How to compute diffraction integral using fast Fourier transform (fft2) ?

Hi there !
The following code computes Fresnel diffraction integral using fft2. It works for (obj.E = ones(Ny, Nx);) and performs the fft2 analysis, but when the input is (obj.E = zeroes(Ny, Nx);), it plots nothing. I checked the same code on python with zeros and it worked but in MATLAB it is not performing fft2 for zeros (gives only zero values). Kindly help me resolve this issue.
The Sheet.m (code):
classdef Sheet
properties
dx
dy
x
y
xx
yy
Nx
Ny
E
end

methods
function obj = Sheet(extent_x, extent_y, Nx, Ny)
obj.dx = extent_x / Nx;
obj.dy = extent_y / Ny;
obj.x = obj.dx * ((0:Nx-1) – floor(Nx/2));
obj.y = obj.dy * ((0:Ny-1) – floor(Ny/2));
[obj.xx, obj.yy] = meshgrid(obj.x, obj.y);
obj.Nx = Nx;
obj.Ny = Ny;
obj.E = zeros(Ny, Nx);
end

function rectangular_slit(obj, x0, y0, lx, ly)
% Creates a slit centered at the point (x0, y0) with width lx and height ly
mask = ((obj.xx > (x0 – lx/2)) & (obj.xx < (x0 + lx/2))) & ((obj.yy > (y0 – ly/2)) & (obj.yy < (y0 + ly/2)));
obj.E = obj.E + mask;
end
end
end

The main code :
% Simulation input
Lx = 1.4;
Ly = 0.4;
Nx = 2500;
Ny = 1500;
sheet = Sheet(2*Lx, 2*Ly, Nx, Ny);
% Slit separation
mm = 1e-3;
D = 128 * mm;
sheet.rectangular_slit(-D/2, 0, 22 * mm, 88 * mm);
sheet.rectangular_slit(D/2, 0, 22 * mm, 88 * mm);
% Distance from slit to the screen (mm)
z = 5000;
% Wavelength (mm)
lambda = 18.5*1e-7;
k = 2*pi / lambda;
% Initialize complex array for phase information
fft_c = fft2(sheet.E .* exp(1i * k/(2*z) * (sheet.xx.^2 + sheet.yy.^2)));
c = fftshift(fft_c);
% Plot with MATLAB
abs_c = abs(c);
% Screen size (mm)
dx_screen = z*lambda/(2*Lx);
dy_screen = z*lambda/(2*Ly);
x_screen = dx_screen * ((1:Nx) – Nx/2);
y_screen = dy_screen * ((1:Ny) – Ny/2);
figure;
subplot(2, 1, 1);
imagesc(x_screen([1 end]), y_screen([1 end]), abs_c);
colormap(gray);
axis equal;
xlabel(‘x (mm)’);
ylabel(‘y (mm)’);
title(‘Probability Density |psi|^2’);
xlim([-2, 2]);
ylim([-1, 1]);
subplot(2, 1, 2);
plot(x_screen, abs(c(Ny/2, :)).^2, ‘LineWidth’, 1);
xlabel(‘x (mm)’);
ylabel(‘Probability Density |psi|^2’);
title(‘Probability Density |psi|^2 along y=0’);
xlim([-2, 2]);Hi there !
The following code computes Fresnel diffraction integral using fft2. It works for (obj.E = ones(Ny, Nx);) and performs the fft2 analysis, but when the input is (obj.E = zeroes(Ny, Nx);), it plots nothing. I checked the same code on python with zeros and it worked but in MATLAB it is not performing fft2 for zeros (gives only zero values). Kindly help me resolve this issue.
The Sheet.m (code):
classdef Sheet
properties
dx
dy
x
y
xx
yy
Nx
Ny
E
end

The main code :
% Simulation input
Lx = 1.4;
Ly = 0.4;
Nx = 2500;
Ny = 1500;
sheet = Sheet(2*Lx, 2*Ly, Nx, Ny);
% Slit separation
mm = 1e-3;
D = 128 * mm;
sheet.rectangular_slit(-D/2, 0, 22 * mm, 88 * mm);
sheet.rectangular_slit(D/2, 0, 22 * mm, 88 * mm);
% Distance from slit to the screen (mm)
z = 5000;
% Wavelength (mm)
lambda = 18.5*1e-7;
k = 2*pi / lambda;
% Initialize complex array for phase information
fft_c = fft2(sheet.E .* exp(1i * k/(2*z) * (sheet.xx.^2 + sheet.yy.^2)));
c = fftshift(fft_c);
% Plot with MATLAB
abs_c = abs(c);
% Screen size (mm)
dx_screen = z*lambda/(2*Lx);
dy_screen = z*lambda/(2*Ly);
x_screen = dx_screen * ((1:Nx) – Nx/2);
y_screen = dy_screen * ((1:Ny) – Ny/2);
figure;
subplot(2, 1, 1);
imagesc(x_screen([1 end]), y_screen([1 end]), abs_c);
colormap(gray);
axis equal;
xlabel(‘x (mm)’);
ylabel(‘y (mm)’);
title(‘Probability Density |psi|^2’);
xlim([-2, 2]);
ylim([-1, 1]);
subplot(2, 1, 2);
plot(x_screen, abs(c(Ny/2, :)).^2, ‘LineWidth’, 1);
xlabel(‘x (mm)’);
ylabel(‘Probability Density |psi|^2’);
title(‘Probability Density |psi|^2 along y=0’);
xlim([-2, 2]); Hi there !
The following code computes Fresnel diffraction integral using fft2. It works for (obj.E = ones(Ny, Nx);) and performs the fft2 analysis, but when the input is (obj.E = zeroes(Ny, Nx);), it plots nothing. I checked the same code on python with zeros and it worked but in MATLAB it is not performing fft2 for zeros (gives only zero values). Kindly help me resolve this issue.
The Sheet.m (code):
classdef Sheet
properties
dx
dy
x
y
xx
yy
Nx
Ny
E
end

The main code :
% Simulation input
Lx = 1.4;
Ly = 0.4;
Nx = 2500;
Ny = 1500;
sheet = Sheet(2*Lx, 2*Ly, Nx, Ny);
% Slit separation
mm = 1e-3;
D = 128 * mm;
sheet.rectangular_slit(-D/2, 0, 22 * mm, 88 * mm);
sheet.rectangular_slit(D/2, 0, 22 * mm, 88 * mm);
% Distance from slit to the screen (mm)
z = 5000;
% Wavelength (mm)
lambda = 18.5*1e-7;
k = 2*pi / lambda;
% Initialize complex array for phase information
fft_c = fft2(sheet.E .* exp(1i * k/(2*z) * (sheet.xx.^2 + sheet.yy.^2)));
c = fftshift(fft_c);
% Plot with MATLAB
abs_c = abs(c);
% Screen size (mm)
dx_screen = z*lambda/(2*Lx);
dy_screen = z*lambda/(2*Ly);
x_screen = dx_screen * ((1:Nx) – Nx/2);
y_screen = dy_screen * ((1:Ny) – Ny/2);
figure;
subplot(2, 1, 1);
imagesc(x_screen([1 end]), y_screen([1 end]), abs_c);
colormap(gray);
axis equal;
xlabel(‘x (mm)’);
ylabel(‘y (mm)’);
title(‘Probability Density |psi|^2’);
xlim([-2, 2]);
ylim([-1, 1]);
subplot(2, 1, 2);
plot(x_screen, abs(c(Ny/2, :)).^2, ‘LineWidth’, 1);
xlabel(‘x (mm)’);
ylabel(‘Probability Density |psi|^2’);
title(‘Probability Density |psi|^2 along y=0’);
xlim([-2, 2]); diffraction, fft2, fresnel, numerical integration, plot MATLAB Answers — New Questions

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