Том 52, № 6 (2016)

Original codes and combinatorial-geometrical computational schemes are presented, which are developed and applied for finding exact analytical formulas that describe the probability of errorless readout of random point images recorded by a scanning aperture with a limited number of threshold levels. Combinatorial problems encountered in the course of the study and associated with the new generalization of Catalan numbers are formulated and solved. An attempt is made to find the explicit analytical form of these numbers, which is, on the one hand, a necessary stage of solving the basic research problem and, on the other hand, an independent self-consistent problem.

Issues related to measuring the information parameters of signals reflected from an object under correlated additive non-Gaussian noise are considered. It is shown that in the presence of correlated non-Gaussian noise, increasing the correlation coefficient increases the generalized signal/noise ratio, which, in turn, improves the measurement accuracy of signal parameters. The obtained dependences confirm that the measurement error of signal information parameters is affected not only by the generalized signal/noise ratio, but also by accounting for the non-Gaussian nature of the additive noise, which leads to a significant improvement in the measurement accuracy of these parameters.

Results of developing control algorithms for an active power filter operating as a fast-response current source are presented which provide a significant improvement in the energy consumption performance in the case of a nonlinear load of arbitrary form with a simultaneous possibility of generating reactive power at the fundamental frequency.

Specific features of half-plane image formation in a spatially noninvariant (aberration-free) coherent optical system of the 2F–2F telecentric type with a limited aperture of the projection objective (in the absence of the spatial frequency filter) are studied. The dependence of the light intensity behavior at a point corresponding to the half-plane edge in the image on the object position is found in an analytical form on the basis of approximating the Fresnel functions by analytical functions. As the half-plane approaches the boundary of the field of vision of the system determined by the objective aperture diameter, the light intensity is demonstrated to deviate significantly from that in the case of the axial position of the half-plane, which may lead to noticeable measurement errors in inspecting the geometric parameters of objects by the projection method in transmitted light.

Results of studying an original method of the modulated optical radiation spectrum analysis and testing a simple detector based on the Fabry–Perot interferometer are reported. The theoretical analysis of detector operation is compared with model experiment results. A possibility of using this analyzer for measuring the characteristics of ultrahigh-frequency modulators of optical radiation operating at modulation frequencies from 10 to 100 GHz and higher is noted.

A method of measuring the velocity of Hilbert-visualized phase structures by means of emulation of two-dimensional spatial filtering of their images formed on the matrix of a digital camcoder is discussed. As an example, visualized fields of the phase optical density in convective flows induced in a high-viscosity fluid are considered. Investigations of this kind of flows are useful for simulating the Earth’s mantle behavior at large depths.

This study describes the laser generation of a 6Zh rhodamine in artificial opals representing single-crystal and heterostructure films. The spectral and angular properties of emission and the threshold characteristics of generation are investigated. In the case where the 6Zh rhodamine was in a bulk opal, the so-called random laser generation was observed. In contrast to this, the laser generation caused by a distributed feedback inside the structure of the photonic bandgap was observed in photonic-crystal opal films.

The development of additive technologies and their application in industry is associated with the possibility of predicting the final properties of a crystallized added material. This paper describes the problem characterized by a dynamic and spatially nonuniform computational complexity, which, in the case of uniform decomposition of a computational domain, leads to an unbalanced load on computational cores. The strategy of partitioning of the computational domain is used, which minimizes the CPU time losses in the serial computations of the additive technological process. The chosen strategy is optimal from the standpoint of a priori unknown dynamic computational load distribution. The scaling of the computational problem on the cluster of the Institute on Laser and Information Technologies (RAS) that uses the InfiniBand interconnect is determined. The use of the parallel code with optimal decomposition made it possible to significantly reduce the computational time (down to several hours), which is important in the context of development of the software package for support of engineering activity in the field of additive technology.