Editing Zone plate

{{Short description|Device used to focus light using diffraction}}
[[Image:Zone plate.svg|right|thumb|210px|Binary zone plate: The areas of each ring, both light and dark, are equal.]]
[[Image:Zonenplatte Cosinus.png|right|thumb|210px|Sinusoidal zone plate: This type has a single focal point.]]

A '''zone plate''' is a device used to [[Focus (optics)|focus]] light or other things exhibiting wave character.<ref name="wmm">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.</ref>  Unlike [[lens (optics)|lenses]] or [[curved mirror]]s, zone plates use [[diffraction]] instead of [[refraction]] or [[Specular reflection|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.<ref>{{ Citation | last = Wood | first = Robert Williams | author-link = Robert Williams Wood | date = 1911 | title = Physical Optics | publisher = The MacMillan Company | place = New York | pages = 37–39 | url = https://books.google.com/books?id=xxtLAAAAYAAJ&q=wood+physical+optics+%22zone+plate%22&pg=PA39 }}</ref>

A zone plate consists of a set of concentric rings, known as [[Fresnel zone]]s, which alternate between being [[opacity (optics)|opaque]] and [[transparency (optics)|transparent]]. Light hitting the zone plate will diffract around the opaque zones. The zones can be spaced so that the diffracted light constructively [[interference (wave propagation)|interferes]] at the desired focus, creating an [[Real image|image]] there.

==Design and manufacture==
To get constructive interference at the focus, the zones should switch from opaque to transparent at radii where<ref>{{cite book|chapter-url=http://xdb.lbl.gov/Section4/Sec_4-4.html|publisher=Center for X-ray Optics and Advanced Light Source, Lawrence Berkeley National Laboratory|access-date=13 January 2015|title=X-Ray Data Booklet|chapter=Zone Plates}}</ref>
 
<math display="block">r_n = \sqrt{n\lambda f + \frac{1}{4}n^2 \lambda^2}</math>

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
<math display="block">r_n \simeq \sqrt{n\lambda f}</math>

For plates with many zones, you can calculate the distance to the focus if you only know the radius of the outermost zone, ''r''<sub>''N''</sub>, and its width, Δ''r''<sub>''N''</sub>:
<math display="block">f = \frac{2r_N \Delta r_N}{\lambda}</math>

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 [[angular resolution|resolution]] of a zone plate depends on the smallest zone width, 
<math display="block">\frac{\Delta l}{\Delta r_N} \approx 1.22</math>

Because of this, the smallest size object you can image, Δ''l'', is limited by how small you can reliably make your zones.

Zone plates are frequently manufactured using [[photolithography|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/m{{sup|2}}).

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 [[holography|transmission hologram]] of a converging lens.

For a smooth zone plate, the opacity (or transparency) at a point can be given by:
<math display="block">\frac{1 \pm \cos\left(kr^2\right)}{2}\,</math>

where <math>r</math> is the distance from the plate center, and <math>k</math> determines the plate's scale.<ref>{{cite book|pages=125|author=Joseph W. Goodman|title=Introduction to Fourier Optics|edition=3rd|year=2005|publisher=Roberts and Company Publishers |isbn=0-9747077-2-4}}</ref>

Binary zone plates use almost the same formula, however they depend only on the sign:
<math display="block">\frac{1 \pm \sgn\left(\cos\left(kr^2\right)\right)}{2}\,</math>

===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
<math display="block">r_n = \sqrt{(n + \alpha)\lambda f + \frac{1}{4}(n + \alpha)^2 \lambda^2}</math>

This reference phase can be chosen to optimize secondary properties such as side lobes.<ref name="wmm" />

==Applications==

===Physics===
There are many [[wavelength]]s of light outside of the visible area of the [[electromagnetic spectrum]] where traditional [[Lens (optics)|lens]] materials like glass are not [[transparency (optics)|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 differing from 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.<ref name="wmm" />

===Photography===
[[File:Christmas with zone plate.jpg|thumb|Example of an image taken with zone plate optics.]]
Zone plates are also used in [[photography]] in place of a [[photographic lens|lens]] or [[pinhole camera|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 (photography)|exposure time]] can be decreased. Common [[f-number]]s 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.<ref>[http://www.physorg.com/news192299313.html New INL gunsight technology should improve accuracy for target shooters, hunters, soldiers], Mike Wall, Idaho National Laboratory, 5 May 2010.</ref><!-- alternative story link https://inlportal.inl.gov/portal/server.pt?open=514&objID=1269&mode=2&featurestory=DA_549448 -->

===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. A specifically designed Fresnel zone plate with blazed phase structures is sometimes called a [[kinoform]].<ref name="s853">{{cite journal | last1=Jordan | first1=J. A. | last2=Hirsch | first2=P. M. | last3=Lesem | first3=L. B. | last4=Van Rooy | first4=D. L. | title=Kinoform Lenses | journal=Applied Optics | publisher=Optica Publishing Group | volume=9 | issue=8 | date=1970-08-01 | pages=1883–1887 | issn=0003-6935 | doi=10.1364/ao.9.001883 | pmid=20094157 | bibcode=1970ApOpt...9.1883J }}</ref>

===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 paraboloid 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;<ref>https://web.archive.org/web/20060827184031/http://www.path.unimelb.edu.au/~dersch/interpolator/interpolator.html Testing Interpolator Quality</ref>
* Image filtering.<ref>http://blogs.mathworks.com/steve/2011/07/22/filtering-fun/ Filtering Fun - Matlab Central</ref>
An open-source zone-plate image generator is available.<ref name="Turkowski, Ken: Zone Plate Test Pattern">https://web.archive.org/web/20200516104605/http://www.realitypixels.com/turk/opensource/#ZonePlate Zone Plate generator, C code. Archived from the [http://www.realitypixels.com/turk/opensource/index.html#ZonePlate original] on 16 May 2020.</ref>

==See also==
*[[Arago spot]]
*[[Diffraction grating]]
*[[Fresnel imager]]
*[[Fresnel lens]]
*[[Fresnel number]]
*[[Fresnel zone antenna]]
*[[Microform]]
*[[Photon sieve]]

==References==
<references/>

==External links==
*[http://www.cxro.lbl.gov/BL612/index.php?content=magneticimaging.html Magnetic Soft X-ray microscopy]
*[http://glsmyth.com/pinhole/zone-plate-patton.asp  Making a photographic zone plate]
*[http://www.whizkidtech.redprince.net/zoneplate/ Whiz Kid Technomagic Zone Plate Designer]
*[https://www.flickr.com/groups/zoneplates/pool/ Examples of zone plate photographs]
*{{cite news|url=https://www.newscientist.com/article/dn13820-telescope-could-focus-light-without-a-mirror-or-lens.html|title=Telescope could focus light without a mirror or lens|work=New Scientist|date=1 May 2008}}
*{{cite web|title=X-ray zone plates|url=http://x-ray-optics.de/index.php/en/types-of-optics/diffracting-optics/fresnel-zone-plates|access-date=2019-11-21|last=Arndt Last}}

{{Photography}}

[[Category:Optical components]]
[[Category:Photography equipment]]