N-zernike.rar_matlab 相位屏_zernike多项式_zernike相位屏_zernike系数_多项式相位

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Class: Psych 221/EE 362 % File: ZernikePolynomial % Author: Patrick Maeda % Purpose: Calculate and Plot Zernike Polynomials % Date: 03.03.03 % % Matlab 6.1: 03.04.03 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % This file calculates and plots the Zernike Polynomial specified by: % n = highest power or order of the radial polynomial term, [a positive integer] % m = azimuthal frequency of the sinusoidal component, [a signed integer] % for a given n, m can take on the values -n, -n+2, -n+4,..., n-4, n-2, n % d = pupil diameter = 2 for normalized pupil coordinates % % The Zernike Polynomial definitions used are derived from: % Thibos, L., Applegate, R.A., Schweigerling, J.T., Webb, R., VSIA Standards Taskforce Members, % "Standards for Reporting the Optical Aberrations of Eyes" % OSA Trends in Optics and Photonics Vol. 35, Vision Science and its Applications, % Lakshminarayanan,V. (ed) (Optical Society of America, Washington, DC 2000), pp: 232-244. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clear all; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Zernike polynomial selection %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% disp('Zernike Polynomial radial order n, azimuthal frequency m, and mode number j') %n=4; %[INPUT] highest power or order of the radial polynomial term %m=4 ; %[INPUT] azimuthal frequency of the sinusoidal component N=50; d=10; r0=1.5; [n,m]=Jx(N); %n = [0 1 1 2 2 2 3 3 3 3 4 4 4 4 4]; %m = [0 1 -1 0 -2 2 -1 1 -3 3 0 2 -2 4 -4]; length_n=length(n); length_m=length(m); %j=0.5*(n*(n+2)+m); %mode number (0 to 36) from single indexing scheme %d=250; %pupil diameter %d=2; PupilDiameter=d; PupilRadius=d/2; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Set-up normalized x,y grid %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% xn=-5:0.05:5; %normalized x-coordinates yn=-5:0.05:5; %normalized y-coordinates %xn=-125:125; %yn=-125:125; z1=zeros(length(xn),length(yn)); a(1)=1; a(2:length(n))=xs(n,m,d,r0); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Compute Zernike polynomial %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for i=1:length_n for j=1:length_m if i==j z=a(i)*zernike(n(i),m(j),xn,yn,d); z1=z1+z; end end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Plot Zernike polynomial %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure % subplot(2,1,1) z1=rot90(z1); z1=flipud(z1); imagesc(xn,yn,z1); colormap gray axis xy axis square %set(gca, 'TickDir', 'out') title('Zernike Polynomial'); %(['Zernike Polynomial Z^{', num2str(m),'}_{', num2str(n),'}'],'FontSize', 10); xlabel('Normalized x pupil coordinate'); ylabel('Normalized y pupil coordinate'); figure % subplot(2,1,2) mesh(xn,yn,z1) %view(-37.5,45) title('Zernike Polynomial Z^N');%(['Zernike Polynomial Z^{', num2str(m),'}_{', num2str(n),'}'],'FontSize', 10); xlabel('Normalized x pupil coordinate'); ylabel('Normalized y pupil coordinate'); zlabel('Amplitude'); % colormap('default') % colormap([0.8 0 0])