非常感谢啊,我手上也有zernike多项式的拟合的源程序,也不知道对不对,不怎么会有 5DJ!:QY!
function z = zernfun(n,m,r,theta,nflag) |3BxNFe`%
%ZERNFUN Zernike functions of order N and frequency M on the unit circle. N!./u(b
% Z = ZERNFUN(N,M,R,THETA) returns the Zernike functions of order N QBd4ok:R
% and angular frequency M, evaluated at positions (R,THETA) on the y1B'_s
% unit circle. N is a vector of positive integers (including 0), and UAGh2?q2
% M is a vector with the same number of elements as N. Each element jS)YYk5
% k of M must be a positive integer, with possible values M(k) = -N(k) ]IH1_?HgP7
% to +N(k) in steps of 2. R is a vector of numbers between 0 and 1, C(vQR~_
% and THETA is a vector of angles. R and THETA must have the same fo~>y
% length. The output Z is a matrix with one column for every (N,M) <8^ws90Y
% pair, and one row for every (R,THETA) pair. DDj:(I?,w
% v >s,*
% Z = ZERNFUN(N,M,R,THETA,'norm') returns the normalized Zernike
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% functions. The normalization factor sqrt((2-delta(m,0))*(n+1)/pi), OVGB7CB]S
% with delta(m,0) the Kronecker delta, is chosen so that the integral wQ8<%qi"L
% of (r * [Znm(r,theta)]^2) over the unit circle (from r=0 to r=1, ji<(}d~L*
% and theta=0 to theta=2*pi) is unity. For the non-normalized <j1r6.E)
% polynomials, max(Znm(r=1,theta))=1 for all [n,m]. i,rX.K}X
% e.W <pI,
% The Zernike functions are an orthogonal basis on the unit circle. 'n}]
% They are used in disciplines such as astronomy, optics, and Y]!&, e,
% optometry to describe functions on a circular domain. KE-0/m4yJ
% gHFQs](G.
% The following table lists the first 15 Zernike functions. ^91Ae!)d
% :i|Bz6Ht4
% n m Zernike function Normalization n<1*cL:8B
% -------------------------------------------------- u/V&1In
% 0 0 1 1 q2/kegAT
% 1 1 r * cos(theta) 2 IY|`$sHb
% 1 -1 r * sin(theta) 2 hV&