- The characteristic equation for a Muller matrix of an arbitrary nondepolarizing optical system is solved, and on this basis
- the problem of independent elements of Muller matrices of nondepolarizing optical systems is solved and on this basis

A new method of object restoration, which is based on the processing of it's several blurred images (blurred from such phenomena as light scattering, diffraction, when electric signals transfer on distance etc.) has been developed. The registered images are to differ from each other by different generation conditions, e.g. the patterns should have various transmission coefficients. The main distinction of the method from existent methods of multiframe image restoration is the possibility of the reconstruction of high spatial frequencies, which are completely blurred with scattering or diffraction. A merit of the method is the possibility of theoretical evaluation of efficiency of the image restoration process without performing model experiments. The patent application has been received.

Methods of image restoration from a single smeared image are developed. In comparison with known methods the main advantage of our methods is the ability to restore with small points of reading into the image. The methods are also applicable for restoration of image registered by space variant imaging systems.

**Key words**: image restoration, unblurring, multiframe image processing, image reconstruction.

The theory of Muller matrices of nondepolarizing optical systems is advanced:

***** eigenpolarizations of all types of nondepolarizing optical systems are investigated; the theorem of necessary and sufficient conditions of orthogonality of eigenpolarizations is proved,

***** in the framework of the Muller matrices formalism the general classification of nondepolarizing optical systems is obtained,

***** polar forms and pseudorepresentations of Muller matrices of nondepolarizing optical systems are obtined,

***** the interior structure of Muller matrices is investigated and their classification is constructed,

*** **a method of determination of Muller matrices is developed and patented.

Some general properties of nondepolarizing optical systems are studied:

- the theorem of necessary and sufficient conditions of nondepolarizing optical systems is proved,
- the polarization degree transformation of an arbitrary nondepolarizing optical system is studied; a degree decrease by partial polarizers in the case of partially polarized illumination is explained,

- the polarizing dependence of energetic characteristics of optical systems is investigated.

Diffraction performance of corner cube retroreflectors

The solution method of the Fraunhofer diffraction problem for a corner cube retroreflector (CCR) has been developed. The diffraction properties of CCR's have been investigated as functions of the following parameters:

The list of selected publications- input plane wave polarization (azimuth, ellipticity and polarization degree),
- refraction indices of CCR and coating (if any, otherwise air is supposed),
- twosided angle deviations (deviations of the right angle between the reflecting facets)

Specialty for CCR without coating it has been ascertained that the illumination polarization modulates the intensity of reflected radiation the CCR twosided angle deviations are different in values and signs. These deviations make diffraction patterns more complicated than one central and six side spots (nodeviation case).

This method has been used to describe CCR diffraction patterns with crossed polarizer and analyzer: a dark cross separating four bright spots. The presence of CCR twosided angle deviations the rightange between the reflecting facets from 90^{î} destroys such pattern structure in general case.

**Keywords:** corner cube retroreflector, Fraunhofer diffraction, polarization.

The results obtained could be used as the basis for essential progress in the Stocks-polarimetry of nondepolarizing optical systems.

We are looking forward to collaboration with all, who are interested in the matrix formalism and, in particular, in the Muller matrix formalism.

The list of selected publications**Keywords: **Muller matrix, nondepolarizing optical systems, polarization, characterictic equation, independent elements.

Methods of assessment of quality of the image registered by focal plane arrays devices (such as CCD, CID and CMOS) are developed on the basis of the Fourier analysis and information theory. Methods allow for parameters such as a signal-to-noise ratio (SNR) and pixel’s geometric parameters (shape of pixel, fill factor and period).

The analytical expression of modulation transfer function (MTF) of the FPA imaging systems with arbitrary pixel geometry is found. When there are no frequencies greater than the Nyquist's one in a spatial object spectrum, it is proved that the object shift does not influence on MTF. In the general case, when there are these frequencies in the spectrum, they are determined. The concept of MTF averaged over shifts and directions of a sinusoidal grating is introduced and the standard derivation and dispersion of MTF are determined. They characterize a degree of the nonisotropic and nonisoplanatic artifacts of FPA. Results of numerical calculations could be used to optimize the geometrical form of pixels.

**Key words**: modulation transfer function (MTF), focal plane arrays (FPA), charge coupled devices (CCD).

Radiation transfer in media with non-spherical scattering particles having preferred spatial orientation

Approximate methods for solving the transfer equation in media with non-spherical scattering particles, which have a preferred spatial orientation have been developed. This situation is typical for solar radiation scattering by ice crystals in high clouds, where scattering particles have elongated form and the mainly vertical orientation originated at the expense of air resistance and particle electrization, and by large raindrops.

In this case, the parameters of a volume element in the transfer equation depend on a direction of light. Based on a number of approximate assumptions about scattering by large non-spherical particles, the approximate methods for calculation of scattered solar radiation density and layer transmittance have been developed. The algorithm for approximate calculation of the angle distribution of the scattered radiation density have been designed.

The calculations show that the transmittance of such a layer may be essentially differ against of the chaotic orientation of scattering particles, especially for oblique incidence of the solar radiation with a large angle. It is also shown that the angle distribution of radiation scattered may have two maxima at a front scattering area. In this case the second maximum position is determined by a medium-attenuation function dependence on the incident light direction.

**Key words: **non-spherical scattering particles, equation of the radiation transfer, multiple scattering.

Radiation transfer in three-dimensional inhomogeneous stochastic media

The radiation transfer in inhomogeneous stochastic scattering media with arbitrary statistics of scattering is developed. The mathematical description of radiation field is developed in the framework of the stochastic radiative transfer theory as a solution of a linear integro-differential transfer equation.

At present, a small-angle method of description of the radiative transfer in media with strongly anisotropic scattering and strongly or weakly fluctuating scattering parameters.

**Key words:** small angle approximation, iteration method, radiative transfer, scattering, three-dimensional inhomogeneous media, intensity, stochastic transfer theory.

Stochastic radiation transfer in a binary Markovian mixture

Some methods of mathematical description of the radiation transfer in macrostochastic scattering media are developed. The scattering media under investigation are, for example, the atmosphere, the ocean, and biotissues consisting of two or more randomly shaped components with distinct scattering parameters. The main aim of these studies is to find a relationship between the statistics of the medium and radiation fields.

Due to the mathematical complexity of the problem, the development of the rather simple but approximate description of the stochastic radiative transfer can be interesting. In accordance with this aim, an approximate analysis of the stochastic laser beam transfer for a special model of the macrostochastic scattering medium, the so called two-component Markovian mixture is given. A typical example of a medium, that could be approximately considered as Marcovian is broken cloud.

The list of selected publications

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**Key words:** stochastic transfer, small angle approximation, intensity, laser beam, scattering, binary Markovian mixture, optical transfer function*. *