An overview of the legal framework of metrology at the international level, in particular, the activities of the intergovernmental International Organization of Legal Metrology, is given. The establishment of the International Organization of Legal Metrology has had an impact on the consolidation of the regulatory framework for metrology at the regional level, especially in the European Union. The reliability, comparability and traceability of measurement results are ensured by international regulatory documents developed by countries in the field of activity of seven international organizations. For international recognition of measurement and test results of any country. There is a need for a system of normative instruments that ensure international law. Strategically, it is necessary to create a legal framework so that it is possible to move from regional politics to global politics. The role of legal metrology at the regional level and the formation of the legislative framework of fundamental metrology in the world are described. The article presents a database of basic documents for solving scientific problems of ensuring the uniformity of measurements at the international level and the main milestones in the history of the formation of the legal framework of the measurement system in Russia for two centuries. The creation of the metrological service of the USSR, and then the state system for ensuring the uniformity of measurements determined new approaches to improving legislation in the field of metrology. Harmonization of the language of measurements and approaches to solving the problems of metrology will ensure the uniformity of measurements not only in individual countries and regions, but also on a global scale.

The methods of management of metrological support of the measuring instrument fleet are considered. The modern situation is described, when the fleet of measuring instruments is heterogeneous and includes both obsolete samples of measuring instruments with a long service life and significant operating time, and the newest, high-tech samples of measuring instruments. At the same time the proportions between the mentioned groups of measuring instruments change over time, as the ageing of measuring instruments and their transition from one group to another takes place. Also the measurement instrument park is renewed as a result of purchases of new and modernization of existing samples. The heterogeneity of the measuring instrument park leads to the necessity of development and application of new methods of management of metrological support of the measuring instrument park, including the use of mathematical modeling. One of the promising methods of metrological management of the measuring instrument fleet based on the risk-oriented approach is proposed. The probability of finding a randomly selected sample of measuring instruments from the measurement instrument park at an arbitrary moment of time in the state of unreadiness for intended use is used as a risk indicator for the measuring instrument park. In accordance with the risk-oriented approach the measuring instrument park is divided into risk classes. The algorithm of assigning measuring instruments to different risk classes is developed, based on solving a series of optimization problems of the fleet operation taking into account the processes of aging and renewal of the fleet of measuring instruments. The results of application of the risk-oriented approach in the problem of modeling of metrological support of heterogeneous fleet of measuring instruments including both modern and obsolete samples with different metrological characteristics, MTBF and lifetime are presented. It is shown that by dividing all samples of measuring instruments into risk classes and carrying out verifications with their close to optimal periodicity and with their tolerance for controlled parameters in each risk class it is possible to minimize the total average risk for the fleet of measuring instruments and at the same time to achieve resource saving.

One of the main tasks of data analysis is to estimate the parameters of a data sample of the constant physical value. Data analysis is required in all areas of experimental physics to obtain reliable measurement results. To describe sample elements with interval uncertainty, the technique of interval analysis and interval statistics is used. In particular, the homogeneity of data in a sample is described using various measures of similarity. A set of three coherence measures is presented that describe different relationships of sample elements. Based on the considered set, a combined measure of sample similarity is proposed, which allows one to simultaneously find external and internal estimates of the value under study. These estimates are important for solving a massive data processing problem, when the sets of samples are obtained under different measurement conditions. The necessary information about interval analysis and various interval arithmetic is provided. The relations between the proposed combined measure and the results of calculations with interval twins and fuzzy sets are considered. This combined measure can be used when solving a massive data processing problem typical for practical and scientific areas of semiconductor physics. A practical example of the use of a combined sample consistency measure when testing solar radiation converters against a reference converter is given as part of the study of their spectral properties and quantum yield.

A method is proposed for selecting the blurriness coefficient of kernel functions for nonparametric estimation of the probability density of a one-dimensional random variable with large volumes of statistical data, for example, obtained by remote sensing of natural objects. In the proposed method for selecting the blurriness coefficient, a regression estimate of the probability density is used. A method for synthesizing a regression probability density estimate is presented. The synthesis of the estimate is based on compression of the initial sample by decomposition of the range of values of a random variable. To decompose the range of values of a random variable, the Heinhold-Gaede rule and the formula for optimal selection of the number of sampling intervals are applied. Two approaches to the selection of the blurriness coefficient of the regression estimation of probability density using the traditional and proposed by the authors optimization methods of nonparametric estimation of probability density are considered. The traditional method of optimizing nonparametric estimation of probability density is based on minimizing its mean square deviation. In the proposed method, the selection of the blurriness coefficients of the kernel functions is based on the conditions of the minimum error of approximation of the regression estimate of the desired probability density. The approximation properties of the regression estimation of probability density using two methods of its optimization are analyzed. The conditions of their competence in estimating the probability densities of random variables with a lognormal distribution law are established. The results obtained allow for development when optimizing a regression estimate of the probability density of a multidimensional random variable.

Moment and compositional approaches to solving the measurement problem of calibration are considered. The use of the moment approach to solving a standard example of thermometer calibration is considered. In this work, this example is solved within the framework of the compositional approach and more accurate and complete results are obtained compared to using the moment approach. This fact is consistent with the assessment of the accuracy of solutions to measurement problems carried out back in 2001 using a more rigorous compositional approach than the moment one: in the problem of calibrating measuring instruments, the moment approach does not fully take into account the inadequacy of functional models, overestimates the accuracy estimates and does not allow obtaining nonlinear models of optimal complexity. To solve the measurement problem within the framework of the compositional approach, this work uses the “MMI-Calibration 3.0” program, which allows taking into account the errors of inadequacy of mathematical models of calibration functions and obtaining tolerance intervals for a given confidence probability. Among polynomials up to the ninth degree inclusive, a three-parameter model of optimal complexity was obtained, the average module of the inadequacy error is 0.002745 °C and the tolerance interval [–0.00828; 0.00761] with a confidence probability of 0.95. Within the framework of the compositional approach, the average module of the error of inadequacy and the kappa criterion used to find a model of optimal complexity are compared. It is shown that the compositional approach fully and strictly describes the solution to the calibration problem without simplifications, allows one to avoid inflated estimates of accuracy, and therefore can serve as an exemplary approach provided that the “MMI-Calibration 3.0” program is used. The simultaneous use of the criteria of the minimum average module of the error of inadequacy and the maximum of the kappa criterion is a necessary and sufficient condition for identifying a model of optimal complexity in the class of polynomials of degree n.

The use of multiparametric optimization of an unknown discrete function in the development of applied solutions for physical systems is considered. Such optimization is practically implemented in real time using modern data transfer protocols at high speed and continuously increasing computing power. To optimize the sensitivity of a modern magnetic sensor based on high-frequency magnetoimpedance in ferromagnetic microconducts, an iterative method of global maximum search, the particle swarm algorithm, has been applied. The output signal of the sensor depends non-linearly on both the internal magnetic properties of the microcircuit and the excitation mode, which requires a certain calibration to establish optimal excitation parameters. The sensor output signals for various excitation parameters and external magnetic fields were measured using an automated installation. The results of the search for the global maximum by the sequential approximation method and the particle swarm method presented in the paper demonstrate the effectiveness of the search algorithm used, the particle swarm algorithm turned out to be the most effective, since it found the global maximum more accurately. With different excitation parameters, the algorithm has always determined the maximum sensitivity when varying the three main parameters of the excitation signal: frequency, amplitude and constant component. The results obtained can be applied in the development of highly sensitive intelligent magnetic sensors and systems based on them.

The article is devoted to the generation of diffractive optical elements and computer holograms for forming three-dimensional images. Possibilities of increasing the speed of diffractive optical elements generation and the quality of reconstructed 3D-objects were investigated. Four methods of optical elements generation were analyzed. The methods use division the 3D-objects into fl at layers. The quality of 3D-object reconstruction and time generation by the methods were assessed. 3D-object reconstruction from generated optical elements was modeled. Optical formation of objects was performed by displaying optical elements onto liquid crystal spatial light modulator. It was found that the best quality of reconstruction was provided by iterative parallel ping-pong and non-convex optimization methods. The optimal ratio of reconstruction quality to generation speed ratio was obtained for the parallel ping-pong method. The possibility of fast formation high-quality three-dimensional scenes consisting of dozens of layers has been demonstrated.

The issues of radiometric calibration of optical-electronic equipment for remote sensing of the Earth in a wide range of spectral radiance have been studied. An alternative method for transmitting a spectral radiance unit from a reference source at the phase transition temperature of pure metals to optical-electronic equipment for remote sensing of the Earth in the infrared wavelength range above 2.5 μm is presented. The method is based on the stepwise transfer of a spectral radiance unit from a reference source through a precision model of a black body with a high level of emissivity and a wide temperature range identical to the temperature range of a wide-aperture black body model with a range of spectral radiance required for calibrating optical-electronic equipment for remote sensing of the Earth. A precision black body model PMBB-60m with an output aperture with a diameter of 30 mm was developed, studied and calibrated in the temperature range of 200–450 K. The calculated value of the effective emissivity of PMBB-60m with coating of the cavity by Aeroglaze Z306 paint is 0.9997. The composition and design of PMBB-60m are described. PMBB-60m can operate both in vacuum conditions and in conditions of inert gas or atmospheric pressure. The metrological characteristics of PMBB-60m , obtained by transferring a temperature unit from the State Standard of the zero digit of a temperature unit in the range from 0 to 3000 °C using a comparator, based on a precision pyrometer TRT II (Heitronics Infrarot Messtechnik GmbH, Germany) are presented. The correction to the PMBB-60m temperature readings in the temperature range of 223.15–450.15 K did not exceed 39 mK according to the results of calibration in the temperature range of 223.15–450.15 K. The results of calculating the expanded uncertainty in the temperature range of 223.15–450.15 K did not exceed 1 K. The values of instability of temperature maintenance PMBB-60m, measured in steps of 10 s for 15 minutes, did not exceed 15 mK in the considered temperature range. The results of calculation of the spectral effective emissivity of PMBB-60m, carried out using the STEEP3 program, are presented.

The need to expand the functionality of systems for monitoring the parameters of the flow of liquid media is substantiated. The advantages of using meters based on the phenomenon of nuclear magnetic resonance to control the parameters of the flow of liquid media are noted. Let us consider the problems that arise during the operation of nuclear magnetic flowmeters-relaxometers operating in two measurement modes (pulse and with periodic modulation of the magnetic field in the nuclear magnetic resonance signal recording system - modulation technique). It is noted that the main problem in the operation of these devices is associated with an increase in the error in measuring liquid flow or the termination of its measurement process with rapid changes in liquid flow. The use of a magnetic tag mode, which allows us to solve this problem, significantly limits the possibilities of using nuclear magnetic resonance flowmeters-relaxometers when used to monitor the parameters of other liquids or with a large increase in the temperature of the flowing medium. A method for creating a magnetic mark at the noise level for measuring liquid flow is proposed. In the method, changing the composition of the flowing medium (including the liquid itself) does not have a significant effect on the formation of a magnetic mark at the noise level in a strong inhomogeneous magnetic field. The results of experimental studies of the nutation line from changes in magnetic field inhomogeneity are presented. A mathematical model has been developed based on the modified Bloch equations and relationships between the magnetic field parameters have been established to implement the magnetic mark mode in the nuclear magnetic resonance signal with magnetization inversion at the noise level. The use of a method makes it possible to make the influence of rapid changes in the value of liquid flow (by a factor of 10 or more) on the flow measurement error insignificant.

A brief overview of contemporary methods for determining the chemical composition of copper alloys and the analytical control methods used is given. It has been shown that to obtain reliable and comparable results of measuring the mass fractions of copper alloys elements in wide ranges of values, the most suitable procedures are based on the X-ray fluorescence method, implemented using portable X-ray fluorescence spectrometers. In order to select the optimal values of the influencing quantities when determining the chemical composition of copper alloys, a robust parameter design of a quantitative chemical analysis procedure was carried out on the X-50 Mobile X-ray fluorescence spectrometer. The use of robust parameter design, as opposed to conducting a full factorial experiment when developing a measurement procedure, makes it possible to optimize measurement conditions and obtain results of the required accuracy with a limited number of experiments and a maximum number of control factors. An example of drawing up an experimental plan for the parameter design of this procedure is given and a statistical analysis of the measurement results is carried out. The optimal measurement conditions (influencing quantities) were analyzed and selected, under which the minimum error in the results of measuring the mass fraction of elements is ensured. The selection of optimal values of the influencing quantities based on the results of robust parameter design of the quantitative chemical analysis procedure made it possible to increase the accuracy of the results of determining the chemical composition of copper alloys and, as a consequence, the reliability of the results of product quality control at relatively low costs for its implementation. This approach can be recommended to analytical laboratories developing procedures of quantitative chemical analysis for metallurgical industry enterprises.