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 "|H0 X#
function z = zernfun(n,m,r,theta,nflag) NUseYU``
%ZERNFUN Zernike functions of order N and frequency M on the unit circle. `CB TZG09
% Z = ZERNFUN(N,M,R,THETA) returns the Zernike functions of order N =6hf'lP
% and angular frequency M, evaluated at positions (R,THETA) on the GbhaibkO
% unit circle. N is a vector of positive integers (including 0), and 78kk"9h'
% M is a vector with the same number of elements as N. Each element aE}u5L$#
% k of M must be a positive integer, with possible values M(k) = -N(k) i@6 kIC
% to +N(k) in steps of 2. R is a vector of numbers between 0 and 1, E6uIp^E
% and THETA is a vector of angles. R and THETA must have the same Zv_<*uzKZ
% length. The output Z is a matrix with one column for every (N,M) f#?R!pR
% pair, and one row for every (R,THETA) pair. DuaOi1Gw
% +Aq}BjD#
% Z = ZERNFUN(N,M,R,THETA,'norm') returns the normalized Zernike ;NEHbLH#F
% functions. The normalization factor sqrt((2-delta(m,0))*(n+1)/pi), kK(,FB
% with delta(m,0) the Kronecker delta, is chosen so that the integral ?:,j9:m?
% of (r * [Znm(r,theta)]^2) over the unit circle (from r=0 to r=1, mi+I)b=
% and theta=0 to theta=2*pi) is unity. For the non-normalized fjf\/%
% polynomials, max(Znm(r=1,theta))=1 for all [n,m]. xE:p)B-]
% {chl+au*l
% The Zernike functions are an orthogonal basis on the unit circle. &e{&<ZVR
% They are used in disciplines such as astronomy, optics, and H~&'`h1
% optometry to describe functions on a circular domain. .nnAI@7E
% >A6lX)
% The following table lists the first 15 Zernike functions. =619+[fK
% Sn0 Gw
% n m Zernike function Normalization X#fI$9a
% -------------------------------------------------- dCBJV
% 0 0 1 1 S&y