Computer-simulated Fresnel diffraction using the Fourier transform

The study of Fresnel diffraction is an integral part of any course in physical optics. Fresnel diffraction occurs when an aperture is illuminated with coherent light and the resulting diffraction pattern appears on a screen, a finite distance from the aperture. In general, the techniques found in standard optics texts' to compute the intensity of the diffraction pattern as a function of position on the screen are limited and aperture-specific. However, as texts on modern optics show, we can formulate Fresnel diffraction in terms of the Fourier transform of a modified aperture function. The article presents a generalized method, using the Fourier transform, for computing and graphically displaying the Fresnel diffraction intensity pattern for any planar aperture. With the advent of the PC and packaged mathematical software containing the fast Fourier transform algorithm, it is now possible to perform these calculations with minimum effort. The advantage of this method is that you can obtain the entire pattern at once, in contrast to the standard methods' point-by-point evaluation process.