# Zernike多项式

ZERNFUN.m 和 ZERNFUN2.m计算了Zernike函数。

Zernike多项式，由无穷数量的多项式完全集组成的，它有两个变量，ρ和θ，它在单位圆内部是连续正交的。需要注意的是，泽尼克多项式仅在单位圆的内部连续区域是正交的，通常在单位圆内部的离散的坐标上是不具备正交性质的。

## Zernike polynomials

ZERNFUN.m and ZERNFUN2.m compute the Zernike functions Znm(r,theta). These functions, which form an orthogonal basis on the unit circle, are used in disciplines such as astronomy, optics, optometry, and ophthalmology to characterize functions and data on a circular domain. ZERNPOL.m computes the Zernike polynomials Znm(r), which are the radial portion of the Zernike functions.

A MATLAB Digest article describing the use of the Zernike functions for analyzing optics data (using a LASIK surgery data as an example) also is available, on the File Exchange as a PDF,

http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=19133&objectType=file

and in HTML at:

http://www.mathworks.com/company/newsletters/digest/2008/jan/zernike.html

zernike.zip (6.61KB)

zernfun.m  zernfun2.m  zernpol.m

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