% Simulation d'un dispositif de Haidinger
close all; clear

e = 0.100e-3
n = 1.5
lambda = 630e-9
f = 0.05;

RGB = spectrumRGB(lambda*1e9)

theta_i_deg = -10:0.2:10;

theta_i = theta_i_deg * pi/180;
delta = 4*pi*e/lambda * sqrt(n^2 - sin(theta_i).^2) - pi;
% theta_t = asin(sin(theta_i/n));
% sep_rayons = 2*e*tan(theta_t);
r = f*theta_i;
I = 4*cos(delta/2).^2;
figure; plot (r,I,'r')

rgb =  I'/max(I) * RGB;
franges_circ (r, I, rgb);
xlabel('x (m)'); ylabel('y (m)')
title ('intensité des franges dans le plan focal')

lam = [450:50:650]*1e-9
col = 'bcgyr';

nl = length(lam);
figure; hold on
for i=1:nl
    delta = 4*pi*e/lam(i) * sqrt(n^2 - sin(theta_i).^2) - pi;
    I(i,:) = 4*cos(delta/2).^2;
    plot(r,I(i,:),col(i))
end
hold off
grid on; 
legend ('bleu','cyan','vert','jaune','rouge')
for i = 1:size(I,2)
    Itot = sum(I,1)/nl;
end

figure; plot(r,Itot)
grid on
title ('lumière blanche')    

% calculons les équivalents RGB des lambda
for i = 1:length(lam)
    rgbi(i,:) = spectrumRGB(lam(i)*1e9);
end
% calibration des RGB pour que la somme des 5 couleurs donne [1 1 1] = blanc
sum_RGB = sum(rgbi,1)
for i = 1:3
    RGBi(:,i) = rgbi(:,i) ./ sum_RGB(i);
end

clear rgb_lam
for i = 1:nl
    max_I = max(I(i,:));
    rgb_lam (i,:,:) =  I(i,:)'/max_I * RGBi(i,:);
end

rgb_tot = sum (rgb_lam,1);
franges_circ (r, Itot, rgb_tot);
xlabel('x (m)'); ylabel('y (m)')
title ('Franges en lumière blanche')