OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 29, Iss. 1 — Jan. 1, 2012
  • pp: 68–77

Design of a general point focusing crystal geometry for x-ray spectroscopy

Sayyed Jalal Pestehe and Golamreza Askari Germi  »View Author Affiliations

JOSA A, Vol. 29, Issue 1, pp. 68-77 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (1376 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A nearly exact general equation for geometrical angular deviations from the Bragg angle over entire curved crystal surfaces is derived using a toroidally curvilinear coordinate system and applied on the nine conventional crystal geometries. Although the derived formula confirms Wittry’s results for the first five cases, it shows considerable differences for the more important cases, such as 45 ° point focusing, general point focusing, and Berreman geometries. The effective scattering areas for the mentioned cases have been derived, plotted, and interpreted. A point-to-point focusing crystal geometry is introduced, and it is shown that it approaches Wittry’s and spherical plane–spherical Johansson geometries as θ B 90 ° and θ B 0 ° , respectively.

© 2012 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(260.1180) Physical optics : Crystal optics
(300.6560) Spectroscopy : Spectroscopy, x-ray
(340.0340) X-ray optics : X-ray optics

ToC Category:
X-ray Optics

Original Manuscript: August 9, 2011
Revised Manuscript: October 15, 2011
Manuscript Accepted: October 20, 2011
Published: December 7, 2011

Pestehe Sayyed Jalal and Askari Germi Golamreza, "Design of a general point focusing crystal geometry for x-ray spectroscopy," J. Opt. Soc. Am. A 29, 68-77 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. B. Berreman, “Single quartz crystal point focusing x-ray monochromator,” Rev. Sci. Instrum. 26, 1048–1052 (1955). [CrossRef]
  2. E. P. Bertin, “Principles and Practice of X-Ray Spectrometric Analysis,” 2nd ed. (Plenum, 1975), p. 200.
  3. D. B. Wittry and S. Sun, “X-ray optics of doubly curved diffractors,” J. Appl. Phys. 67, 1633–1638 (1990). [CrossRef]
  4. D. B. Wittry and S. Sun, “X-ray optics of doubly curved diffractors II,” J. Appl. Phys. 71, 564–568 (1992). [CrossRef]
  5. D. B. Wittry and D. M. Golijanin, “Large aperture point focusing diffractor for x-rays,” Appl. Phys. Lett. 52, 1381–1382 (1988). [CrossRef]
  6. Z. W. Chen, F. Wei, and D. Gibson, “Advance in detection of low sulfur content by wavelenght dispersive XRF,” X-Ray Optical Systems Inc., 30 Corporate Circle, Albany, New York 12203 (2003).
  7. Z. W. Chen, T. N. Mailb, F. Z. Weia, C. A. MacDonald, and W. M. Gibson, “Focused beam total reflection x-ray fluorescence with low power sources coupled to doubly curved crystal optics,” Spectrochim. Acta B 60, 471–478 (2005). [CrossRef]
  8. M. Krämer, K. Kuzushita, S. Maeo, T. Utaka, and K. Taniguchi, “Design of a doubly-curved crystal to improve X-ray fluorescence analysis of aerosol particles,” Spectrochim. Acta B 63, 1408–1414 (2008). [CrossRef]
  9. Z. W. Chen, W. M. Gibson, and H. Huang, “High definition x-ray fluorescence: principles and techniques,” ID 318171, X-Ray Optics and Instrumentation, Inc., 15 Tech Valley Drive, East Greenbush, New York 12061, USA (2008).
  10. K. Yamamura, K. Ueda, M. Nagano, N. Zettsu, S. Maeo, S. Shimada, T. Utaka, and K. Taniguchi, “Fabrication of damage-free Johansson-type doubly curved crystal spectrometer substrate by numerically controlled local wet etching,” Nucl. Instrum. Methods Phys. Res. A 616, 281–284 (2010). [CrossRef]
  11. D. M. Golijanin and D. B. Wittry, “Microprobe x-ray fluorescence: new developments in an old technique,” in Microbeam Analysis 1988: Proceedings of the 23rd Conference of the Microbeam Analysis Society, D.E.Newbury, ed. (San Francisco Press, 1988), p. 397–402.
  12. D. B. Wittry, “Scanning monochrometer crystal and method of formation,” U.S. Patent No. 4,807,268 (21 February 1989).
  13. D. W. Berreman, J. Stamatoff, and S. J. Kennedy, “Doubly curved crystal point-focusing x-ray monochromators: geometrical and practical optics,” Appl. Opt. 16, 2081–2085 (1977). [CrossRef] [PubMed]
  14. E. M. Latush and M. I. Mazuritsky, “A focusing x-ray diffractor: effect of the crystal bending parameters on the spectral resolution,” Tech. Phys. Lett. 28, 142–144 (2002). [CrossRef]
  15. M. M. Stepanenko, “A spectral resolution of Johann-type x-ray spectrometers,” Plasma Devices Oper. 17, 191–200 (2009). [CrossRef]
  16. Z. W. Chen and D. B. Wittry, “Microanalysis by monochromatic microprobe x-ray fluorescence—physical basis, properties and future prospects,” J. Appl. Phys. 84, 1064–1073 (1998). [CrossRef]
  17. D. B. Wittry and N. C. Barbi, “X-ray crystal spectrometers and monochromators in microanalysis,” Microsc. Microanal. 7, 124–141 (2001).
  18. N. Gao and Z. Chen, “A microbeam wavelength-dispersive x-ray fluorescence system and its application for thin-film analysis,” Rev. Sci. Instrum. 76, 123104 (2005). [CrossRef]
  19. D. B. Wittry, W. Z. Chang, and R.Y. Li, “X-ray optics of diffractors curved to a logarithmic spiral,” J. Appl. Phys 74, 3534–3540(1993). [CrossRef]
  20. D. B. Wittry and S. Sun, “Focusing properties of curved x-ray diffractors,” J. Appl. Phys. 68, 387–391 (1990). [CrossRef]
  21. W. Z. Chang and D. B. Wittry, “Synthesis of x-ray intensity profiles for x-ray optical systems with curved cliff ractors,” J. Appl. Phys. 74, 2999–3008 (1993). [CrossRef]
  22. D. B. Wittry and W. Z. Chang, “Evaluation of crystal diffractor parameters for curved diffractors,” J. Appl. Phys. 72, 3440–3446 (1992). [CrossRef]
  23. D. B. Wittry and S. Sun, “Properties of curved x-ray diffractors with stepped surfaces,” J. Appl. Phys 69, 3886–3892(1991). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited