Aperture and diffraction

A simple Mathematica trick allows to play with an aperture and see how diffraction affects it. On the left we have an interactive polygon (or it could be some other interactive graphics). We take that image as array of 1’s and 0’s and apply Fourier transform to it. That would give the “beam shape at infinity“, to get the shadow at some finite distance, the original array is pre-multiplied by exp(-i*k*x^2). Finally, interpret the result of the Fourier transform as the amplitude at the screen and convert it to black-and-white image (on the right).