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, 6 IvAs-%W
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, %n$f#Ml_r
这个,跟我们用zygo干涉仪直接拟合出的36项zernike系数,有何关系呢? uH\EV`@'
那些系数是通过对29525*10阶的矩阵每列的值算出来的嘛? [8'?G5/n
wR_mJMk_
;1&"]N%
V Rv4p5
JSUD$|RiJ
function z = zernfun(n,m,r,theta,nflag) i*$+>3Q-
%ZERNFUN Zernike functions of order N and frequency M on the unit circle. .>W [
% Z = ZERNFUN(N,M,R,THETA) returns the Zernike functions of order N !/G}vu
% and angular frequency M, evaluated at positions (R,THETA) on the $}vk+.!*1
% unit circle. N is a vector of positive integers (including 0), and i$kB6B#==
% M is a vector with the same number of elements as N. Each element oG)T>L[&
% k of M must be a positive integer, with possible values M(k) = -N(k) q
4Pv\YO
% to +N(k) in steps of 2. R is a vector of numbers between 0 and 1, "rMfe>;FJ
% and THETA is a vector of angles. R and THETA must have the same `,4yGgD!4
% length. The output Z is a matrix with one column for every (N,M) x<I[?GT=
% pair, and one row for every (R,THETA) pair. JWHsTnB
% +pYgh8w@
% Z = ZERNFUN(N,M,R,THETA,'norm') returns the normalized Zernike {XU!p: x
% functions. The normalization factor sqrt((2-delta(m,0))*(n+1)/pi), syu/"KY^!
% with delta(m,0) the Kronecker delta, is chosen so that the integral M"*NV(".g
% of (r * [Znm(r,theta)]^2) over the unit circle (from r=0 to r=1, w6Gez~8
% and theta=0 to theta=2*pi) is unity. For the non-normalized 4D&