Last time, I only gave the formula, not the code , Many partners said they didn't agree very much . Send the code directly today

by HPC_ZY

The formula

Zernike in Cartesian coordinates （Zernike） coefficient

Code

Functions that generate Zernike polynomials ( normalization ）

%  Functions that generate Zernike polynomials 
function [x,y,z] = getZernikeBasicFunc()
x = -1:0.01:1;
[x,y] = meshgrid(x);
[theta,r] = cart2pol(x,y);
z{
    1} = ones(size(x)).*1/sqrt(pi);
z{
    2} = r .* cos(theta).*2/sqrt(pi);
z{
    3} = r .* sin(theta).*2/sqrt(pi);
z{
    4} = r.^2 .* cos(2.*theta).*sqrt(6/pi);
z{
    5} = (2.*r.^2 - 1) .* sqrt(3/pi);
z{
    6} = r.^2 .* sin(2.*theta) .* sqrt(6/pi);
z{
    7} = r.^3 .* cos(3.*theta) .* sqrt(8/pi);
z{
    8} = (3.*r.^3 - 2.*r) .* cos(theta) .* sqrt(8/pi);
z{
    9} = (3.*r.^3 - 2.*r) .* sin(theta) .* sqrt(8/pi);
z{
    10} = r.^3 .* sin(3.*theta) .* sqrt(8/pi);
z{
    11} = r.^4 .* cos(4.*theta) .* sqrt(10/pi);
z{
    12} = (4.*r.^4 - 3.*r.^2) .* cos(2.*theta) .* sqrt(10/pi);
z{
    13} = (6.*r.^4 - 6.*r.^2 + 1).*sqrt(5/pi);
z{
    14} = (4.*r.^4 - 3.*r.^2) .* sin(2.*theta).*sqrt(10/pi);
z{
    15} = r.^4 .* sin(4.*theta).*sqrt(10/pi);
for n = 1:15
   z{
    n}(r>1) = nan; 
   z{
    n} = z{
    n}/max(abs(z{
    n}(:)));
end

Usage and display

%  Generate 
[x,y,z] = getZernikeBasicFunc();
%  Two display modes 
figure
for n = 1:15
	subplot(3,5,n),pcolor(x,y,z{
    n}), shading interp
	axis square
	axis off
	colorbar
end

figure
for n = 1:15
	subplot(3,5,n),mesh(x,y,z{
    n}), shading interp
	axis square
	colorbar
end

other

Nothing else