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 00'R1q4
function z = zernfun(n,m,r,theta,nflag) 2G8f4vsC[
%ZERNFUN Zernike functions of order N and frequency M on the unit circle. c+/SvRx^>
% Z = ZERNFUN(N,M,R,THETA) returns the Zernike functions of order N Ij
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% and angular frequency M, evaluated at positions (R,THETA) on the ![Z'jCpy
% unit circle. N is a vector of positive integers (including 0), and oc,a
% M is a vector with the same number of elements as N. Each element 6elmLDMni\
% k of M must be a positive integer, with possible values M(k) = -N(k) Exox&T
% to +N(k) in steps of 2. R is a vector of numbers between 0 and 1, 4r!8_$fN?G
% and THETA is a vector of angles. R and THETA must have the same dm1WC:b
% length. The output Z is a matrix with one column for every (N,M)
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% pair, and one row for every (R,THETA) pair. ajuwP1I
% <">tB"="b
% Z = ZERNFUN(N,M,R,THETA,'norm') returns the normalized Zernike mT;1KE{J{
% functions. The normalization factor sqrt((2-delta(m,0))*(n+1)/pi), :tY;K2wDM
% with delta(m,0) the Kronecker delta, is chosen so that the integral [ZS}P
% of (r * [Znm(r,theta)]^2) over the unit circle (from r=0 to r=1, <U=:N~L
% and theta=0 to theta=2*pi) is unity. For the non-normalized F{\MIuoy
% polynomials, max(Znm(r=1,theta))=1 for all [n,m]. -E#!`~&V
% f5+a6s9
% The Zernike functions are an orthogonal basis on the unit circle. ba^cw}5
% They are used in disciplines such as astronomy, optics, and 3k;*xjv6@
% optometry to describe functions on a circular domain. <4,>`#NEo
% yw`xK2(C$
% The following table lists the first 15 Zernike functions. lL~T@+J~
% w?A&X