采用matlab编程,其主函数如下,可以模拟各阶的zernike多项式: P! cfe@;<4
%Display the Zernike function Z(n=5,m=1) +q*WY*gX
clc zu/BDyF
clear "qh~wK J
a=5;%%%%%%%%%%Z的阶数下标 (:er~Y}
b=1;%%%%%%%%%%Z的阶数的上标 (E(J}r~E
x = -1:0.01:1; R?62gH
[X,Y] = meshgrid(x,x); Mbm'cM&}
[theta,r] = cart2pol(X,Y); da'1H
idx = r<=1; qkXnpv
z = nan(size(X)); /tdRUX
z(idx) = zernfun(a,b,r(idx),theta(idx)); ^k J>4
figure(1) 2`d KnaF|
pcolor(x,x,z), shading interp fM/~k>wl
axis square, colorbar Q Uy7Q$W
xlabel('X'); G]v BI=
ylabel('Y'); ?kM2/a"{G
title(['Zernike function Z^a_b','(r,\theta)']) ^=Dz)95c
figure(2) Phq"A[4=O
mesh(x,x,z) f/PqkHF
xlabel('X'); QJ\+u
ylabel('Y'); H~$*R7~
title(['Zernike function Z^a_b','(r,\theta)'])