Diffraction and Fourier Transform

This applet is based on the fast Fourier transform algorithm. It can calculate the 2D Fourier transform (FT) of a density function ρ(x) which is either periodic or non periodic yielding the function G(S). It can also calculate the inverse FT, namely FT-1 not only of G(S) but also of ∣G(S)∣2 and other variations.

The density function ρ(x) can be drawn by hand on the screen. For example, a crystal structure can be simulated and its FT can be calculated. The corresponding Patterson function can be obtained by inverse FT.

Pictures can also be uploaded and the corresponding FT and FT-1 can be obtained. The user can for example exchange the phases and amplitudes of Fourier transformed pictures.

The effect of resolution can also be tested by limiting the extension of the periodicity of the pattern along two separate dimensions.