Computer Optics

179-189

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

Alongside phase singularities (optical vortices), there may be light fields with polarization singularities (PS), i.e. isolated intensity nulls with radial, azimuthal, or radial-azimuthal polarization around them. Here, we study Gaussian beams with several arbitrarily located PS. An analytic expression is obtained for their complex amplitude. A partial case is studied when the PS are at the vertices of a regular polygon. If the beam has one or two PS, then these are points with radial polarization. If there are four PS, then two of the points will have azimuthal polarization. It is shown that while propagating in free space, the PS can appear only in a discrete set of planes, in contrast to the phase singularities, which exist in any transverse plane. In the case of two PS, it is shown that their polarization transforms from radial in the initial plane to azimuthal in the far field.

197-211

Authors: Kharitonov S.I., Khonina S.N.

In this paper, we have developed a mathematical base for describing the propagation of waves in a metal waveguide in a cylindrical coordinate system. The transformation of a conical wave with circular polarization into a cylindrically polarized vortex beam is shown on the basis of the expansion of the field in vector cylindrical modes. The results of modeling, based on the expansion in plane waves, qualitatively agree with theoretical calculations.

219-226

Authors: Doskolovich L.L., Bezus E.A., Kazanskiy N.L.

We present a method for calculating a spectral multifocal diffractive lens that forms a given set of fixed-position foci at multiple operating wavelengths. It is based on minimizing a function represented as a squared absolute value of difference between the complex amplitudes of beams formed by the relief of a spectral lens at the given wavelengths and the complex transmission functions of multifocal lenses calculated for these wavelengths. As an example, we calculated zone plates that form three fixed foci at three and four operating wavelengths. The results obtained may find application in the development and creation of new multifocal contact and intraocular lenses with reduced chromatic aberrations.

236-243

Authors: Plastun A.S., Konyukhov A.I.

With the help of numerical simulation, we study the propagation of light in an all-glass photonic crystal fiber. A comparison of the spectral characteristics of a fiber with the idealized hexagonal structure and a fiber with transverse profile deformations is conducted. The calculations use methods based on a spatial Fourier transform. It is shown that total internal reflection modes and the fundamental mode of the photonic bandgap can be excited simultaneously. Structural deformation of a photonic crystal fiber results in the shifting and narrowing of the photonic bandgap. Excitation of the total internal reflection modes leads to increased absorption on the boundaries of the spectral band of the fiber.

248-253

Authors: Grebenyuk A.A., Ryabukho V.P.

In optical coherence microscopy (OCM) with a given numerical aperture (NA) of the objectives the transverse resolution can be increased by increasing the numerical aperture of illumination (NAi). However, this may also lead to attenuation of the signal with defocus preventing the effective numerically focused 3D imaging of the required sample volume. This paper presents an approach to structuring the illumination aperture, which allows combining the advantages of increased transverse resolution (peculiar to high NAi) with small attenuation of the signal with defocus (peculiar to low NAi) for high-resolution numerically focused 3D imaging in OCM.

263-266

Authors: Kalinin N.V., Saleev V.A.

Calcite is the most thermodynamically stable polymorphic phase of the CaCO3 crystal. It is widely used in modern optical instruments operating in the infrared and visible wavelengths of electromagnetic radiation. In particular, due to its anisotropic properties, calcite is used in polarization optics devices. Ab initio quantum mechanical modeling of the Raman and infrared spectra of calcite makes it possible to better understand the structure and nature of the chemical bonds of the compound, and find the optimal conditions for the effective use of unique properties of calcite in photonics tools. The calculations are performed within the framework of the density functional theory in the CRYSTAL program, using the “hybrid” B3LYP functional and the all-electronic bases of the STO-6G, PO-TZVP and BSD atomic orbitals of the Gaussian type. The obtained results for the elastic constants, Raman and infrared spectra of calcite agree satisfactorily with the available experimental data for the basic sets of POB-TZVP and BSD.

273-282

Authors: Fedotov N.G., Syemov A.A., Moiseev A.V.

We consistently describe the theoretical basis of a new geometric method of analysis and recognition of three-dimensional (3D) images. The description of a scanning technique for forming a hypertrace transform and its mathematical model are given. This method, unlike the existing ones, enables 3D images to be analyzed directly from their 3D shape, without first simplifying them or constructing plane projections. We substantiate the selection of a particular scanning tool and the need to construct a reference spherical grid to address the problem of the rotational invariance of the 3D image recognition. A mathematical apparatus of the stochastic realization of the scanning technique based on stochastic geometry and functional analysis is developed. We introduce a new mathematical tool for 3D image analysis – a hypertrex matrix that allows spatial objects of complex shape and structure to be recognized by constructing a single mathematical model of the 3D image. We describe a new type of 3D image features that have an analytic structure -- hypertryplet features, whose analytical structure makes possible an automatic generation of a large number of features with predetermined properties. Results of the experimental verification are presented, demonstrating the accurate calculation of features for 3D image recognition and proving the adequacy of the developed mathematical apparatus.

291-296

Authors: Lebedev M.A., Rubis A.Yu., Vizilter Yu.V., Vygolov O.V.

In our previous works dealing with detecting differences in images in the case of substantial variations in brightness and geometry of an object, we proposed a morphological scheme for image analysis based on diffusion and reference mosaic filters. The filters were defined through the heat kernels of the similarity of image fragments. In this paper, we propose an implementation of this morphological scheme using original reference Earth mover's distance (EMD) filters, in which the optimal matrices of the mutual similarity of mosaic forms are calculated through a linear programming method.

306-311

Authors: Rubis A.Yu., Lebedev M.A., Vizilter Yu.V., Vygolov O.V., Zheltov S.Yu.

In a previous work, we proposed a Comparative Morphology (CM) construction scheme that generalized Pytyev's Morphological Image Analysis approach onto a wider range of practical image comparison applications. Within a Guided Contrasting framework, a filtering procedure and a related change detection algorithm were developed. In this work, we propose a class of CM filtering in which Mathematical Morphology operators introduced by Serra are used as smoothing operators that offer monotonically non-increasing (non-decreasing) filtering, in contrast to linear diffusion filtering and non-linear median filtering. The results of experiments on change detection based on the new CM filtering are discussed in comparison with other morphological procedures.

320-327

Authors: Yablokova L.V., Golovashkin D.L.

The work is devoted to the synthesis of block algorithms of the FDTD method. In particular, the simultaneous difference solution of d’Alembert's and Maxwell's equations is considered. Accounting for the computer memory hierarchical structure allows the calculation time to be reduced up to six times when compared with the known software implementations of the method.

338-342

Authors: Perminov N.S., Smirnov M.A., Nigmatullin R.R., Talipov A.A., Moiseev S.A.

A comparative analysis of the method of histograms and the sequence of the ranged amplitudes (SRA) for statistical parametrization of the operation regime of a single-photon avalanche photodetector has been performed. It was shown that in addition to providing all the information that can be obtained using the histogram method, the SRA method also provides a quick and robust description of the dark counts of the detector for a shorter (compared to histograms) noise sample of ~103points. The revealed advantages open prospects for introducing the SRA method in the software of high-sensitivity photodetectors.