lens_calculator.m

%% simulations for optical systems

% 2-lenses system

% numerical simulation of magnification
f_1 = [-1000:1000]; 
f_2 = [1:1000];
u_1 = 1:500;

% single lens
v_1 = zeros(length(f_1),length(u_1));
for i = 1:length(f_1) 
    for ii= 1:length(u_1)
        v_1(i,ii) = (f_1(i)*u_1(ii)) / (u_1(ii)-f_1(i));
    end
end
figure, p=plot(v_1(:,50:50:500)); hold on
legend(string_array,'Location','SouthWest')
xlabel('focal length, mm')
ylabel('virtual image distance, mm')

% two lens system: magnification
m = zeros(length(f_1),length(f_2),length(u_1));
d = zeros(length(f_1),length(f_2),length(u_1));
for i = 1:length(f_1) 
    for ii = 1:length(f_2)
        for iii = 1:length(u_1)
            
            m(i,ii,iii) = (150*(f_1(i)*u_1(iii))/(u_1(iii) - f_1(i))) / (u_1(iii) * 150*f_2(ii)/(150-f_2(ii)));
            
        end
    end
end
% visualize exemple
m1 = squeeze(m(:,:,400));
figure, %subplot(121), 
imagesc(1./m1,[-5 5]), colorbar, axis square, 
ylabel('focal length of lens 1, mm')
xlabel('focal length of lens 2, mm')
title('de-magnification factor, object size to image size, u1 = 400 mm, v2=150 mm','FontSize',12,'FontWeight','bold')
subplot(122), imagesc( (abs(m1)>=1/4).* (abs(m1)<=1/3) ), axis square
ylabel('focal length of convex lens, mm')
xlabel('distance screen to first lens, mm')
title('bands of demagnfication factor between 3x and 4x')

% find size of region of space with right magnification
% as a function of object distance to first lens
high_cutoff  = 3.5;
low_cutoff = 3;
magnification_binary = zeros(size(m));
magnification_region_size = zeros(size(m,3));
for iii = 1:length(u_1)
    magnification_region_size(iii) = numel(find((abs(squeeze(m(:,:,iii)))>=1/high_cutoff).* ...
        (abs(squeeze(m(:,:,iii)))<=1/low_cutoff)))/(size(m,1)*size(m,2));
    magnification_binary(:,:,iii) = (abs(squeeze(m(:,:,iii)))>=1/high_cutoff).* ...
        (abs(squeeze(m(:,:,iii)))<=1/low_cutoff);
end
% two lens system: distance between lenses, as function of focal lengths,
% and object position
% initial conditions, mm
v_2 = 150; 
% u1 = 30;
d = zeros(length(f_1),length(f_2),length(u_1));
for i = 1:length(f_1) 
    for ii = 1:length(f_2)
        for iii = 1:length(u_1)
            
            d(i,ii,iii) = f_2(ii)*v_2/(v_2-f_2(ii)) - f_1(i)*u_1(iii)/(u_1(iii)-f_1(i));
       
        end
    end
end
d1 = squeeze(d(:,:,50));
figure, %subplot(121), 
imagesc(d1,[-500 500]), colorbar, axis square, 
ylabel('focal length of lens 1, mm')
xlabel('focal length of lens 2, mm')
title('distance between lenses, u1= 50 mm')
subplot(122), imagesc( (abs(m1)>=1/4).* (abs(m1)<=1/3) ), axis square
ylabel('focal length of convex lens, mm')
xlabel('distance screen to first lens, mm')
title('bands of demagnfication factor between 3x and 4x')


% binarize solutions
m_binary = zeros(length(f_1),length(f_2),length(u_1));
for iii = 1:length(u_1)
    m_binary(:,:,iii) = (abs(m(:,:,iii))>=1/4).* (abs(m(:,:,iii))<=1/3);
end


figure, contour3(u_1,f_2,1./abs(squeeze(m(60,:,:))),1000)

ftest = [60,75,100,125,150,175,200,250,300,400,500,750]
for j = 1:length(ftest)
    figure, imagesc(1./abs(squeeze(m(ftest(j),:,:)))), title(['f1 =  ', num2str(ftest(j))])
end


% minimize distance between lenses

u1 = 1:100;
f1 = 60:5:1000;
d = zeros(length(f1),length(u1));
for i = 1:length(f1) 
    for ii = 1:length(u1)
        d(i,ii) = f1(i)*u1(ii) / (u1(ii)-f1(i));
    end
end