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Applied Optics

Applied Optics


  • Editor: Glenn D. Boreman
  • Vol. 44, Iss. 33 — Nov. 20, 2005
  • pp: 7098–7105

Fundamental spatial resolution of an x-ray pore optic

Arjan L. Mieremet and Marco W. Beijersbergen  »View Author Affiliations

Applied Optics, Vol. 44, Issue 33, pp. 7098-7105 (2005)

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We investigate the fundamental spatial resolution of an x-ray pore optic as a function of the pore dimensions, the photon energy, and the focal length. We achieve this by calculating the shape of the focal spot, using diffraction integrals such that the half-energy width is determined. Quantitative results are presented for the X-Ray Evolving Universe Spectroscopy (XEUS) telescope, showing that a resolution of better than 2 arc sec half-energy width is possible by use of an optic with pore sizes of approximately 0.5 mm.

© 2005 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(110.7440) Imaging systems : X-ray imaging
(340.7470) X-ray optics : X-ray mirrors
(350.1260) Other areas of optics : Astronomical optics

ToC Category:
X-ray Optics

Original Manuscript: May 3, 2005
Revised Manuscript: July 11, 2005
Manuscript Accepted: July 13, 2005
Published: November 20, 2005

Arjan L. Mieremet and Marco W. Beijersbergen, "Fundamental spatial resolution of an x-ray pore optic," Appl. Opt. 44, 7098-7105 (2005)

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  1. A. N. Parmar, M. Arnaud, X. Barcons, J. Bleeker, G. Hasinger, H. Inoue, G. Palumbo, M. Turner, “Science with XEUS: the X-ray Evolving Universe Spectroscopy Mission,” in UV and Gamma-Ray Space Telescope Systems, G. Hasinger, M. J. Turner, eds., Proc. SPIE5488, 388–393 (2004). [CrossRef]
  2. M. Bavdaz, D. Lumb, A. Peacock, “XEUS mission reference design,” in UV and Gamma-Ray Space Telescope Systems, G. Hasinger, M. J. Turner, eds., Proc. SPIE5488, 829–836 (2004). [CrossRef]
  3. M. Beijersbergen, M. Bavdaz, A. Peacock, E. Tomaselli, R. Fairbend, J.-P. Boutot, S. Flyckt, A. Brunton, G. Price, G. Fraser, C. Herrmann, M. Krumrey, E. Ziegler, A. Freund, “High-resolution micropore x-ray optics produced with microchannel plate technology,” in Advances in X-Ray Optics, A. Freund, T. Ishikawa, A. Khounsary, D. Mancini, A. Michette, S. Oestreich, eds., Proc. SPIE4145, 188–192 (2001). [CrossRef]
  4. M. Beijersbergen, S. Kraft, R. Guenther, A. Mieremet, M. Collon, M. Bavdaz, D. Lumb, A. Peacock, “Silicon pore optics: novel lightweight high-resolution X-ray optics developed for XEUS,” in UV and Gamma-Ray Space Telescope Systems, G. Hasinger, M. J. Turner, eds., Proc. SPIE5488, 868–874 (2004). [CrossRef]
  5. H. Wolter, “Spiegelsysteme streifenden Einfalls als abbildende Optiken für Röntgenstrahlen,” Ann. Phys. 10, 94–114 (1952). [CrossRef]
  6. M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, 1999), pp. 412–516. [CrossRef]
  7. F. Pedrotti, L. Pedrotti, Introduction to Optics (Prentice-Hall, 1987), pp. 323–348.
  8. The exact solution for the prefactor z can be found by solution of the equation ∫02(sin x/x)2dx= ½∫0∞ (sin x/x)2dx. This equation can be rewritten9 into [cos(2z) − 1]/(2z) + Si(2z) = π/4, where Si is the sine-integral function, giving z = 0.850. This solution has to be divided by π to yield the relative position of the HEW with respect to the first zero points of the central peak of the diffraction pattern.
  9. I. S. Gradsteyn, I. M. Ryzhik, Table of Integrals, Series and Products, 6th ed. (Academic, 2000).

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