Application of Fraunhofer diffraction patterns for calculation of fractal dimension

Abstract

In this paper the modificated method of calculation of fractal dimension is described. The method is based on effective averaging procedure and deals with the number of fractal generation levels. The existing methods of calculation of fractal dimension need the information about structure factor or scaling factor, which are generally unknown for real objects. The offered algorithm of calculation fractal dimensions allows to calculate fractal dimension of object with a relative error less than 1%. Thus for calculation of dimension there is no necessity to reveal the factor of structure and scaling factor. The method was checked on the wide range of two-dimensional fractals with exact self-similarity and different values of fractal dimension.