Optical diffraction on fractals

Abstract

Diffraction experiments are performed on two-dimensional deterministic fractals such as Cantor bars or Vicsek fractals. We show that the intensity I(q) which is scattered at a wave vector q by a fractal grating is simply its optical Fourier transform. This allows a direct determination of the Hausdorff dimension D and of other geometrical characteristics of fractals. Applications of this analog method to experimentally obtained aggregates are discussed.