Evgeni N. Terentiev

Problem of the radiovision system resolution improvement in millimeter-wave range

At the Faculty of Physics of Moscow State University experimental researches of the working radiovision systems on the base of phased antenna array and radio optical systems with the sensors rules are carried out. Since 1980 the system of Sun radio observation in 3-mm wavelength range created by the specialists of Bauman Moscow State Technical University is exploited. Investigations in the mathematical modeling of image formation systems in wide wavelength range with different receiving schemes and with distortion compensation task solution and super-resolution are conducted by mathematician and physicists.

On the problem of beam focusing in the turbulent atmosphere

Two parts of the problem were analyzed. The first one is the adequate description of turbulence. The result is the simulation of the evolution of the refractive index due to turbulence. The second one is the beam focusing on condition that the refractive index is subject to spatial and temporal variations. The turbulence was simulated with the aid of the solution to the Navier-Stokes equations. Three kinds of initial conditions were used: (i) the vortical field was given, the velocity divergence (dilatation) being zero and the temperature being constant; (ii) the velocity divergence was given, the vorticity being zero and the temperature being constant; (iii) there is a temperature distribution, the vorticity and the dilatation being zero. In all cases, the initial values of the density are constant. The problem is set in the infinite space, the initial data being random functions. The solution of the Navier- Stokes equations was reduced to the solution of integral equations of the Volterra type. The iterative procedure was used. The comparison of the subsequent iterations allows to conclude that the convergence takes place. The problem of compensation for turbulent distortions of a laser beam was solved. The resolving function determines the necessary deformation of the mirror. The knowledge of the resolving function indicates the way to the beam focusing in the turbulent atmosphere.

Laser beam propagation through an ensemble of vortex rings in air

The problem of the evolution of an ensemble of vortex rings in air has been solved. The full system of the Navier -Stokes equations was used. The parametrix method was applied. The calculations were performed for a wide range of the ring parameters (circular and elliptic cross-sections, various diameters of the rings, their different orientation in the space etc.). The initial value problem is as follows. The vorticity has non-zero value only inside the rings at initial instant, the density and the temperature being constant everywhere at t=0. If the density is known, then it is possible to find the refractive index. The solution to the Navier-Stokes equations is an oscillating one. Thus the refractive index is an oscillating function with respect to time. These results enable to model turbulence in an adequate way without using the Taylor frozen turbulence hypothesis. The evolution of the frequency spectrum of the density fluctuations was obtained. These results were compared with Tatarskiis data. The intensity of a laser beam propagating through the ensemble of vortex rings in air was found with the aid of the parabolic equation method. A numerical procedure is set forth which allows to solve the problems of superresolution without using regularization methods. The task is as follows. There is a set of experimental data and an instrument function (with some error). We change the domain in such a manner that the corresponding MTF has nowhere zero values. The procedure enables to solve problems of focusing in the turbulent atmosphere.

Local-linear method of super-resolution for compensation of image distortions using new model of turbulence

Atmospheric turbulence is one of the important factors that influence on scene spatial resolution. In order to restore an image with minimum distortions one must know the correlation function for fluctuations of refractive index and the distorting PSF as a result. Grid-generated turbulence is a classic example of homogeneous and isotropic turbulence. Statistical properties of this flow have been investigated experimentally. In our case of grid-generated turbulence the statistical properties are distinct from the Kolmogorovs two-thirds law. Calculations performed on the basis of the linearized three-dimensional unsteady Navier-Stokes equations gave similar results. We modelled laser beam propagation through turbulent atmosphere and obtained numerical data for the distortion of images. The distortion of PSF and the set of resolving functions were found according to the structure function. The problem of compensation of distortions caused by turbulence was solved with the aid of a new local-linear super-resolution method. This method allows to resolve turbulent distortions of PSF at low signal-to-noise ratio.

Superresolution when PSF is indefinite

Situation when Point Spread Function (PSF) of the device is indefinite or it is roughly appreciated takes place almost always. In an optical wave range PSF (optics + atmosphere) is frequently indefinite, because of an indefinite conditions of scattering and turbulence of an atmosphere. The antenna pattern or PSF of radio telescopes cannot be measured. The near zone of the radio telescopes is so big that it does not allow to measure the antenna pattern or PSF by the ground based methods. The methods of evaluation of PSF on details of the images are considered in the repot. The received estimation of PSF is used for the solution of task (compensation of PSF distortions) super-resolution.

Problems of precise air-spatial monitoring

The designers of modern devices of vision prefer to choose a scanning step of receiving system antenna with some less size than the main lobe of Point Spread Function (PSF). They tell such systems are good constructed. However there is a problem of additional increase of resolution for such well constructed receiving system. This problem is naturally connected with improvement of mathematical models. The report is devoted to development and applications of local-linear method of additional enhancement of resolution for such receiving system in radio vision and optics.

Optimization of radiovision systems in millimeter-wave range

Method of optimization is considered to improve resolution and noise properties of millimeter-wave radio vision system. Conditions of optimal measurements are realized by coincidence of bandwidths both of signals and device.

Grid turbulence and its interaction with a shock wave

Turbulent fluctuations of density and pressure in air and argon in a shock tube have been investigated as well as their interaction with a shock wave reflected from a perforated plate at the end of a shock tube. Air and argon were used as test gases. The Mach number of the incident shock was 1.9–3.9, that one of the reflected shock was 1.4–2.4. The turbulent length scale behind the incident shock was measured as well as that one behind the reflected shock. The last value is a few times less than the former. It was established that there is overpressure in the turbulent flow behind the reflected shock. The value of the overpressure is 12% in argon and 9% in air.

Density oscillations generated by vortex rings and their effect on scintillation of a Gaussian beam

Density oscillations in the vicinity of vortex rings in air have been investigated. The calculations were fulfilled on the basis of the Navier-Stokes equations. We used series expansions of unknown functions in powers of a parameter which characterizes vorticity. As a result, we got a non-uniform system of parabolic differential equations with constant coefficients. The frequency of oscillations depends only on the dimensions and the shape of the ring in the case of small vorticity (weak turbulence). We analyzed oscillations generated by rings with circular cross-section. The size of the rings varied in a wide range. It includes inertial range and dissipation range. It is interesting to note that first of all the amplitude of oscillations increases, reaches its maximum and then decreases up to zero. These data can be used for modeling the propagation of a Gaussian beam through the turbulent atmosphere. We analyzed intensity fluctuations (scintillations) of the beam after the passage through the non-uniform region which contains vortex rings. We considered an ill-posed problem (that of super-resolution) connected with image restoration. In such cases if the input data are slightly changed, the solution may vary considerably. The proposed procedure is as follows. We change the instrument function in such a manner that it will be reversible one within the limits of accuracy. The procedure enables to solve some problems referring to the turbulent atmosphere. Ke

Problems related to the beam propagation in the tubulent atmosphere

Related problems are as follows: (i) evolution of the vortical structures which play an important role in turbulence; (ii) laser beam propagation through turbulence; (iii) object-targeting problem. The parametrix method was used. The convergence of the coupled iterative procedure was discussed. We investigated the influence of a point thermal source on the vorticity of a cylindrical vortex. We revised the 3D object-targeting problem.