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, Y'v[2s
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, TdtV (
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? %opBJ
那些系数是通过对29525*10阶的矩阵每列的值算出来的嘛? }3pM,.
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function z = zernfun(n,m,r,theta,nflag) }z3j7I
%ZERNFUN Zernike functions of order N and frequency M on the unit circle. h^M_yz-f
% Z = ZERNFUN(N,M,R,THETA) returns the Zernike functions of order N !jCgTo
y
% and angular frequency M, evaluated at positions (R,THETA) on the x#rgFY,TY
% unit circle. N is a vector of positive integers (including 0), and O%bbyR2
% M is a vector with the same number of elements as N. Each element K/Q"Z*
% k of M must be a positive integer, with possible values M(k) = -N(k) (O.%Xbx3
% to +N(k) in steps of 2. R is a vector of numbers between 0 and 1, Cux(v8=n
% and THETA is a vector of angles. R and THETA must have the same P3M$&::D-
% length. The output Z is a matrix with one column for every (N,M) B9v>="F
% pair, and one row for every (R,THETA) pair. |3H+b,M5
% 1+l 8%G=hB
% Z = ZERNFUN(N,M,R,THETA,'norm') returns the normalized Zernike Dk1& <} I
% functions. The normalization factor sqrt((2-delta(m,0))*(n+1)/pi), )^2eC<t
% with delta(m,0) the Kronecker delta, is chosen so that the integral tFN >]`Z
% of (r * [Znm(r,theta)]^2) over the unit circle (from r=0 to r=1, n3^(y"q
% and theta=0 to theta=2*pi) is unity. For the non-normalized Z8$}Rpo
% polynomials, max(Znm(r=1,theta))=1 for all [n,m]. g=*jKSZ
% &q