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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 31, Iss. 2 — Feb. 1, 2014
  • pp: 363–372

Diffraction theory for azimuthally structured Fresnel zone plate

Thordis Vierke and Jürgen Jahns  »View Author Affiliations

JOSA A, Vol. 31, Issue 2, pp. 363-372 (2014)

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A conventional Fresnel zone plate (FZP) consists of concentric rings with an alternating binary transmission of zero and one. In an azimuthally structured Fresnel zone plate (aFZP), the light transmission of the transparent zones is modulated in the azimuthal direction, too. The resulting structure is of interest for extreme ultraviolet and x-ray imaging, in particular, because of its improved mechanical stability as compared to the simple ring structure of an FZP. Here, we present an analysis of the optical performance of the aFZP based on scalar diffraction theory and show numerical results for the light distribution in the focal plane. These will be complemented by calculations of the optical transfer function.

© 2014 Optical Society of America

OCIS Codes
(110.7440) Imaging systems : X-ray imaging
(220.4000) Optical design and fabrication : Microstructure fabrication
(350.1260) Other areas of optics : Astronomical optics
(050.1965) Diffraction and gratings : Diffractive lenses
(110.4235) Imaging systems : Nanolithography
(220.4241) Optical design and fabrication : Nanostructure fabrication

ToC Category:
Optical Design and Fabrication

Original Manuscript: September 27, 2013
Revised Manuscript: December 16, 2013
Manuscript Accepted: December 18, 2013
Published: January 23, 2014

Thordis Vierke and Jürgen Jahns, "Diffraction theory for azimuthally structured Fresnel zone plate," J. Opt. Soc. Am. A 31, 363-372 (2014)

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  1. A. Heuberger, “X-ray lithography,” J. Vac. Sci. Technol. B 6, 107–121 (1985). [CrossRef]
  2. W. Chao, B. D. Harteneck, J. A. Liddle, and D. T. Attwood, “Soft x-ray microscopy at a spatial resolution better than 15 nm,” Nature 435, 1210–1213 (2005). [CrossRef]
  3. D. T. Attwood, Soft X-Rays and Extreme Ultraviolet Radiation: Principles and Applications (Cambridge University, 1999).
  4. 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]
  5. G. Schmahl and D. Rudolph, “High-power zone plates as image forming systems for soft x-rays,” Optik 29, 577–585 (1969).
  6. J. Als-Nielsen, D. Jacquemain, K. Kjaer, F. Leveiller, M. Lahav, and L. Leiserowitz, “Principles and applications of grazing incidence x-ray and neutron scattering from ordered molecular monolayers at the air-water interface,” Phys. Rep. 246, 251–313 (1994). [CrossRef]
  7. L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft x-rays with photon sieves,” Nature 414, 184–188 (2001). [CrossRef]
  8. G. Andersen, “Large optical photon sieves,” Opt. Lett. 30, 2976–2978 (2005). [CrossRef]
  9. Q. Cao and J. Jahns, “Focusing analysis of the pinhole photon sieve: individual far-field model,” J. Opt. Soc. Am. A 19, 2387–2393 (2002). [CrossRef]
  10. I. Mitsuishi, Y. Ezoe, M. Koshiishi, M. Mita, Y. Maeda, N. Y. Yamasaki, K. Mitsuda, T. Shirata, T. Hayashi, T. Takano, and R. Maeda, “Evaluation of the soft x-ray reflectivity of micropore optics using anisotropic wet etching of silicon wafers,” Appl. Opt. 49, 1007–1011 (2010). [CrossRef]
  11. A. W. Lohmann, Optical Information Processing (TU Ilmenau University, 2006).
  12. C. W. McCutchen, “Generalized aperture and the three-dimensional diffraction image,” J. Opt. Soc. Am. 54, 240–242 (1964). [CrossRef]
  13. J. Jahns and S. Helfert, Introduction to Micro- and Nanooptics (VCH-Wiley, 2012).
  14. J. Jahns and S. J. Walker, “Two-dimensional array of diffractive microlenses fabricated by thin film deposition,” Appl. Opt. 29, 931–936 (1990). [CrossRef]
  15. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1964).
  16. Q. Cao and J. Jahns, “Modified Fresnel zone plates that produce sharp Gaussian focal spots,” J. Opt. Soc. Am. A 20, 1576–1581 (2003). [CrossRef]

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