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 L
dyTB@
function z = zernfun(n,m,r,theta,nflag) 1s@%q
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%ZERNFUN Zernike functions of order N and frequency M on the unit circle. alB[/.1
% Z = ZERNFUN(N,M,R,THETA) returns the Zernike functions of order N AO"pm
% and angular frequency M, evaluated at positions (R,THETA) on the $Z8=QlG>
% unit circle. N is a vector of positive integers (including 0), and *'q6#\#.
% M is a vector with the same number of elements as N. Each element h;(#^+LH
% k of M must be a positive integer, with possible values M(k) = -N(k) D3BNA]P\2@
% to +N(k) in steps of 2. R is a vector of numbers between 0 and 1, 6IyD7PQ
% and THETA is a vector of angles. R and THETA must have the same zld[uhc>
% length. The output Z is a matrix with one column for every (N,M) l0%qj(4`6&
% pair, and one row for every (R,THETA) pair. i& ,Wg8#R
% !gm;g}]szG
% Z = ZERNFUN(N,M,R,THETA,'norm') returns the normalized Zernike &&\HE7*
% functions. The normalization factor sqrt((2-delta(m,0))*(n+1)/pi), !qjIhZi
% with delta(m,0) the Kronecker delta, is chosen so that the integral j(*ZPo>oD
% of (r * [Znm(r,theta)]^2) over the unit circle (from r=0 to r=1, 1aQR9zg%
% and theta=0 to theta=2*pi) is unity. For the non-normalized .7"]/9oB
% polynomials, max(Znm(r=1,theta))=1 for all [n,m]. SK@%r
% $B3<"
% The Zernike functions are an orthogonal basis on the unit circle. X$<s@_#1
% They are used in disciplines such as astronomy, optics, and 4Sq[I
% optometry to describe functions on a circular domain. A_mVe\(*M
% j~ )GZV
% The following table lists the first 15 Zernike functions. \ $PB~-Z
% Qq. ht
% n m Zernike function Normalization NLz[F`I
% -------------------------------------------------- 9
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% 0 0 1 1 #_b
U/rk)*
% 1 1 r * cos(theta) 2 4%(\y"T
% 1 -1 r * sin(theta) 2 [1\k'5rp
% 2 -2 r^2 * cos(2*theta) sqrt(6) 0L5n<<