Alexander V. Kovalchuk

Fractal description of rough surfaces

The multifractal description of rough surfaces is discussed and the mechanisms for generation of fractal and multifractal height distributions of inhomogeneities for rough surfaces are simulated. The original technique for estimating the spectrum of singularities is proposed for the study of these distributions.

Study of optical field diffracted by multifractals

Diffraction of radiation by the Cantor set based multifractals is studied. The connection between the dimension of an objects supporting fractal and its level is searched for, as well as one between the multifractals construction parameter, singularity spectra, and asymmetry parameters of its diffraction pattern. It has been shown that the singularity spectrum has a maximum whose position depends on the objects supporting fractal dimension. At the same time, a singularity spectrums half-width and near-field intensity asymmetry coefficient ought to be acceptable for evaluation of the object construction ratio parameter, and the magnitude of the asymmetry coefficient at the saturation zone depends on the level of the objects supporting fractal.

Optical diagnostics of asymmetrical fractal structures

Diffraction of radiation by asymmetric Cantor fractals and diffraction gratings is studied. Asymmetry parameters of an object and its diffraction field are compared. It has been shown that the asymmetry coefficient of optical fields diffracted by the asymmetric fractals is acceptable for evaluation of the asymmetry degree of the studied fractals. Empirical relations among the fractal level, asymmetry of the object fractal and coefficient of asymmetry for the field diffracted on it have been obtained.

Diffraction of radiation on Cantor fractals

In this paper we investigate some properties of the diffraction field due to Cantor bars, which are a 1-D fractal and are one of the most well known regular fractals. By 1-D fractal we mean that the smallest Euclidian dimension of a space where a fractal exists is one. We investigate spatial complexity in optical fields resulting from diffraction of a plane wave by such fractals. For this purpose we employ the theory of stochastic and chaotic oscillations. There are several parameters which are commonly used to characterize the dimension of a chaotic system, namely, Liapunov exponent, dimension, and entropy. We use fractal dimension d for fractals and correlation exponent v for the diffraction field. In the present paper, the correlation exponent v is used as a parameter characterizing the spatial complexity of an optical field. This parameter gives the quantity of spatial harmonics with uncommesurable periods.

Diffraction of an optical field on multifractals

Diffraction of radiation by the Cantor set based multifractals is studied. Connection between the dimension of an objects supporting fractal and its level is searched for as well as one between the multifractals construction parameter, singularity spectra, and asymmetry parameters of its diffraction pattern. It has been shown that the singularity spectrum has a maximum whose position depends on the objects supporting fractal dimension. At the same time, a singularity spectrum half-width and near-field intensitys asymmetry coefficient occur to be acceptable for evaluation of the object construction ratio parameter, and magnitude of the asymmetry coefficient at saturation zone depends on the level of the objects supporting fractal.

Optical measurements of the structure parameters of random and fractal objects

Optical correlation diagnostics of random and fractal objects is considered. A promising fractal approach for the object structure diagnostics is discussed. The possibility for measurement of a correlation dimension of complexity, and Cantor fractals asymmetry are shown.

Diagnostic of asymmetrical fractals structure

Diffraction of radiation by asymmetric Cantor fractals and diffraction gratings is studied. Asymmetry parameters of an object and its diffraction field are compared. It has been shown that the asymmetry coefficient of optical fields diffracted by the asymmetric fractals arises to be acceptable for evaluation of the asymmetry degree of the studied fractals. As empirical relations among fractal level, asymmetry of the object fractals, and coefficients of asymmetry of the field diffracted on them have been obtained.

Fractal properties of rough surfaces

The multifractal description of rough surfaces is discussed and the mechanisms for analysis of fractal and multifractal height distributions of inhomogeneities for rough surfaces are simulated. The original technique for estimating the spectrum of singularities is proposed for studying these distributions. Further, the application of the wavelet analysis for quantitative characterization of fractal distributions associated with rough surfaces and for determination of the position of singularities of these structures is presented.

Feasibility of optical correlation diagnostics of multifractals

Diffraction of radiation by Cantor set based multifractals is studied. Connection among dimension and level of an objects supporting fractal as well as its multifractal construction parameter and its diffraction patterns singularity spectra and asymmetry parameters is searched. It has been shown that the position of singularity spectrum maximum depends on the dimension of the objects supporting fractal, singularity spectrum half-width as well as near- field patterns asymmetry coefficient occurs to be acceptable for evaluation of the object construction ratio parameters, length of asymmetry coefficient saturation zone depends on the level of the objects supporting fractal.

Diffraction of light by asymmetric amplitude fractals

Diffraction of radiation by the asymmetric Cantor fractals is studied. Asymmetry parameters of an object and its diffraction field are compared. The fields asymmetry is estimated employing its statistical moments. It has been shown that the statistical asymmetry coefficient of optical fields diffracted by the asymmetric fractals occurs to be acceptable for evaluation of the asymmetry degree of the studied fractals. An empirical relations among fractal level, asymmetry of the object fractals, and coefficients asymmetry of the field diffracted on them measured at the certain zones have been obtained.