# Talk:Zone plate

WikiProject Physics (Rated Start-class, Mid-importance)
This article is within the scope of WikiProject Physics, a collaborative effort to improve the coverage of Physics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Start  This article has been rated as Start-Class on the project's quality scale.
Mid  This article has been rated as Mid-importance on the project's importance scale.
WikiProject Technology (Rated C-class)
This article is within the scope of WikiProject Technology, a collaborative effort to improve the coverage of technology on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
C  This article has been rated as C-Class on the project's quality scale.

## Not Invented by Fresnel

The zone plate seems to have been invented by Lord Rayleigh, as evidenced by his notebook entry on 4/11/1871: "The experiment of blocking out the odd Huygens zones so as to increase the light at centre succeeded very well." —Preceding unsigned comment added by 128.112.50.118 (talk) 20:15, 14 April 2008 (UTC)

What does a spiral diffraction grating form? lysdexia 16:33, 22 Oct 2004 (UTC)

I don't think that a spiral diffraction grating forms any sort of coherent image, because it would pass through light at all radii somewhere, rather than like a fresnel lens, only passing through light at radii that will constructively interfere to produce focused images. Laura Scudder 01:22, 6 Nov 2004 (UTC)

## should move this to "zone plate lens"

Zone plates are useful for more than just lenses. They are good for testing video systems, printing processes, image scaling algorithms, alpha blending, gamma correction errors... AlbertCahalan 01:20, 16 Jun 2005 (UTC)

Then you should add descriptions of these uses here. The general rule of thumb is to write on one topic until the article becomes long enough to spin subtopics out as their own articles rather than vice versa. In other words, this article should strive to collect all uses of zone plates until enough material is here for spin-offs, at which point the appropriate spin-off topics should be apparent by the article's organization. So far I only wrote about uses I know of personally, and no one has added to that section since then. --Laura Scudder | Talk 07:29, 16 Jun 2005 (UTC)

Problems with zone plates are:

• INSANE chromatic aberration (linear z-dispersion with wavelength)
• Multiple orders of diffraction (the spot that has the 1st order in focus also shows the higher orders unfocused)
• VERY low efficiency (about 1/100 of the photons actually get where they are supposed to)

Using the formulae given produce different results for zone radii. If you use the chirp formula to generate a zoneplate scaled to the the size of the last ring as computed by using the fl * lamda * ringnumber formula then the inner rings seem to be off. For instance, generating a binary zoneplate using the chirp function means, I think, that the zero crossings are the zone boundaries. These boundaries don't match as stated above. Mrpinhole (talk) 19:38, 18 December 2008 (UTC)MrPinhole 18 dec 08

## Given formula for radii only approximate

The Formula given for the radius is only valid as an approximation when the radius of the zone plate is much less than the focal distance, otherwise higher order terms come into play. The exact formula can be found by application of Pythagoras: The distance from a point at radius r on the zone plate to the focus, a perpenidcular distance f from the the zone plate, is ${\displaystyle {\sqrt {r^{2}+f^{2}}}}$. Thus the optical path difference (OPD) as r varies is ${\displaystyle {\sqrt {r^{2}+f^{2}}}-f}$. The radius of the nth half-period zone, rn occurs when the OPD is n half-wavelengths: ${\displaystyle {\sqrt {r_{n}^{2}+f^{2}}}-f=n\lambda /2}$. Expanding this square root with the binomial expansion and taking only the first two terms yields the approximate formula ${\displaystyle r_{n}={\sqrt {n\lambda f}}}$, but rearranging without making any approximations gives the correct formula ${\displaystyle r_{n}={\sqrt {n\lambda f+{\frac {n^{2}\lambda ^{2}}{4}}}}}$.131.111.213.211 14:38, 16 January 2006 (UTC)

## "Video" section

Regarding the discussion in relation to video resolution: Is this really a zone plate? Isn't it just a high-frequency test sample? That is, doesn't it have nothing to do with diffraction? 155.212.242.34 17:52, 29 October 2007 (UTC)

It's both, of course. Yes, it's a test target and not a piece of optics, but it's still the "zone plate" pattern. See [1] (under THE SINUSOIDAL ZONE PLATE) for a reference (and, given that it links here, probably the inspiration for adding the section in the first place). Andrew Rodland 04:50, 4 December 2007 (UTC)

## Relation between free parameters

The article uses the focal length f as the free parameter in the early part but then switches to another parameter k which is not defined. Comparing the r_n for n=1 with the zero of the cosine (pi/2) gives me k=2*pi/(4*lambda*f+lambda^2), but I'm not sure if that interpretation is correct. --Ralf Muschall (talk) 19:01, 20 February 2012 (UTC)

## Free plate pictures (CC0)

Just in case, this page has two free as in Creative Commons Zero/Public Domain zone plates: http://www.thetenthplanet.de/archives/3859 — Preceding unsigned comment added by 37.209.110.47 (talk) 16:46, 23 April 2014 (UTC)

## Relation to a Fresnel lens

I removed the following material, because the claimed connection between the Fresnel zone plate and the Fresnel lens is not supported by a citation. It's not clear to me that the claimed connection is true. --Srleffler (talk) 05:02, 28 May 2014 (UTC)

Wave propagation can be calculated by summing over all possible ray paths. For short wavelengths, it is usually only where many paths sum coherently, meaning that they have close to the same phase (are on the same half of the complex plane), that propagation is significant, because contributions with different phases cancel each other. (For electromagnetic radiation, for example, opposite fields cancel.)

A zone plate works by blocking the paths with contributions of the opposite phase. If a phase shifter such as a refractive material is available, one can increase the collected light (or other wave) by replacing the absorbing rings with half wavelength phase delays.<ref name="wmm" /> Side lobes can be reduced by sloping these dielectric rings thicker on the inner side than on the outer. With optimal slope of the dielectric or other phase shifter, (in the thin lens approximation) the contributions from all parts of the lens can be the same, making it an ideal lens for one wavelength. The jump between zones can be any integer number of wavelengths. If there is a range in wavelengths (the source is not monochromatic), then the zones are not coherent with each other, but still coherent within each zone. The diffraction limit of the resolution is then determined by the width of each zone, and the zones add incoherently (with random phase). This is called a Fresnel lens.[citation needed] If there is only one such zone, it is a conventional lens.