Generation of fractal speckle using computer-generated holograms and its application to speckle correlometry

When a diffuser is illuminated by the coherent light with intensity distributions obeying a negative power law, speckle fields with fractal properties are produced. Such a random field is called fractal speckles. Fractal speckles have extremely long spatial correlation functions of the intensity distributions in comparison with ordinary speckles. It implies that fractal speckles may extend measurement ranges in various metrological applications based on the spatial correlation of speckles. We report the generation of fractal speckles using computer-generated holograms based on the method of stationary phase and the iterative Fourier transform algorithm, and its application to speckle correlometry is discussed.