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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 20 — Jul. 10, 2012
  • pp: 4638–4659

Toward the diffraction limit with transmissive x-ray lenses in astronomy

Christoph Braig and Peter Predehl  »View Author Affiliations

Applied Optics, Vol. 51, Issue 20, pp. 4638-4659 (2012)

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We develop an analytical approach to refractive, blazed diffractive, and achromatic x-ray lenses of scalable dimensions for energies from 1 to 20 keV. Based on the parabolic wave equation, their wideband imaging properties are compared and optimized for a given spectral range. Low-Z lens materials for massive cores and rugged alternatives, such as polycarbonate or Si for flat Fresnel components, are investigated with respect to their suitability for diffraction-limited high-energy astronomy. Properly designed “hybrid” combinations can serve as an approach to x-ray telescopes with an enhanced efficiency throughout the whole considered band, nearly regardless of their inherent absorption.

© 2012 Optical Society of America

OCIS Codes
(340.7440) X-ray optics : X-ray imaging
(050.1965) Diffraction and gratings : Diffractive lenses

ToC Category:
X-ray Optics

Original Manuscript: March 23, 2012
Revised Manuscript: May 3, 2012
Manuscript Accepted: May 7, 2012
Published: July 2, 2012

Christoph Braig and Peter Predehl, "Toward the diffraction limit with transmissive x-ray lenses in astronomy," Appl. Opt. 51, 4638-4659 (2012)

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  1. W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft x-ray microscopy at a resolution better than 15 nm,” Nature 435, 1210–1213 (2005). [CrossRef]
  2. A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy x-rays,” Nature 384, 49–51 (1996). [CrossRef]
  3. B. Lengeler, C. G. Schroer, M. Kuhlmann, B. Benner, T. F. Günzler, O. Kurapova, F. Zontone, A. Snigirev, and I. Snigireva, “Refractive x-ray lenses,” J. Phys. D 38, A218–A222(2005). [CrossRef]
  4. D. Attwood, Soft X-Rays and Extreme Ultraviolet Radiation: Principles and Applications (Cambridge University, 1999).
  5. C. G. Schroer and B. Lengeler, “Focusing hard x-rays to nanometer dimensions by adiabatically focusing lenses,” Phys. Rev. Lett. 94, 054802 (2005). [CrossRef]
  6. S. Rehbein, S. Heim, P. Guttmann, S. Werner, and G. Schneider, “Ultrahigh-resolution soft x-ray microscopy with zone plates in high orders of diffraction,” Phys. Rev. Lett. 103, 110801 (2009). [CrossRef]
  7. G. K. Skinner, “Diffractive-refractive optics for high energy astronomy—II. Variations on the theme,” Astron. Astrophys. 383, 352–359 (2002). [CrossRef]
  8. 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]
  9. C. Braig and P. Predehl, “Large-scale diffractive x-ray telescopes,” Exp. Astron. 21, 101–123 (2006). [CrossRef]
  10. C. Braig and P. Predehl, “Efficient Fresnel x-ray optics made simple,” Appl. Opt. 46, 2586–2599 (2007). [CrossRef]
  11. G. K. Skinner, Z. Arzoumanian, W. C. Cash, N. Gehrels, K. C. Gendreau, P. Gorenstein, J. F. Krizmanic, M. C. Miller, J. D. Phillips, R. D. Reasenberg, C. S. Reynolds, R. M. Sambruna, R. E. Streitmatter, and D. L. Windt, “The Milli-Arc-Second Structure Imager, MASSIM: a new concept for a high angular resolution x-ray telescope,” Proc. SPIE 7011, 70110T (2008). [CrossRef]
  12. G. K. Skinner, “Diffractive x-ray telescopes,” X-Ray Opt. Instrum. 2010, 743485 (2010). [CrossRef]
  13. P. Gorenstein, “Focusing x-ray optics for astronomy,” X-Ray Opt. Instrum. 2010, 109740 (2010). [CrossRef]
  14. 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,” Atomic Data Nucl. Data Tables 54, 181–342 (1993). [CrossRef]
  15. B. X. Yang, “Fresnel and refractive lenses for x-rays,” Nucl. Instrum. Methods Phys. Res. A 328, 578–587 (1993). [CrossRef]
  16. C. Braig, P. Predehl, and E.-B. Kley, “Efficient extreme ultraviolet transmission gratings for plasma diagnostics,” Opt. Eng. 50, 066501 (2011). [CrossRef]
  17. Y. V. Kopylov, A. V. Popov, and A. V. Vinogradov, “Application of the parabolic wave equation to x-ray diffraction optics,” Opt. Commun. 118, 619–636 (1995). [CrossRef]
  18. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).
  19. C. Braig, and P. Predehl, “Advanced Fresnel x-ray telescopes for spectroscopic imaging,” Exp. Astron. 27, 131–155(2009). [CrossRef]
  20. D. T. Grubb, “Radiation damage and electron microscopy of organic polymers,” J. Mater. Sci. 9, 1715–1736 (1974). [CrossRef]
  21. F. Barkusky, A. Bayer, C. Peth, and K. Mann, “Direct photoetching of polymers using radiation of high energy density from a table-top extreme ultraviolet plasma source,” J. Appl. Phys. 105, 014906 (2009). [CrossRef]
  22. B. Lengeler, J. Tümmler, A. Snigirev, I. Snigireva, and C. Raven, “Transmission and gain of singly and doubly focusing refractive x-ray lenses,” J. Appl. Phys. 84, 5855–5861 (1998). [CrossRef]
  23. J. Krizmanic, G. Skinner, and N. Gehrels, “Formation flying for a Fresnel lens observatory mission,” Exp. Astron. 20, 497–503 (2005). [CrossRef]
  24. B. Lengeler, C. Schroer, J. Tümmler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, “Imaging by parabolic refractive lenses in the hard x-ray range,” J. Synchrotron Rad. 6, 1153–1167 (1999). [CrossRef]
  25. J. Krizmanic, B. Morgan, R. Streitmatter, N. Gehrels, K. Gendreau, Z. Arzoumanian, R. Ghodssi, and G. Skinner, “Development of ground-testable phase Fresnel lenses in silicon,” Exp. Astron. 20, 299–306 (2005). [CrossRef]

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