Computer Optics

311-318

Authors: V.V. Kotlyar, S.S. Stafeev

Tight focusing of light with mth-order circular-azimuthal polarization was investigated. This is a new type of inhomogeneous hybrid polarization that combines the properties of mth order cylindrical polarization and circular polarization. Using the Richards-Wolf formalism, we obtained analytical expressions in the focal spot for the projections of the electric and magnetic field, the intensity distribution, the projections of the Poynting vector, and the spin angular momentum. It was shown theoretically and numerically that at the focus, the intensity has 2(m+1) local maxima located on a circle centered on an on-axis intensity null. It was shown that 4m vortices of a transverse energy flow were produced at the focus, with their centers located between the local intensity maxima. It was also shown that in the focal plane, the transverse energy flow changes the direction of rotation 2(2m+1) times around the optical axis. It is interesting that the longitudinal projection of the spin angular momentum at the focus changes sign 4m times. In those areas of the focal plane where the transverse energy flow rotates counterclockwise, the longitudinal projection of the spin angular momentum is positive, and the polarization vector rotates counterclockwise in the focal plane. Conversely, if the energy flow rotates clockwise, the polarization vector rotates clockwise, and the longitudinal projection of the spin angular momentum is negative. Numerical simulations are in agreement with the theoretical investigation.

324-330

Authors: R.V. Kutluyarov, D.M. Fatkhiev, I.V. Stepanov, E.P. Grakhova, V.S. Lyubopytov, A.K. Sultanov

We propose and numerically verify a design of the photonic integrated circuit for in-plane generation of a 1st azimuthal order vortex mode in dielectric rectangular waveguides. Radiation is introduced into the proposed structure in a standard way through two grating couplers. Applying a mode coupling and specific phase shift, a field with the required amplitude-phase distribution is formed directly in the output waveguide. The geometric dimensions of the device are simulated and optimized to fit the technological parameters of the silicon-on-insulator platform.

340-349

Authors: D.V. Lyakin, V.P. Ryabukho

The effect of the width of the angular spectrum (numerical aperture) of a broadband-frequency wave-field probing a layered object on the signal of an autocorrelation low-coherence interferometer (ALCI) under spatially coherent and incoherent illumination of the entrance pupil is considered. It is found that under incoherent illumination an increase in the width of the angular spectrum of the field leads to a decrease in the amplitude, a change in the shape and position of the measuring signals of the interferometer due to decorrelation of the object field partial components which have reflected from various interlayer boundaries inside the object. In the case of coherent illumination, the ALCI signal is formed in a confocal mode, which leads to the amplitude extraction of the measurement signals are determined by the mutual correlations between a partial component reflected from the boundary on which the probing field was focused, and partial components of this field which have reflected from other boundaries within the object. This effect makes it possible to determine parameters of the internal layered structure of an object doing without apriori structure-related information. In this case, an increase in the numerical aperture of the probing light beam leads to an increase in the systematic error in determining the optical thicknesses of the layers, which can be estimated on the basis of the obtained expressions.

356-363

Authors: A.I. Kashapov, L.L. Doskolovich, D.A. Bykov, E.A. Bezus, D.V. Nesterenko

Optical properties of a resonant trilayer metal-dielectric-metal (MDM) structure that consists of an upper metal layer, a dielectric layer, and a metal substrate are investigated. Using a multiple wave interference model, we prove that the reflection coefficient of the MDM structure may strictly vanish. The existence of a reflectance zero makes it possible to use the MDM structure as an optical differentiator. The numerical simulation results presented demonstrate the possibility of optical computation of the first derivative with respect to either time or spatial variable. The obtained results may find application in novel analog optical computing and optical information processing systems.

372-381

Authors: V.A. Mikhailov, N.V. Troshkin

In this paper we investigate non-Markovian evolution of a two-level system (qubit) in a bosonic bath under influence of an external classical fluctuating environment. The interaction with the bath has the Lorentzian spectral density, and the fluctuating environment (stochastic field) is represented by a set of Ornstein-Uhlenbeck processes. Each of the subenvironments of the composite environment is able to induce non-Markovian dynamics of the two-level system. By means of the numerically exact method of hierarchical equations of motion, we study steady states of the two-level system, evolution of the reduced density matrix and the equilibrium emission spectra in dependence on the frequency cutoffs and the coupling strengths of the subenvironments. Additionally, we investigate the impact of the rotating wave approximation (RWA) for the interaction with the bath on accuracy of the results.

394-398

Authors: A.V. Demin, E.N. Sechak, S.P. Prisyazhnyuk

The article presents results of the development and research of a hyperspectral imaging spectrometer for analyzing borehole fluids in real operating conditions in the spectral range from 0.35 microns to 2.1 microns. A mathematical model and an algorithm for identifying the borehole fluid by composition and percentage content based on the results of hyperspectral image analysis are developed.

405-417

Authors: S. Madenda, A. Darmayantie

This paper describes the use of some color spaces in JPEG image compression algorithm and their impact in terms of image quality and compression ratio, and then proposes adaptive color space models (ACSM) to improve the performance of lossy image compression algorithm. The proposed ACSM consists of, dominant color analysis algorithm and YCoCg color space family. The YCoCg color space family is composed of three color spaces, which are YCcCr, YCpCg and YCyCb. The dominant colors analysis algorithm is developed which enables to automatically select one of the three color space models based on the suitability of the dominant colors contained in an image. The experimental results using sixty test images, which have varying colors, shapes and textures, show that the proposed adaptive color space model provides improved performance of 3 % to 10 % better than YCbCr, YDbDr, YCoCg and YCgCo-R color spaces family. In addition, the YCoCg color space family is a discrete transformation so its digital electronic implementation requires only two adders and two subtractors, both for forward and inverse conversions.

427-437

Authors: A.S. Shirokanev, N.A. Andriyanov, N.Y. Ilyasova

For diabetic retinopathy treatment, laser coagulation is used in modern practice. During the laser surgery process, the parameters of laser exposure are selected manually by a doctor, which requires the doctor to have sufficient experience and knowledge to achieve a therapeutic effect. On the basis of mathematical modeling of the laser coagulation process, it is possible to estimate the crucial parameters without performing an operation. However, the retina has a rather complex structure, and when even low-cost numerical methods are used for modeling, it takes a long time to obtain a result. In this regard, the development of time-efficient algorithms for three-dimensional modeling is an urgent task, since the use of such algorithms will provide a compre-hensive study within a limited time. In this paper, we study the execution time of algorithms that implement various variations in the application of the splitting method and the finite difference method, adapted to the set problem of heat conduction. The study reveals the most efficient algorithm, which is then vectorized and implemented using the CUDA technology. The study was carried out using Intel Core i7-10875H and Nvidia RTX 2080 MAX Q and showed that an analog of the vector algorithm, focused on solving a multidimensional heat conduction problem, provides an acceleration of no more than 1.5 times compared to the sequential version. The developed vector-based algorithm, focused on the application of the sweep method in all directions of the three-dimensional problem, significantly reduces the time spent on copying into the memory of the video card and provides a 40-fold acceleration in comparison with the sequential three-dimensional modeling algorithm. On the basis of the same approach, a parallel algorithm of mathematical modeling was developed, which provided a 20-fold acceleration at full processor load.

449-460

Authors: Y.V. Vizilter, O.V. Vygolov, S.Y. Zheltov

We consider the statistical properties of different mosaic filters. We demonstrate that in Pitiev's morphology, the measure of shape complexity is directly related to the shape simplicity measure based on morphological correlation coefficient (MCC). Based on MCC, we introduce the normalized morphological simplification index (NMSI). Using NMSI, we show that the simpler the mosaic shape, the more shape simplification is provided by the corresponding Pyt'ev projector. For the examples of mean and median mosaic filters, we address the problem of different operator comparison. In this context we introduce the concept of statistically simplifying morphological operators. Morphological correlation of mosaic shape and diffusion mosaic operator is considered. We prove that the NMSI for the diffusion mosaic operator is not related to the complexity for the corresponding diffusion shape kernel. Thus, a principal qualitative difference in the relationship between relational and operator models for diffuse and projective mosaic linear filters is demonstrated.