1. T. Stone and N. George, "Hybrid diffractive-refractive lenses and achromats," Appl. Opt. 27, 2960-2971 (1988).
    [CrossRef] [PubMed]
  2. N. Davidson, A. A. Friesem, and E. Hasman, "Analytic design of hybrid diffractive-refractive achromats," Appl. Opt. 32, 4770-4774 (1993).
    [CrossRef] [PubMed]
  3. K. C. Johnson, "Dispersion-compensated Fresnel lens," U.S. patent 5,161,057 (3 November 1992).
  4. G. Skinner, P. von Ballmoos, N. Gehrels, and J. Krizmanic, "Fresnel lenses for x-ray and gamma-ray astronomy," Proc. SPIE 5168, 459-470 (2004).
    [CrossRef]
  5. P. Gorenstein, "Role of diffractive and refractive optics in x-ray astronomy," Proc. SPIE 5168, 411-419 (2004).
    [CrossRef]
  6. Y. Wang, W. Yun, and C. Jacobsen, "Achromatic Fresnel optics for wideband extreme-ultraviolet and x-ray imaging," Nature 424, 50-53 (2003).
    [CrossRef] [PubMed]
  7. G. K. Skinner, "Design and imaging performance of achromatic diffractive-refractive x-ray and gamma-ray Fresnel lenses," Appl. Opt. 43, 4845-4852 (2004).
    [CrossRef] [PubMed]
  8. G. K. Skinner, "Diffractive-refractive optics for high energy astronomy-II. Variations on the theme," Astron. Astrophys. 383, 352-359 (2002).
    [CrossRef]
  9. B. X. Yang, "Fresnel and refractive lenses for x-rays," Nucl. Instrum. Methods Phys. Res. A 328, 578-587 (1993).
    [CrossRef]
  10. C. Braig and P. Predehl, "Large-scale diffractive x-ray telescopes," Exp. Astron. 21, 101-123 (2006).
  11. S. E. Strom, L. M. Stepp, and B. Gregory, "Giant segmented mirror telescope: a point design based on science drivers," Proc. SPIE 4840, 116-128 (2003).
    [CrossRef]
  12. B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30000 eV, Z = 1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
    [CrossRef]
  13. A. F. Holleman and E. Wiberg, Lehrbuch der Anorganischen Chemie (Walter de Gruyter, 1995).
  14. ESPI Metals, Ashland, Oregon, http://www.espi-metals.com (2005).
  15. Island Pyrochemical Industries, New York, http://www.islandgroup.com (2005).
  16. American Elements Inc., Los Angeles, Calif., http://www.americanelements.com (2006).
  17. E. M. Dufresne, D. A. Arms, S. B. Dierker, R. Clarke, N. R. Pereira, and D. Foster, "Lithium metal for x-ray refractive optics," Appl. Phys. Lett. 79, 4085 (2001).
    [CrossRef]
  18. D. A. Arms, E. M. Dufresne, R. Clarke, S. B. Dierker, N. R. Pereira, and D. Foster, "Refractive optics using lithium metal," Rev. Sci. Instrum. 73, 1492-1494 (2002).
    [CrossRef]
  19. N. R. Pereira, E. M. Dufresne, D. A. Arms, and R. Clarke, "Large aperture x-ray refractive lens from lithium," Proc. SPIE 5539, 174-184 (2004).
    [CrossRef]
  20. E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, "High-efficiency multilevel zone plates for keV x-rays," Nature 401, 895-898 (1995).
    [CrossRef]
  21. M. Revnivtsev, M. Gilfanov, R. Sunyaev, K. Jahoda, and C. Markwardt, "The spectrum of the cosmic x-ray background observed by RXTE/PCA," Astron. Astrophys. 411, 329-334 (2003).
    [CrossRef]
  22. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).
  23. M. Young, "Zone plates and their aberrations," J. Opt. Soc. Am. A 62, 972-976 (1972).
    [CrossRef]
  24. L. Strüder, "High-resolution imaging x-ray spectrometers," Nucl. Instr. Methods Phys. Res. A 454, 73-113 (2000).
    [CrossRef]

2004

N. R. Pereira, E. M. Dufresne, D. A. Arms, and R. Clarke, "Large aperture x-ray refractive lens from lithium," Proc. SPIE 5539, 174-184 (2004).
[CrossRef]

G. Skinner, P. von Ballmoos, N. Gehrels, and J. Krizmanic, "Fresnel lenses for x-ray and gamma-ray astronomy," Proc. SPIE 5168, 459-470 (2004).
[CrossRef]

P. Gorenstein, "Role of diffractive and refractive optics in x-ray astronomy," Proc. SPIE 5168, 411-419 (2004).
[CrossRef]

G. K. Skinner, "Design and imaging performance of achromatic diffractive-refractive x-ray and gamma-ray Fresnel lenses," Appl. Opt. 43, 4845-4852 (2004).
[CrossRef] [PubMed]

2003

Y. Wang, W. Yun, and C. Jacobsen, "Achromatic Fresnel optics for wideband extreme-ultraviolet and x-ray imaging," Nature 424, 50-53 (2003).
[CrossRef] [PubMed]

M. Revnivtsev, M. Gilfanov, R. Sunyaev, K. Jahoda, and C. Markwardt, "The spectrum of the cosmic x-ray background observed by RXTE/PCA," Astron. Astrophys. 411, 329-334 (2003).
[CrossRef]

S. E. Strom, L. M. Stepp, and B. Gregory, "Giant segmented mirror telescope: a point design based on science drivers," Proc. SPIE 4840, 116-128 (2003).
[CrossRef]

2002

G. K. Skinner, "Diffractive-refractive optics for high energy astronomy-II. Variations on the theme," Astron. Astrophys. 383, 352-359 (2002).
[CrossRef]

D. A. Arms, E. M. Dufresne, R. Clarke, S. B. Dierker, N. R. Pereira, and D. Foster, "Refractive optics using lithium metal," Rev. Sci. Instrum. 73, 1492-1494 (2002).
[CrossRef]

2001

E. M. Dufresne, D. A. Arms, S. B. Dierker, R. Clarke, N. R. Pereira, and D. Foster, "Lithium metal for x-ray refractive optics," Appl. Phys. Lett. 79, 4085 (2001).
[CrossRef]

2000

L. Strüder, "High-resolution imaging x-ray spectrometers," Nucl. Instr. Methods Phys. Res. A 454, 73-113 (2000).
[CrossRef]

1995

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, "High-efficiency multilevel zone plates for keV x-rays," Nature 401, 895-898 (1995).
[CrossRef]

1993

B. X. Yang, "Fresnel and refractive lenses for x-rays," Nucl. Instrum. Methods Phys. Res. A 328, 578-587 (1993).
[CrossRef]

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30000 eV, Z = 1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
[CrossRef]

N. Davidson, A. A. Friesem, and E. Hasman, "Analytic design of hybrid diffractive-refractive achromats," Appl. Opt. 32, 4770-4774 (1993).
[CrossRef] [PubMed]

1988

1972

M. Young, "Zone plates and their aberrations," J. Opt. Soc. Am. A 62, 972-976 (1972).
[CrossRef]

Arms, D. A.

N. R. Pereira, E. M. Dufresne, D. A. Arms, and R. Clarke, "Large aperture x-ray refractive lens from lithium," Proc. SPIE 5539, 174-184 (2004).
[CrossRef]

D. A. Arms, E. M. Dufresne, R. Clarke, S. B. Dierker, N. R. Pereira, and D. Foster, "Refractive optics using lithium metal," Rev. Sci. Instrum. 73, 1492-1494 (2002).
[CrossRef]

E. M. Dufresne, D. A. Arms, S. B. Dierker, R. Clarke, N. R. Pereira, and D. Foster, "Lithium metal for x-ray refractive optics," Appl. Phys. Lett. 79, 4085 (2001).
[CrossRef]

Barrett, R.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, "High-efficiency multilevel zone plates for keV x-rays," Nature 401, 895-898 (1995).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Braig, C.

C. Braig and P. Predehl, "Large-scale diffractive x-ray telescopes," Exp. Astron. 21, 101-123 (2006).

Cabrini, S.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, "High-efficiency multilevel zone plates for keV x-rays," Nature 401, 895-898 (1995).
[CrossRef]

Clarke, R.

N. R. Pereira, E. M. Dufresne, D. A. Arms, and R. Clarke, "Large aperture x-ray refractive lens from lithium," Proc. SPIE 5539, 174-184 (2004).
[CrossRef]

D. A. Arms, E. M. Dufresne, R. Clarke, S. B. Dierker, N. R. Pereira, and D. Foster, "Refractive optics using lithium metal," Rev. Sci. Instrum. 73, 1492-1494 (2002).
[CrossRef]

E. M. Dufresne, D. A. Arms, S. B. Dierker, R. Clarke, N. R. Pereira, and D. Foster, "Lithium metal for x-ray refractive optics," Appl. Phys. Lett. 79, 4085 (2001).
[CrossRef]

Davidson, N.

Davis, J. C.

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30000 eV, Z = 1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
[CrossRef]

Di Fabrizio, E.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, "High-efficiency multilevel zone plates for keV x-rays," Nature 401, 895-898 (1995).
[CrossRef]

Dierker, S. B.

D. A. Arms, E. M. Dufresne, R. Clarke, S. B. Dierker, N. R. Pereira, and D. Foster, "Refractive optics using lithium metal," Rev. Sci. Instrum. 73, 1492-1494 (2002).
[CrossRef]

E. M. Dufresne, D. A. Arms, S. B. Dierker, R. Clarke, N. R. Pereira, and D. Foster, "Lithium metal for x-ray refractive optics," Appl. Phys. Lett. 79, 4085 (2001).
[CrossRef]

Dufresne, E. M.

N. R. Pereira, E. M. Dufresne, D. A. Arms, and R. Clarke, "Large aperture x-ray refractive lens from lithium," Proc. SPIE 5539, 174-184 (2004).
[CrossRef]

D. A. Arms, E. M. Dufresne, R. Clarke, S. B. Dierker, N. R. Pereira, and D. Foster, "Refractive optics using lithium metal," Rev. Sci. Instrum. 73, 1492-1494 (2002).
[CrossRef]

E. M. Dufresne, D. A. Arms, S. B. Dierker, R. Clarke, N. R. Pereira, and D. Foster, "Lithium metal for x-ray refractive optics," Appl. Phys. Lett. 79, 4085 (2001).
[CrossRef]

Foster, D.

D. A. Arms, E. M. Dufresne, R. Clarke, S. B. Dierker, N. R. Pereira, and D. Foster, "Refractive optics using lithium metal," Rev. Sci. Instrum. 73, 1492-1494 (2002).
[CrossRef]

E. M. Dufresne, D. A. Arms, S. B. Dierker, R. Clarke, N. R. Pereira, and D. Foster, "Lithium metal for x-ray refractive optics," Appl. Phys. Lett. 79, 4085 (2001).
[CrossRef]

Friesem, A. A.

Gehrels, N.

G. Skinner, P. von Ballmoos, N. Gehrels, and J. Krizmanic, "Fresnel lenses for x-ray and gamma-ray astronomy," Proc. SPIE 5168, 459-470 (2004).
[CrossRef]

Gentili, M.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, "High-efficiency multilevel zone plates for keV x-rays," Nature 401, 895-898 (1995).
[CrossRef]

George, N.

Gilfanov, M.

M. Revnivtsev, M. Gilfanov, R. Sunyaev, K. Jahoda, and C. Markwardt, "The spectrum of the cosmic x-ray background observed by RXTE/PCA," Astron. Astrophys. 411, 329-334 (2003).
[CrossRef]

Gorenstein, P.

P. Gorenstein, "Role of diffractive and refractive optics in x-ray astronomy," Proc. SPIE 5168, 411-419 (2004).
[CrossRef]

Gregory, B.

S. E. Strom, L. M. Stepp, and B. Gregory, "Giant segmented mirror telescope: a point design based on science drivers," Proc. SPIE 4840, 116-128 (2003).
[CrossRef]

Gullikson, E. M.

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30000 eV, Z = 1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
[CrossRef]

Hasman, E.

Henke, B. L.

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30000 eV, Z = 1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
[CrossRef]

Holleman, A. F.

A. F. Holleman and E. Wiberg, Lehrbuch der Anorganischen Chemie (Walter de Gruyter, 1995).

Jacobsen, C.

Y. Wang, W. Yun, and C. Jacobsen, "Achromatic Fresnel optics for wideband extreme-ultraviolet and x-ray imaging," Nature 424, 50-53 (2003).
[CrossRef] [PubMed]

Jahoda, K.

M. Revnivtsev, M. Gilfanov, R. Sunyaev, K. Jahoda, and C. Markwardt, "The spectrum of the cosmic x-ray background observed by RXTE/PCA," Astron. Astrophys. 411, 329-334 (2003).
[CrossRef]

Johnson, K. C.

K. C. Johnson, "Dispersion-compensated Fresnel lens," U.S. patent 5,161,057 (3 November 1992).

Kaulich, B.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, "High-efficiency multilevel zone plates for keV x-rays," Nature 401, 895-898 (1995).
[CrossRef]

Krizmanic, J.

G. Skinner, P. von Ballmoos, N. Gehrels, and J. Krizmanic, "Fresnel lenses for x-ray and gamma-ray astronomy," Proc. SPIE 5168, 459-470 (2004).
[CrossRef]

Markwardt, C.

M. Revnivtsev, M. Gilfanov, R. Sunyaev, K. Jahoda, and C. Markwardt, "The spectrum of the cosmic x-ray background observed by RXTE/PCA," Astron. Astrophys. 411, 329-334 (2003).
[CrossRef]

Pereira, N. R.

N. R. Pereira, E. M. Dufresne, D. A. Arms, and R. Clarke, "Large aperture x-ray refractive lens from lithium," Proc. SPIE 5539, 174-184 (2004).
[CrossRef]

D. A. Arms, E. M. Dufresne, R. Clarke, S. B. Dierker, N. R. Pereira, and D. Foster, "Refractive optics using lithium metal," Rev. Sci. Instrum. 73, 1492-1494 (2002).
[CrossRef]

E. M. Dufresne, D. A. Arms, S. B. Dierker, R. Clarke, N. R. Pereira, and D. Foster, "Lithium metal for x-ray refractive optics," Appl. Phys. Lett. 79, 4085 (2001).
[CrossRef]

Predehl, P.

C. Braig and P. Predehl, "Large-scale diffractive x-ray telescopes," Exp. Astron. 21, 101-123 (2006).

Revnivtsev, M.

M. Revnivtsev, M. Gilfanov, R. Sunyaev, K. Jahoda, and C. Markwardt, "The spectrum of the cosmic x-ray background observed by RXTE/PCA," Astron. Astrophys. 411, 329-334 (2003).
[CrossRef]

Romanato, F.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, "High-efficiency multilevel zone plates for keV x-rays," Nature 401, 895-898 (1995).
[CrossRef]

Skinner, G.

G. Skinner, P. von Ballmoos, N. Gehrels, and J. Krizmanic, "Fresnel lenses for x-ray and gamma-ray astronomy," Proc. SPIE 5168, 459-470 (2004).
[CrossRef]

Skinner, G. K.

G. K. Skinner, "Design and imaging performance of achromatic diffractive-refractive x-ray and gamma-ray Fresnel lenses," Appl. Opt. 43, 4845-4852 (2004).
[CrossRef] [PubMed]

G. K. Skinner, "Diffractive-refractive optics for high energy astronomy-II. Variations on the theme," Astron. Astrophys. 383, 352-359 (2002).
[CrossRef]

Stepp, L. M.

S. E. Strom, L. M. Stepp, and B. Gregory, "Giant segmented mirror telescope: a point design based on science drivers," Proc. SPIE 4840, 116-128 (2003).
[CrossRef]

Stone, T.

Strom, S. E.

S. E. Strom, L. M. Stepp, and B. Gregory, "Giant segmented mirror telescope: a point design based on science drivers," Proc. SPIE 4840, 116-128 (2003).
[CrossRef]

Strüder, L.

L. Strüder, "High-resolution imaging x-ray spectrometers," Nucl. Instr. Methods Phys. Res. A 454, 73-113 (2000).
[CrossRef]

Sunyaev, R.

M. Revnivtsev, M. Gilfanov, R. Sunyaev, K. Jahoda, and C. Markwardt, "The spectrum of the cosmic x-ray background observed by RXTE/PCA," Astron. Astrophys. 411, 329-334 (2003).
[CrossRef]

Susini, J.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, "High-efficiency multilevel zone plates for keV x-rays," Nature 401, 895-898 (1995).
[CrossRef]

von Ballmoos, P.

G. Skinner, P. von Ballmoos, N. Gehrels, and J. Krizmanic, "Fresnel lenses for x-ray and gamma-ray astronomy," Proc. SPIE 5168, 459-470 (2004).
[CrossRef]

Wang, Y.

Y. Wang, W. Yun, and C. Jacobsen, "Achromatic Fresnel optics for wideband extreme-ultraviolet and x-ray imaging," Nature 424, 50-53 (2003).
[CrossRef] [PubMed]

Wiberg, E.

A. F. Holleman and E. Wiberg, Lehrbuch der Anorganischen Chemie (Walter de Gruyter, 1995).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Yang, B. X.

B. X. Yang, "Fresnel and refractive lenses for x-rays," Nucl. Instrum. Methods Phys. Res. A 328, 578-587 (1993).
[CrossRef]

Young, M.

M. Young, "Zone plates and their aberrations," J. Opt. Soc. Am. A 62, 972-976 (1972).
[CrossRef]

Yun, W.

Y. Wang, W. Yun, and C. Jacobsen, "Achromatic Fresnel optics for wideband extreme-ultraviolet and x-ray imaging," Nature 424, 50-53 (2003).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

E. M. Dufresne, D. A. Arms, S. B. Dierker, R. Clarke, N. R. Pereira, and D. Foster, "Lithium metal for x-ray refractive optics," Appl. Phys. Lett. 79, 4085 (2001).
[CrossRef]

Astron. Astrophys.

G. K. Skinner, "Diffractive-refractive optics for high energy astronomy-II. Variations on the theme," Astron. Astrophys. 383, 352-359 (2002).
[CrossRef]

M. Revnivtsev, M. Gilfanov, R. Sunyaev, K. Jahoda, and C. Markwardt, "The spectrum of the cosmic x-ray background observed by RXTE/PCA," Astron. Astrophys. 411, 329-334 (2003).
[CrossRef]

At. Data Nucl. Data Tables

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30000 eV, Z = 1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
[CrossRef]

J. Opt. Soc. Am. A

M. Young, "Zone plates and their aberrations," J. Opt. Soc. Am. A 62, 972-976 (1972).
[CrossRef]

Nature

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, "High-efficiency multilevel zone plates for keV x-rays," Nature 401, 895-898 (1995).
[CrossRef]

Y. Wang, W. Yun, and C. Jacobsen, "Achromatic Fresnel optics for wideband extreme-ultraviolet and x-ray imaging," Nature 424, 50-53 (2003).
[CrossRef] [PubMed]

Nucl. Instr. Methods Phys. Res. A

L. Strüder, "High-resolution imaging x-ray spectrometers," Nucl. Instr. Methods Phys. Res. A 454, 73-113 (2000).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A

B. X. Yang, "Fresnel and refractive lenses for x-rays," Nucl. Instrum. Methods Phys. Res. A 328, 578-587 (1993).
[CrossRef]

Proc. SPIE

G. Skinner, P. von Ballmoos, N. Gehrels, and J. Krizmanic, "Fresnel lenses for x-ray and gamma-ray astronomy," Proc. SPIE 5168, 459-470 (2004).
[CrossRef]

P. Gorenstein, "Role of diffractive and refractive optics in x-ray astronomy," Proc. SPIE 5168, 411-419 (2004).
[CrossRef]

S. E. Strom, L. M. Stepp, and B. Gregory, "Giant segmented mirror telescope: a point design based on science drivers," Proc. SPIE 4840, 116-128 (2003).
[CrossRef]

N. R. Pereira, E. M. Dufresne, D. A. Arms, and R. Clarke, "Large aperture x-ray refractive lens from lithium," Proc. SPIE 5539, 174-184 (2004).
[CrossRef]

Rev. Sci. Instrum.

D. A. Arms, E. M. Dufresne, R. Clarke, S. B. Dierker, N. R. Pereira, and D. Foster, "Refractive optics using lithium metal," Rev. Sci. Instrum. 73, 1492-1494 (2002).
[CrossRef]

Other

C. Braig and P. Predehl, "Large-scale diffractive x-ray telescopes," Exp. Astron. 21, 101-123 (2006).

A. F. Holleman and E. Wiberg, Lehrbuch der Anorganischen Chemie (Walter de Gruyter, 1995).

ESPI Metals, Ashland, Oregon, http://www.espi-metals.com (2005).

Island Pyrochemical Industries, New York, http://www.islandgroup.com (2005).

American Elements Inc., Los Angeles, Calif., http://www.americanelements.com (2006).

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

K. C. Johnson, "Dispersion-compensated Fresnel lens," U.S. patent 5,161,057 (3 November 1992).

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Figures (23)

Fig. 1
Fig. 1

(Color online) Dispersion corrected hybrid x-ray lens (Ref. [8]). Absorption effects of an additional support layer will be ignored in this work. The detector usually covers an order of 103 resolution elements in diameter.

Fig. 2
Fig. 2

(Color online) Focal length dispersion of hybrid lenses compared to pure diffractive ones (dashed line). Limits on the DOF (hatched and crosses) give spectral acceptance, shown for N = 100 .

Fig. 3
Fig. 3

Differential modulation transfer function of hybrid lenses designed with s = 2 (dark gray) and s = 5 (light gray). See text for details.

Fig. 4
Fig. 4

(Color online) Absorption-induced angular resolution of compact achromatic objectives. The step near N = 7 N 0 is attributable to the first fringe transition. The transmission T ( s ) is given in %.

Fig. 5
Fig. 5

Schematic view of the segmented aperture. The innermost of the T N = 7 rings is obstructed ( r o b s ) . The lower right inset illustrates the detailed structure with gray–white Fresnel zones and black segment boundaries.

Fig. 6
Fig. 6

Cross section of segmented achromatic optics. For the sake of simplicity, this lens contains only T N = 7 rings, from which the innermost one is obstructed. The aspect ratio is defined for the outermost segments.

Fig. 7
Fig. 7

Fourier diffraction pattern of individual segments. The superimposed PSF is obtained from rotated intensity distributions for transparent (left, s = 0 ) and absorptive (right, s = 7.5 ) refractive prisms.

Fig. 8
Fig. 8

(Color online) Angular resolution of segmented achromatic objectives for segment zone numbers N related to the critical one N 0 . The transmission for zone ratios at approximately s 7 is given in %.

Fig. 9
Fig. 9

Achromatic luminous power as a function of the zone ratio N / N 0 . Absorption-induced degraded spatial resolution and transmission force a distinct maximum in A e f f × Δ E , located at N = 5 N 0 for monolithic versions.

Fig. 10
Fig. 10

Achromatic luminous power as a function of the zone ratio N / N 0 . Absorption-induced degraded spatial resolution and transmission force a distinct maximum in A e f f × Δ E , located at N 7.5 N 0 for segmented versions.

Fig. 11
Fig. 11

(Color online) Critical zone number N 0 of solid-state low-Z materials (according to Ref. [9]), based on standard tables (Ref. [12]). Data from real samples are drawn in dashed curves.

Fig. 12
Fig. 12

Impurities of commercially available Li samples, given in ppm for elements of atomic number Z. Light gray bars refer to sample 1 ( 99.96 % ) , dark gray bars represent sample 2 ( 99.99 % ) .

Fig. 13
Fig. 13

Critical zone number N 0 of common solid-state low-Z compounds, including hydrides X m H n .

Fig. 14
Fig. 14

Ratio between the aperture and detector radii for different obstructions and fields of view. Data in brackets include absorption effects for optimized arrangements (see text).

Fig. 15
Fig. 15

Optimized luminous powers of segmented, filled apertures ( a = 0 ) for various materials. For arbitrary focal spots, the scaling law is A e f f × Δ E ( P S F ) 2 .

Fig. 16
Fig. 16

Effective area of some optimized achromatic Fresnel optics compared to that of Chandra and XMM-Newton (without losses). Widths of bars represent spectral tolerances.

Fig. 17
Fig. 17

(Color online) Higher-order focusing with achromatic Fresnel optics. The absorption-neglected response is shown for 10 2 and 10 3 zones as a function of the fractional energy.

Fig. 18
Fig. 18

Calculation of geometric aberrations will be based on that notation. Figure adapted from Born and Wolf (Ref. [22]).

Fig. 19
Fig. 19

Aplanatic sandwich profile for segmented hybrid objectives with small f ratios. Components are drawn separately for the sake of clarity.

Fig. 20
Fig. 20

(Color online) Residual third-order aberrations of compact versions for ϕ = 80   mas . In conjunction with δ = 6 × 10 6 , the outermost f ratio ( 1.88 × 10 6 ) describes the worst case of Li optics at 4 keV. All other examples from Tables 3 and 4 show even smaller absolute errors. Spherical errors with ϕ = 0 are drawn separately (dashed curves).

Fig. 21
Fig. 21

(Color online) Possible implementation of compact apertures. Optical active rods (see enlarged inset) are stabilized by the numerous honeycombs into which the lens is divided. Gray levels visualize the radial transmission profile.

Fig. 22
Fig. 22

Torsional tolerances Δ φ z in arc sec of the detector unit for various fields of view r F O V , which are given in units of radial resolution elements.

Fig. 23
Fig. 23

Spectral selectivity of semiconductor devices (hatched) compared to the dispersion-corrected bandwidth (straight lines) for zone numbers 5 × 10 2 N 2 × 10 4 .

Tables (11)

Tables Icon

Table 1 Conversion for Segmented Apertures

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Table 2 Accuracy of the Prismatic Approximation

Tables Icon

Table 3 Compact Telescopes Made of Li and Be

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Table 4 Compact Telescopes Made of Plastics

Tables Icon

Table 5 Segmented Telescopes Made of Li

Tables Icon

Table 6 Segmented Telescopes Made of Be

Tables Icon

Table 7 Compact A eff × Δ E (103 cm2 keV)

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Table 8 Focal Spots in m th Diffraction Order

Tables Icon

Table 9 Segmented A eff × Δ E (103 cm2 keV)

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Table 10 Diffraction-Limited Compact Lens Tilts

Tables Icon

Table 11 Scaled-Down Lenses Made of C16H14O3

Equations (364)

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10 2 1 0 3   eV
F 1 = F Z 1 + F L 1 ,   with   d d E F ( E ) = 0.
F Z , L R 2 E h c N ^ Z , L 1 ,   with   N ^ L E 1 ,
N ^ Z , L
F Z , L ( E )
E c
N Z N N ^ Z
N L N ^ L ( E c )
F Z E
n = 1 δ i β
F L δ 1 ( E )
E c δ ( E c ) δ ( E c ) = sig ( F L ) N Z N L .
F L
N Z , L > 0
δ ( E c )
δ ( E ) = α E 2
( F L < 0 )
N Z 2 N L
C 16 H 14 O 3
N Z = 2 ( 1 + ε ) N L
ε 2 × 10 3
N Z = 2 N L
N L N Z
F ( E ) = 2 F Z [ 1 + ( Δ E 2 E ) 2 + O ( Δ E 2 E ) 3 ] ,
Δ E / E
2 Δ z DOF = ± λ ( NA ) 2 ,   with   NA R / F
Δ E = N 1 E
Δ E = 2 N 1 / 2 E .
Δ E
F ( E c )
N 0 δ / ( 2 π β )
s N / N 0
s 1
s = 10 2
s 6
I s ( r ) = 1 π ( 0 1 e s 4 ( 1 τ 2 ) J 0 ( r τ ) τ d τ ) 2 ,
τ σ / R
R 2 I s ( r ) = 1
J 0
0 τ 1
T ( s ) = 2 s 1 [ 1 exp ( s / 2 ) ] ,
s = 2
s = 5
( s > 0 )
s = 2
s = 5
s = 12
s 7
10 3
10 4   km
N
T N
N = T N N
1 k T N
φ k ( 0 )
x [ x ]
r k = ( k / T N ) 1 / 2
φ k , q = φ k ( 0 ) + 2 π ( q 1 ) [ π k + k 1 k k 1 ] 1 .
k 1
( 1 h 2 π ) h k ( r ) = N 4 [ k T N ( r R ) 2 ] ,
h 2 π λ c / δ ( λ c )
T N
A s e g = Δ t m a x / Δ r min
Δ t m a x = h 2 π N / 4
± 1
Δ r n ( k ) ± R N 1 T N / k   for   k 1 .
I ˜ N ( κ )
k , j
s k # ( seg ) k
I ˜ N ( κ ) = k = k T N j = 1 s k | k , j ( κ ) | 2 ,
κ
k [ a 2 T N ] + 1
k > 1
k , j
0 a 1
T N
Δ ϵ η N ( a ) T N
η N ( a )
h k ( r )
N / N 0
κ = ( u , v )
I ^ s ( κ ) 1 2 e s / 4  cos ( u ) + e s / 2 ( s / 4 ) 2 + u 2 sin 2 ( v / 2 ) ( v / 2 ) 2 ,
0 < φ 2 π
I s ( κ ) 0 2 π I ^ s ( κ ) d φ   with   κ = κ ( cos   φ ,  sin   φ ) .
PSF
PSF = Q ( s ) PSF ( 0 )
Q ( s )
s = N / N 0
N 0
N
T N = 5
k o b s 4
s = 7.5
Δ ϵ inc η N ( a ) T N Q ( s ) Δ ϵ c o h ,
Δ ϵ c o h = α λ R 1
α = 0.535
( Δ ϵ c o h )
( Δ ϵ i n c )
η N ( a )
Q ( s )
PSF
N
PSF = 2 α η N ( a ) N 1 R Q ( s ) .
N
N
N
A e f f × Δ E
π R 2 T ( s )
N
N 10 N 0
A e f f × Δ E = π ( PSF α Q s ) 2 N 0 N ( 1 e N 2 N 0 ) E
PSF
α = 0.535
Q s
4 s Q s Q s + e s / 2 ( 1 + e s / 2 s 4 s Q s Q s ) = 1 ,
Q s
d Q / d s
s = 5.0
s 12
s > 5
lim N 0 ( A e f f × Δ E ) s 3 .
s = 5
3 s 7
N 0
s > 5
A e f f × Δ E = π ( PSF α Q s ) 2 N 0 N ( 1 e N 2 N 0 ) ( a ) E .
0 a 1
( a ) = ( 1 a 2 ) η N 2 ( a )
η N ( a ) 3
a = T N 1 / 2
Q s
s o p t 7.5
N
N 0
( B 10 H 14 )
( C 16 H 14 O 3 )
N 0
10 2
f 1 , k + i f 2, k
N 0
N 0 = k f 1 , k 0 ( E ) 2 π k f 2 , k 0 ( E ) = j m j f 1 , j 0 ( E ) 2 π j m j f 2 , j 0 ( E ) .
m j
N 0
Z > 20
F e 26 , 27 Co , or 28 Ni
( C 8 H 8 )
( C 22 H 10 N 2 O 5 )
N 0
9   keV
20   keV
2 π
10 5 10 4   m
X m H n
B 10 H 14
BeH 2
10 3   m
7 × 10 2 cm 2
10 3   m
10 5
7.5 × 10 4   m
A e f f × Δ E
cm 2   keV
10 4   arc   sec
11.8   keV
17.3   keV
5.3 × 10 4   m
8.0 × 10 4   m
2.2 × 10 4 cm 2   keV
17.3   keV
4.0 × 10 4 cm 2   keV
C 16 H 14 O 3
10   keV
PSF
5 × 10 4   m
20   keV
1.6 × 10 4   m
5.7 × 10 4 cm 2   keV
4 × 10 3   m
7.5 × 10 4   m
10 7   m
t max
10 2   m
10 3   km
W F 2
T N
A max ( s e g ) 3
Δ ϵ
10 3   arc   sec
A e f f × Δ E
N 0
PSF
6   keV
17   keV
( PSF ) 2
z m = m 2 F
m 1 E
m 1 PSF
T m ( m 1 E ) = 2 N 0 ( E / m ) m N ( 1 e m N 2 N 0 ( E / m ) ) ,
m × N
Δ E = 2 ( m N ) 1 / 2 E .
m 2
20   keV
6 × 10 2 cm 2   keV
3.7 × 10 4   km
m > 2
PSF > 10 3   m
s o p t 7.5
m = 1
A e f f × Δ E γ m
γ 7
1.77   mm
2.70   mm
SNR A e f f × Δ E ( n ¯ s ) 1 / 2 b g t ,
n ¯ s
n ¯ b
b g = ( 1 + n ¯ b n ¯ s A P S F A e f f Ω ) 1 / 2 .
Ω = 2 π
n ¯ b ( E ) = n ¯ 0 E Γ
n ¯ 0 = ( 9.8 ± 0.3 ) s 1
cm 2 keV 1 sr 1
Γ = 1.42 ± 0.02
20   keV
10 4 cm 2
A PSF ( A e f f ) 1 10 7
E 4   keV
10 s 1
cm 2 keV 1
10 5 s 1 cm 2 keV 1
10 4 n ¯ s ( tot )
10 3 cm 2   keV
10 6   s
Δ ϵ x , y
A s e g 2
r n = ( n / N ) 1 / 2 R
± 0.5 °
10 3   arc   sec
h 1 , 2 ( r )
h 1 , 2 ( r ) = R 2 r 2 2 ξ 1 , 2 + γ R 4 r 4 8 ξ 1 , 2 3 + O ( r 6 ) ,
γ 0
F = 2 F Z
p 1 + q 1 = 2 F 1
Ψ Z , L ( 4 ) = 1 4 m = 0 2 ( J m K m ) σ 4 m ( F Z m 3 F L m 3 ) ϕ m ,
Ψ Z , L ( 4 ) ( Ψ Z , Ψ L 1 , 2 ) ( 4 )
J m ( q , θ )
J 0 = U Z ( q ) 2 , J 1 = 2 V Z ( q ) cos θ , J 2 = 1 + 2 cos 2 θ .
U Z ( q )
V Z ( q )
U Z ( q ) = 1 3 ( G q G q 2 ) , V Z ( q ) = 2 G q 1 ,
G q q 1 F Z . Ψ Z ( 4 )
Ψ L 1 , 2 ( 4 )
( L 1 , L 2 )
K m ( 1 , 2 ) ( n , θ )
K 0 ( 1 , 2 ) = 1 2 U L 1 , 2 ( n ) , K 1 ( 1 , 2 ) = 2 V L 1 , 2 ( n ) cos   θ ,
U L 1 ( n )
V L 1 ( n )
U L 1 ( n ) = 2 + n ( ( n 2 ) n + b 1 ) ( n 1 ) 2 n , V L 1 ( n ) = n 2 n 1 ( n 1 ) n .
b 1 = γ 1
K 2 ( 1 , 2 ) = 2 cos 2 θ + W L 1 , 2 ( n )
W L 1 , 2 = 1 + n 1
q > 0
U L 2 ( n ) = q 2 2 + 3 n n + q 1 + 3 n n 1 + n 2 + b 2 ( n 1 ) 2 ,
q q 1 F L 2
b 2 = b 1
V L 2
V L 2 ( n ) = q 2 n + 1 n + n n 1 .
Δ ϵ = σ Ψ ( 4 )   with   Ψ ( 4 ) = Ψ L 1 ( 4 ) + Ψ Z ( 4 ) + Ψ L 2 ( 4 ) ,
σ σ ( cos   θ ,  sin   θ )
q = 2 3 F
ξ 1 , 2
1 + b 1 , 2 = γ
ξ 1 , 2 F δ ( ± 2 + δ ) , γ 6 δ ,
n = 1 δ ϵ R
δ 1
| Δ ϵ f , ϕ | = ϕ 2 2 f cos 2 θ + ( δ / 2 ) 2 sin 2 θ .
2 π Δ ϵ θ 2 0 2 π | Δ ϵ f , ϕ | 2 d θ ,
δ 1
10 6   m
γ = 0
ξ 1 , 2 = ± 2 F δ
( 3 f ) 1 ϕ 2 Δ ϵ θ ( 11 f 3 δ ) 1 + ( 2 f ) 1 ϕ 2 .
1 ° ϕ + 1 °
10 6   arc   sec
( L 1 )
p = F = q
ξ 1 = F δ
γ = 0
Δ ϵ x = 1 2 f ( ϕ 2 2 1 ) cos   θ + ϕ ( 1 + 2 cos 2 θ ) ,
Δ ϵ y = 1 4 f ( δ ϕ 2 + 4 1 ) sin   θ + 2 ϕ   sin   θ   cos   θ ,
( 8 δ f 2 )
Δ ϵ θ ( 8 δ f 3 ) 1 1 + 5 ( ϕ f ) 2 .
10 % 20 %
10 2   m
10 6   m
10 4
10 2
ϕ det
1 / cos ( ϕ det )
Δ x det
3 × 10 1 PSF
Δ x det 2 × 10 4   m
Δ z D O F = ± N 1 F
± 2
± 3   km
± 4
± 5   km
± 8   km
± 40
± 110   m
± 60   m
10 2   eV
Δ E FWHM = 2.355 ω ENC 2 + E ω ,
ω = 3.65   eV
( e / hole )
F
5 e
10   keV
20   keV
10 2   keV
10 2   m
10   keV
10 5 m
6.4   keV
7 × 10 6   m
N 0
K α
N 250
20   keV
A max ( s e g )
A max ( s e g )
N = 100
s = 2
s = 5
N = 7 N 0
T ( s )
T N = 7
( r o b s )
T N = 7
s = 0
s = 7.5
N
N 0
s 7
N / N 0
A e f f × Δ E
N = 5 N 0
N / N 0
A e f f × Δ E
N 7.5 N 0
N 0
( 99.96 % )
( 99.99 % )
N 0
X m H n
( a = 0 )
A e f f × Δ E ( P S F ) 2
10 2
10 3
ϕ = 80   mas
δ = 6 × 10 6
( 1.88 × 10 6 )
ϕ = 0
Δ φ z
r F O V
5 × 10 2 N 2 × 10 4

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