# Diffraction pattern of plane wave through Circular Aperture

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syed khaleduzzaman on 26 Oct 2022
Commented: Bjorn Gustavsson on 27 Oct 2022
I have done diffraction pattern for infinite slit (in the y-dir.) with a =10 microns (total opening = 20 microns). but cannot do same thing for circular aperture with Diameter = 15 microns. Here is my code for slit aperture. Requesting for circular aperture-plane wave diffraction pattern solution.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This program creates a plane wave function U(r), the transmission
% profile of a 20 um slit p(x), and a combination of the two, g(x),
% a distance away d computed from the user input Fresnel number.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear all
% cwd = pwd;
% cd(tempdir);
% pack
% cd(cwd)
posx=[];
posy=[];
% posy=[];
lambda=1.31; % wavelength
k=(2*pi)/lambda;
z=1;
Nf=input('Enter Fresnel Number: ');
slit=10;
d=(slit^2)/(lambda*Nf);
%d=input('Enter distance of observation plane in microns: ');
Ur=[];
aperture=[];
% 2-D Plane Wave Amplitude U(x)
for x=-30:1:30
for y=-30:1:30
posx=[posx x];
posy=[posy y];
u=exp(-j*k*z); % plane wave
Ur=[Ur u];
% begin slit definition
if (x>=-slit)&(x<=slit)
amp=1;
else
amp=0;
end %
aperture=[aperture amp];
end
IU=abs(Ur).^2;
% Complex Wave after Aperture f(x)
fx=Ur.*aperture;
If=abs(fx).^2;
% g(x) and Intensity Determination |g(x)|^2
hx=[];
aa=[];
ho=(j/(lambda*d))*exp(-j*k*d);
for a=-70:0.025:70
aa=[aa a];
const=(-j*pi)/(lambda*d);
h1=a^2;% Fresnel Appx. of transfer function of free space
h2=exp(const*h1);
hx=[hx h2];
end
hhx=ho*hx;
gx=conv2(fx,hhx,'same'); % direct convolution
Ig=abs(gx).^2;
% intensity normalization
maxg1=max(Ig);
% Pupil Function p(x,y)
figure(1);
plot(posx, aperture);
title('Slit Transmission Profile');
xlabel('X-Distance (microns)');
ylabel('Transmission Value');
% Aperture Function f(x,y)
figure(2);
plot(posx,If);
xlabel('X-Distance (microns)');
ylabel('Normalized Intensity');
% Observation Plane g(x)
figure(3);
plot(posx,Ig/maxg1);
t1=sprintf('Aperture Affected Beam Pattern (Nf=%f, d=%f microns)',Nf,d);
title(t1);
xlabel('X-Distance (microns)');
ylabel('Normalized Intensity');

Bjorn Gustavsson on 26 Oct 2022
Your first problem is surely that all your variables are 1-D arrays and it seems you still only model some kind of linear aperture. To model a circular aperture you will need to model a fully 2-D circular aperture. Start by making posx and posy 2-D arrays and then make aperture into a circular pupil.
Bjorn Gustavsson on 27 Oct 2022
You're welcome, happy that it helped.

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