№ 796 (2014)

УДК 537.958:621.372.8
В.М. Фітьо, В.В. Ромах, Я.В. Бобицький
Національний університет “Львівська політехніка”,
кафедра фотоніки
АНАЛІЗ ПЛАНАРНИХ ХВИЛЕВОДІВ МЕТОДОМ ЗБУРЕННЯ
© Фітьо В.М., Ромах В.В., Бобицький Я.В., 2014

Використано метод визначення сталих поширення планарних хвилеводів за наяв¬ності збурення діелектричної проникності. Метод ґрунтується на представленні поля збуреного хвилеводу у вигляді лінійної комбінації полів незбуреного хвилеводу з деякими коефіціє¬нтами. Проведено розрахунки для хвилеводів, які не впливають на випроміню¬вання (па¬сивні), поглинають чи підсилюють його (активні). Ця теорія є наближеною, коли врахо¬вуються лише направлені моди, проте може бути точною, коли немає взаємодії між модами.
Ключові слова: підсилення, направлена мода, діелектрична проникність, планар¬ний хвилевід, стала поширення.

V.M. Fitio, V.V. Romakh, Ya.V. Bobitski
Lviv Polytechnic National University
Department of Photonics
ANALYSIS OF PLANAR WAVEGUIDES BY PERTURBATION METHOD
© Fitio V.M., Romakh V.V., Bobitski Ya.V., 2014

One of the important tasks today in the field of communications and information technologies is the ability to provide high-speed data transmission using fiber-optic communication lines. The presence of existing homo- and heterostructures in semiconductor lasers cannot implement this task due to the fact that at high-frequency modulation these structures generate a large number of modes, i.e., wavelengths. As an alternative, distributed feedback lasers (DFB lasers) are used which active medium is similar to a waveguide that includes a periodic structure, namely a grating. A waveguide indicates that active layer has greater refractive index than layers surround it. In a grating which is formed at layer interface of structure, Bragg reflection occurs providing single-mode generation in spite of spatial failure due to a standing wave in active medium.
As to the theory of distributed feedback lasers, it is well developed and studied when first order Bragg conditions are carried out. Instead, there is another situation for higher order Bragg conditions (second, third). In particular, the theory for analysis of waveguide lasers to satisfy second order conditions is described, but it is only applied to active waveguides with surface relief gratings; in addition, representation of the fields in active waveguide is not quite complete. Also, the fields are not sufficiently presented for waveguides with bulk gratings resulting radiation is expected only from waveguide top, but at small angles to the axes x (i.e., almost perpendicular to a waveguide) and z (beam generated is propagating in a substrate) it is not provided by the theory. The theory of propagation of plane only reflective wave in periodic medium with gain and without it is worked out, and generation conditions at implementation of second and higher order Bragg conditions are obtained. But there is no possible to use this theory directly for waveguide DFB lasers because it is not clear how fields and waveguide mode constants of planar waveguides are calculated.
Therefore, the aim of this work is a usage of method to find propagation constants of waveguide modes at perturbation presence which is determined by change of waveguide permittivity during pumping. This method is based on fact that field of unperturbed waveguide is represented as linear combination of unperturbed waveguide fields with coefficients which depends on coordinate along which waveguide modes propagate. As a result, systems of second order differential equations are obtained. In this paper, both passive (permittivity ε(x) is a real function) and active (ε(x) becomes imaginary values) waveguides without grating in a structure are considered. Using both the perturbation method and approach based on Fourier transform, symmetric and asymmetric waveguides are analyzed, and propagation constants of guided modes are found. Good coincidence of results obtained by these methods is observed. Difference is only in last digits of propagation constants; it appears due to rounding. Theory used is approximate because only guided modes are taken into account, but it can be accurate when there is no interaction between modes of unperturbed waveguide.
Key words: gain, guided mode, permittivity, planar waveguide, propagation constant.

Література – 11

УДК 621.396.96
С.Є. Фабіровський
Національний університет “Львівська політехніка”
СУБПІКСЕЛЬНА ОБРОБКА ЗОБРАЖЕНЬ У СИСТЕМАХ МОНІТОРИНГУ ВИДИМОГО ДІАПАЗОНУ ХВИЛЬ
© Фабіровський С.Є., 2014

Наведено аналіз методів підвищення роздільної здатності, технології субпіксельної обробки зображень, оцінка варіантів побудови оптичних систем. У межах роботи проаналізовано шляхи підвищення роздільної здатності, вказано переваги та недоліки методів.
Ключові слова: обробка зображень, субпіксельна обробка зображень, просторова роздільна здатність, оптичний давач, ПЗЗ лінійка, інтерполяція, деконволюція, відновлення, аерокосмічне знімання, дистанційне зондування Землі.

S.E. Fabirovskyy
Lviv Polytechnic National University
SUBPIXEL IMAGE PROCESSING IN MONITORING
SYSTEMS OF VISIBLE WAVELENGTHS
© Fabirovskyy S.E., 2014

This paper is devoted to considering of ways to improve the resolution, principles and methods of subpixel imaging technology, assessment of the development status and the latest research developments. Modern approaches to improving the spatial resolution as the main parameter of satellite images are based on algorithmic search and design solutions as the technology of manufacturing image sensors exhaust its potential for improvement. One of the major tasks of remote monitoring is to improve the quality of images, which is determined by parameters such as resolution. Resolution of digital images, in its turn, is determined by the number of pixels of which it is composed. The need for high resolution usually is accompanied by the need to capture the largest possible surface area. However, reducing the pixel size and increasing their number is limited by technological factors and is associated with difficulties of the operation and handling. Pixel size of CCD is technology limited. Increasing of pixels number and hence the resolution will increase the size (length) of CCD line. As the result, there is need to use more expensive optics, weight of which is greater or reduce the focal length of the optical system.
The solution to this situation is the use of subpixel processing. The advantages of subpixel imaging include the possibility to increase the spatial resolution without changing the optical system. The essence of the subpixel processing is constructive two CCD lines shifted by half a pixel with respect to each other. Use of subpixel imaging technology allows to increase the resolution of the instrument, or, in case of saving a lower resolution, to reduce the focal length of the system and reduce the weight and volume of the optical system, which is crucial for monitoring systems. During subpixel imaging, there are high requirements to the board processor, memory and bandwidth of the radio frequency channel of system.
The need to increase the resolution a monitoring systems helps to find new, more effective, methods to increase resolution. The paper analyzes ways of increasing resolution the advantages and disadvantages of existing techniques are analyzed. The scope of subpixel processing methods in existing monitoring systems of visible wavelength range is considered. The need to further improvement monitoring systems resolution helps to find new, more effective methods of signal processing and filtering.
The studied modern methods of subpixel image processing effectively increase the resolution. Thus, based on the analysis, we can conclude that increasing the system resolution should be conducted by subpixel processing methods that require improvement.
Key words: image processing, subpixel image processing, spatial resolution, optical sensor, CCD line, interpolation, deconvolution, aerospace survey, remote sensing of the Earth, restoration.

Література – 14

УДК 621.372.061
Ю.І. Шаповалов, Б.А. Мандзій, Д.Р. Бачик
Національний університет “Львівська політехніка”
ПРО ЗМЕНШЕННЯ ГРОМІЗДКОСТІ МАТЕМАТИЧНОЇ
МОДЕЛІ ЛІНІЙНОГО ПАРАМЕТРИЧНОГО КОЛА

© Шаповалов Ю.І., Мандзій Б.А., Бачик Д.Р., 2014

Досліджено вплив вибору змінних диференціального рівняння, що описує лінійне параметричне коло у часовій області, на зменшення громіздкості такого рівняння. Запропоновано правила формування системи лінійних диференціальних рівнянь кола, що забезпечують її прийнятну громіздкість.
Ключові слова: лінійне параметричне коло, частотний символьний метод.

Yu.I. Shapovalov, B.А. Mandziy, D.R. Bachyk
Lviv Polytechnic National University
ABOUT THE DECREASE BULKINESS OF MATHEMATICAL
MODEL OF LINEAR PERIODICALLY TIME-VARIABLE CIRCUIT
© Shapovalov Yu.I., Mandziy B.А., Bachyk D.R., 2014

In this paper are investigated the influence of variables the differential equation describing the linear periodically time-variable circuits in the time domain on decrease of bulkiness such equation. Rules of forming a system of linear differential equations of circuit that provide its acceptable bulkiness are proposed. Communication of voltages and currents on elements of an electric circuit looks like algebraic, differential and integral equations. As showed computer experiments, on the bulkiness of system of the equations, that describe in particular LPTV circuit and its further transformation in time domain, essentially influences presence of integrated expressions in this system. Since the input and output variables are usually given you must to choose such method of formation of system of equations, which would provide absence in it integral expressions. The first rule of formation of the system of equations of circuit is as follows: to provide absence the integral expressions in the system of equations describing a circle in the time domain, as variables in it need to choose the voltage on the capacitor and current in the inductor. One of the perspective methods of forming of equations is the tabular method. By the tabular method in system of equations as variables are selected nodal voltages, currents and voltages on the elements of the circuit, and the equations themselves may be formulated so that the integral expressions were absent. It follows the second rule of formation of system of differential equations which is as follows: in the absence of other requirements, mathematical model of circuit in the time domain advisable to form by the tabular method that provides absence the integral expressions in equations without additional action to remove them. In addition, the tabular method does not impose restrictions on the structure and elements of circuit. Under condition of performance of the presented two rules the system of the equations describing a circuit less bulky than without it. Normally in such systems variables which do not interest the researcher further are eliminated, and the equation in which there are only two variables is formed. Bulkiness of the last equation too can be different, and it depends on what variables left in it. The third rule of forming a differential equation that describes a circle in the time domain and that provides acceptable bulkiness is as follows: despite the fact which variables of circuit is an output variables, in a mathematical model of circuit that was formed by a rule 2, we eliminate all variables, except what correspond to an input signal and a parametric element. If sources of input signal or parametric elements in the circuit a few then such equations necessary to form few - one for each pair of “input - parametric element.” The differential equation that formed by the three rules using method L.A. Zadeh is transferred into the frequency domain and is solved by the frequency symbolic method. As a result we receive symbolic parametric transfer functions which are a basis for formation of a frequency symbolic model of each parametric element. Such models in turn are a basis for creation of frequency symbolic model of circuit as a whole. Such frequency symbolic model of circuit contains or determines output signals. Values of output signals of circuit may be are converted to the time domain.
Key words: linear periodically time-variable circuits, frequency symbolic method.

Література – 7

УДК 621.391:519.21
Р. М. Юзефович
Фізико-механічний інститут ім. Г. В. Карпенка НАН України, Львів

ОЦІНЮВАННЯ ВЗАЄМОСПЕКТРАЛЬНИХ КОМПОНЕНТІВ
ПЕРІОДИЧНО НЕСТАЦІОНАРНИХ ВИПАДКОВИХ СИГНАЛІВ

© Юзефович Р. М., 2014

Проаналізовано властивості оцінок взаємоспектральних компонентів, що знахо¬дять на основі перетворень Фур’є згладжених оцінок взаємокореляційних компо¬нентів. Виведено формули для зміщення та дисперсії оцінок, що описують залежність цих величин від довжини відрізка реалізації, точки усічення корелограми, форми зглад¬жувального вікна та спектральних характеристик сигналу. Наведено приклад оціню¬вання взаємоспектральних компонентів амплітудно- та фазомодульованих сигналів.
Ключові слова: періодично нестаціонарні випадкові сигнали, взаємокореляційна функція, взаємоспектральна густина, дисперсія, зміщення оцінки.

R. M. Yuzefovych
Karpenko Physico-mechanical institute NAS Ukraine, Lviv

AN ESTIMATION OF CROSS-SPECTRAL COMPONENTS
FOR PERIODICALLY NON-STATIONARY RANDOM PROCESSES

© Yuzefovych R. M., 2014

Correlations between harmonic components of random processes is a feature of signal non-stationarity. In the case of periodically non-stationary random processes (PNRP) correlate harmonics distant one from another on frequencies, what multiple to value T, T - period of non-stationarity [1, 2]. Since faults appearance in rotating elements of mechanical systems leads to periodical non-stationarity of vibration signals when searching of correlations between harmonic components can lay in the base for defects detection [1, 3–5]. For description of such correlations used spectral components, which are Fourier coefficients of varying spectral density and at the same time are the Fourier transformations of correlation components. For widening of vibration diagnostics capabilities reasonable to provide a cross-spectral analysis of vibration signals measured at different points of mechanical system. It gives possibility to investigate spatial properties of signals and to solve tasks of defects localization with higher effectiveness [6, 7].
The properties of cross-spectral components estimators, based on Fourier transformation of smoothed estimators of cross-correlation components, are analyzed. The formulae for estimator bias and variance, which describe dependence of these values on realization length, point of correlogram cutoff, smoothing window form and signal spectral characteristics, are derived. The examples of cross-spectral components estimation for amplitude- and phase modulated signals are given. It is proved that variances of cross-spectral components estimators depend on all of spectral components, which are present in Fourier decomposition of varying spectral density of periodically non-stationary random processes. It is shown that statistical analysis of stationary approximation of PNRP can not be made within stationary model but only within the PNRP, which approximation it is.
Key words: periodically non-stationary random signals, cross-correlation function, cross-spectral density, variance, estimator bias.

Література – 7

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