A zone plate is a device used to focus light or other things exhibiting wave character.[1] Unlike lenses or curved mirrors, zone plates use diffraction instead of refraction or reflection. Based on analysis by French physicist Augustin-Jean Fresnel, they are sometimes called Fresnel zone plates in his honor. The zone plate's focusing ability is an extension of the Arago spot phenomenon caused by diffraction from an opaque disc.[2]
A zone plate consists of a set of concentric rings, known as Fresnel zones, which alternate between being opaque and transparent. Light hitting the zone plate will diffract around the opaque zones. The zones can be spaced so that the diffracted light constructively interferes at the desired focus, creating an image there.
Design and manufacture
To get constructive interference at the focus, the zones should switch from opaque to transparent at radii where
\( {\displaystyle r_{n}={\sqrt {n\lambda f+{\frac {1}{4}}n^{2}\lambda ^{2}}}} \) [3]
where n is an integer, λ is the wavelength of the light the zone plate is meant to focus and f is the distance from the center of the zone plate to the focus. When the zone plate is small compared to the focal length, this can be approximated as
\( {\displaystyle r_{n}\simeq {\sqrt {n\lambda f}}}. \)
For plates with many zones, you can calculate the distance to the focus if you only know the radius of the outermost zone, rN, and its width, ΔrN:
\( {\displaystyle f={\frac {2r_{N}\Delta r_{N}}{\lambda }}} \)
In the long focal length limit, the area of each zone is equal, because the width of the zones must decrease farther from the center. The maximum possible resolution of a zone plate depends on the smallest zone width,
\( {\displaystyle {\frac {\Delta l}{\Delta r_{N}}}\approx 1.22} \)
Because of this, the smallest size object you can image, Δl, is limited by how small you can reliably make your zones.
Zone plates are frequently manufactured using lithography. As lithography technology improves and the size of features that can be manufactured decreases, the possible resolution of zone plates manufactured with this technique can improve.
Continuous zone plates
Unlike a standard lens, a binary zone plate produces intensity maxima along the axis of the plate at odd fractions (f/3, f/5, f/7, etc.). Although these contain less energy (counts of the spot) than the principal focus (because it is wider), they have the same maximum intensity (counts/m2).
However, if the zone plate is constructed so that the opacity varies in a gradual, sinusoidal manner, the resulting diffraction causes only a single focal point to be formed. This type of zone plate pattern is the equivalent of a transmission hologram of a converging lens.
For a smooth zone plate, the opacity (or transparency) at a point can be given by:
\( {\displaystyle {\frac {1\pm \cos \left(kr^{2}\right)}{2}}\,} \)
where r is the distance from the plate center, and k determines the plate's scale.[4]
Binary zone plates use almost the same formula, however they depend only on the sign:
\( {\displaystyle {\frac {1\pm \operatorname {sgn} \left(\cos \left(kr^{2}\right)\right)}{2}}\,} \)
Free parameter
It does not matter to the constructive interference what the absolute phase is, but only that it is the same from each ring. So an arbitrary length can be added to all the paths
\( {\displaystyle r_{n}={\sqrt {(n+\alpha )\lambda f+{\frac {1}{4}}(n+\alpha )^{2}\lambda ^{2}}}} \)
This reference phase can be chosen to optimize secondary properties such as side lobes.[1]
Applications
Physics
There are many wavelengths of light outside of the visible area of the electromagnetic spectrum where traditional lens materials like glass are not transparent, and so lenses are more difficult to manufacture. Likewise, there are many wavelengths for which there are no materials with a refractive index significantly larger than one. X-rays, for example, are only weakly refracted by glass or other materials, and so require a different technique for focusing. Zone plates eliminate the need for finding transparent, refractive, easy-to-manufacture materials for every region of the spectrum. The same zone plate will focus light of many wavelengths to different foci, which means they can also be used to filter out unwanted wavelengths while focusing the light of interest.
Other waves such as sound waves and, due to quantum mechanics, matter waves can be focused in the same way. Wave plates have been used to focus beams of neutrons and helium atoms.[1]
Photography
Example of an image taken with zone plate optics.
Zone plates are also used in photography in place of a lens or pinhole for a glowing, soft-focus image. One advantage over pinholes (aside from the unique, fuzzy look achieved with zone plates) is that the transparent area is larger than that of a comparable pinhole. The result is that the effective f-number of a zone plate is lower than for the corresponding pinhole and the exposure time can be decreased. Common f-numbers for a pinhole camera range from f/150 to f/200 or higher, whereas zone plates are frequently f/40 and lower. This makes hand held shots feasible at the higher ISO settings available with newer DSLR cameras.
Gunsights
Zone plates have been proposed as a cheap alternative to more expensive optical sights or targeting lasers.[5]
Lenses
Zone plates may be used as imaging lenses with a single focus as long as the type of grating used is sinusoidal in nature.
Reflection
A zone plate used as a reflector will allow radio waves to be focused as if by a parabolic reflector. This allows the reflector to be flat, and so easier to make. It also allows an appropriately patterned Fresnel reflector to be mounted flush to the side of a building, avoiding the wind loading that a parabaloid would be subject to.
Software testing
A bitmap representation of a zone plate image may be used for testing various image processing algorithms, such as:
Image interpolation and image resampling;[6]
Image filtering.[7]
An open-source zone-plate image generator is available.[8]
See also
Arago spot
Diffraction grating
Fresnel imager
Fresnel lens
Fresnel number
Fresnel zone antenna
Photon sieve
References
G. W. Webb, I. V. Minin and O. V. Minin, “Variable Reference Phase in Diffractive Antennas”, IEEE Antennas and Propagation Magazine, vol. 53, no. 2, April. 2011, pp. 77-94.
Wood, Robert Williams (1911), Physical Optics, New York: The MacMillan Company, pp. 37–39
"Zone Plates". X-Ray Data Booklet. Center for X-ray Optics and Advanced Light Source, Lawrence Berkeley National Laboratory. Retrieved 13 January 2015.
Joseph W. Goodman (2005). Introduction to Fourier Optics (3rd ed.). p. 125. ISBN 0-9747077-2-4.
New INL gunsight technology should improve accuracy for target shooters, hunters, soldiers, Mike Wall, Idaho National Laboratory, 5 May 2010.
https://web.archive.org/web/20060827184031/http://www.path.unimelb.edu.au/~dersch/interpolator/interpolator.html Testing Interpolator Quality
http://blogs.mathworks.com/steve/2011/07/22/filtering-fun/ Filtering Fun - Matlab Central
https://web.archive.org/web/20200516104605/http://www.realitypixels.com/turk/opensource/#ZonePlate Zone Plate generator, C code. Archived from the original on 16 May 2020.
vte
Photography
Terminology
35 mm equivalent focal length Angle of view Aperture Black and white Chromatic aberration Circle of confusion Color balance Color temperature Depth of field Depth of focus Exposure Exposure compensation Exposure value Zebra patterning F-number Film format
Large Medium Film speed Focal length Guide number Hyperfocal distance Metering mode Orb (optics) Perspective distortion Photograph Photographic printing Photographic processes Reciprocity Red-eye effect Science of photography Shutter speed Sync Zone System
Genres
Abstract Aerial Aircraft Architectural Astrophotography Banquet Conceptual Conservation Cloudscape Documentary Ethnographic Erotic Fashion Fine-art Fire Forensic Glamour High-speed Landscape Lomography Nature Neues Sehen Nude Photojournalism Pictorialism Pornography Portrait Post-mortem Selfie Social documentary Sports Still life Stock Straight photography Street Vernacular Underwater Wedding Wildlife
Techniques
Afocal Bokeh Brenizer Burst mode Contre-jour Cyanotype ETTR Fill flash Fireworks Harris shutter HDRI High-speed Holography Infrared Intentional camera movement Kirlian Kite aerial Long-exposure Macro Mordançage Multiple exposure Night Panning Panoramic Photogram Print toning Redscale Rephotography Rollout Scanography Schlieren photography Sabattier effect Slow motion Stereoscopy Stopping down Strip
Slit-scan Sun printing Tilt–shift
Miniature faking Time-lapse Ultraviolet Vignetting Xerography
Composition
Diagonal method Framing Headroom Lead room Rule of thirds Simplicity Golden triangle (composition)
Equipment
Camera
light-field field instant pinhole press rangefinder SLR still TLR toy view Darkroom
enlarger safelight Film
base format holder stock available films discontinued films Filter Flash
beauty dish cucoloris gobo hood hot shoe monolight Reflector snoot Softbox Lens
Wide-angle lens Zoom lens Telephoto lens Manufacturers Monopod Movie projector Slide projector Tripod
head Zone plate
History
Timeline of photography technology Analog photography Autochrome Lumière Box camera Calotype Camera obscura Daguerreotype Dufaycolor Heliography Painted photography backdrops Photography and the law Glass plate Visual arts
Digital
photography
Digital camera
D-SLR
comparison MILC camera back Digiscoping Digital versus film photography Film scanner Image sensor
CMOS APS CCD Three-CCD camera Foveon X3 sensor Image sharing Pixel
Color
photography
Color Print film
Chromogenic print Reversal film Color management
color space primary color CMYK color model RGB color model
Photographic
processing
Bleach bypass C-41 process Cross processing Developer Digital image processing Dye coupler E-6 process Fixer Gelatin silver process Gum printing Instant film K-14 process Print permanence Push processing Stop bath
Lists
Most expensive photographs Photographers
Norwegian Polish street women
Hellenica World - Scientific Library
Retrieved from "http://en.wikipedia.org/"
All text is available under the terms of the GNU Free Documentation License
