下面这个函数大家都不会陌生,计算zernike函数值的,并根据此可以还原出图像来, t_^X$pL
我输入10阶的n、m,r,theta为38025*1向量,最后得到的z是29525*10阶的矩阵, nfSbM3D]h
这个,跟我们用zygo干涉仪直接拟合出的36项zernike系数,有何关系呢? ^zzP.
那些系数是通过对29525*10阶的矩阵每列的值算出来的嘛? %
2$/JZ
"5R~(+~<@
?'86d_8
K_)eWf0a
Q/uwQo/
function z = zernfun(n,m,r,theta,nflag) e}/Lk5q!
%ZERNFUN Zernike functions of order N and frequency M on the unit circle. J]lrS
% Z = ZERNFUN(N,M,R,THETA) returns the Zernike functions of order N jp8@vdRg
% and angular frequency M, evaluated at positions (R,THETA) on the RqEH|EUZ
% unit circle. N is a vector of positive integers (including 0), and gI^oU4mq
% M is a vector with the same number of elements as N. Each element X+L) -d
% k of M must be a positive integer, with possible values M(k) = -N(k) DI+]D~N
% to +N(k) in steps of 2. R is a vector of numbers between 0 and 1, 3$.deYa$R
% and THETA is a vector of angles. R and THETA must have the same ^k5ll=}
% length. The output Z is a matrix with one column for every (N,M) |F,R&<2
% pair, and one row for every (R,THETA) pair. "k*PA\U
% 3.22"U\1:
% Z = ZERNFUN(N,M,R,THETA,'norm') returns the normalized Zernike ;c~cet4
% functions. The normalization factor sqrt((2-delta(m,0))*(n+1)/pi), uH/w\v_I
% with delta(m,0) the Kronecker delta, is chosen so that the integral @1.QEyXG
% of (r * [Znm(r,theta)]^2) over the unit circle (from r=0 to r=1, B~o\+n
% and theta=0 to theta=2*pi) is unity. For the non-normalized j
8*ZF
% polynomials, max(Znm(r=1,theta))=1 for all [n,m]. - p3Re9
% *.L81er5~
% The Zernike functions are an orthogonal basis on the unit circle. kB?al#`
% They are used in disciplines such as astronomy, optics, and w0w G-R ?
% optometry to describe functions on a circular domain. Y<1QY?1sd
% i1H\#;`$
% The following table lists the first 15 Zernike functions. Eskb9^A
% M@ed>.
% n m Zernike function Normalization G!K]W:m
% -------------------------------------------------- IDnC<