Optimal resolution with extreme depth of focus

R. L. Gordon*, G. W. Forbes

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


When the focal depth is required to be much larger than the wavelength, λ, the effective NA of the beam with optimal resolution is much less than unity. An aperture that is much larger than this beam's footprint is then of no consequence. Such beams that maximize the mean encircled energy fraction within a cylindrical focal region are shown to depend on only a single parameter, ω, that is proportional to the ratio of the square of the cylinder's radius to the product of its length and λ. A linear combination of Hermite- or Laguerre-Gaussian modes is used to represent these fields in two and three dimensions, respectively. For small ω, the results are compared both to asymptotic expansions and to optimal Gaussian and Bessel-Gauss beams.

Original languageEnglish
Pages (from-to)277-286
Number of pages10
JournalOptics Communications
Issue number1-6
Publication statusPublished - 1 May 1998


  • apodization
  • bessel-Gauss beams
  • depth of focus
  • gaussian beams


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