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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 21, Iss. 4 — Apr. 1, 2004
  • pp: 561–571

Comprehensive focusing analysis of various Fresnel zone plates

Qing Cao and Jürgen Jahns  »View Author Affiliations


JOSA A, Vol. 21, Issue 4, pp. 561-571 (2004)
http://dx.doi.org/10.1364/JOSAA.21.000561


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Abstract

A series-form expression for the individual diffracted field of a general annular ring is derived from the Rayleigh–Sommerfeld diffraction integral. It can be used for the accurate and fast simulation of any diffractive focusing element composed of concentric transparent rings. We present a comprehensive analysis, based on the leading term and the linear superposition principle, of the focusing performances of various Fresnel zone plates. Many problems, such as the equivalent aperture function, the diffraction efficiency, the focal spot pattern, the suppression of higher orders and the appearance of “fractional orders,” and the explanation for the appearance of Fraunhofer diffraction patterns, are analytically investigated in detail. Because of the great similarity between Fresnel zone plates and multilevel diffractive lenses, most of the obtained results are also applicable to multilevel diffractive lenses.

© 2004 Optical Society of America

OCIS Codes
(110.0110) Imaging systems : Imaging systems
(220.2560) Optical design and fabrication : Propagating methods
(340.7440) X-ray optics : X-ray imaging
(350.3950) Other areas of optics : Micro-optics
(350.4600) Other areas of optics : Optical engineering

History
Original Manuscript: August 14, 2003
Revised Manuscript: November 12, 2003
Manuscript Accepted: December 3, 2003
Published: April 1, 2004

Citation
Qing Cao and Jürgen Jahns, "Comprehensive focusing analysis of various Fresnel zone plates," J. Opt. Soc. Am. A 21, 561-571 (2004)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-21-4-561


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References

  1. A. V. Baez, “Fresnel zone plate for optical image formation using extreme ultraviolet and soft x radiation,” J. Opt. Soc. Am. 51, 405–412 (1961). [CrossRef]
  2. C. D. Pfeifer, L. D. Ferris, W. M. Yen, “Optical image formation with a Fresnel zone plate using vacuum-ultraviolet radiation,” J. Opt. Soc. Am. 63, 91–95 (1973). [CrossRef]
  3. G. Schmahl, D. Rudolph, P. Guttmann, O. Christ, “Zone plates for x-ray microscopy,” in X-ray Microscopy, G. Schmahl, D. Rudolph, eds. (Springer-Verlag, Berlin, 1984), Vol. 43, pp. 63–74.
  4. A. Boivin, “On the theory of diffraction by concentric arrays of ring-shaped apertures,” J. Opt. Soc. Am. 42, 60–64 (1952). [CrossRef]
  5. G. S. Waldman, “Variations on the Fresnel zone plate,” J. Opt. Soc. Am. 56, 215–218 (1966). [CrossRef]
  6. D. J. Stigliani, R. Mittra, R. G. Semonin, “Resolving power of a zone plate,” J. Opt. Soc. Am. 57, 610–613 (1967). [CrossRef]
  7. H. Arsenault, “Diffraction theory of Fresnel zone plates,” J. Opt. Soc. Am. 58, 1536 (1968). [CrossRef]
  8. M. Bottema, “Fresnel zone-plate diffraction patterns,” J. Opt. Soc. Am. 59, 1632–1638 (1969). [CrossRef]
  9. M. Young, “Zone plates and their aberrations,” J. Opt. Soc. Am. 62, 972–976 (1972). [CrossRef]
  10. M. Novotny, “A new series representation of the Fresnel diffraction field of axially symmetrical filters,” Opt. Acta 24, 551–565 (1977). [CrossRef]
  11. J. A. Sun, A. Cai, “Archaic focusing properties of Fresnel zone plates,” J. Opt. Soc. Am. A 8, 33–35 (1991). [CrossRef]
  12. B. Xiao, “Equivalent field of paraxial diffraction of a zone plate,” Opt. Lett. 19, 1940–1942 (1994). [CrossRef] [PubMed]
  13. R. Chmelı́k, “Analytical description of wave fields in focal regions of diffractive lenses,” J. Mod. Opt. 43, 1463–1471 (1996). [CrossRef]
  14. E. H. Anderson, V. Boegli, L. P. Muray, “Electron beam lithography digital pattern generator and electronics for generalized curvilinear structures,” J. Vac. Sci. Technol. B 13, 2529–2534 (1995). [CrossRef]
  15. E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000). [CrossRef]
  16. M. J. Simpson, A. G. Michette, “Imaging properties of modified Fresnel zone plates,” Opt. Acta 31, 403–413 (1984). [CrossRef]
  17. L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, R. Seemann, “Sharper images by focusing soft x-rays with photon sieves,” Nature (London) 414, 184–188 (2001). [CrossRef]
  18. Q. Cao, J. Jahns, “Focusing analysis of the pinhole photon sieve: individual far-field model,” J. Opt. Soc. Am. A 19, 2387–2393 (2002). [CrossRef]
  19. Q. Cao, J. Jahns, “Nonparaxial model for the focusing of high-numerical-aperture photon sieves,” J. Opt. Soc. Am. A 20, 1005–1012 (2003). [CrossRef]
  20. G. E. Artzner, J. P. Delaboudinière, X. Y. Song, “Photon sieves as EUV telescopes for solar orbiter,” in Innovative Telescopes and Instrumentation for Solar Astrophysics, S. L. Keil, S. V. Avakyan, S. I. Vavilov, eds., Proc. SPIE4853, 158–161 (2003). [CrossRef]
  21. M. Howells, http://www-esg.lbl.gov/esg/personnel/howells/Xraysieves.pdf . The opinion that the suppression of higher orders results from the use of different ratios d/w for different pinholes is presented in this reference, where d is the diameter of an individual pinhole and w is the width of the corresponding local half-zone of the underlying TFZP.
  22. Q. Cao, J. Jahns, “Modified Fresnel zone plates that produce sharp Gaussian focal spots,” J. Opt. Soc. Am. A 20, 1576–1581 (2003). [CrossRef]
  23. A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990). [CrossRef]
  24. J. Jahns, S. J. Walker, “Two-dimensional array of diffractive microlenses fabricated by thin film deposition,” Appl. Opt. 29, 931–936 (1990). [CrossRef] [PubMed]
  25. S. Sinzinger, J. Jahns, Microoptics, 2nd ed. (Wiley-VCH, Weinheim, Germany2003), Subsect. 6.3.6.
  26. M. Kuittinen, H. P. Herzig, “Encoding of efficient diffractive microlenses,” Opt. Lett. 20, 2156–2158 (1995). [CrossRef] [PubMed]
  27. U. Levy, D. Mendlovic, E. Marom, “Efficiency analysis of diffractive lenses,” J. Opt. Soc. Am. A 18, 86–93 (2001). [CrossRef]
  28. J. E. Harvey, “Fourier treatment of near-field scalar diffraction theory,” Am. J. Phys. 47, 974–980 (1979). [CrossRef]
  29. W. H. Southwell, “Validity of the Fresnel approximation in the near field,” J. Opt. Soc. Am. 71, 7–14 (1981). [CrossRef]
  30. C. J. R. Sheppard, M. Hrynevych, “Diffraction by a circular aperture: a generalization of Fresnel diffraction theory,” J. Opt. Soc. Am. A 9, 274–281 (1992). [CrossRef]
  31. R. Ashman, M. Gu, “Effect of ultrashort pulsed illumination on foci caused by a Fresnel zone plate,” Appl. Opt. 42, 1852–1855 (2003). [CrossRef] [PubMed]
  32. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Subsect. 2.1.5.
  33. C. Vassallo, “Wide-angle BPM and power conservation,” IEE Electron. Lett. 31, 130–131 (1995). [CrossRef]
  34. C. Vassallo, “Limitations of the wide-angle beam propagation method in nonuniform systems,” J. Opt. Soc. Am. A 13, 761–770 (1996). [CrossRef]
  35. Q. Cao, X. Deng, “Power carried by scalar light beams,” Opt. Commun. 151, 212–216 (1998). [CrossRef]
  36. M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975). [CrossRef]
  37. G. P. Agrawal, M. Lax, “Free-space wave propagation beyond the paraxial approximation,” Phys. Rev. A 27, 1693–1695 (1983). [CrossRef]
  38. Q. Cao, X. Deng, “Corrections to the paraxial approximation of an arbitrary free-propagation beam,” J. Opt. Soc. Am. A 15, 1144–1148 (1998). [CrossRef]
  39. Q. Cao, “Corrections to the paraxial approximation solutions in transversely nonuniform refractive-index media,” J. Opt. Soc. Am. A 16, 2494–2499 (1999). [CrossRef]
  40. G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed. (Cambridge U. Press, Cambridge, UK1966), p. 46.

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