Fraunhofer Diffraction - Multiple Square Apertures

Hello all!

I'm stuck for some days trying to get the diffraction pattern from a binary grating / square period grating / multi-aperture square screen... whatever you want to call it.

Imagine I have a 8 * 5 square apertures grating. Something like this:

The intensity profile from a single aperture is easy to calculate:

% Clean all
clc;
close all;
clear all;

% Light Source
lambda = 550e-9;                    % Wavelength [m]
k = (2*pi)/lambda;                  % Wavenumber [m^-1]
Io = 100;                           % Relative intensity

% Aperture
a = 1e-6;                           % Aperture size X-axis [m]
b = 1e-6;                           % Aperture size Y-axis [m]

% Screen
R = 1e-3;                           % Distance aperture-screen [m]
dsize = 0.5e-2;                     % Square size [m]
dpix = 1000;                        % Dimension [pixel]
X = -dsize:2*dsize/dpix:dsize;      % Screen X-axis
Y = X;                              % Screen Y-axis

% Intensity Profile
alpha = k*a*X/(2*pi*R);                     % Periodic parameter X-axis
beta = k*b*Y/(2*pi*R);                      % Periodic parameter Y-axis
I = Io*(sinc(alpha).^2)'*(sinc(beta).^2);   % Intensity profile

% Print
fig = figure();
imshow(I);

To calculate the same for a 8 * 5 grating, I have to do a convolution of my unit-square aperture by a comb function. I will get an infinite pattern.

I already search and according with some answers I could use the "repmat" function to get a 8*5 section of that infinite pattern

Then I just have to multiply it by rectangular (sinc) function to get a non-infinite pattern. But I'm struggle with it.

Could you advise me?

Thank you in advance.

Answer 1

[Cédric Pereira]

Could it be right?

% Clean all
clc;
close all;
clear all;

% Light Source
lambda = 550e-9;                    % Wavelength [m]
k = (2*pi)/lambda;                  % Wavenumber [m^-1]
Io = 100;                           % Relative intensity

% Aperture
a = 1e-6;                           % Aperture size X-axis [m]
b = 1e-6;                           % Aperture size Y-axis [m]

% Screen
R = 1e-3;                           % Distance aperture-screen [m]
dsize = 0.5e-2;                     % Square size [m]
dpix = 1000;                        % Dimension [pixel]
X = -dsize:2*dsize/dpix:dsize;      % Screen X-axis
Y = X;                              % Screen Y-axis

% Intensity Profile
alpha = k*a*X/(2*pi*R);                     % Periodic parameter X-axis
beta = k*b*Y/(2*pi*R);                      % Periodic parameter Y-axis
I = Io*(sinc(alpha).^2)'*(sinc(beta).^2);   % Intensity profile

% Square Aperture on Matrix
I2 = repmat(I,16);                          % Replicate square aperture on matrix

% Total Area
V = linspace(-8008,8008,16016);
M = sinc(V).^2'*sinc(V).^2;                 % Rectangular area

% Final Result
I3 = I2.*M*10^16;

% Print
fig = figure();
imshow(I3);

Why do I have some bright central lines?

[Divya P]

Hey could you tell me that what you have reffered to get this code ? And is this has any article?