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[交流] CODEV fringe Zernike MATLAB实现

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laughvn

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擦汗
2024-5-29 14:47

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发表于 2024-3-18 14:44 | 显示全部楼层 |阅读模式

<blockquote>function [z,zer]= CodevFringeZernike(res,flag)

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laughvn

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楼主| 发表于 2024-3-18 14:45 | 显示全部楼层

function [z,zer]= CodevFringeZernike(res,flag)
% ref1 - Optical Shop Testing, Third Edition (2007) P517 TABLE 13.5.
% ref2 - https://blog.csdn.net/xsz591541060/article/details/124275188
% ref3 - Zemax中Zernike Standard多项式 https://zhuanlan.zhihu.com/p/667867516
% 参数j： Zernike多项式的序号
% 参数res：Zernike多项式的分辨率
relative = 1;%设置为单位圆
x = linspace(-relative,relative,res);
[x,y] = meshgrid(x,x);
[theta,rho] = cart2pol(x,y);% 由(x,y)换算(r,theta)
z{1} = ones(size(x)); %Piston
z{2} = rho .* cos(theta); %x tilt
z{3} = rho .* sin(theta); %y tilt
z{4} = (2.*rho.^2 - 1); %Defocus
z{5} = rho.^2 .* cos(2.*theta); %Primary astigmatism at 45°
z{6} = rho.^2 .* sin(2.*theta); %Primary astigmatism at 0°
z{7} = (3.*rho.^3 - 2.*rho) .* cos(theta); %Primary y coma
z{8} = (3.*rho.^3 - 2.*rho) .* sin(theta); %Primary x coma
z{9} = (6.*rho.^4 - 6.*rho.^2 + 1); %Primary spherical
z{10} = rho.^3 .* cos(3.*theta);
z{11} = rho.^3 .* sin(3.*theta);
z{12} = (4.*rho.^4 - 3.*rho.^2) .* cos(2.*theta); %Secondary astigmatism at 0°
z{13} = (4.*rho.^4 - 3.*rho.^2) .* sin(2.*theta); %Secondary astigmatism at 45°
z{14} = (10.*rho.^5 - 12.*rho.^3 + 3.*rho) .* cos(theta); %Secondary x coma
z{15} = (10.*rho.^5 - 12.*rho.^3 + 3.*rho); %Secondary y coma
z{16} = (20.*rho.^6 - 30.*rho.^4 + 12.*rho.^2 + 1); %Secondary spherical
z{17} = rho.^4 .* cos(4.*theta);
z{18} = rho.^4 .* sin(4.*theta);
z{19} = (5.*rho.^5 - 4.*rho.^3) .* cos(3.*theta);
z{20} = (5.*rho.^5 - 4.*rho.^3) .* sin(3.*theta);
z{21} = (15.*rho.^6 - 20.*rho.^4 + 6.*rho.^2) .* cos(2.*theta);
z{22} = (15.*rho.^6 - 20.*rho.^4 + 6.*rho.^2) .* sin(2.*theta);
z{23} = (35.*rho.^7 - 60.*rho.^5 + 30.*rho.^3 - 4.*rho) .* cos(theta);
z{24} = (35.*rho.^7 - 60.*rho.^5 + 30.*rho.^3 - 4.*rho) .* sin(theta);
z{25} = (70.*rho.^8 - 140.*rho.^6 + 90.*rho.^4 - 20.*rho.^2 + 1);
z{26} = rho.^5 .* cos(5.*theta);
z{27} = rho.^5 .* sin(5.*theta);
z{28} = (6.*rho.^6 - 5.*rho.^4) .* cos(4.*theta);
z{29} = (6.*rho.^6 - 5.*rho.^4) .* sin(4.*theta);
z{30} = (21.*rho.^7 - 30.*rho.^5 + 10.*rho.^3) .* cos(3.*theta);
z{31} = (21.*rho.^7 - 30.*rho.^5 + 10.*rho.^3) .* sin(3.*theta);
z{32} = (56.*rho.^8 - 105.*rho.^6 + 60.*rho.^4 - 10.*rho.^2) .* cos(2.*theta);
z{33} = (56.*rho.^8 - 105.*rho.^6 + 60.*rho.^4 - 10.*rho.^2) .* sin(2.*theta);
z{34} = (126.*rho.^9 - 280.*rho.^7 + 210.*rho.^5 - 60.*rho.^3 + 5.*rho) .* cos(theta);
z{35} = (126.*rho.^9 - 280.*rho.^7 + 210.*rho.^5 - 60.*rho.^3 + 5.*rho) .* sin(theta);
z{36} = (252.*rho.^10 - 630.*rho.^8 + 560.*rho.^6 - 210.*rho.^4 + 30.*rho.^2 - 1);
z{37} = (924.*rho.^12 - 2772.*rho.^10 + 3150.*rho.^8 - 1680.*rho.^6 + 420.*rho.^4 - 42.*rho.^2 + 1);
zer = zeros(res,res,37);
for n = 1:37
if flag == 1
z{n}(rho>relative) = 0; % 只保留单位圆内的数据
end
% z{n} = z{n}/max(abs(z{n}(:)));
zer(:,:,n) = z{n};
%z{n} = z{n}/max(abs(z{n}(:)));归一化
end
end
%%demo
% res = 256;
% z = CodevFringeZernike(res,1);
% figure;
% for n = 1:37
% subplot(5,8,n);imshow(z{n},[]);colormap jet;colorbar;xlabel(['Z',num2str(n)]);
% end

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