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, Ec]|p6a3
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, UQT'6* !
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? 7m1KR#j
那些系数是通过对29525*10阶的矩阵每列的值算出来的嘛? |L:Cn J
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function z = zernfun(n,m,r,theta,nflag) cHD%{xlb
%ZERNFUN Zernike functions of order N and frequency M on the unit circle. u oVNK
% Z = ZERNFUN(N,M,R,THETA) returns the Zernike functions of order N H+ZSPHs
% and angular frequency M, evaluated at positions (R,THETA) on the |M5-5)
% unit circle. N is a vector of positive integers (including 0), and UAYd?r
% M is a vector with the same number of elements as N. Each element y,m2(V
% k of M must be a positive integer, with possible values M(k) = -N(k) 9dKul,c
% to +N(k) in steps of 2. R is a vector of numbers between 0 and 1, !3}deY8;#
% and THETA is a vector of angles. R and THETA must have the same j9y3hQ+q
% length. The output Z is a matrix with one column for every (N,M) \4bWWy
% pair, and one row for every (R,THETA) pair. :tGYs8UK
% 0 bSA_
% Z = ZERNFUN(N,M,R,THETA,'norm') returns the normalized Zernike >+9JD%]x]
% functions. The normalization factor sqrt((2-delta(m,0))*(n+1)/pi), &%F@O<:
% with delta(m,0) the Kronecker delta, is chosen so that the integral 8cVzFFQP
% of (r * [Znm(r,theta)]^2) over the unit circle (from r=0 to r=1, U/w. M_S
% and theta=0 to theta=2*pi) is unity. For the non-normalized ]=&L