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VNA Tools—A Metrology Software Supporting the Digital Traceability Chain -
Metrological Assessment of pHT in TRIS Buffers Within Artificial Seawater: Implications for High-Salinity Reference Materials -
Quantifying the Performance of Distributed Large-Volume Metrology Systems for Dynamic Measurements: Methodology Development
Journal Description
Metrology
Metrology
is an international, peer-reviewed, open access journal on the science and technology of measurement and metrology, published quarterly online by MDPI.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within ESCI (Web of Science), Scopus and other databases.
- Journal Rank: CiteScore - Q2 (Engineering (miscellaneous))
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 32.8 days after submission; acceptance to publication is undertaken in 6.4 days (median values for papers published in this journal in the second half of 2025).
- Recognition of Reviewers: APC discount vouchers, optional signed peer review, and reviewer names published annually in the journal.
- Journal Cluster of Instruments and Instrumentation: Actuators, AI Sensors, Instruments, Metrology, Micromachines and Sensors.
Impact Factor:
1.5 (2024);
5-Year Impact Factor:
1.6 (2024)
Latest Articles
Non-Contact Damage Detection in Concrete Using Laser Doppler Vibrometry and Various Excitation Methods
Metrology 2026, 6(2), 35; https://doi.org/10.3390/metrology6020035 - 21 May 2026
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A substantial share of reinforced-concrete infrastructure assets has reached an age where deterioration mechanisms such as cracking, delamination, and voiding may develop, potentially increasing safety risks and maintenance demands. Conventional condition assessment commonly relies on localized intrusive testing (e.g., coring) and manual sounding,
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A substantial share of reinforced-concrete infrastructure assets has reached an age where deterioration mechanisms such as cracking, delamination, and voiding may develop, potentially increasing safety risks and maintenance demands. Conventional condition assessment commonly relies on localized intrusive testing (e.g., coring) and manual sounding, which can be disruptive, labor-intensive, and partly subjective. Vibration-based Non-Destructive Testing (NDT) provides an alternative by exciting the structure and evaluating changes in its dynamic response. In contrast to previous studies, which typically assess a single excitation method in isolation, this study provides a systematic side-by-side comparison of three vibration-based NDT excitation approaches: mechanical impact using a custom compressed-air impact device, acoustic excitation, and shaker excitation. All three methods were evaluated under identical measurement conditions. The vibration response is measured using Laser Doppler Vibrometry (LDV), enabling non-contact acquisition of frequency-response signatures. A custom mechanical excitation device was developed and evaluated, and the results indicate that it provides stable and repeatable excitation with good defect discrimination. Experiments on specimens with representative defect types show that mechanical impact and shaker excitation yield the most repeatable and discriminative response features, whereas acoustic excitation provides insufficient signal-to-noise ratios (SNRs) for the smallest tested specimens. Among the evaluated setups, the Qsources surface-mounted shaker and the compressed-air impact device provided the most promising laboratory results. However, the large electrodynamic shaker was used mainly as a controlled reference excitation method, and scalable field inspection would require more compact and automated excitation solutions. The goal of this work is therefore to support the development of efficient LDV-based non-contact inspection methods for safer and more reliable monitoring of reinforced-concrete infrastructure.
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Open AccessArticle
Fourier-Transform-Based Metrology for Whispering Gallery Mode Spectra in Soft Photonic Microcavities
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Sadok Kouz and Abdel I. El Abed
Metrology 2026, 6(2), 34; https://doi.org/10.3390/metrology6020034 - 17 May 2026
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We present a Fourier-transform (FT)-based framework for quantitative analysis of whispering gallery mode (WGM) spectra in soft photonic microcavities. By treating the WGM spectrum as a quasi-periodic signal, the method enables robust extraction of the optical path length
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We present a Fourier-transform (FT)-based framework for quantitative analysis of whispering gallery mode (WGM) spectra in soft photonic microcavities. By treating the WGM spectrum as a quasi-periodic signal, the method enables robust extraction of the optical path length directly in the frequency domain, avoiding explicit peak identification and reducing sensitivity to background and spectral overlap. This quantity is used as a primary measurand within a unified metrological formulation: when the cavity radius R is known, it yields the effective refractive index ; when the refractive index n is known, it provides an inferred geometric path length . Following the Guide to the Expression of Uncertainty in Measurement (GUM), we establish the measurement models and evaluate the uncertainty budget, identifying the FSR determination as the dominant contribution (relative uncertainty ), with secondary contributions from radius measurement ( ) and negligible influence from wavelength calibration. The framework is applied to two representative soft photonic systems as complementary test and consistency cases. For Rhodamine B-doped mesoporous silica microcapsules ( ), we obtain , corresponding to a porosity of via Bruggeman effective medium theory, in close agreement with independent BET measurements ( ). For surfactant-stabilized Rhodamine 640-doped benzyl alcohol microdroplets, the method identifies dominant Fourier-domain periodicities and yields inferred geometric path lengths consistent with near-equatorial mode propagation. An additional droplet analysis gives an FT-inferred radius of , in close agreement with the microscopy-estimated radius of approximately . By combining Fourier-domain analysis with explicit measurement modeling and uncertainty quantification, this work establishes FT-WGM spectroscopy as a reproducible and generalizable tool for single-particle metrology in complex soft-matter microcavities.
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Open AccessCommunication
A Study on Thin-Film Dispersion Interference Spectral Measurement by Integrating Deep Learning and Physical Model Fitting
by
Tong Wu, Haopeng Li, Chenxu Liu, Chuan Zhang, Jiahao Wu, Jingwei Yu, Jianjun Liu, Zepei Zheng, Bosong Duan, Anyu Sun and Bingfeng Ju
Metrology 2026, 6(2), 33; https://doi.org/10.3390/metrology6020033 - 15 May 2026
Abstract
In the context of the increasing demands of precision manufacturing and nanotechnology, especially for emerging fields such as Oxide oxide films in Nuclear nuclear fuel assemblies, the measurement of multi-layer inhomogeneous thin films faces significant challenges. Traditional spectroscopic interference thickness measurement techniques have
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In the context of the increasing demands of precision manufacturing and nanotechnology, especially for emerging fields such as Oxide oxide films in Nuclear nuclear fuel assemblies, the measurement of multi-layer inhomogeneous thin films faces significant challenges. Traditional spectroscopic interference thickness measurement techniques have limitations in handling dispersion interference, parameter coupling, and the efficient solution of nonlinear inverse problems. This study proposes a new model that integrates deep learning and physical model fitting. It constructs a theoretical model of multi-layer thin-film interference spectroscopy based on the Lorentz–Drude formula, uses a generative adversarial network (GAN) for initial structure analysis, and builds a two-layer optimization framework of “deep learning rough positioning—physical model fine fitting”. The research aims to break through the limitations of traditional methods, improve measurement accuracy and anti-noise ability, and provide a key technical support for emerging fields.
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(This article belongs to the Special Issue Measuring by Light: Innovations in Optical Measurement and Sensing for Advanced Metrology)
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Open AccessArticle
Wheelset Wear Condition Evaluation Based on High-Precision Online Measurement of Geometric Parameters
by
Saisai Liu, Qixin He, Wenjie Fu, Qiang Han and Qibo Feng
Metrology 2026, 6(2), 32; https://doi.org/10.3390/metrology6020032 - 8 May 2026
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Train wheel wear is a critical factor affecting train operational safety, making the accurate and objective evaluation of wheel wear condition essential. However, current approaches are still constrained by inadequate measurement accuracy and incomplete evaluation methods. To address this issue, this study proposes
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Train wheel wear is a critical factor affecting train operational safety, making the accurate and objective evaluation of wheel wear condition essential. However, current approaches are still constrained by inadequate measurement accuracy and incomplete evaluation methods. To address this issue, this study proposes an integrated method for the high-precision measurement and wear condition evaluation of train wheels. A multi-sensor data fusion-based measurement method is developed to synchronously acquire key wear-related parameters, including wheel diameter, flange height, and flange thickness. Based on the measured data, a matter-element model combined with game-theoretic weighting is established to evaluate wheel wear condition. Experimental results show that the proposed online measurement method for in-service wheels achieves standard deviations below 0.15 mm, and the measurement errors satisfy the requirements of Chinese railway industry standards. The evaluation results derived from the high-precision measurement data indicate that wheel wear condition gradually deteriorates with increasing service mileage, and that flange height wear is the dominant factor affecting the wear grade. These findings are consistent with actual operating conditions. The proposed method integrates high-precision multi-parameter measurements with wear condition evaluation, providing a reliable technical basis for wheel condition monitoring and predictive maintenance in rail transit.
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Open AccessArticle
Algorithm for Calculation of Pitch Diameter of Parallel Thread Gauge
by
Vedran Šimunović, Gorana Baršić and Nenad Ferdelji
Metrology 2026, 6(2), 31; https://doi.org/10.3390/metrology6020031 - 5 May 2026
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The main difficulty of pitch diameter calculation arises during the determination of the coordinates of the probing element and screw surface contact. This paper proposes a mathematical model for pitch diameter calculation of thread gauges using a two-ball stylus for internal thread calibration
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The main difficulty of pitch diameter calculation arises during the determination of the coordinates of the probing element and screw surface contact. This paper proposes a mathematical model for pitch diameter calculation of thread gauges using a two-ball stylus for internal thread calibration and three wires for external thread calibration. To describe the geometry of the thread and probing element, a non-linear equation system has been established and solved numerically. The solution of this system gives the actual contact points of the probing element with the thread profile. Pitch diameter is calculated directly without any further corrections. This mathematical model can be applied to parallel threads without any restrictions regarding lead and flank angles. Calculation of the rake correction is therefore avoided completely. The authors provide functional PHP/HTML code that can be easily integrated into any PHP-based website. Additionally, an open-access web tool has been developed that enables the direct calculation of thread pitch diameter from measured values, as well as the coordinates of the actual contact points between the thread profile and the measuring elements.
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Open AccessCommunication
Interferometric Surface Profile Measurement Based on Radial Polarization and Wavelength Variation
by
Yen-Chang Chu, Wei-En Bi, Jing-Heng Chen and Kun-Huang Chen
Metrology 2026, 6(2), 30; https://doi.org/10.3390/metrology6020030 - 4 May 2026
Abstract
A radial-polarization-based interferometric method is proposed for measuring object surface profiles. In the proposed approach, a radially polarized beam is generated by transmitting a linearly polarized beam through a zero-order vortex half-wave plate and is then introduced into a modified Twyman–Green interferometer, in
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A radial-polarization-based interferometric method is proposed for measuring object surface profiles. In the proposed approach, a radially polarized beam is generated by transmitting a linearly polarized beam through a zero-order vortex half-wave plate and is then introduced into a modified Twyman–Green interferometer, in which the test specimen is placed in one interferometric arm. By introducing a small variation in the wavelength illumination, two interferometric intensity patterns are recorded using a CMOS camera. The corresponding phase difference distribution is retrieved from the recorded intensities and subsequently used to reconstruct the surface profile of the specimen. The feasibility of the proposed method is experimentally validated by measuring a standard gauge block, and the results show good agreement with theoretical predictions. Owing to its simple optical configuration, ease of alignment, high measurement accuracy, and rapid measurement capability, the proposed method demonstrates strong potential for practical surface profile measurement applications.
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(This article belongs to the Special Issue Measuring by Light: Innovations in Optical Measurement and Sensing for Advanced Metrology)
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Open AccessCommunication
High-Frequency Coupled-Resonator CMUT with Stepped Cavity for Enhanced Sensitivity and Bandwidth in Acoustic Emission Detection
by
Sulaiman Mohaidat, Mohammad Okour, Mutaz Al Fayad and Fadi Alsaleem
Metrology 2026, 6(2), 29; https://doi.org/10.3390/metrology6020029 - 28 Apr 2026
Abstract
Acoustic emission (AE) monitoring in metal additive manufacturing (AM) requires compact sensors capable of high-frequency operation, broad bandwidth, and high sensitivity. However, increasing structural stiffness to achieve high resonance frequencies typically reduces electromechanical sensitivity. This work presents a finite element study of a
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Acoustic emission (AE) monitoring in metal additive manufacturing (AM) requires compact sensors capable of high-frequency operation, broad bandwidth, and high sensitivity. However, increasing structural stiffness to achieve high resonance frequencies typically reduces electromechanical sensitivity. This work presents a finite element study of a coupled-resonator capacitive micromachined ultrasonic transducer (CMUT) designed to address this trade-off. The proposed architecture integrates three mechanically coupled silicon membranes with a stepped capacitive cavity that increases capacitance while preserving structural stiffness, enabling enhanced sensitivity without compromising high-frequency operation. COMSOL Multiphysics simulations were used to evaluate modal characteristics and frequency response under DC pre-stressed conditions. Modal coupling produced closely spaced resonances that broadened the effective bandwidth, while the stepped cavity significantly increased voltage output through improved electromechanical coupling. Compared to a single-resonator flat-cavity design, the coupled stepped-cavity configuration demonstrated nearly a threefold enhancement in output voltage while maintaining operation near 100 kHz. Additionally, adjusting the central resonator length enabled controlled frequency tuning for scalable array implementation. These results establish a proof of concept for a high-frequency, high-sensitivity micro-electro-mechanical systems (MEMS) CMUT architecture suitable for distributed AE monitoring in advanced manufacturing environments.
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(This article belongs to the Special Issue Applied Industrial Metrology: Methods, Uncertainties, and Challenges)
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Eccentricity Correction Methods for Circular Targets in Perspective Projection
by
Frank Liebold and Hans-Gerd Maas
Metrology 2026, 6(2), 28; https://doi.org/10.3390/metrology6020028 - 20 Apr 2026
Abstract
In a perspective projection, a circular target appears as an ellipse for an oblique view. Herein, the ellipse center obtained from image coordinate measurement operators differs from the projection of the circle center. This discrepancy is called eccentricity and may lead to systematic
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In a perspective projection, a circular target appears as an ellipse for an oblique view. Herein, the ellipse center obtained from image coordinate measurement operators differs from the projection of the circle center. This discrepancy is called eccentricity and may lead to systematic errors. This article documents the significance of these discrepancies and discusses five different correction methods that can be applied in the image space or as a model adaptation. Two of the methods include the determination of the circle radius and thus also offer a possibility to define the scale. The eccentricity correction procedures are validated in a series of experiments, which proved that even extreme eccentricity effects can be fully compensated. In the experiment on the approaches including scale determination, the precision and accuracy of the scale definition is investigated, obtaining relative accuracies of 0.5–1%.
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(This article belongs to the Special Issue Advances in Optical 3D Metrology)
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Open AccessTechnical Note
Moody Revisited: Least-Squares Solutions of the Union Jack Surface Plate Measurement Method
by
Han Haitjema
Metrology 2026, 6(2), 27; https://doi.org/10.3390/metrology6020027 - 13 Apr 2026
Abstract
For the calibration of surface plate, the classical Moody method is still commonly used. In this method the straightness of a number of lines over a surface plate in a union-jack configuration is measured and combined into a flatness measurement. The measurement of
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For the calibration of surface plate, the classical Moody method is still commonly used. In this method the straightness of a number of lines over a surface plate in a union-jack configuration is measured and combined into a flatness measurement. The measurement of the two center lines is used to determine so-called closure errors. A shortcoming of this method is that it gives an ambiguous value for the central height and that the measurements of the central lines are not involved in the evaluation. This research shows how the lines can be incorporated in the measurement evaluation in a least-squares sense. This gives a measurement redundancy leading to an 18% reduction in the uncertainty. Also, it is shown that a further reduction in the uncertainty is possible when using the gravity vector as a common reference, as can be done when using electronic levels. A least-squares evaluation of measurements taken in this way gives an even further redundancy, leading to a reduction in the uncertainty of 29% relative to the traditional evaluation according to the Moody method. This is illustrated with an actual measurement example and additional Monte Carlo simulations.
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(This article belongs to the Special Issue Feature Papers Collection: Celebration of the First Impact Factor of Metrology)
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Open AccessArticle
Shrinkage Estimation to Minimize Error in Measurement Estimates and Consensus Values
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Robin Willink
Metrology 2026, 6(2), 26; https://doi.org/10.3390/metrology6020026 - 9 Apr 2026
Abstract
This paper considers the measurement of a quantity when a nominal value or previous estimate is available, which is the case with a quantity designed to be zero or which might be the case when a consensus value is to be calculated in
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This paper considers the measurement of a quantity when a nominal value or previous estimate is available, which is the case with a quantity designed to be zero or which might be the case when a consensus value is to be calculated in a measurement comparison. If an upper bound can be placed on the magnitude of the difference between the nominal value and the true value, then the mean square error of the overall measurement procedure can be reduced by a statistical method known as shrinkage estimation. We describe the method for use in an individual measurement, but we give a deeper analysis assuming the context of a measurement comparison.
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(This article belongs to the Collection Measurement Uncertainty)
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Open AccessArticle
Metrological Aspects of Soft Sensors for Estimating the DC-Link Capacitance of Frequency Inverters
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Vinicius S. Claudino, Antonio L. S. Pacheco, Gabriel Thaler and Rodolfo C. C. Flesch
Metrology 2026, 6(2), 25; https://doi.org/10.3390/metrology6020025 - 4 Apr 2026
Abstract
The capacitance of the DC link is an important variable for the prediction of remaining useful life and failures in frequency inverters. The direct measurement of the DC-link capacitance in inverters operating under load is technically challenging and generally impractical. Recently, a great
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The capacitance of the DC link is an important variable for the prediction of remaining useful life and failures in frequency inverters. The direct measurement of the DC-link capacitance in inverters operating under load is technically challenging and generally impractical. Recently, a great focus has been given to data-based soft sensors for estimating this variable. These methods, however, are evaluated based only on the estimate errors, and do not take into account the metrological aspects of these estimators. This paper proposes an uncertainty analysis method based on Monte Carlo simulations and bootstrapping that can be applied to all recently published methods for end-of-life (EOL) estimation based on data-driven regression and neural networks. A state-of-the-art model of EOL monitoring based on capacitance estimation was evaluated using the proposed framework, and an experimental study with a frequency converter drive for a brushless DC motor was performed, considering multiple output frequencies, loads and DC-link capacitance conditions. The output distributions are not symmetrical and show that the variable with the most significant impact in the propagated uncertainty is the DC link voltage. The results show confidence interval widths ranging from 12 μF to 61 μF, with wider confidence intervals obtained at higher power setpoints.
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(This article belongs to the Collection Measurement Uncertainty)
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Open AccessArticle
Experimental Study of High-Frequency Current Transformer for Partial Discharge Detection Using Frequency and Impulse Metrics
by
Laura Della Giovanna, Francesco Guastavino and Eugenia Torello
Metrology 2026, 6(2), 24; https://doi.org/10.3390/metrology6020024 - 1 Apr 2026
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This study presents a characterization method for High-Frequency Current Transformers (HFCTs) intended for partial discharge (PD) measurement in on-line acquisition systems designed for AI-based processing and clustering. The primary objective is to analyze how key design parameters, ferrite core material, and number of
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This study presents a characterization method for High-Frequency Current Transformers (HFCTs) intended for partial discharge (PD) measurement in on-line acquisition systems designed for AI-based processing and clustering. The primary objective is to analyze how key design parameters, ferrite core material, and number of turns, influence HFCT frequency response, attenuation, and sensitivity, thereby providing a basis for optimized sensor design when data analysis is to be performed by means of AI-based algorithms. The investigation focuses on the influence of different ferrite core materials and varying secondary turn numbers on the frequency spectrum and the response to IEC 60270-compliant calibrator impulses Both concentrated and well-distributed HFCT secondary winding configurations are analyzed to evaluate their impact on signal behavior and sensitivity. The experimental results are compared with a simplified theoretical model to validate performance trends and identify key design factors. The HFCT response to IEC 60270-compliant calibrator impulses is examined to assess its suitability for PD measurement systems and monitoring. The results highlight the critical role of core selection and the number of turns in shaping HFCT bandwidth, attenuation, and impulse response, which are essential for accurate and reliable PD detection in continuous monitoring systems to perform the diagnostic of the electrical insulation condition. This diagnostic approach is based on the detection of partial discharge (PD) activity over time, with the objective of identifying evolving phenomena by monitoring the amplitude and characteristics of the signals associated with different defects. Therefore, accurate separation of signals originating from different defects and from noise is essential. These results provide a foundation for designing HFCT sensors suitable for integration into advanced diagnostic frameworks, AI-aided for Condition-Based Maintenance (CBM).
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Open AccessArticle
A Cost-Effective Cylindrical Capacitive Sensor for Liquid Dielectric Characterization from 1 to 30 MHz
by
Thet Pai Oo, Thipamas Phakaew, Muhammad Uzair, Prayoot Akkaraekthalin, Wutthinan Jeamsaksiri and Suramate Chalermwisutkul
Metrology 2026, 6(2), 23; https://doi.org/10.3390/metrology6020023 - 1 Apr 2026
Abstract
A cost-effective and practical method for characterizing the dielectric properties of liquids at 1 MHz is presented in this article. A cylindrical parallel-plate capacitive sensor was developed, in which the circular end plates function as electrodes and the sidewall is formed by a
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A cost-effective and practical method for characterizing the dielectric properties of liquids at 1 MHz is presented in this article. A cylindrical parallel-plate capacitive sensor was developed, in which the circular end plates function as electrodes and the sidewall is formed by a thin polyvinyl chloride ring cut from a standard water pipe to enclose the liquid sample. Dielectric constant values of air, distilled water, ethanol, and methanol were determined through analytical calculations, electromagnetic simulations, and experimental measurements at 1 megahertz. Consistent results were obtained across all methods, and the extracted values were found to agree well with theoretical values, yielding extraction errors of 0.06% for methanol and 1.85% for ethanol with respect to theoretical values from the literature. A calibration technique was applied in which air and water were used as reference materials with known dielectric constants, effectively mitigating uncertainties associated with sensor geometry, spacer material, and fringing fields. Through this work, a practical and effective technique for dielectric characterization at low frequency has been demonstrated, with core validation of four reference materials (air, deionized water, ethanol, and methanol) at 1 MHz and an additional application example in which cow’s milk is characterized over 10–30 MHz. The 10–30 MHz measurement demonstrates the applicability of the proposed method in the low megahertz region, while the primary validation is conducted at 1 MHz. The technique is applicable to a wide range of applications in materials science, chemical, and biomedical engineering.
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(This article belongs to the Special Issue Applied Industrial Metrology: Methods, Uncertainties, and Challenges)
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Open AccessArticle
Interlaboratory Comparison of SI-Traceable Flow Metering Calibration Facilities with Gaseous Carbon Dioxide
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Ara Abdulrahman, Gabriele Chinello, Revata Seneviratne, Kurt Rasmussen, Dennis van Putten and Pier Giorgio Spazzini
Metrology 2026, 6(2), 22; https://doi.org/10.3390/metrology6020022 - 24 Mar 2026
Abstract
Carbon capture, utilization, and storage (CCUS) plays an important role in meeting the European Union’s target to reduce greenhouse gas emissions by 55% by 2030 and become carbon neutral by 2050. Accurate flow metering is required throughout the carbon capture and storage (CCS)
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Carbon capture, utilization, and storage (CCUS) plays an important role in meeting the European Union’s target to reduce greenhouse gas emissions by 55% by 2030 and become carbon neutral by 2050. Accurate flow metering is required throughout the carbon capture and storage (CCS) chain to meet fiscal and regulatory requirements. To establish accurate CO2 flow metering, flow meters must be calibrated with traceability to international standards of measurement at relevant flow conditions. To ensure confidence, reliability, and comparability of calibration results, calibration facilities perform interlaboratory comparisons. However, there is currently a lack of CO2 gas flow meter calibration facilities. The flow metering calibration facilities of VSL, NEL, INRIM, DNV, and FORCE participated in an interlaboratory comparison with CO2 up to 400 m3/h and 31 bar(a) to compare the calibration results with several flow metering principles. At the intermediate-scale facilities of NEL, VSL, and INRIM, the difference in results between the VSL and INRIM facilities were within the facilities’ CMC values, while NEL’s facility showed a significant difference primarily due to vibrational relaxational effects of CO2 with small critical flow Venturi nozzles. At the large-scale facilities of NEL, DNV, and FORCE, 91% of the test points passed the equivalency criteria in the range of 20 m3/h to 400 m3/h with a Coriolis meter, confirming traceability for carbon dioxide across the facilities. Overall, the interlaboratory comparison has made it possible for the CCUS industry to calibrate gaseous CO2 flow meters with traceability to international standards.
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(This article belongs to the Special Issue Applied Industrial Metrology: Methods, Uncertainties, and Challenges)
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Open AccessArticle
Metrological Validation of Low-Cost DS18B20 Digital Temperature Sensors Using the TH-001 Procedure: Calibration Models, Uncertainty, and Reproducibility
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Juan Antonio Rodríguez-Rama, Leticia Presa Madrigal, Alfredo Marín Lázaro, Javier Maroto Lorenzo, Ana García Laso, Jorge L. Costafreda Mustelier and Domingo A. Martín-Sánchez
Metrology 2026, 6(1), 21; https://doi.org/10.3390/metrology6010021 - 23 Mar 2026
Cited by 1
Abstract
This study presents the metrological validation of encapsulated DS18B20 digital temperature sensors. Eight units were tested, and seven were analysed (sensor 8 was excluded owing to a systematic failure). The evaluation was performed using a standard comparison calibration, where Tref was defined
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This study presents the metrological validation of encapsulated DS18B20 digital temperature sensors. Eight units were tested, and seven were analysed (sensor 8 was excluded owing to a systematic failure). The evaluation was performed using a standard comparison calibration, where Tref was defined as the mean of two calibrated Pt-100 probes in a Julabo DYNEO DD 601F thermostatic bath, following the TH-001 procedure of the Spanish Centre of Metrology (CEM). Four validation tests were performed: Test 1 (E1, 20 to 75 °C), Test 2 (E2, 20 to 72 °C), and with an extended range, Test 3 (E3, −12 to 86 °C) and Test 4 (E4, −12 to 86 °C; repetition to assess reproducibility relative to E3), with 10 steady-state readings per setpoint. Erroneous readings were defined and removed (probe 3, Test 4), and set points without valid readings from probe 4 above 68 °C were excluded. Without data processing, the errors were consistent with the manufacturer’s stated ±0.5 °C, despite an inter-probe bias. Several correction models were evaluated (offset, affine linear, polynomial, and segmented); the probe-specific affine linear model provided the best overall compromise, reducing MAE (Mean Absolute Error) to 0.046 to 0.130 °C and RMSE (Root Mean Square Error) to 0.057 to 0.169 °C. The process uncertainty is dominated by the traceability of the Pt-100 probes and the effective nonuniformity of the isothermal volume, which limits the achievable accuracy. The results support the use of individually calibrated DS18B20 sensors for continuous monitoring, provided that the effective operating range is maintained.
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(This article belongs to the Special Issue Feature Papers Collection: Celebration of the First Impact Factor of Metrology)
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Open AccessArticle
Uncertainty Assessment of S-Parameters in Vector Network Analyzers Under De-Embedding Conditions
by
Jiangmiao Zhu, Yifan Wang, Chaoxian Fu, Kaige Man and Kejia Zhao
Metrology 2026, 6(1), 20; https://doi.org/10.3390/metrology6010020 - 11 Mar 2026
Abstract
This study proposes a method to quantify uncertainty in the scattering parameter (S-parameter) measurements when using de-embedding techniques. After calibrating the measurement setup with reference standards, de-embedding algorithms are employed to extract the intrinsic S-parameter of the device under test (DUT). This process
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This study proposes a method to quantify uncertainty in the scattering parameter (S-parameter) measurements when using de-embedding techniques. After calibrating the measurement setup with reference standards, de-embedding algorithms are employed to extract the intrinsic S-parameter of the device under test (DUT). This process introduces additional complexity to the uncertainty analysis. This study investigates the sources of uncertainty inherent to vector network analyzer (VNA) measurements. Subsequently, a covariance matrix-based approach is employed to propagate these uncertainties, culminating in the quantification of S-parameter uncertainty. The effectiveness of the proposed is determined by comparing the measured S-parameters of power dividers and couplers to their nominal values, considering parameters such as balance, coupling, and voltage standing wave ratio (VSWR). Additionally, an uncertainty analysis is conducted for the power divider’s S-parameters, tracing the uncertainty sources back to the calibration standards.
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(This article belongs to the Collection Measurement Uncertainty)
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Open AccessArticle
Modelling Dissemination of Mass with Buoyancy Correction from Volume and Density of Weights
by
Jaroslav Zůda
Metrology 2026, 6(1), 19; https://doi.org/10.3390/metrology6010019 - 7 Mar 2026
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Dissemination of unit of mass is one of the key processes in mass metrology and involves a large number of measurements to determine the mass of weights across a wide range (e.g., 1 mg–10 kg in the case of the Czech Metrology Institute,
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Dissemination of unit of mass is one of the key processes in mass metrology and involves a large number of measurements to determine the mass of weights across a wide range (e.g., 1 mg–10 kg in the case of the Czech Metrology Institute, CMI). Evaluation of such measurements can be challenging, and to address this, the European Metrology Programme for Innovation and Research (EMPIR) project 19RPT02 “Improvements of the realisation of the mass scale” developed RealMass software solution (currently available in version 1.1) and a draft calibration procedure. However, standard procedures usually assume either identical densities of the weights or use the volume of the weights for buoyancy correction. In the latter case, if the volume is not known, the usual approach is to estimate it by dividing the nominal mass by the density. If the weights differ in either volume or density, these procedures lead to incorrect results. CMI developed a model and evaluation script to address these issues. The comparison data show that the developed model is consistent with the results obtained by RealMass software and other examples. The examples given in the text show how incorrect assumptions can lead to incorrect results and how they are evaluated by the approach presented in this paper.
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Open AccessArticle
Geometrical Prediction of Copper-Coated Solid-Wire Deposition by Wire-Arc Additive Manufacturing Based on Artificial Neural Networks and Support Vector Machines
by
Miroslav Petrov, Grazia Lo Sciuto, Evgeni Tongov, Yavor Sofronov, Georgi Todorov, Todor Todorov, Valentin Mishev, Antonio Nikolov and Krum Petrov
Metrology 2026, 6(1), 18; https://doi.org/10.3390/metrology6010018 - 6 Mar 2026
Abstract
Wire and arc additive manufacturing is a promising technology for fabricating large and complex metallic components. Wire arc methods, like MIG and MAG, use an electric arc to melt and deposit metal wire layer-by-layer. The improvement of the surface depends on the multi-bead
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Wire and arc additive manufacturing is a promising technology for fabricating large and complex metallic components. Wire arc methods, like MIG and MAG, use an electric arc to melt and deposit metal wire layer-by-layer. The improvement of the surface depends on the multi-bead overlapping model. However, the high quality of multi-layer deposits is reduced by structural irregularities, such as geometric defects, poor fusion, and reduced mechanical properties of the weld bead. The analysis of a single weld bead that solidifies on a base material can be carried out to improve the geometry of the microstructure, to improve the mechanical properties, and to understand the relationship between welding parameters and the bead dimensions. In the present study, current metal welding technologies and strategies in wire-arc additive manufacturing were discussed, and different weld bead geometries using BÖHLER SG2 solid wire were realized, varying the robot’s trajectory length and welding speed. The computational models are proposed to create a dependence between the controllable welding input parameters and resulting geometrical weld bead outputs (width, height, length, and radius) for prediction and optimization. These models, using techniques such as support vector machines and artificial neural networks, can be a good tool for controlling quality by understanding these input–output relationships. However, the SVM has revealed a superior performance based on metrics for the nonlinear and intricate relationships between the geometrical weld beads and welding parameters.
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(This article belongs to the Special Issue Applied Industrial Metrology: Methods, Uncertainties, and Challenges)
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Control-Enhanced Hamiltonian Optimization for Quantum Parameter Estimation in Many-Body Systems
by
Hong Tao
Metrology 2026, 6(1), 17; https://doi.org/10.3390/metrology6010017 - 5 Mar 2026
Abstract
Quantum metrology uses the principles of quantum mechanics to improve the accuracy of parameter estimation so that it can surpass the classical limit. However, noise and the challenge of preparing multipartite entangled states hinder practical applications. In this work, we use the Lipkin-Meshkov-Glick
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Quantum metrology uses the principles of quantum mechanics to improve the accuracy of parameter estimation so that it can surpass the classical limit. However, noise and the challenge of preparing multipartite entangled states hinder practical applications. In this work, we use the Lipkin-Meshkov-Glick model as the experimental platform and the quantum parameter estimation package QuanEstimation as a tool to improve the quantum parameter estimation in many-body systems by using Hamiltonian control optimization. We apply auto-GRAPE, PSO, and DE algorithm to optimize the time-dependent control field. Our results show that the optimal control strategy can significantly enhance the quantum Fisher information and reduce the quantum Cramér-Rao bound even under environmental noise. These findings provide a way to achieve the parameter estimation limit in a noisy environment and promote the development of practical quantum metrology applications.
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(This article belongs to the Special Issue Measuring by Light: Innovations in Optical Measurement and Sensing for Advanced Metrology)
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Evaluating Measurement Uncertainty Using Measurement Models with Arguments Subject to a Constraint
by
Adriaan M. H. van der Veen, Gertjan Kok and Kjetil Folgerø
Metrology 2026, 6(1), 16; https://doi.org/10.3390/metrology6010016 - 2 Mar 2026
Abstract
Measurement models that have a chemical composition as one of the arguments require special attention when used with the law of propagation of uncertainty from the Guide to the expression of uncertainty in measurement. The constraint that the amount fractions in a composition
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Measurement models that have a chemical composition as one of the arguments require special attention when used with the law of propagation of uncertainty from the Guide to the expression of uncertainty in measurement. The constraint that the amount fractions in a composition add exactly to unity not only affects the covariance matrix associated with the composition, but also impacts the differentiation of the measurement model to obtain the expressions and values of the sensitivity coefficients. Differentiating the measurement model with respect to each variable individually is not possible as it involves evaluating the model for infeasible inputs, leading to an undefined output. In this work, a numerical method for constrained partial differentiation is presented, enabling the use of the law of propagation of uncertainty for measurement models with compositions as one of their arguments. The numerical method enables treating the measurement model as a black box and using it with measurement models in the form of an algorithm. The numerical method is demonstrated by showing how the uncertainty associated with composition, temperature and pressure can be propagated through an equation of state, in this case, the GERG-2008 equation of state. It is shown that this differentiation can be completed in a few simple steps, requiring only a valid implementation of the measurement model that provides an output value for given input quantities. The numerical differentiation method applies in principle to all differentiable functions of a composition.
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(This article belongs to the Collection Measurement Uncertainty)
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