OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 25 — Dec. 3, 2012
  • pp: 27212–27221

Three-level filter for increased depth of focus and Bessel beam generation

Colin JR Sheppard and Shalin Mehta  »View Author Affiliations

Optics Express, Vol. 20, Issue 25, pp. 27212-27221 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (2340 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A novel axially-symmetric filter for increasing focal depth and generating an approximation to a Bessel beam is proposed. It consists of an array of rings of strength –1,0 and 1. The design is based on an analytic solution, and combines high resolution in the transverse direction with good efficiency. One presented design increases the depth of focus compared with a standard lens by more than 30 times, with a very flat axial intensity distribution over this range. Effects of discretization are discussed. Various different approaches to increasing depth of focus are compared, to put the new design into perspective.

© 2012 OSA

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(050.1940) Diffraction and gratings : Diffraction
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(110.6980) Imaging systems : Transforms
(350.6980) Other areas of optics : Transforms

ToC Category:
Diffraction and Gratings

Original Manuscript: July 17, 2012
Revised Manuscript: August 23, 2012
Manuscript Accepted: August 23, 2012
Published: November 19, 2012

Colin JR Sheppard and Shalin Mehta, "Three-level filter for increased depth of focus and Bessel beam generation," Opt. Express 20, 27212-27221 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: “non-diffracting” beams,” Laser Photon. Rev.4(4), 529–547 (2010). [CrossRef]
  2. J. H. McLeod, “The axicon: A new type of optical element,” J. Opt. Soc. Am.44(8), 592–597 (1954). [CrossRef]
  3. J. Dyson, “Circular and spiral diffraction gratings,” Proc. R. Soc. Lond. A Math. Phys. Sci.248(1252), 93–106 (1958). [CrossRef]
  4. G. B. Airy, “The diffraction of an annular aperture,” Phil. Mag. Ser. 318, 1–10 (1841).
  5. J. W. S. Rayleigh, “On the diffraction of object glasses,” Mon. Not. R. Astron. Soc.33, 59–63 (1872).
  6. G. C. Steward, “IV Aberration diffraction effects,” Phil. Trans. Roy. Soc. London Ser. A225(626-635), 131–198 (1926). [CrossRef]
  7. E. H. Linfoot and E. Wolf, “Diffraction images in systems with an annular aperture,” Proc. Phys. Soc. B66(2), 145–149 (1953). [CrossRef]
  8. B. J. Thompson, “Diffraction by semitransparent and phase annuli,” J. Opt. Soc. Am.55(2), 145–149 (1965). [CrossRef]
  9. G. Yang, “An optical pickup using a diffractive optical element for a high-density optical disc,” Opt. Commun.159(1-3), 19–22 (1999). [CrossRef]
  10. H. F. Wang and F. Gan, “High focal depth with a pure-phase apodizer,” Appl. Opt.40(31), 5658–5662 (2001). [CrossRef] [PubMed]
  11. E. R. Dowski and W. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt.34(11), 1859–1866 (1995). [CrossRef] [PubMed]
  12. C. J. R. Sheppard and T. Wilson, “Gaussian-beam theory of lenses with annular aperture,” IEE J. Microwaves Opt. Acoust.2(4), 105–112 (1978). [CrossRef]
  13. J. Durnin, “Exact solutions for nondiffracting beams. I. the scalar theory,” J. Opt. Soc. Am. A4(4), 651–654 (1987). [CrossRef]
  14. C. J. R. Sheppard, “Binary phase filters with a maximally-flat response,” Opt. Lett.36(8), 1386–1388 (2011). [CrossRef] [PubMed]
  15. C. J. R. Sheppard, J. Campos, J. C. Escalera, and S. Ledesma, “Three-zone pupil filters,” Opt. Commun.281(14), 3623–3630 (2008). [CrossRef]
  16. F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64(6), 491–495 (1987). [CrossRef]
  17. A. J. Cox and J. D’Anna, “Constant-axial-intensity nondiffracting beam,” Opt. Lett.17(4), 232–234 (1992). [CrossRef] [PubMed]
  18. M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys.47(3), 264–267 (1979). [CrossRef]
  19. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett.99(21), 213901 (2007). [CrossRef] [PubMed]
  20. M. R. Arnison, C. J. Cogswell, C. J. R. Sheppard, and P. Török, “Wavefront coding fluorescence microscopy using high aperture lenses,” in Optical Imaging and Microscopy P. Török and F.-J. Kao, eds. (Springer, 2003), pp. 143–168.
  21. R. Boivin and A. Boivin, “Optimized amplitude filtering for superresolution over a restricted field - I. Achievement of maximum central irradiance under an energy constraint,” Opt. Acta (Lond.)27, 857 (1980).
  22. C. J. R. Sheppard and Z. S. Hegedus, “Axial behaviour of pupil plane filters,” J. Opt. Soc. Am. A5(5), 643–647 (1988). [CrossRef]
  23. Y. S. Xu, J. Singh, C. J. R. Sheppard, and N. G. Chen, “Ultra long high resolution beam by multi-zone rotationally symmetrical complex pupil filter,” Opt. Express15(10), 6409–6413 (2007). [CrossRef] [PubMed]
  24. V. F. Canales, J. E. Oti, and M. P. Cagigal, “Three-dimensional control of the focal light intensity distribution by analytically designed phase masks,” Opt. Commun.247(1-3), 11–18 (2005). [CrossRef]
  25. Z. Bouchal, J. Wagner, and M. Olivik, “Bessel beams in the focal region,” Opt. Eng.34(6), 1680–1688 (1995). [CrossRef]
  26. Y. Kozawa and S. Sato, “Sharper focal spot formed by higher-order radially polarized laser beams,” J. Opt. Soc. Am. A24(6), 1793–1798 (2007). [CrossRef] [PubMed]
  27. Y. Kozawa, T. Hibi, A. Sato, H. Horanai, M. Kurihara, N. Hashimoto, H. Yokoyama, T. Nemoto, and S. Sato, “Lateral resolution enhancement of laser scanning microscopy by a higher-order radially polarized mode beam,” Opt. Express19(17), 15947–15954 (2011). [CrossRef] [PubMed]
  28. C. J. R. Sheppard, “Synthesis of filters for specified axial properties,” J. Mod. Opt.43(3), 525–536 (1996). [CrossRef]
  29. M. R. Foreman, S. S. Sherif, P. R. T. Munro, and P. Török, “Inversion of the Debye-Wolf diffraction integral using an eigenfunction representation of the electric fields in the focal region,” Opt. Express16(7), 4901–4917 (2008). [CrossRef] [PubMed]
  30. T. Čižmár and K. Dholakia, “Tunable Bessel light modes: engineering the axial propagation,” Opt. Express17(18), 15558–15570 (2009). [CrossRef] [PubMed]
  31. J. Wang, W. Chen, and Q. W. Zhan, “Engineering of high purity ultra-long optical needle field through reversing the electric dipole array radiation,” Opt. Express18(21), 21965–21972 (2010). [CrossRef] [PubMed]
  32. H. F. Wang, L. Shi, B. Luk`yanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2(8), 501–505 (2008). [CrossRef]
  33. C. J. R. Sheppard, S. Rehman, N. K. Balla, E. Y. S. Yew, and T. W. Teng, “Bessel beams: Effects of polarization,” Opt. Commun.282(24), 4647–4656 (2009). [CrossRef]
  34. X. Hao, C. F. Kuang, T. T. Wang, and X. Liu, “Phase encoding for sharper focus of the azimuthally polarized beam,” Opt. Lett.35(23), 3928–3930 (2010). [CrossRef] [PubMed]
  35. C. J. R. Sheppard and S. Rehman, “Highly convergent focusing of light based on rotating dipole polarization,” Appl. Opt.50(22), 4463–4467 (2011). [CrossRef] [PubMed]

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.

Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited