zernikepolynomial.m

利用Zernike多项式来描述人眼眼底波前畸变的matlab程序,其中还有PSF和MTS的计算,PPT的详细讨论,非常游泳

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%
% 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
% 
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%
% 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. 
%
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clear all;

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% Zernike polynomial selection
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disp('Zernike Polynomial radial order n, azimuthal frequency m, and mode number j')
n=3                 %[INPUT] highest power or order of the radial polynomial term
m=-1                 %[INPUT] azimuthal frequency of the sinusoidal component
j=0.5*(n*(n+2)+m)   %mode number (0 to 36) from single indexing scheme
d=2;                %pupil diameter
PupilDiameter=d
PupilRadius=d/2

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% Set-up normalized x,y grid
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xn=-1:0.02:1;   %normalized x-coordinates
yn=-1:0.02:1;   %normalized y-coordinates

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% Compute Zernike polynomial
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z=zernike(n,m,xn,yn,d);

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% Plot Zernike polynomial
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figure
subplot(2,1,1)
z=rot90(z);
z=flipud(z);
imagesc(xn,yn,z);
colormap gray
axis xy
axis square
%set(gca, 'TickDir', 'out')
title(['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,z)
%view(-37.5,45) 
title(['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])