Use FFT2 on the GPU to Simulate Diffraction Patterns

Define the Coordinate System

Before you simulate the light that has passed through an aperture, define a coordinate system. To get the correct numerical behavior for calling fft2, arrange x and y so that the zero value is in the correct place.

N2 is half the size in each dimension.

N2 = gpuArray(1024);
[gx,gy] = meshgrid(-1:1/N2:(N2-1)/N2);

Simulate the Diffraction Pattern for a Rectangular Aperture

Simulate the effect of passing a parallel beam of monochromatic light through a small rectangular aperture. The two-dimensional Fourier transform describes the light field at a large distance from the aperture. Start by forming aperture as a logical mask based on the coordinate system. The light source is a double-precision version of the aperture. The far-field light signal is found using fft2.

aperture = (abs(gx)<4/N2).*(abs(gy)<2/N2);
lightsource = double(aperture);
farfieldsignal = fft2(lightsource);

Display the Light Intensity for a Rectangular Aperture

Calculate the far-field light intensity from the magnitude squared of the light field. Use fftshift to aid visualization.

farfieldintensity = real(farfieldsignal.*conj(farfieldsignal));

imagesc(fftshift(farfieldintensity));
axis("equal");
axis("off");
title("Rectangular Aperture Far-field Diffraction Pattern");

Simulate Young's Double-Slit Experiment

One of the most famous experiments in optics is Young's double-slit experiment which shows light interference when an aperture comprises two parallel slits. A series of bright points is visible where constructive interference takes place. Form the aperture representing two slits. Restrict the aperture in the y direction to ensure that the resulting pattern is not entirely concentrated along the horizontal axis.

slits = (abs(gx)<=10/N2).*(abs(gx)>=8/N2);
aperture = slits.*(abs(gy)<20/N2);
lightsource = double(aperture);
farfieldsignal = fft2(lightsource);

Display the Light Intensity for Young's Double-Slit

Calculate and display the intensity as before.

farfieldintensity = real(farfieldsignal.*conj(farfieldsignal));
imagesc(fftshift(farfieldintensity));
axis("equal"); 
axis("off");
title("Double Slit Far-field Diffraction Pattern");