### INFORMATION TECHNOLOGIES AND SYSTEMS

SCHEDULING SETS OF COMPOSITE APPLICATIONS WITH SOFT DEADLINES IN TIME WINDOWS OF HETEROGENEOUS COMPUTING ENVIRONMENTS
Bochenina Klavdiya O., Butakov Nikolay A., Boukhanovsky Alexander V

295

The loading performance of heterogeneous computing resources under user deadline requirements to results of calculation necessitates the use of specialized planning algorithms of the tasks execution. Such algorithms should consider both the specifics of the distributed environment (the level of utilization, types of resources) and possible data relationship between parts of the design scenario. The proposed algorithms implement per-task, phasic and clusterization approaches to planning sets of composite applications with a soft deadline requirements in conditions of partial availability of computing resources. Comparative efficiency of the developed algorithms for scheduling sets of the composite applications on heterogeneous resources is investigated. Presented experimental results demonstrate that: a) the use of information about the availability of resources and the tasks completion timing can significantly improve the scheduling quality; b) clusterization approach is superior to stage and per-task according to integral criterion of scheduling efficiency.

ANALYSIS OF PROCESS QUALITY IN TIME-VARIANT DISCRETE MULTICHANNEL SYSTEMS
Pavlov Andrey S., Ushakov Anatoly Vladimirovich

302

Time-variant discrete multiple-input multiple-output systems with a regular discrete time intervals of separate channels are considered. A method of analysis of process quality in such systems is presented. Scalar evaluation of the vector processes in the systems are realized by singular value decomposition of special matrices. The method feasibility in evaluation of the system performance is demonstrated by majorant and minorant estimates of generally accepted indicators of quality. Algorithmic maintenance using Sylvester matrix equation with variable matrix components is constructed with the account of the discrete nature of the time-variant multiple-input multiple-output systems.

### COMPUTER TECHNIQUE

THE KALMAN FILTER PROPERTIES IN TRANSITION REGIME
Kaplin Alexander Yu., Stepanov Mikhail G., Yarmolich Alexey G.

311

The conditions providing high accuracy of the Kalman filter in transition regime are considered. Relations between the respective values of parameters of state equations and measurement are determined. A simple rule for preliminary evaluation of the transition process nature is formulated. By the example of practically important problem of Kalman estimation of exponentially-correlated random process, application of the proposed rules is illustrated by presented calculations with different initial data.

GORDON—MILLS—WELCH SEQUENCES OF PERIOD N = 1023
Victor G. Starodubtsev, Popov Anton M.

318

А full list of testing polynomials for Gordon—Mills—Welch sequences of period N = 1023 are derived on the basis of a developed algorithm of forming data sequences. The principle dissimilarity from sequences with a smaller period is the possibility to create several GMW-sequences with different equivalent linear complexity (ELC) determined as the degree of testing polynomial hGMW(x) for each basic Msequence (MS) with the primitive testing polynomial hMS(x). This is a consequence of existence of six primitive polynomials in the finite field of GF(25), in contrast to the fields of GF(23) and GF(24) with two primitive polynomials in each. For each of the six MS of period N=31 acting as a characteristic sequence for MS matrix representation of period N=1023, it is possible to use the other five different MS to form five different GMW-sequences. It is shown that on the base of every MS with the period N=1023 it is possible to build five GMW-sequences. One of the GMW-sequences has a testing polynomial of the eightieth degree, two sequences — polynomials of fortieth degree, and two sequences — polynomials of the twentieth degree.

### OPTICAL AND OPTO-ELECTRONIC INSTRUMENTS AND SYSTEMS

APPLICATION OF CROSS-SHEAR INTERFEROMETRY IN HOLOGRAPHY FOR CONTROL OF GEOMETRIC PARAMETERS OF DIFFUSE-REFLECTING SURFACES
Prokopenko Victor T., Majorov Evgeniy E., Mashek Alexander Ch., Tsygankova Galina A., Khaidarov Andrey G., Abramian Volodia K., Zaitsev Yury E., Khaidarov Gennady G.

331

Various methods of interference fringes tuning are evaluated. The features of two-beam holographic registration and reconstruction of the original and perturbed states of a diffuse reflecting surface are considered. Quantitative assessment of measurement error is carried out; the deviation of one of the supporting beams at 10–5 rad is shown to lead to phase shift of the object wave for 0,22 of the interference fringe and to the error in the phase of the interference fringe δφ = 2π·0,22. The possibility of applying shear interferometry instead of two-beam interferometry allows to use a single reference beam and thus improve the measurement accuracy for two orders of magnitude. The phase difference between the beams at the output of transverse shear interferometer (Jamin interferometer) is analyzed. The result allows to estimate the measuring range of the displacement vector magnitude; the maximum and the minimum value of the measured offset are determined to be 1,5 mm and 0,01 μm respectively.

DEVELOPMENT OF A SENSITIVE ELEMENT FOR FIBER-OPTIC STRAIN GAUGE BASED ON BRAGG GRATINGS
Munko Anna S., Varzhel Sergey V., Arkhipov Sergey Vladimirovich, Kirill A. Konnov

340

The problem of stability of optical fiber strain gauge sensing element under simultaneous variations of deformation and temperature is considered. Fiber Bragg gratings is used as one of the most promising sensor elements of fiber-optic gauges. A sensing element based on two Bragg gratings with different specially selected coatings is developed. It is shown that the structure of the developed sensing element allows for separation of the influence of strain from temperature effects.

DETERMINING COORDINATES OF LOCAL MAXIMA OF LIGHT SIGNAL INTENSITY IN DIFFRACTION PATTERN OF THE SURFACE WITH PERIODIC STRUCTURE
Kofnov Oleg V., Lebedev Eugeny L., Mikhailenko Alexander V.

347

An automatic searching method for local maxima of light intensity distribution along diffraction pattern image is presented. The proposed approach consists in slicing the initial intensity oscillation diagram by approximation function for average values so that the required diffraction peaks will lie above the approximating curve, and therefore the local extrema can be found with any algorithm searching for maximum in an uninterrupted segment. Calculated coordinates of local maxima can be used for determining geometrical parameters of periodical structures with the double Fourier transform method. The method is recommended for the use in automatic quality control.

CALCULATION OF BACKLASHES IN CONJUGATION OF OPTICAL COMPONENTS OF A LENS AND ITS ADJUSTMENT
Latyev Svyatoslav M, Tabachkov Alexey G., Frolov Dmitry N., Krynin Lev I., Gnezdilova Mariyа S.

353

Calculation of probable backlashes in plantings details of objective lens and influence of conditions of unit assembly and adjustment on lens centering and image quality are considered. Characteristics of the fields of scattering and errors tolerances of backlashes of conjugated details are analyzed for the probable values of the resulting backlashes. Being casual errors, backlashes are noted to posess a significant regular component caused by regular errors in conjugated components dimensions. Assembly of a lens with horizontal chassis position is shown to allow for reduction of backlashes influence on the accuracy of lens components centering as compared to the "vertical" arrangement when the lens centering breaks because of errors of the diameters of the lens components. To achieve the required quality of generated image, it is necessary to consider the effect of violation of centering of the lens components on aberration at the center and at the edge of the image field.

### SCIENTIFIC AND PRACTICAL DEVELOPMENTS

ELECTRIC BREAKDOWN OF AIR BY NANOSECOND PULSES OF ELECTROMAGNETIC RADIATION
Andrey P. Aleoshkin , Timothy O. Myslivtsev, Bakursky Klim V., Мoskalyev Viktor M.

359

Dielectric toughness of air under the exposure to powerful electromagnetic pulses is evaluated with the use of results of theoretical and experimental studies of high-frequency and pulsed gas discharge. The main attention is paid to the impact of pulses of nanosecond duration. The results presented in the form of semi-empirical formulas and graphs are valid at atmospheric pressure below 10 Torr corresponding to altitudes of up to 30 km.

STUDY OF HYDRODYNAMIC PROCESSES IN LIQUIDS UNDER THE INFLUENCE OF POWERFUL MICROSECOND YB,ER:GLASS LASER PULSES
Belikov Andrei , Gagarsky Sergey V., Andrey N. Sergeev, Smirnov N Sergey

367

Results of the study of hydrodynamic processes induced in liquid by the Yb,Er:Glass (wavelength of 1,54 μm) laser radiation pulses of microsecond duration with an energy of 100±5 mJ are presented. The investigations carried out using three methods — acoustic signal detection, optical probing, and high-speed video recording – allow for objective and comprehensive picture of excited processes. The correlation between data obtained using these methods are established. The analysis of images and oscillograms demonstrates that the laser pulses, delivered in a bulk of saline (0,9 % sodium chloride aqueous solution) via quartz-quartz optical fiber with a core diameter of 470 μm, induce thermoelastic waves and the formation of steam-gas cavity (bubble). Dynamics of optical properties of the liquid under exposure to Yb,Er:Glass laser pulse appears to be related mostly to the bubble formation. It is shown that the build-up stage of the steamgas cavity occurs at 5—10 s after the beginning of adiabatic laser exposure with the energy of about 100 mJ. The cavity reaches the maximum size (up to 3 mm in diameter) at 140 s (on average) relative to laser pulse rising edge. After that, it collapses to the critical size of 0.5 mm at about 120 s and detaches from the fiber end surface. The presented data on the steam-gas cavity size dynamics may be useful when optimizing the temporal and energy parameters of laser radiation for laser processing of submerged objects, including effective and safe treatment of biological objects.

SURFACE PLASMON-RESONANCE SENSOR FOR EXPRESS ANALYSES
Dukin Roman V., Shandybina Galina D., Kuzmin Evgeny V.

375

Surface plasmon resonance sensors are considered in Kretzmann configuration with different types of wave beams: parallel, diverging, and converging. Statistical measurements of the angle of total internal reflection of prism carried out in parallel wave beam with stepwise variation of the incidence angle, demonstrate high measurement accuracy of the method. Conversion from a discrete method to the measures of the entire diverging beam aperture allows to cover large range of angles, including the angles of total internal reflection and surface plasmon resonance, with a single measure. Therefore, the productivity of measurement process significantly increases without loss of accuracy. Changing the shape of the resonance curve in the transition from discrete to the aperture method is correlated with changes in the conditions of surface plasmons excitation. The large width of the resonance curve leads to a decrease in sensitivity of the method, and at the same time reduces significantly the time of measurements.

### BRIEF NOTES

IMPROVING THE ACCURACY OF LINNIK MICROINTERFEROMETER
Kirillovsky Vladimir K., Gubaidullin Kamil R.

381

Modernization of Linnik microinterferometer is performed with the aim of expanding the instrument capabilities and simplify processing of results. An additional optical unit is introduced for image transfer to sensitive area of the matrix. Computer processing of interference pattern is applied. These innovations greatly helpe to improve the methodology of research conducted using microinterferometer Linnik.