# Zernike "modes"

## Italian translation: modi dei polinomi di Zernike

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 15:59 Nov 22, 2008
English to Italian translations [PRO]
Medical - Medical (general) / Optometry
 English term or phrase: Zernike "modes" We are talking about Zernike polynomials in Optometry. The term "modes" appears frequently: -Individual modes of Zernike polynomials..; -The coefficient C (...) varies according to the number of modes in the Zernike polynomials. At the beginning of the text we have: -The individual modes, or terms, in the polynomial.. I found "termini di Zernike" and "metodo Zernike" but not "modi".
 Local time: 07:43
 Italian translation:modi dei polinomi di Zernike Explanation:io interpreto il passaggio per spiegare le "forme" o "modi" dei polinomi di Zernike, che in optometria servono a rappresentare le aberrazioni ottiche. Forse può essere utile quanto spiegato nell'articolo: http://www.optikon.com/it/articles/keratron_023/media/TheAbe...
Selected response from:

Carla Sordina
Italy
Local time: 07:43
 Grazie, ho riscontrato lo stesso utilizzo di "modi Zernike" anche in altri documeti.4 KudoZ points were awarded for this answer

4 +3mode/funzioni base
 texjax DDS PhD
3 +1modi dei polinomi di Zernike
 Carla Sordina
3modalità di Zernike
 xxxluciby

31 mins   confidence:
zernike \"modes\"
modalità di Zernike

Explanation:

www.fe.infn.it/venerdi/VENERDIHOME_file/pdf08/ricci/ricci.p...

 xxxlucibyCanadaLocal time: 23:43Specializes in fieldNative speaker of: ItalianPRO pts in category: 12

46 mins   confidence: peer agreement (net): +3
zernike "modes"
mode/funzioni base

Explanation:
http://research.opt.indiana.edu/Library/WavefrontReporting/W...

mode è un termine statistico = moda al singolare, mode al plurale, che corrisponde al numero di osservazioni che compare con maggior frequenza.
Lo vedi nel grafico.

The Zernike basis functions, or "modes" as they are often called, are systematically arranged into a periodic table with the shape of a pyramid as shown in Fig. 3. Each row in the pyramid corresponds to a given order of the polynomial component of the function and each column corresponds to a different meridional frequency. By convention, harmonics in cosine phase are assigned positive frequencies and harmonics in sine phase are assigned negative frequencies. Although the each mode can be assigned a single reference number, a more natural numbering system is a double-script notation which designates each basis function according to its order and frequency. The radial order is used as a subscript and the meridional frequency is used as a superscript to unambiguously and conveniently identify each mode.

Given this catalog of fundamental building blocks, we may now describe the aberration structure of an eye mathematically as the weighted sum of Zernike basis functions. [...]

This development leads to our final topic, which is to explore various ways of displaying the spectrum of aberration coefficients associated with a Zernike expansion. To visualize the 2-dimensional Zernike spectrum as a pyramid, we can assemble a collection of sub-regions in our graph that correspond to the pyramid of Zernike basis functions. Within each sub-region we can show information about the corresponding Zernike mode. For example, we can display the value of the Zernike coefficients of a single eye, or the mean of a population of eyes, using a pyramid of rectangular blocks. As shown in Fig. 4A, the intensity of each block indicates the value of the coefficient for the corresponding mode. White signifies a large positive value, black signifies a large negative value, and grey signifies zero. The advantage of this visualization scheme is that it permits an immediate visual assessment of the relative magnitude of the various modes that make up the aberration structure of an eye.

 texjax DDS PhDLocal time: 02:43Specializes in fieldNative speaker of: ItalianPRO pts in category: 891

agree
 17 mins
-> Grazie, e buon WE

agree
 22 hrs
-> grazie

agree
 1 day 15 mins
-> grazie

50 mins   confidence: peer agreement (net): +1
zernike "modes"
modi dei polinomi di Zernike

Explanation:
io interpreto il passaggio per spiegare le "forme" o "modi" dei polinomi di Zernike, che in optometria servono a rappresentare le aberrazioni ottiche.
Forse può essere utile quanto spiegato nell'articolo:
http://www.optikon.com/it/articles/keratron_023/media/TheAbe...

 Carla SordinaItalyLocal time: 07:43Native speaker of: ItalianPRO pts in category: 8
 Grazie, ho riscontrato lo stesso utilizzo di "modi Zernike" anche in altri documeti.

agree  Roland_Lelaj: D'accordo. Qui un riferimento sui modi: http://www.arcetri.astro.it/~riccardi/tesi/node54.html
 6 hrs
-> Grazie Roland

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