70 lines
1.8 KiB
Matlab
70 lines
1.8 KiB
Matlab
clc
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clear
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%% User choices %%
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x_max = 2; % maximum x in mm
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f1 = 100; % focal length of the 1st lens of the telescope in mm
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f2 = 100; % focal length of the 2nd lens of the telescope in mm
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r = 0.5; % radius of the beam in mm
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lambda = 1e-3; % wavelength in mm
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N = 2^10; % number of points
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%%%%%
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k0 = 2 * pi / lambda; % wavenumber
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Lz = 2 * (f1 + f2); % z-limit of visualization in mm
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Lx = 2 * x_max; % x-limit of visualization in mm
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dz = Lz / (N - 1);
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dx = Lx / (N - 1);
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dkx = 2 * pi / Lx;
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z = 0:dz:Lz; % z coordinate array
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x = -Lx/2:dx:Lx/2; % x coordinate array
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kx = -pi/dx:dkx:pi/dx; % kx coordinate array
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tau1 = exp(1i * k0 * x.^2 * 0.5 / f1); % 1st lens phase function
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tau2 = exp(-1i * k0 * x.^2 * 0.5 / f2); % 2nd lens phase function
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E = exp(-(x / r).^2); % Gaussian beam
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% E = rect(x / (2 * r)); % Uniform beam
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t = 0; % iterator for z
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n = 1; % counter
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I = zeros(N, N); % resulting intensity
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while t <= f1
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E = exp(-1i * k0 * dz) * ifft(fftshift(exp(-1i * sqrt(k0^2 - kx.^2) * dz) .* fftshift(fft(E))));
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I(n, :) = abs(E);
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t = t + dz;
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n = n + 1;
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end
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E = E .* tau1;
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while t <= 2 * f1 + f2
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E = exp(-1i * k0 * dz) * ifft(fftshift(exp(-1i * sqrt(k0^2 - kx.^2) * dz) .* fftshift(fft(E))));
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I(n, :) = abs(E);
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t = t + dz;
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n = n + 1;
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end
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E = E.*tau1;
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while t <= 2 * (f1 + f2)
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E = exp(-1i * k0 * dz) * ifft(fftshift(exp(-1i * sqrt(k0^2 - kx.^2) * dz) .* fftshift(fft(E))));
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I(n, :) = abs(E);
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t = t + dz;
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n = n + 1;
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end
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figure
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imagesc(z, x, rot90(I))
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line([f1 f1], [-x_max x_max], 'Color','red','LineStyle','--');
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line([2*f1+f2 2*f1+f2], [-x_max x_max], 'Color','red','LineStyle','--');
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colorbar
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title(sprintf("Kepler telescope with {f_1 =} %.2f mm and {f_2} = %.2f mm", f1, f2))
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xlabel("z, mm")
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ylabel("x, mm")
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% colormap(gray)
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