%
%
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% Optical Imaging and Spectroscopy
%
% David J. Brady
% Duke University
% www.opticalimaging.org
%
% Aliased filter images Figures 7.9 and 7.10
%
figure(1);set(gcf,'color','white');
figure(2);set(gcf,'color','white');
xrange=linspace(-2,62,512);
yrange=linspace(-2,14,128);
%
% one wavelength is 4 samples
%
[x,y]=meshgrid(xrange,yrange);
imgD=(1+cos(2*pi*((x+2).^2/128+(y+2).^2/200)))/2;
figure(1);subplot(5,1,1,'align');imagesc(xrange(19:497),yrange(9:120),imgD(9:120,19:497));colormap 'gray'; 
title('0bject field'); axis image;
figure(2);subplot(5,1,1);plot(xrange(19:497),imgD(64,19:497),'-k');axis tight;
title('0bject field');
fnumber=1;
h=jinc(sqrt((x-30).^2+(y-6).^2)/fnumber).^2;
h=h(33:98,225:288);
imgL=conv2(imgD,h,'same');
imgL=imgL/max(max(imgL));
figure(1);subplot(5,1,2,'align');imagesc(xrange(19:497),yrange(9:120),imgL(9:120,19:497));colormap 'gray'; 
title('Optically filtered');axis image;
figure(2); subplot(5,1,2);plot(xrange(19:497),imgL(64,19:497),'-k');axis tight;
title('Optically filtered');
% Effect of down sampling
%
% sampling at one half wavelength scale
%
dSr=kron(eye(256),[1 1 ])/2;
dSl=kron(eye(64),[1 1])/2;
dxrange=linspace(-2,62,256);
dyrange=linspace(-2,14,64);
imgLd1=dSl*imgL*dSr';
figure(1);subplot(5,1,3,'align');imagesc(dxrange(10:248),dyrange(5:60),imgLd1(5:60,10:248));colormap 'gray'; 
title('Critically sampled');axis image;
figure(2);subplot(5,1,3);plot(dxrange(10:248),imgLd1(32,10:248),'-k');axis tight;
title('Critically sampled');
% sampling at one  wavelength scale
%
dSr=kron(eye(128),[1 1 1 1])/4;
dSl=kron(eye(32),[1 1 1 1])/4;
dxrange=linspace(-2,62,128);
dyrange=linspace(-2,14,32);
imgLd1=dSl*imgL*dSr';
figure(1);subplot(5,1,4,'align');imagesc(dxrange(5:124),dyrange(3:30),imgLd1(3:30,5:124));colormap 'gray'; 
title('2x undersampled'); axis image;
figure(2);subplot(5,1,4);plot(dxrange(5:124),imgLd1(16,5:124),'-k');axis tight;
title('2x undersampled ');
% sampling at two  wavelength scale
%
dSr=kron(eye(64),[1 1 1 1 1 1 1 1])/8;
dSl=kron(eye(16),[1 1 1 1 1 1 1 1])/8;
dxrange=linspace(-2,62,64);
dyrange=linspace(-2,14,16);
imgLd1=dSl*imgL*dSr';
figure(1);subplot(5,1,5,'align');imagesc(dxrange(3:62),dyrange(2:15),imgLd1(2:15,3:62));colormap 'gray'; 
title('4x undersampled '); axis image;xlabel('\lambda f/#');
figure(2);subplot(5,1,5);plot(dxrange(3:62),imgLd1(8,3:62),'-k');axis tight;
title('4x undersampled');xlabel('\lambda f/#');
h=figure(2);
set(h,'papersize',[6 9]);
hp=figure(1);
set(hp,'papersize',[6 9]);