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<gYf -E+
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, +~v3D^L15
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? 4s+J-l
那些系数是通过对29525*10阶的矩阵每列的值算出来的嘛? 5eZg+ O
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function z = zernfun(n,m,r,theta,nflag) )LS+M_
%ZERNFUN Zernike functions of order N and frequency M on the unit circle. :."n@sA@
% Z = ZERNFUN(N,M,R,THETA) returns the Zernike functions of order N 5a/
A_..+I
% and angular frequency M, evaluated at positions (R,THETA) on the uq1(yyWp(
% unit circle. N is a vector of positive integers (including 0), and ]oZ,{Q5~
% M is a vector with the same number of elements as N. Each element 8~L.6c5U
% k of M must be a positive integer, with possible values M(k) = -N(k) g he=mQ-
% to +N(k) in steps of 2. R is a vector of numbers between 0 and 1, +^% &8<
% and THETA is a vector of angles. R and THETA must have the same gT\y&
% length. The output Z is a matrix with one column for every (N,M) E9+O\"e9
% pair, and one row for every (R,THETA) pair. T>:g
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% y0y;1N'KK
% Z = ZERNFUN(N,M,R,THETA,'norm') returns the normalized Zernike 0 6v5/Xf
% functions. The normalization factor sqrt((2-delta(m,0))*(n+1)/pi), yl;$#aZB
% with delta(m,0) the Kronecker delta, is chosen so that the integral )T~ +>+t
% of (r * [Znm(r,theta)]^2) over the unit circle (from r=0 to r=1, MxvxY,~{0
% and theta=0 to theta=2*pi) is unity. For the non-normalized !6i
% polynomials, max(Znm(r=1,theta))=1 for all [n,m]. '~x_
% TKs@?Q,J
% The Zernike functions are an orthogonal basis on the unit circle. ^eT>R,aB
% They are used in disciplines such as astronomy, optics, and m_O=X8uj"D
% optometry to describe functions on a circular domain. 1*`JcUn,>
% ,IX4Zo"a
% The following table lists the first 15 Zernike functions. t6>Qe
% RgzSaP;;
% n m Zernike function Normalization oDiv9jm
% -------------------------------------------------- Spw=+z<<Ub
% 0 0 1 1 VlXy&oZ
% 1 1 r * cos(theta) 2 dCJR,},\f
% 1 -1 r * sin(theta) 2 w5JC 2
% 2 -2 r^2 * cos(2*theta) sqrt(6) Qmh(+-Mp(
% 2 0 (2*r^2 - 1) sqrt(3) vWfef~}~
% 2 2 r^2 * sin(2*theta) sqrt(6) lSsFI30
% 3 -3 r^3 * cos(3*theta) sqrt(8) 9(gOk
% 3 -1 (3*r^3 - 2*r) * cos(theta) sqrt(8) 5T@'2)BI=
% 3 1 (3*r^3 - 2*r) * sin(theta) sqrt(8) */h9 "B
% 3 3 r^3 * sin(3*theta) sqrt(8) 'C4Ll2
% 4 -4 r^4 * cos(4*theta) sqrt(10) thboHPml{
% 4 -2 (4*r^4 - 3*r^2) * cos(2*theta) sqrt(10) *[/Xhx"
% 4 0 6*r^4 - 6*r^2 + 1 sqrt(5) H"
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