采用matlab编程,其主函数如下,可以模拟各阶的zernike多项式: FQQ@kP$.
%Display the Zernike function Z(n=5,m=1) at=D&oy4"+
clc G+fd.~aGE
clear oAC^4-Ld
a=5;%%%%%%%%%%Z的阶数下标 C*$|#.l
b=1;%%%%%%%%%%Z的阶数的上标 ]|;7R^o3|
x = -1:0.01:1; >]^>gUmq
[X,Y] = meshgrid(x,x); yI lV[_
[theta,r] = cart2pol(X,Y); F"Uh/EO<
idx = r<=1; XEa~)i{O
z = nan(size(X)); \!m!ibr
z(idx) = zernfun(a,b,r(idx),theta(idx)); df!+T0
figure(1) vB=;_=^i1
pcolor(x,x,z), shading interp {$3j/b
axis square, colorbar k RQ~hRT6
xlabel('X'); QZ?O;K1|y
ylabel('Y'); Euqjxz
title(['Zernike function Z^a_b','(r,\theta)']) 2(hvv-
figure(2) Ko@zk<~"[
mesh(x,x,z) KxGKA
xlabel('X'); )K8P+zn~
ylabel('Y'); P4i3y{$V
title(['Zernike function Z^a_b','(r,\theta)'])