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 AL5Vu$V~n}
function z = zernfun(n,m,r,theta,nflag) 7w1wr)qSB
%ZERNFUN Zernike functions of order N and frequency M on the unit circle. i{I~mrm/'\
% Z = ZERNFUN(N,M,R,THETA) returns the Zernike functions of order N 98.>e
% and angular frequency M, evaluated at positions (R,THETA) on the gqWupL
% unit circle. N is a vector of positive integers (including 0), and /W<>G7%.
% M is a vector with the same number of elements as N. Each element 0D8K=h&e
% k of M must be a positive integer, with possible values M(k) = -N(k) Y-0?a?q2Fr
% to +N(k) in steps of 2. R is a vector of numbers between 0 and 1, "U\JV)N
% and THETA is a vector of angles. R and THETA must have the same ,<:!NF9
% length. The output Z is a matrix with one column for every (N,M) #Eb5: ;
% pair, and one row for every (R,THETA) pair. D13Rx 6b
% ^V%rag
% Z = ZERNFUN(N,M,R,THETA,'norm') returns the normalized Zernike xTGxvGv8
% functions. The normalization factor sqrt((2-delta(m,0))*(n+1)/pi), @JW@-9/
% with delta(m,0) the Kronecker delta, is chosen so that the integral *Y@nVi
% of (r * [Znm(r,theta)]^2) over the unit circle (from r=0 to r=1, o!~Jzd.=h
% and theta=0 to theta=2*pi) is unity. For the non-normalized ltFq/M
% polynomials, max(Znm(r=1,theta))=1 for all [n,m]. +t2SzQ j>
% 0 u?{\
% The Zernike functions are an orthogonal basis on the unit circle. F_bF
% They are used in disciplines such as astronomy, optics, and HV/c c"
% optometry to describe functions on a circular domain. 7r{83_B
%
+D1 d=4
% The following table lists the first 15 Zernike functions. srV.)Ur
% 2!Bd2
% n m Zernike function Normalization -rKO
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% -------------------------------------------------- )z8!f}:De=
% 0 0 1 1 "k Te2iS
% 1 1 r * cos(theta) 2 FW"^99mrnb
% 1 -1 r * sin(theta) 2 $#|gLVOQ
% 2 -2 r^2 * cos(2*theta) sqrt(6)
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