采用matlab编程,其主函数如下,可以模拟各阶的zernike多项式: S|RUc}(
%Display the Zernike function Z(n=5,m=1) i"!j:YEo
clc r`0oI66B/
clear viS7+E|O
a=5;%%%%%%%%%%Z的阶数下标 kafj?F
b=1;%%%%%%%%%%Z的阶数的上标 G"<} s
mB
x = -1:0.01:1; ''EFh&F
[X,Y] = meshgrid(x,x); `@ Ont+
[theta,r] = cart2pol(X,Y); -Ze2]^#dl
idx = r<=1; +r =p,leb
z = nan(size(X)); j =b-Y
z(idx) = zernfun(a,b,r(idx),theta(idx)); g>f_'7F&
figure(1) !Ie={BpzbZ
pcolor(x,x,z), shading interp O`0A#h&No
axis square, colorbar Y5Z<uD
xlabel('X'); q&k?$rn
ylabel('Y');
(>x_fDv
title(['Zernike function Z^a_b','(r,\theta)']) [E%Ov0OC
figure(2) &f>1/"lnd\
mesh(x,x,z) _"";SqVB
xlabel('X'); <Okl.Iz>
ylabel('Y'); M6b6lhg
title(['Zernike function Z^a_b','(r,\theta)'])