Simulation of the optically inhomogeneous
scattering structures using fractal multilayer model
I.S. Nefedov 
, D.A. Zimnyakov 
Institute of Radio Engineering and Electronics of Russian
Ac. Sci., Saratov Branch, Russia;
Saratov State University, Saratov, Russia
To describe formation of the scattering fields produced by diffraction of the coherent beams on optically inhomogeneous structures random amplitude-phase screen approach can be used (see, e.g. [1]). This model allows to characterize scattering structures by means of statistical and correlation analysis of the scattered light intensity fluctuations in terms of boundary field formation. Negligibly small thickness of the scattering media in the direction of light propagation is proposed in this case and the usage of this approach for volume-scattering objects requires to take into account the relationships between parameters of the volume distributions of refractive index fluctuations and boundary field characteristics. Pre-fractal multilayer model has been examined as a particular case of volume scattering structure. To reconstruct the amplitude and phase distributions of the boundary field behind the screen the following model has been used. Diffractional effects accompaning the illuminating beam propagation through the screen have been neglected and we have consider smooth fluctuations (with the characteristical scales significantly larger that the wavelength and screen thickness) of the structure parameters across the illuminated area. So, we have one-dimensional approach for the description of the screen structure in the light propagation direction. Basic parameters of the used pre-fractal model are the number of the layers and refractive indices for all layers. Structure topology has been proposed to be described as Cantor pre-fractal. Transfer matrix method has been used to calculate boundary field parameters. Transfer matrix Cantor pre-fractal of the N-th level generation may be obtained using the following iteration procedure:
This procedure
is started from the finite N-th step of fractal construction and
carried out to the first step. 
is the transfer matrix for a
minimal pre-fractal layer and 
is the transfer matrix for an
intermediate layer. So, 
is the transfer matrix of N-th
level pre-fractal.
Results of simulation for different multilayer pre-fractal structures are presented, analysis of the influence of model parameters (such as number of layers and fractal dimension) on the boundary field characteristics is carried out. Some possibilities of this model usage for the description of scattering properties of the biotissues are discussed.