Zone Plate Equations
Zone Plate Equations
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