Computer Optics

590-597

Authors: D. A. Bykov, L. L. Doskolovich

Diffraction of a 3D optical beam from a resonant multilayer structure (phase-shifted Bragg grating) is considered. It is shown that the said structure enables optical computation of the spatial Laplace operator of the electromagnetic field components of the incident beam. The computation of the Laplacian is performed in reflection at normal incidence. Presented numerical results demonstrate high quality of the Laplace operator computation. The beam transformation performed in transmission is also investigated.

606-613

Authors: S.S. Stafeev, L. O’Faolain, M.I. Shanina, A.G. Nalimov, V.V. Kotlyar

Using a binary microlens of diameter 14 µm and focal length 532 nm (numerical aperture NA = 0.997), we focus a 633-nm laser beam composed of a mixture of radially and linearly polarized waves obtained by reflection of a linearly polarized Gaussian beam from a gold-coated subwavelength binary four-zone diffractive optical microelement (micropolarizer) of size 100×100 µm to a near-surface, near-circular focal spot of size (0.37±0.02)λ and (0.39±0.02)λ, where λ is wavelength. A linearly polarized light beam forms an elliptical focal spot with diameters (0.35±0.02)λ and (0.41±0.02)λ. Both focal spots have the area of 0.133λ². Subwavelength focusing using two microoptical components (a binary microlens and a micropolarizer) is suggested for the first time.

619-622

Authors: D.I. Zavershinskiy , N.E.Molevich

Earlier, we demonstrated the possibility of energy transfer from unstable acoustic waves into Alfven waves due to a process of three-wave interaction of collinear waves. In this paper, we briefly discuss cooling mechanisms and possible heating scenarios of an optically thin plasma medium. The upper layers of the solar atmosphere have been chosen as the model medium. By the use of two cooling function models we obtain temperature intervals in which the instability can take place and calculate acoustic increments for all heating scenarios.

629-637

Authors: S.A. Degtyarev, A.V. Ustinov, S.N. Khonina

We show that the near-field nanofocusing of the electromagnetic field is possible to implement not only by means of metallic but also dielectric structures with sharp edges. The effect of the extraordinary enhancement of the longitudinal electric field component near the sharp edges of an optical element microrelief is shown using vector Rayleigh-Sommerfeld integrals. A finite element method is used for modeling the diffraction of the electromagnetic radiation by the edges of high-refractive-index metal and dielectric structures. It is shown that the focal spot size (full width at half-maximum) depends on the radius of curvature of the sharp tip. An optical scheme for sharp focusing, which consists of a concentrator collecting and directing the radiation onto a nano-focuser, is offered. A refractive axicon is suggested as the concentrator that directs the radiation on its vertex where an aluminium or silicon nanosphere is located (a nanofocuser). Illumination of this focuser by an optical vortex beam provides the nanofocusing with high diffraction efficiency. It is necessary to illuminate an axicon by a vortex beam of the first order or by a radially polarized beam. The scheme proposed is able to confine the radiation within a light spot of size l/400 at the half maximum of the intensity.

643-650

Authors: A.O. Gorbunova, I.P. Zavershinskii, N.E. Molevich, D.P. Porfirev

Numerical simulation of non-stationary vortical plasma-gas-dynamic structures formed in a swirl flow in the open tube under the RF-electromagnetic field is conducted. It is shown that when the external RF-field coincides with the resonator’s eigenfrequency, an abrupt jump of gas-dynamic fluctuations and corresponding changes in the discharge structure take place.

658-662

Authors: A.A. Kovalev, V.V. Kotlyar, A.P. Porfirev

With use of a liquid crystal phase-only spatial light modulator, we generate form-invariant Half-Pearcey laser beams (HP-beams), which were recently proposed by the present authors [Computer Optics, v. 38, no. 2 (2014)]. It is experimentally shown that upon propagation the HP-beams preserve their shape up to a scale and rotate by 180 degrees. These beams have the ability to auto-focus and reconstruct their intensity pattern after partial distortion by an amplitude defect (property of self-healing). The amplitude and phase of the HP-beam were encoded with the modified two-phase algorithm. Ignoring the amplitude and using only the phase leads to greater distortions of the HP-beam comparing with the two-phase encoding algorithm.

670-680

Authors: S.N. Khonina, A.V. Ustinov, S.A. Degtyarev

We consider the diffraction of Gaussian beams by a cylindrical axicon whose numerical aperture (NA) is close to or higher than a limiting value (when the incident wave is assumed not to pass through an element). Three models of diffraction were considered: the ray approach, the vector wave theory with a thin optical element approximation and the solution of Maxwell’s equations by the finite elements method. Although in the ray approach the limiting NA corresponds to the total internal reflection (TIR), the analysis of the ray path has shown that with increasing NA (narrowing axicon’s angle) a proportion of energy leaks through the lateral sides, forming a diverging beam. In the wave theory, energy dissipation in lateral directions also occurs, but evanescent waves play a special role in the element’s near-field zone. In this case, the analytical estimations for the electric field components have been obtained in a thin element approximation. Application of the finite element method to Maxwell’s equations has shown that for optimal concentration of energy at the refractive element’s tip its NA should be increased (by narrowing the axicon’s angle or by increasing the material refractive index) only until the TIR occurs. The further increase of the NA results in both the reflection of rays from the flat surface and their output from the lateral sides.

686-688

Authors: I.V. Alimenkov, Y.Z. Pchelkina

Solutions of the expanded pulse-propagation equation are derived in elementary functions in optical fibers for competing nonlinearit.

695-703

Authors: A.G. Poleshchuk, A.G. Sedukhin, V.I. Trunov,V.G. Maksimov

A theoretical and experimental study of a Hartmann sensor intended for measurements of light beam wavefronts and implemented on the basis of multielement amplitude masks with apodized apertures is presented. We perform a comparative analysis of the optical performance of the amplitude masks with hard-edge circular apertures and half-tone masks (HTMs) with apodized apertures forming smooth fast decaying optical responses on a photosensor. A technique for fabricating chromium HTMs is developed, which is based on laser thermochemical method of recording. This technique includes two main stages: first – the exposure of a chromium film by a focused laser beam, whose power is varied in a smooth and nonlinear manner versus the required density of HTM’s structure, and second – the developing of the film in a selective etcher. Specimens of HTMs consisting of 64×64 Gaussian apertures were fabricated and applied in a modified Hartmann sensor to measure the wavefront of powerful laser systems.

710-716

Authors: A.V. Belashov, N.V. Petrov, I.V. Semenova

A method for calculating the difference between two arbitrary spatial phase distributions reconstructed from digital holograms is presented. The method is promising for application in double-exposure digital holographic interferometry, especially for the evaluation of phase variations in heavily noised or speckle-structure-modulated digital holograms, because it does not use the phase unwrapping procedure for each reconstructed spatial phase distribution. Instead, by analogy with classical double-exposure holographic interferometry, an interference pattern formed by two reconstructed object waves is calculated first. The interferogram thus obtained is then processed as a digital hologram by the same method that was used for reconstruction of physically recorded holograms. The advantages of the proposed method are demonstrated by both by the numerical computation of the difference of the phase distributions of speckle-structure-modulated wavefronts and the experimental observation of the laser-induced temperature gradients in an aqueous solution of a photosensitizer.

722-726

Authors: A.P. Porfirev, R.V. Skidanov

We demonstrate optical trapping and movement of a carbon nanoparticle agglomeration with both a single optical bottle beam and arrays of such traps. Diffractive optical elements (DOE) designed by a method based on a superposition of the Bessel beams were employed for the generation of the optical traps. Due to the structure of the generated traps, we were able to carry out a three-dimensional movement of trapped microscopic objects.

737-742

Authors: R.V. Kutluyarov, A.H. Sultanov, V.H. Bagmanov

We consider interaction of polarization-mode dispersion (PMD), Kerr-nonlinearities and chromatic dispersion and its effect on the quality of WDM-transmission in a fiber link. We simulate the propagation of RZ- and NRZ-coded signals in a multispan link with optical amplification and chromatic dispersion compensation. For some fiber realizations signal impairments reduction occurs in the case of PMD and nonlinearities interaction as compared to the case of nonlinear transmission with no PMD. This signal enhancement is related to the pulse compression and this phenomenon is determined by the frequency dependence of PMD.

749-756

Authors: A.A. Zvekov, A.V. Kalenskii, A.P. Nikitin, B.P. Aduev

The radiative transfer equation in a slab with Fresnel boundaries was solved by the spherical harmonics method in the case of a transparent medium containing aluminum nanoparticles. A computer program was developed, the angular radiance distribution on the slab boundaries and in the slab center were calculated. It was concluded that Fresnel boundary conditions make the angular distribution on the slab boundaries asymmetric. The use of angular radiance distribution for solving the reverse problems of scattering spectroscopy was discussed.

763-769

Authors: A.N. Agafonov, B.O. Volodkin, A.K. Kaveev, B.A. Knyazev, G.I. Kropotov, V.S. Pavelyev, K.N. Tukmakov, Yu.Yu. Choporova

Experimental results on forming pre-given laser modes from an illuminating Gaussian beam of a terahertz Novosibirsk Free Electron Laser (NovoFEL) at the wavelength of 141 mm by use of binary silicon diffractive optical elements are presented. The experimental results are in good agreement with the results of computer simulation.

777-781

Authors: L.L. Doskolovich, E.A. Bezus, D.A. Bykov

We analyze the performance of a diffraction-grating-based Offner spectrometer. We use the paraxial approximation to derive analytical expressions for the spatial and spectral point spread function for each diffraction order. We show that a disruptive effect of the diffraction orders overlap occurs. However, it can be compensated for by means of simple image post-processing.

790-793

Authors: E.V. Myasnikov

This paper considers two approaches to the hierarchical decomposition of the feature space to improve the efficiency of the non-linear dimensionality reduction method. The first approach suggested by the author of the paper is based on the decomposition of the original feature space using hierarchical clustering. The second original approach is based on a hierarchical decomposition of the target space by using a KD-Tree. The approaches analyzed are evaluated in terms of the efficiency of the non-linear dimensionality reduction method.

804-810

Authors: N.L. Kazanskiy, V.I. Protsenko, P.G. Serafimovich

Comparison of two streaming systems: Apache Storm and IBM InfoSphere Streams was performed in solving image sliding window filtering task. Analysis was focused on two parameters: throughput and memory consumption. Profiling was held under CentOS operating systems running on two virtual machines for each system. First, the most cheap in developing cost realizations were compared. After analysis optimization of memory consumption was performed. Final suggestions on applicability of two systems were made at the end of the article.

818-824

Authors: М.А. Shcherbakov, A.P. Panov

Different approaches to the construction of digital nonlinear filters that operate by use of local image properties are offered. Structures of nonlinear filters with variable nonlinear-component weight and parametric adaptation are considered. The effectiveness of the proposed methods of filtering is illustrated by the examples of the additive Gaussian and impulse noise suppression.

833-842

Authors: M.A. Dryuchenko, A.A. Sirota

A steganography algorithm based on a relatively low-frequency spatial deformation of full color image fragments is considered. Correlation properties for the color channels of images are used for extraction of hidden data. Results of the algorithm application are presented.

851-855

Authors: N.Yu. Ilyasova, A.V. Kupriyanov, R.A. Paringer

The computer diagnostic system of eye diseases is considered. To improve the quality of diagnostics we propose an algorithm for the informative features formation, using methods of discriminant analysis. The method for receiving an informtiveness estimation is described. The research confirming the efficiency of the formed features for classification of images of an fundus was conducted by means of classification by support vector machine. The algorithm possesses a sufficient level of universality and may be applied to increase the informtiveness of any feature set.

865-870

Authors: A.Yu. Kruchinin

We introduce an algorithm for the recognition of two-dimensional industrial codes DataMatrix that would allow one to identify codes applied by a shock-point or a drip method on the surface with a complex background. The algorithm can be adapted to a varying background by changing the binarization mode.

881-885

Authors: M.S. Kasparyan

We introduce a generalized sine-cosine transform (GSCT). Analytical conditions of orthogonality of these transformations are derived. A theorem that allows one to find the relation between the GSCT coefficients in the orthogonal case is proven. Fast algorithms for computing the GSCT are considered and their complexity is analyzed.

372-376

Authors: N.V. Golovastikov, D.A. Bykov, L.L. Doskolovich

The diffraction of a 2D optical beam upon a multilayer Bragg structure is considered. It is shown that phase-shifted Bragg grating can perform spatial integration in transmission of a 2D incident beam in the vicinity of the angular frequency associated with the excitation of a quasi-guided mode confined to the defect layer. The integration is fulfilled with an exponential weight function which fades away as the quality factor of the resonance increases. Beam propagation simulation results are in close agreement with provided theoretical description.

380-385

Authors: E.S. Kozlova, V.V. Kotlyar

Truncated ellipsoid which all parallel incident rays collects on it’s flat surface is designed. Simulation by (FD)2TD method of focusing of femtosecond pulse (duration 1.24 fs and the carrier wavelength λ = 532 nm) by a silica truncated microellipsoid with smaller cross-sectional diameter of 1.16 mm showed that the ellipsoid gives an elliptical focus spot with a smaller diameter FWHM = 0,38 λ. At the same time the pulse duration at the focus of a few percent smaller than the duration of the incoming pulse.

393-396

Authors: D.A. Kozlov , V.V. Kotlyar

In this paper we provide a numerically obtained result for analytical solution for the problem of monochromatic nonparaxial Gaussian beam diffraction by uniform dielectric cylinder, which yields a focal spot outside the cylinder with linear sizes twice less than the diffraction limit in the free space in case of cylinder radius comparable with the wavelength. Although the radius of cylinder is only two times larger than the wavelength, the produced intensity in focal spot is 48 times larger than the maximal intensity of incident Gaussian beam. Two percent deviation from the resonant radius (for a fixed wavelength) causes the focal spot increase in half, and the resulted intensity in focal spot drop to value of 12 times greater than the incident beam intensity. Obtained solution corresponds to the growth of the Bessel function of order 18 coefficient in E-field amplitude Bessel series expansion.

402-411

Authors: A.V. Ustinov, S.N. Khonina

In previous studies we shown on the basis of the geometrical-optical analysis that the fracxicon (generalized optical element of the parabolic lens and the linear axicon) formally produces an infinitely large value of the intensity on the optical axis. Within frame of the paraxial wave model this caustic effect was not found. In this paper, we consider plane wave diffraction on the fracxicon in nonparaxial wave model and we show that at high numerical aperture the fracxicon with an exponent close to 3/2, is actually analogue of the hyperbolic lens optimally focusing incident beam.

418-424

Authors: G.I. Greisukh, E.G. Ezhov, S.V. Kazin, Z.A. Sidyakina, S.A. Stepanov

Adverse impact of the diffraction orders on visually assess the quality of the image formed by refractive-diffractive optical system is investigated. It is shown that if the microstructure of diffractive lenses used in the optical system has a saw-tooth profile and brightness variations in the photographed scenes that are not extreme, the adverse diffraction orders practically not reduce of the system's frequency-contrast characteristic, and the halo does not have any significant negative impact for visual perception of the image.

435-442

Authors: S.V. Kravchenko, M.A. Moiseev, L.L. Doskolovich

New optimization method for design of refractive optical elements with two free-form surfaces is presented. Algorithm of design consists of two parts: generation of initial approximation and the further optimization of outer surface parameters from condition of producing prescribed illuminance distribution. As an example the optical element generating uniformly illuminated rectangular region with angular sizes 60° × 40° with extended 1x1 mm Lambertian light source is computed. The light efficacy of optical element is about 88,5% and the relative root-mean-square error of generated illuminance distribution is less than 8,5 %.

449-455

Authors: K.V. Borisova, M.A. Moiseev, L.L. Doskolovich, E.S. Andreev

A numerical-analytical approach is proposed for designing reflective surface producing prescribed irradiance distribution on the curve with specified shape. Method consists of two steps: computation of eikonal function on curve and reconstruction of the reflective surface using precomputed eikonal function. Reflective surface generating spiral line and module of backlight system for displays are designed. The simulation results demonstrate high-quality of the proposed method: light efficiency of backlight system is 86.5 % and uniformity of illuminance distribution is 93 %.

463-468

Authors: R.V. Skidanov, S.V. Ganchevskaya

Was considered the formation of Bessel beams by vortex axicons with different topological charges patterns. Presented the results of mathematical simulation and experiments.

476-481

Authors: V.G. Volostnikov, S.A. Kishkin, S.P. Kotova

The paper brings forward a theoretical study of the usability of the mathematical apparatus of spiral beams for problems of the contour images identification. The estimation of the approach offered is given in the light of its advantages and shortcomings, numerical simulation results are offered and the method applications aspects are analyzed in the context of actual practical tasks.

489-493

Authors: A.M. Belov, V.V. Myasnikov

The paper presents a method of atmospheric correction of spaceborne hyperspectral images. The method based on approximate solution of MODTRAN transmittance equation using simultaneous analysis of spaceborne and airborne hyperspectral images.

503-510

Authors: D.A. Zherdev, N.L. Kazanskiy, V.A. Fursov

In the work study the object recognition problem by the radar signatures of scattering reflected electromagnetic radiation. As template we use diagrams that made by computing the scattering field of 3d object models. The conjugation index with so-called support subspace that formed by attribute vectors of recognition class used in recognition as metric distance. Recognition quality in depending upon the dimension of support subspaces is studied. In work give comparison of result obtained by support vector machine and the compute correlation index with average class vector.

521-528

Authors: Y.Y. Ogorodnikov, R.T. Faizullin

The paper presents two heuristic methods of recognizing zero bits satisfiability problem. The first is based on the reduction of the satisfiability problem to an equivalent problem of minimizing a continuous smooth function by method of successive approximations, extended by changing the order of calculation of variables. Another way is to reduce to a system of linear algebraic equations with symmetric diagonally dominant matrix.

539-549

Authors: A.A. Agafonov, V.V. Myasnikov

A problem of traffic flow analysis and prediction in city transport network is considered in this paper. The proposed algorithm uses GPS / GLONASS data of public transport location as input. Projecting this information on a transport network graph, as well as using additional filtering, we estimate traffic flow parameters. These parameters are used for short-term (up to 1 hour) prediction of road conditions in the city transport network. There is proposed a new method which consists of several steps to construct prediction. First, the transport graph is divided into a number of subgraphs by a territorial basis. Second, we use a dimension reduction method based on principal components analysis to describe the spatio-temporal distribution of traffic flow condition in the subgraphs. Third, an elementary prediction for each of the subgraphs is formed using the potential functions method with the measure of the subgraphs descriptions closeness introduced by analogy with bilateral filtering and support vector machine. Fourth, the additional elementary prediction is calculated using the known scalar and vector Box–Jenkins time series prediction models. Fifth, we construct the result prediction for each of the subgraphs using an adaptive linear composition of elementary predictions. At last, the traffic flow parameters are calculated as a linear combination of predictions for subgraphs of the city transport network. We have also made experimental investigations of transport network in Samara to evaluate the prediction accuracy of the proposed algorithm. The advantages of the proposed solution in comparison with existing ones are provided.

555-563

Authors: A.V. Verichev, V.A. Fedoseev

The paper presents a digital watermarking scheme robust to geometric distortions of an image. The proposed scheme is based on Delaunay tessellation built on a set of feature points. Various feature points extraction methods are outlined and the best one for the watermarking scheme is chosen. Embedding and extracting algorithms are presented, emphasize being on the procedures of perceptual masking of the embedded watermark according to the human visual system. Numerical experiments are performed to demonstrate robustness of the proposed watermarking scheme to a wide range of geometric distortions.

574-579

Authors: D.G. Asatryan, V.V. Kurkchiyan, L.R. Kharatyan

In this paper, novel method for texture analysis and classification based on using image structural properties is proposed. It is known that the Human Visual System successfully perceives an image content by visualized collection of existing edges. In this paper, we propose to use the collection of gradient magnitudes as the characteristics of the structure of an image. Gradient magnitude is assumed to be a random variable with two-parameter Weibull distribution, and as a characteristic of the proximity of the two images we use a special measure of proximity of the parameter estimates of the corresponding distributions. Classification is made by method of comparison with the etalon using the database of the University of Heidelberg (Germany) which contains 10 texture classes. As an etalon is used the set of average values of the parameters estimates of the Weibull distribution, calculated by the magnitude gradients of training set of texture, and comparison is performed using the proposed proximity measure. The analysis revealed two virtually indistinguishable classes, and for the remaining eight classes it is shown that the classification error on the average is about 18%.

162-170

Authors: V.V. Kotlyar, A.A. Kovalev, R.V. Skidanov, V.A. Soifer

We considered a new three-parameter family of rotating asymmetric Bessel-Gaussian beams (aBG-beams) with integer and fractional orbital angular momentum (OAM). Complex amplitude of aBG-beams is proportional to a Gaussian function and to n-th order Bessel function with complex argument. These beams have finite energy. The asymmetry ratio of the aBG-beam depends on the real parameter c ≥ 0. For c = 0, the aBG-beam coincides with the conventional radially symmetric Bessel-Gaussian beam, with increasing c intensity distribution of the aBG-beam takes the form of Crescent. At c >> 1, the beam is widening along the vertical axis while shifting along the horizontal axis. In initial plane, the intensity distribution of asymmetric Bessel-Gaussian beams has a countable number of isolated zeros located on the horizontal axis. Locations of these zeros correspond to optical vortices with unit topological charges and opposite signs on different sides of the origin. During the beam propagation, centers of these vortices rotate around the optical axis along with the entire beam at a non-uniform rate (for large c >> 1): they will rotate by 45 degrees at a distance of the Rayleigh range, and then by another 45 degrees during the rest distance. For different values of the parameter c zeros in the transverse intensity distribution of the beam change their location and change the OAM of the beam. Isolated intensity zero on the optical axis corresponds to an optical vortex with topological charge of n. Laser beam with the shape of rotating Crescent has been generated by using a spatial light modulator...

181-187

Authors: N.L. Kazanskiy, P.G. Serafimovich

In this paper we propose and numerically investigate an all-optical temporal integrator based on a photonic crystal cavity. We show that an array of photonic crystal cavities enables high-order temporal integration. The effect of the value of the cavity’s free spectral range on the accuracy of the integration is considered. The influence of the coupling coefficients in the resonator array on the integration accuracy is demonstrated. A compact integrator based on a photonic crystal nanobeam cavity is designed, which allows high-precision integration of optical pulses of subpicosecond duration.

193-197

Authors: A.A. Kovalev, V.V. Kotlyar, S.G. Zaskanov

We obtain a new solution of the paraxial Helmholtz equation that describes a family of three-dimensional and two-dimensional structurally stable half-Pearcey beams (HP-beams). HP-beams generalize Pearcey beams obtained in Opt. Express, 20, 18955 (2012), since these Pearcey beams can be considered as the sum of two first-order HP-beams. Three-dimensional HP-beams have angular spectrum of plane waves, which is non-zero at a half of parabola. For functions of HP-beams complex amplitudes, the orthogonality properties have been revealed. For two-dimensional HP-beam acceleration and deceleration of trajectory has been shown for areas before and beyond the focal plane respectively.

204-206

Authors: I. V. Alimenkov, Yu.G. Pchelkina

We found in quadratures the solution of expanded pulse – propagation equation for optical fibers for an arbitrary nonlinearity.

213-222

Authors: A.V. Ustinov, S.N. Khonina

The theoretical analysis of plane wave diffraction by axicon in the zone of evanescent waves is executed. The received analytical estimations are qualitatively in accordance with results of numerical calculations in nonparaxial scalar wave model.

229-236

Authors: A.G. Nalimov, L. O'Faolain, S.S. Stafeev, M.I. Shanina, V.V.Kotlyar

A four zone subwavelength binary diffraction optical micro element (size of 100x100 mkm) for polarization transformation from linear to radial was calculated and designed. A grating period was equal to 400 nm, a height of the element was equal to 110 nm in a gold film for a wavelength of 633 nm. Simulation by FDTD method and Rayleight-Zommerfeld integral shown, that despite only four zones used for polarization transformation to four different angles there are radial polarized light beam in the far field with smooth angle dependence on the beam circle observation position. Experimentally shown that in the near field, depending on the direction of the axis of the polarizer on the output light are two zones 4-zone trace element for one or the other diagonal, which proves the presence of radial polarization in the reflected beam.

243-248

Authors: A.P. Porfirev, R.V. Skidanov

We propose a new method of shaping nondiffracting hollow optical beams (HOB’s), the intensity distribution of the cross-section of which have the shape of the simple geometrical figures. This method is based on interference of two coaxial Bessel beams. These beams can be used as optical traps for controlled manipulation of non-spherical microobjects.

256-270

Authors: N.L. Kazanskiy, S.I. Kharitonov, S.N. Khonina, S.G. Volotovskiy, Yu.S. Strelkov

Article is devoted to simulation of hyperspectrometer based on the use of linear variable filters. We regarded possibilities of recovery of spectral pixels of images based on the solution of the integral equation. The paper presents estimates of the size of the scattering spots depending on the parameters of the spectral filter. Numerical results showed that a significant deterioration in resolution occurs only in the case of short-optical systems.

281-286

Authors: E.A. Zimichev, N.L. Kazanskiy, P.G. Serafimovich

A complex spectral–spatial classification scheme for hyperspectral images is proposed and explored. The key feature of method is using widespread and simple enough algorithms while having high precision. The method combines the results of a pixel wise support vector machine classification and the segmentation map obtained by partitional clustering using majority voting. The k-means++ clusterization algorithm is used for image clustering. Principal component analysis is used to prevent redundant processing of similar data. The proposed method provides improved precision and speed of hyperspectral data classification.

297-303

Authors: A.Yu. Denisova, V.V. Myasnikov

The authors propose two algorithms of linear spectral mixture analysis for hyperspectral images using base map. Base map data are used to refine coefficients of spectral mixture on the edges of map objects (in first algorithm) and acquire spectral signatures of small objects (in second algorithm), that does not occupy any pixel on input image entirely. The set of mixed signatures may be already known with undefined coefficients or unknown with extraction on one of the stages of the algorithm.

314-321

Authors: O.O. Evsutin

This paper is aimed at receiving orthogonal bases families from the evolving states of cellular automata. I suggest a comparison technique of the appropriate orthogonal transformations in respect of noises, shown as a result of information losses on the restored data elements.

330-334

Authors: P.S. Bogdanov, V.M. Chernov

In this paper fractal dimension of fundamental domain boundary for all possible ternary quasicanonical numerical system in the ring of Eisenstein integers is calculated. Modified method that was used by W. Gilbert and J. Thuswaldner for computing of fundamental domain boundary fractal dimension for canonical numerical system is considered.

343-350

Authors: V.P. Bessmeltsev, E.D. Bulushev

We investigated the possibility of fast quality control of laser micromachining of surface based on optical measurements. The main objective is to match CAD-model and 3D geometry of the machined surface. We found that standard matching algorithms have either low performance or are ineffective at high noise level or at presence of geometrical distortion. The algorithm based on Ciratefi algorithm, which previously wasn’t used for image registration, was developed. The performance of algorithm was increased by using an iterative search of optimum based on image pyramid. The testing of algorithm on height maps of objects formed by laser methods showed its high accuracy and performance.

356-368

Authors: A.A. Agafonov, V.V. Myasnikov

The problem of precise arrival time of public transport is considered in this paper. There is proposed a new prediction algorithm based on adaptive composition model using elementary prediction. A small number of adaptive parameters characterizes each elementary prediction algorithm. Adaptability means that parameters of the constructed compositions depend on a number of control parameters of the model, which includes the following factors: weather conditions, traffic density, driving dynamics, prediction horizon, etc. Adaptability is achieved by introducing a hierarchical decomposition range of control parameters used in regression tree. We made experimental investigations on real routes of city public transport in Samara to evaluate the prediction accuracy of the proposed algorithm. We also explain the advantages of the proposed solution in comparison with existing ones.

4-10

Authors: V.V. Kotlyar, A.A. Kovalev, V.A. Soifer

This paper introduces a new family of diffraction-free asymmetric elegant Bessel beams (EB-beams) with fractional orbital angular momentum (OAM). EB-beams are modes of free space and described by the n-th order Bessel function of the first kind with a complex argument. Functions of complex amplitudes of EB-beams are orthogonal by continuous scaling parameter and not orthogonal on a discrete parameter (topological charge). The intensity distribution of EB-beams has a countable number of isolated zeros of intensity, located on the horizontal axis. These zeros are centers of optical vortices with unit topological charge and opposite signs on different sides of the origin. Isolated intensity zero on the optical axis generates an optical vortex with topological charge of n. OAM of the EB-beams is (n + 0,69777)h per photon, where h is the Planck's constant.

20-27

Authors: E.Yu. Buldygin, D.L. Golovashkin, L.V. Yablokova

The technique of searching of the collateral finite – difference solution of a wave equation and set of equations of Maxwell is offered, allowing to combine advantage and to avoid shortcomings of both made mention numerical methods of nanophotonics (to reduce expenses of memory and to apply well-known TF/SF and PML techniques). In a two – dimensional case on test examples convergence of such decision, possibility of imposing of PML-ayers and a task of an incident wave on the TF/SF technology are shown.

31-37

Authors: A.A. Kovalev, V.V. Kotlyar, S.G. Zaskanov

We propose a method of obtaining solution of the paraxial Helmholtz equation which describes two-dimensional light beams accelerating on a finite interval of the trajectory. Method based on complex conjugation and shift along the longitudinal coordinate (parallel to the optical axis) of the complex amplitude of the slowing light beams. Using this method we obtained Fresnel and Laplace beams, as well as "half-Bessel" beams, accelerating along the trajectory in a form of square root. It has been observed that the well-known Hermite-Gaussian light beams are also accelerating beams with a hyperbolic trajectory. In contrast to well-known diffraction-free accelerating Airy beams all beams, which we consider, are converging upon propagation.

42-50

Authors: A.V. Ustinov, S.N. Khonina

Theoretical and numerical analysis of flat beam diffraction by fracxicon with value of power less than unity are performed within the nonparaxial scalar model. Using integration by parts of the Rayleigh-Sommerfeld integral of first type and applying the modified method of stationary phase we obtain the expression of the axial complex distribution satisfying the boundary conditions for on the optical axis. The results obtained by numerical integration show good agreement with analytical estimates. Numerical examples show that the divergent fracxicon allows to form an extended axial light line with diameter of the order of the wavelength longer and more uniform than provides a linear axicon.

57-66

Authors: S.V. Alferov, S.V. Karpeev, S.N. Khonina, O.Yu. Moiseev

Experimentally investigated a focusing of inhomogeneously polarized laser beams formed by the sector polarizing plates. The analysis of noise distortion beams formed different types of plates is performed. Focusing is implemented by a micro-objective with high numerical aperture and by a diffraction axicon with moderate numerical aperture. It's experimentally shown that beam distortion by noise have a little effect on the intensity distribution in the center of the focus area due to its high frequency nature. It is in agreement with the simulation results.

72-80

Authors: V.V. Kotlyar, S.S. Stafeev, A.Yu. Feldman

It was experimentally shown that square microsteps with width of 0.4 um, 0.5 um, 0.6 um, 0.8 um and height of 500 nm illuminated by linearly polarized laser light with wavelength λ = 633 nm formed near its’ surface focal spots (photonic nanojets) with intensity that is 6 times higher than the intensity of incident light and diameters of 0.44λ, 0.43λ, 0.39λ and 0.47λ (less than the diffraction limit 0.51λ). When the square width was smaller than the wavelength, the focal spot was located inside the step. When the square width was larger than the wavelength, the focal spot was located outside the step and looks like a handle.

87-93

Authors: M.V. Gashnikov, N.I. Glumov

We consider the use of compression method based on hierarchical grid interpolation to compress the hyperspectral images. Approximation of the spectral channels is proposed to improve the efficiency of the method. Recommendations for setting the parameters of the method formulated. Numerical experiments compared to JPEG method implemented.

105-111

Authors: A.A.Vaniev

Article is devoted to the development of methods and criteria for identification of multiple moving objects observed by passive optical digital locator. Approaches to the development of methods of identification of multiple moving objects are examined. Mathematical model of the promising measuring system and some results of practical research are provided. The developed model can be used in various measurement and control systems, real-time observation for the separate estimation of motion of objects in the group.

118-126

Authors: A.A. Sirota, A.Y. Ivankov

Different approaches to block image processing applied to the reconstruction of super-resolution images using the Kalman filter are analyzed. The results of the various approaches are represented.

131-138

Authors: S.S. Sadykov, Yu.A. Bulanova, E.A. Zakharova

This paper proposes a technology of computer diagnosis of tumors in mammary gland of three main types: cyst, fibroadenoma, and breast cancer. It is noted that the use of such technology in the health care setting reduces the chance of missing a tumor when viewing mammograms, are at an early stage of development, but also minimizes the subjectivity of diagnosis. Work on a set of technologies studied real mammograms from MIAS database with known diagnoses. The results of experiments that show the possibility of using the developed based on this technology integrated cabinet in mammography as for general research and well as for screening.

148-153

Authors: M.S. Kasparyan

Introduce an analog cosine transform on the pre-fractal region. From fractal discrete Fourier transform output discrete cosine transform on two-dimensional domains associated with the fundamental domains of number systems in imaginary quadratic rings. It is shown that this transformation is orthogonal.