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 %b!-~
Y.
function z = zernfun(n,m,r,theta,nflag) udqS'g&
%ZERNFUN Zernike functions of order N and frequency M on the unit circle. @9G- m(?*
% Z = ZERNFUN(N,M,R,THETA) returns the Zernike functions of order N e;95a
% and angular frequency M, evaluated at positions (R,THETA) on the Xa9TS"
% unit circle. N is a vector of positive integers (including 0), and omX?Bl
% M is a vector with the same number of elements as N. Each element 2&(sa0*y
% k of M must be a positive integer, with possible values M(k) = -N(k) p9ZXbAJ{
% to +N(k) in steps of 2. R is a vector of numbers between 0 and 1, o>D
% and THETA is a vector of angles. R and THETA must have the same %:C ]7gQ
% 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. RMYP"
% C*70;:b
% Z = ZERNFUN(N,M,R,THETA,'norm') returns the normalized Zernike `iShJz96
% functions. The normalization factor sqrt((2-delta(m,0))*(n+1)/pi), YE+$H%Jl!
% with delta(m,0) the Kronecker delta, is chosen so that the integral ]> !<G8=N
% of (r * [Znm(r,theta)]^2) over the unit circle (from r=0 to r=1, Owv+1+B
% and theta=0 to theta=2*pi) is unity. For the non-normalized '_0]vupvY
% polynomials, max(Znm(r=1,theta))=1 for all [n,m]. wo^Sy41bF
% 3TuC+'`G
% The Zernike functions are an orthogonal basis on the unit circle. c9Es%@]
% They are used in disciplines such as astronomy, optics, and SS.jL)
% optometry to describe functions on a circular domain. rnm03 '{
% MQ/
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% The following table lists the first 15 Zernike functions. Q[ieaL6&
% v Y|!
% n m Zernike function Normalization &~DTZgY
% -------------------------------------------------- n]!fO
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% 0 0 1 1 Ju` [m
% 1 1 r * cos(theta) 2 &