A brief description of the main methods for determining the fine structure constant is given. It is shown that the exact value of the fine structure constant is important for the new International System of Units and for fundamental metrology. Recent measurement results and theoretical calculations of the fine structure constant, as well as its possible space-time variations, are presented. The results of laboratory experiments on the search for long-term variations of the fine structure constant are presented. The astrophysical and cosmological observational data on possible variability of the fine structure constant are presented. The possibility of slightly lower values of the fine structure constant in the remote past as compared to its modern value, as well as the existence of unresolved problems related to possible space-time variations of the fine structure constant and the spread of the results of its precise laboratory measurements, are noted. Despite the absence of experimentally confirmed long-term variations of the fine structure constant at a high level of accuracy, possible practical applications of the results are noted, namely, the construction of an optical frequency standard with high stability and frequency reproduction accuracy based on the ytterbium-171 ion and a laser frequency synthesizer which may replace the caesium frequency standard.

It is carried out the comparative analysis of some theoretical and phenomenological relations among constants of the extended Standard Model for electromagnetic, strong and weak interactions of fundamental particles (further the extended Standard Model) in order to find possible correlations for constants in the quark and lepton sectors. Availability of such correlations may attest to some connections for constants in the framework of a theory more general than the extended Standard Model. A number of theoretical relations among constants are considered and an accuracy of fulfi llment of these relations obtained in the main approximation of the extended Standard Model is evaluated. Then phenomenological relations between masses of current and constituent quarks and their mixing angles are considered. A typical estimation of accuracy of these theoretical and phenomenological relations is obtained. A phenomenological relation for constituent quark masses and a mixing angle for quarks is suggested. The quark-lepton complementarity relation for quark and neutrino mixing angles is verifi ed. Functional dependences for coupling constants of electromagnetic, strong and weak interactions on the square of a four-dimensional vector of energy and momentum are represented. An example of a grand unifi cation theory is demonstrated together with possible levels of spontaneous violation of its gauge symmetry to the gauge symmetry of the extended Standard Model.

It is pointed out that additional Higgs particles are appeared at these levels of spontaneous violation. The quark-lepton complementarity relation verifi ed in the article for quark and neutrino mixing angles can be a consequence of a fundamental link between Cabibbo-Kobayashi-Maskava and Pontecorvo-Maki-Nakagava-Sakata matrices in a future grand unifi cation theory. In this case the received result will promote finding of such theory.

The quality of the image formed by the optical system is determined by its modulation transfer function at various spatial frequencies. To ensure the uniformity of measurements of the modulation transfer function and create a reference base for the reproduction, storage and transmission of modulation transfer function, the State primary standard of optical power units for eyeglass optics GET 205-2013 was improved in terms of reproducing the modulation transfer function in the wavelength range 450–1550 nm. The composition, principle of operation and main metrological characteristics of the State primary standard of units of optical power and modulation transfer function of eyeglass optics and objectives GET 205-2025 are presented. The GET 205-2025 includes an installation for measuring the modulation transfer function of optical systems and a set of reference lenses. GET 205-2025 ensures the uniformity of measurements of the modulation transfer function of optical systems in the spectral range of discrete wavelength values 450–1550 nm and allows you to transfer the modulation transfer function by comparison using a comparator to working standards. From working standards by direct measurement, the modulation transfer function is transferred to modulation transfer function measuring instruments: modulation transfer function measuring devices, contrast transfer function measuring systems, optical benches, optical system quality control stations.

The theoretical foundations of mathematical processing of indirect measurement results in the form of a quotient are considered. In practice, the results and accuracy indicators are represented by approximate formulas obtained by the linearization method. The correct presentation of the results with this method provides for the determination of the systematic error of the result by an additional assessment of the degree of approximation of the formulas. It is shown that the systematic error of an indirect measurement result can be determined with known arithmetic means and standard deviations of the measurement results necessary to obtain the desired value. It is almost impossible to clarify the value of the variance without considering the distribution laws of random errors in measurement results. It is established that the analytical formula for the quotient of random variables, derived within the framework of the necessary and suffi cient conditions for the Taylor series expansion of the quotient of random variables, can be represented as a linear function of random errors of the measurement results required to obtain the desired value. For the specifi ed linear function, based on theorems on the numerical characteristics of functions of random arguments, exact formulas are obtained that describe the mathematical expectation and variance and coincide with the formulas used in practice as approximate ones. Formulas representing the result of indirect measurements as a quotient are obtained by a method different from the linearization method, which allows these formulas to be considered exact, i.e. there is no need to evaluate the accuracy of their approximation. The results of the conducted studies are intended for use by a wide range of people involved in measurements in various fi elds of science and technology, and may be useful to instrument makers, metrologists, students of relevant specialties at universities and postgraduates.

Conformity assessment of measuring equipment, which can also be called verification, can be provided within the process of calibration in accredited calibration laboratories in accordance with the requirements of ISO/IEC 17025:2017 “General requirements for the competence of testing and calibration laboratories” on customer's request. However, the task execution in practice is often associated with significant difficulties due to the lack of laboratory personal's knowledge in the fi eld of probability theory and theoretical metrology, as well as the absence of clear and unambiguous rules for the task execution methods. The paper describes and analyzes the process of performing conformity assessment, which can be applied to any type of measuring equipment, and considers its particular elements, such as equipment requirements, decision rule, risk of a false decision and measurement uncertainty. The rules for performing conformity assessment for geometrical product specifications standardized in international standards ISO 14253 series are analyzed here. By using the example of calibration of a geometrical product specifications measuring instrument, such as a caliper, the article presents three scenarios of conformity assessment, based on different decision rules and different evaluation methods of measurement uncertainty. The statements of conformity acquired from the different scenarios of the caliper conformity assessment were inconsistent; they were analyzed and the above-mentioned scenarios were assessed for their validity in practice. The research results can be used for the development of conformity assessment procedures in accredited calibration laboratories performing the measurements of geometrical product specifications as well as the other types of measurement; they will also contribute to improving the qualification level of specialists involved in the conformity assessment and verification activities of various objects.

The efficiency of estimating the traditional numerical characteristics of multimodal symmetric and asymmetric distribution laws of a one-dimensional random variable with large amounts of statistical data is considered. To circumvent the problem of large samples, the formulas for discretization of the interval of values of a random variable by Sturgess, Brooks-Carruthers, Heinhold-Gaede and the formula for optimal discretization proposed by the authors of this article were used. For this purpose, data arrays have been formed that allow us to evaluate the numerical characteristics of the laws of distribution of random variables, taking into account their discrete values. Estimates of mathematical expectation, mean square deviation, coefficients of asymmetry and kurtosis are calculated from the transformed data sets. Estimates of the numerical characteristics of the considered distribution laws for continuous and discrete random variables with different volumes of initial statistical data are compared. The efficiency of methods for estimating the numerical characteristics of multimodal distribution laws based on initial statistical information and the results of transforming this information using the specifi ed discretization formulas has been established. The reliability of comparing the performance indicators of the studied methods was confirmed using the Kolmogorov-Smirnov criterion. It is shown that the Heinhold-Gaede formula and the optimal discretization formula proposed by the authors are more effective than the Sturgess and Brooks-Carruthers discretization formulas. The obtained results can be used in processing remote sensing data of natural objects, which are characterized by a large volume of statistical information and multimodal laws of distribution of spectral features.

In order to reduce the number of erroneous water management decisions, it is necessary to have sufficiently strict metrological support for studies of the composition and properties of natural waters. The use of standard methods requires expanding the scope of hydromonitoring and increasing the accuracy of the data obtained in order to ensure their representativeness, including the ability to refl ect general trends and transfer the results of the study to a wider range of objects. As a possible alternative to standard methods, it is proposed to analyze the accumulated measurement information using fuzzy logic. A methodology for applying the methods and mathematical apparatus of fuzzy (multi-valued) logic to solve metrological water-ecological problems has been developed and tested using the example of water quality assessment. Using fuzzy logic methods, the infl uence of four cause factors “Leaching”, “Weathering and sedimentation”, “Anthropogenic discharges”, “Self-purification” on the effect factor “Decrease in water quality against background” in the fi ve-level Harrington scale adopted in expert statistical assessment was studied. Using the software package of fuzzy logic MatLab Fuzzy Logic, forecasts of changes in water quality depending on four factors were obtained. The method of assessing the quality of natural water was tested on a specific example of setting up a fuzzy system for assessing water quality.

It was found that the risks of errors still exist, but they were significantly reduced by taking into account poorly formalized linguistic information from expert hydrologists. The possibility of using the method for an a priori assessment of the probable consequences of changes in factors infl uencing the decline in water quality and taking preventive measures to optimize the operation of the water use system was shown.

Improving the accuracy of measurements in dynamic goniometry is inextricably linked with achieving the ultimate accuracy of the optical null indicator. This device is part of angle measuring devices operating on the principle of a dynamic goniometer. The autocollimator-null-indicator, when its optical axis coincides with the normal to the controlled reflecting surface, generates an electric pulse, which is used to read the readings of the angular scale of the dynamic goniometer. The ultimate accuracy of the autocollimator-null-indicator is determined by its random error. The random error of measurements of the constant angular position of a reflecting mirror at different times of the day was experimentally studied. It is shown that external noises prevail during daytime measurements – various vibrations, air and external lighting fluctuations, which depend on the distance between the autocollimator-null-indicator and the mirror, and during nighttime measurements the influence of external effects on the measurement results is minimal, which made it possible to obtain the measurement error at night at the flicker noise level. The experimental data are analyzed using the methods of mathematical statistics, Allan variance and wavelet analysis. It is determined that the arrays of random variables characterizing the random error are non-stationary. The minimum value of the random error of the autocollimator-null-indicator was 0.001″.

The presented results are of interest to specialists developing and using optoelectronic devices based on the autocollimator.

The problem of optical reconstruction of object images using display of quantized computer-generated holograms on a high-speed digital micromirror device is considered. The quantization of light distributions is widely used for information storage, transmission, processing and compression. To determine the most universal hologram quantization method, four iterative, four noniterative quantization methods, and two methods proposed earlier by the authors of this paper and based on noniterative analysis of the intensity distribution histogram, are investigated. The processing (quantization) rate and quality of images optically reconstructed with computer-generated holograms were analyzed for the methods. The holograms were displayed on a digital micromirror device. Object images were reconstructed in laser light. The quality of reconstruction was assessed using quality metrics such as structural similarity index, correlation coefficient and speckle contrast. It was found that the quality of reconstructed images for the histogram methods is higher by 19 % compared to non-iterative methods and by 15 % compared to resource-intensive iterative methods. The rate of hologram quantization by the developed histogram methods is an order of magnitude higher than the rate of iterative methods. Joint accounting of relative intensity and the specifi ed quality metrics is realized by calculation of the target function. The target function of histogram methods exceeds its values of non-iterative and iterative methods by 5 and 2 %, respectively. The obtained results demonstrate the advantages of the histogram methods (high quality of quantization and little time of image processing), in comparison with the other ones for image reconstruction from binary holograms. Thus the histogram quantization methods are recommended for optical reconstruction of volumetric scenes, compression of holographic data, and high-speed modulation of light fi elds.

The future space experiment «Sun-Terahertz» is aimed at studying the Sun in the unexplored terahertz range, obtaining new data on the terahertz radiation of the Sun, solar active regions and solar fl ares. The scientific equipment being developed is a set of eight detectors sensitive to radiation of various frequencies in the range 0.4–12.0 THz. In this paper, we consider the expected spectral characteristics of scientific equipment and briefl y describe the method of their experimental verification by installing an additional cutoff filter. Two methods for increasing the frequency selectivity of detectors are considered. To assess the sensitivity of the detectors, an experiment was conducted to measure solar radiation using a single-channel model, which is a complete analogue of the detector of scientific equipment with the ability to replace bandpass terahertz filters. Also, a two-axis rotating platform and a cloud sensor were made for the single-channel model. Based on the results of the experimental verification, conclusions were made about the sensitivity of the detectors of scientific equipment and the possibility of improving the characteristics in terms of frequency selectivity. This article may be useful to experimenters involved in spectrometric scientific devices based on optoacoustic converters (Golay cell) and other sensitive elements.

A modified method for efficient spectral and correlation-based spatio-temporal signal processing is presented, designed for operation under conditions of high dynamic variability in input signal intensity and varying frequency-time resources of digital processing. The method is based on adapting algorithms and refining the goals and tasks of signal processing. A methodology has been developed to achieve high instrumental resolution of signals based on spectral and/or correlation features. The study addresses aspects of improving the efficiency of spatio-temporal signal processing, which are relevant for radio engineering measurement systems with digital phased antenna arrays and moving target selection systems. The previously proposed adaptive method of reversible spectral analysis, developed by the author, has been modernized for use in spatio-temporal signal processing. The updated method takes into account the variability (type changes) of processed signals and introduces measures to reduce the dynamic range requirements of the input signal stream by utilizing coarse (low-bit and binary) statistics. The frequency nomenclature has been expanded to include temporal and spatial spectra of distribution laws (characteristic functions). Technical (hardware and software) constraints, such as the use of coarse signal quantization, are also considered. Processing efficiency is achieved through the application of a whitening operation (rejection of dominant components) for passive interference prior to the main stage – the reversible spectral analysis method — and through the use of traditional stochastic algorithms. This includes increasing sample sizes (apertures, windows) and improving the convergence rate of measurements in the basic Monte Carlo method. The results obtained can be applied in radio engineering measurement complexes, including radar systems, for tasks such as radio and radio technical monitoring, as well as for measuring range and bearing coordinates.

An overview of the application of optical tomography methods in the fi eld of biological and physicochemical research is given. The capabilities of existing methods are described. However, the capabilities of optical tomography in the study of cell biology have not yet been fully explored. At present, much attention is paid to the study of blood cells, in particular erythrocytes, using optical tomography. A method for studying the redistribution of hemoglobin molecules in single native erythrocytes with a change in the osmolarity of the medium has been developed. The method is based on the principles of differential optical tomography and its modifications. This method allows obtaining information on changes in morphological and physiological parameters of cells in real time without using exogenous labels as a contrast for visualization. An original algorithm for processing differential tomography data is proposed: restoration of phase images of individual erythrocytes. As a result of data processing, three-dimensional images of changes in the refractive index during two hours of exposure of the erythrocyte in a hypoosmolar medium are obtained. Several cell parameters, including morphology and dry mass of proteins, and their changes in the medium under conditions different from normal physiological conditions in vivo were calculated. Changes in cell morphology, a decrease in dry mass, and three-dimensional maps of intracellular hemoglobin distribution were obtained. It was found that significant changes in the refractive index in the erythrocyte cytoplasm with a change in the tonicity of the solution are observed in the nearmembrane layer. This method can find application in applied research in biology and medicine to assess the general physical properties of various cells under normal or abnormal conditions, including blood cells, bacteria, neurons, algae, cancer cells, etc.

The article considers changes in water properties under the influence of various external factors and points out the absence of a generally accepted technique for accounting for the effect of air on distilled water. The possibility of instrumental assessment of the effect of carbon dioxide CO₂ on the electrical conductivity of distilled water is analyzed. For this purpose, the inertia of CO₂ gas exchange at the water/air interface in sealed conductometric cells with a degree of filling with distilled water within 10–100 % and water heating (cooling) rates of 0.04–2.00 °C·min^–1 was experimentally studied. A method for numerical assessment of the inertia of CO₂ gas exchange at the water/air interface using a special coefficient of gas exchange inertia is proposed. This coefficient is calculated based on the ratio of the change in the specific electrical conductivity of water to the average value of this parameter in the “heating – cooling” mode. When measuring the electrical conductivity of water, its temperature varied within 20–55 °C. Based on the results of the experiments, the dependences of the gas exchange inertia coefficient on the water heating rate at different cell filling factors were obtained. It was shown that the gas exchange inertia is maximum at the maximum water heating (cooling) rate and minimum cell filling with water. The highest value of the CO₂ gas exchange inertia coefficient in the experiments was about 8 %. The results obtained can be used in practice for quantitative assessment of the permeability of the water/air interface for CO₂ molecules under various external influences on water.