Features of Speckle Fractal Structures Propagation in Free Space

The diffraction transformation of scaling and statistical characteristics of speckle fractal fields is considered. For their model representation, the properties of the two-dimensional Weierstrass function with random phases of its harmonics and the Rayleigh law of intensity distribution are used. The characteristics of the light field at different distances from the initial plane are estimated by the method of its expansion in plane waves in combination with the coating method. It showed that during the propagation of light speckle beams, fractality in the transverse distribution of the field amplitude is preserved, but the values of the fractal dimension can change noticeably. In this case, scaling takes place in the spatial spectrum of radiation. This property ensures high efficiency of using fractal speckle structures in art therapy and ophthalmology.