Zone Plate Equations

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Zone Plate Equations

15zones.gif

Variables

  • f = focal length
  • λ = wavelength
  • ρr = phase variation
  • rm = radius of mth zone
  • m = zone number
  • 1 ≤ N ≤ ∞

Definitions

  • GZP = Geometric Zone Plate, paraxial, f# > 10
  • IZP = Interferometric Zone Plate, f# < 10
  • GHZP = Generalized Holographic Zone Plate

Equations

  • For GZP: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r_m = \sqrt{2 m \lambda f}, \, \phi_r = \pi r^2 / (\lambda f)}
  • For IZP: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r_m = \sqrt{2 m \lambda f + {(m \lambda)}^2}}
  • For GHZP: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r_m = \sqrt{2 m \lambda f + {(m \lambda / N)}^2}}

Properties of Zone Plates

  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \text{Minimum zone width } \simeq 2\lambda f\sharp \simeq \text{ minimum spot size}}
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \text{Depth of focus } \simeq 2 \lambda {f\sharp}^2}
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f = \frac{f_m^2}{2 m \lambda}, \, f\sharp = \frac{1}{2 N A} = \frac{f}{D i a}}
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \text{Chromatic aberration } \Delta \lambda \simeq \lambda / m} (m = number of zones illuminated)
  • Hybrid condition (f zone)/(f lens) = (n-1)/λ (dispers const.))
  • Hybrid Achromats typically use GZP pattern and less than 300 zones

Last modified on 9/22/97