Metrology doi: 10.3390/metrology6020033

Authors: Tong Wu Haopeng Li Chenxu Liu Chuan Zhang Jiahao Wu Jingwei Yu Jianjun Liu Zepei Zheng Bosong Duan Anyu Sun Bingfeng Ju

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.

Metrology doi: 10.3390/metrology6020032

Authors: Saisai Liu Qixin He Wenjie Fu Qiang Han Qibo Feng

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.

Metrology doi: 10.3390/metrology6020031

Authors: Šimunović Baršić Ferdelji

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.

Metrology doi: 10.3390/metrology6020030

Authors: Yen-Chang Chu Wei-En Bi Jing-Heng Chen Kun-Huang Chen

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.

Metrology doi: 10.3390/metrology6020029

Authors: Sulaiman Mohaidat Mohammad Okour Mutaz Al Fayad Fadi Alsaleem

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.

Metrology doi: 10.3390/metrology6020028

Authors: Frank Liebold Hans-Gerd Maas

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%.

Metrology doi: 10.3390/metrology6020027

Authors: Han Haitjema

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.

Metrology doi: 10.3390/metrology6020026

Authors: Robin Willink

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.

Metrology doi: 10.3390/metrology6020025

Authors: Vinicius S. Claudino Antonio L. S. Pacheco Gabriel Thaler Rodolfo C. C. Flesch

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.

Metrology doi: 10.3390/metrology6020024

Authors: Laura Della Giovanna Francesco Guastavino Eugenia Torello

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).

Metrology doi: 10.3390/metrology6020023

Authors: Thet Pai Oo Thipamas Phakaew Muhammad Uzair Prayoot Akkaraekthalin Wutthinan Jeamsaksiri Suramate Chalermwisutkul

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.

Metrology doi: 10.3390/metrology6020022

Authors: Ara Abdulrahman Gabriele Chinello Revata Seneviratne Kurt Rasmussen Dennis van Putten Pier Giorgio Spazzini

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.

Metrology doi: 10.3390/metrology6010021

Authors: Juan Antonio Rodríguez-Rama Leticia Presa Madrigal Alfredo Marín Lázaro Javier Maroto Lorenzo Ana García Laso Jorge L. Costafreda Mustelier Domingo A. Martín-Sánchez

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.

Metrology doi: 10.3390/metrology6010020

Authors: Jiangmiao Zhu Yifan Wang Chaoxian Fu Kaige Man Kejia Zhao

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.

Metrology doi: 10.3390/metrology6010019

Authors: Jaroslav Zůda

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.

Metrology doi: 10.3390/metrology6010018

Authors: Miroslav Petrov Grazia Lo Sciuto Evgeni Tongov Yavor Sofronov Georgi Todorov Todor Todorov Valentin Mishev Antonio Nikolov Krum Petrov

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.

Metrology doi: 10.3390/metrology6010017

Authors: Hong Tao

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.

Metrology doi: 10.3390/metrology6010016

Authors: Adriaan M. H. van der Veen Gertjan Kok Kjetil Folgerø

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.

Metrology doi: 10.3390/metrology6010015

Authors: Carlos Otávio Damas Martins José Carlos Bizerra Costa Junior Luciano Volcanoglo Biehl Jorge Luís Braz Medeiros

The characterization of mechanical properties in heat-treated carbon steels, which is crucial for quality control, traditionally relies on destructive testing. This study evaluated the reliability of the non-destructive ultrasonic technique as a metrological alternative for AISI 1045 steel. Samples subjected to six heat treatment conditions (Annealing, Normalizing, Quenching, and Tempering) were characterized by hardness, metallography, and ultrasound. Through linear regression analyses, the multiparametric model combining sound velocity, attenuation, and FWHM demonstrated exceptional metrological precision, resulting in a coefficient of determination of (R2 = 96.687%). The metrological robustness of the model was validated by quantifying the Expanded Uncertainty (U), following the GUM (Guide to the Expression of Uncertainty in Measurement). It is concluded that the multiparametric ultrasonic methodology is an accurate, robust, and non-destructive alternative for the quantitative determination of Vickers Hardness in AISI 1045 steels, contributing to the optimization of industrial processes and metrological rigor.

Metrology doi: 10.3390/metrology6010014

Authors: Rahul Kumar Michele Norgia

Optical measurement technologies have emerged as indispensable tools in modern metrology, offering precision, noninvasive measurement capabilities, and remarkable versatility across diverse scientific and industrial applications [...]

Metrology doi: 10.3390/metrology6010013

Authors: Zimu Zhou Enrique A. Lopez-Guerra Iulica Zana Vu Nguyen Nguyen Quoc Huy Tran Violet Huang Bojun Zhou Gary Qian Michael Kwan Peter Wilkens Chester Chien

Accurate and high-efficiency film metrology remains a key challenge in High-Volume Manufacturing (HVM), where conventional spectroscopic reflectometry and white light interferometry (WLI) are either limited by model dependence or throughput. In this work, we extend the measurable film-thickness range of reflectometry to at least 50 µm through a new model-free algorithm, the Linearized Reflectance Zero-Crossing (LRZ) method. The approach builds upon the previously reported Linearized Reflectance Extrema (LRE) technique but eliminates the sensitivity to spectral sampling and fringe attenuation that degrade performance in the thick-film regime. By linearizing phase response and extracting Zero-Crossing positions in wavenumber space, LRZ provides robust and repeatable thickness estimation without iterative fitting, achieving comparable accuracy with much higher computational efficiency than conventional model-based methods. Validation using more than 80 measurements on alumina films over NiFe substrates shows excellent correlation with WLI (r = 0.97) and low gauge repeatability and reproducibility (GR&R < 3%). Moreover, LRZ achieves an average Move-Acquire-Measure (MAM) time of approximately 2 s, which is about 7 times faster than WLI. The proposed method enables fast, accurate, and model-independent optical metrology for thick films, offering a practical solution for advanced HVM process control.

Metrology doi: 10.3390/metrology6010012

Authors: Ionuț-Alin Dumitrache Andrei George Totu Ana-Maria Dumitrache Mihai Vlăduț

Dimensional verification of turbomachinery rotors requires traceable accuracy on functional data and dense coverage of freeform blades. This study quantifies the expanded measurement uncertainty (U95) for a centrifugal rotor inspected with a bridge-type CMM (Nikon Altera 10.10.8) and a structured-light scanner (ATOS Compact Scan 5M Rev.1), using repeated measurements in accordance with ISO 10360 and ISO 15530-3. The CMM achieved U95 ≈ 4–6 µm on bores, whereas optical scanning yielded U95 ≈ 12–18 µm on freeform blade regions. Cross-system results exhibited systematic offsets, indicating that the two methods are not directly interchangeable in absolute terms. Nevertheless, they are complementary: CMM ensures datum traceability, while optical scanning enables rapid full-field blade assessment, supporting uncertainty-aware hybrid inspection.

Metrology doi: 10.3390/metrology6010011

Authors: Jorge Palacios Moreno Pierre Mertiny

Unidirectional glass fiber-reinforced thermoplastic (UGFT) composite tapes are promising recyclable structural materials for applications such as composite pressure pipes. However, their durability under hydrothermal environments remains a critical concern. This study emphasizes metrology-driven evaluation of aging behavior in polypropylene-based UGFT tapes. Specimens were conditioned at 95 °C in a deionized-water environment for up to 4 weeks, and multiple complementary measurement techniques were applied to quantify degradation. Mass-change metrology was performed to characterize water uptake kinetics and establish diffusion-driven aging progression. Tensile testing enabled quantitative assessment of mechanical strength retention, defining a >25% reduction in strength as a threshold for significant deterioration. Acoustic emission (AE) acted as the central non-destructive monitoring method, capturing high-fidelity waveforms generated during loading. AE waveform descriptors, such as amplitude, rise time, and frequency content, served as measurable indicators of internal damage mechanisms including matrix cracking, interfacial debonding and fiber breakage. To process large AE datasets, principal component analysis was used for dimensionality reduction, followed by k-means clustering to group signals by damage type. Optical microscopy provided microstructural verification of these classifications. The integrated metrological framework demonstrates a reliable pathway to monitor, identify, and quantify damage evolution in hydrothermally aged UGFT structures.

Metrology doi: 10.3390/metrology6010010

Authors: Clément Moreau Julie Lemesle François Berkmans David Páez Margarit Thomas Carlier François Blateyron Maxence Bigerelle

This study investigates two measurement campaigns: extended time and short time, to determine the stability of roughness measurements, focusing on the Sdr parameter. Extended-time measurements were conducted using the most sensitive instrument available to follow metrological fluctuations. The results revealed that Sdr exhibits the clearest trend and the highest dispersion among all roughness parameters, making it the most relevant indicator for tracking temporal deviations. Other parameters, such as Sa, Sq, and Sds, also emerged as potential candidates. These results were validated through a stability analysis (SI), showing that Sdr is the worst stable roughness parameter. To ensure the robustness of the findings and be closer to the real conditions, a short-time assessment was performed using a dedicated measurement plan performed on multiple instruments. The results confirmed that measurement fluctuations are instrument-dependent, but similar results are found across the same technologies (CSI(S) and CSI(B)). The short-time study included a quality inspection, a drift/stability analysis employing AR (2) models on the time series data systematically and a relevance measurement assessment using ANOVA. The study was conducted using a full-scale roughness analysis and could potentially be applied to a multiscale approach. These findings highlight the ability of Sdr to monitor metrological fluctuation during a long-time acquisition and according to a dedicated measurement plan.

Metrology doi: 10.3390/metrology6010009

Authors: Thet Pai Oo Thipamas Phakaew Muhammad Uzair Rungsima Yeetsorn Prayoot Akkaraekthalin Wutthinan Jeamsaksiri Suramate Chalermwisutkul

This work presents microwave sensing of ethanol concentration in ethanol–water mixtures using a low-cost 3D-printed cavity resonator. The objective is to realize a customizable liquid sensor that combines high measurement accuracy with inexpensive, in-house fabrication. The cylindrical cavity is fabricated from polylactic acid using fused deposition modeling and metallized on its inner surface with copper tape. The resonator operates in the TM010 mode with a resonant frequency of 3 GHz. A standard 1.5 mL centrifuge tube is used as a modular sample holder and inserted through a circular opening in the top endcap of the cavity. The quality factor of the air-filled cavity is 200, which decreases to 37.3 when the cavity is loaded with deionized water. As an application example, ethanol concentrations in ethanol–water mixtures are determined using both the resonant frequency and the peak magnitude of the transmission coefficient (|S21|). For ethanol concentrations between 20% and 100%, the concentration can be accurately extracted from the resonant frequency alone: a quartic calibration curve yields a coefficient of determination R2=0.9992, an average sensitivity of approximately 8.4 MHz/% ethanol, and a mean absolute error of about 0.58% on the calibration set. In addition, a cubic calibration based on the peak ∣S21∣ over the 0–90% concentration range achieves a mean absolute error of approximately 0.52% on the calibration set and about 0.55% on an independent validation set covering 5–85% ethanol. Comparison with conventionally machined metal cavities shows that the proposed 3D-printed cavity achieves a high Q-factor at significantly lower cost and can be fabricated in-house using a standard 3D printer. These results demonstrate metrologically relevant performance in terms of low error and high sensitivity using a low-cost and easily replicable platform for microwave liquid sensing in biomedical and chemical engineering applications.

Metrology doi: 10.3390/metrology6010008

Authors: Fernando M. Janeiro Pedro M. Ramos

Accurate and efficient frequency estimation is essential in many scientific fields and has led to the development of various algorithms. Commonly used methods involve applying the Discrete Fourier Transform followed by spectral interpolation. This approach faces challenges especially under low signal-to-noise ratio conditions. To mitigate this limitation, the Generalized Fractional Interpolated Discrete Fourier Transform for frequency estimation of rectangular-windowed sinewaves is proposed. This non-iterative algorithm enhances frequency estimation by employing spectral components at fractional steps of the Discrete Fourier Transform frequency resolution. A non-iterative, closed-form equation for frequency estimation is derived, enabling efficient computation. The proposed algorithm is evaluated through numerical simulations and compared with existing interpolation methods for different frequencies, signal-to-noise ratios, and number of acquired samples. The method is validated using experimentally acquired sinewave signals.

Metrology doi: 10.3390/metrology6010007

Authors: David Gorman Claire Pottier Marta Cibrian Samual Johnston

Limitations associated with traditional automation approaches within manufacturing have driven the pursuit of more flexible and intelligent robot guidance methods. One promising development in this area is the integration of external multitarget six degrees of freedom (6 DoF) distributed large-volume metrology (DLVM) into the control loop. Although multiple standards exist across dimensional metrology, motion tracking, indoor positioning, robot guidance, and machine tool accuracy, there is no harmonised, technology-agnostic standard that fully encompasses the unique challenges of 6 DoF DLVM systems for dynamic applications. This work identifies key gaps in the current standards’ landscape and presents a technology-agnostic candidate test methodology intended to support future standardisation of dynamic DLVM performance evaluation. The method provides a metrologically grounded spatial reference path and a temporal alignment strategy so that position and orientation errors can be reported in the intrinsic coordinates of the path. The paper covers the basic principle of the test, artefact construction, synchronisation strategies, preliminary error modelling, and a baseline uncertainty approach, and reports representative results from initial prototype trials on a multi-nodal distance-camera DLVM system. The prototype results demonstrate feasibility and highlight temporal sampling and traceable timing as current limiting factors for fully deconvolving latency and pose error; these aspects are therefore positioned as instrumentation requirements and the focus of ongoing work.

Metrology doi: 10.3390/metrology6010006

Authors: Raquel Quendera Maria João Nunes Ana Luísa Fernando Carla Palma Sara Moura Olivier Pellegrino João Alves e Sousa

Anthropogenic CO2 emissions drive ocean acidification through changes in the carbonate system, lowering seawater pH. In contrast, salinity variations arise from physical processes such as freshwater fluxes and circulation. This study reports the preparation and Harned cell characterization of three equimolal TRIS buffer solutions (0.01 mol·kg−1, 0.025 mol·kg−1, and 0.04 mol·kg−1) in artificial seawater (ASW) matrices with practical salinities of 35 and 50 and temperatures of 20 °C, 25 °C, and 30 °C. Determined pHT values achieved expanded uncertainties (UpHT ≤ 0.006), meeting Global Ocean Acidification Observing Network (GOA-ON) “climate” quality standards. Absolute salinity (SA) was concurrently measured via density (TEOS-10), revealing systematic deviations from practical salinity due to TRIS content. A nonlinear regression model was developed to predict pHT as a function of salinity, temperature, and TRIS molality, with r2 = 0.99998. These results provide a robust dataset for developing Certified Reference Materials (CRMs) for pHT calibration under climate-relevant high-salinity environments at different temperature conditions, offering a practical tool for high-accuracy calibration in variable marine conditions.

Metrology doi: 10.3390/metrology6010005

Authors: Ioulia Chikina

Impedance diagnostics is commonly employed in the study of transport phenomena in conducting media of different sizes. A common reason for choosing the more complex method of exciting the conductive medium at finite frequencies (ac mode) instead of the relatively simple method of excitation at zero frequency (dc mode) is to eliminate the influence of contact phenomena on the current–volt charateristic (IVC) during dc measurements. In this paper, we analyze relaxation phenomena in electrolytes with linear electrohydrodynamics in terms of dopant density nd. It is shown that the requirement of linearity on nd of the electrohydrodynamics of dilute solutions cannot be satisfied by the Debye–Huckel–Onsager theory of electrolyte conductivity. A linear alternative based on the fundamental principles of the theory of transport in finely dispersed two-phase systems is proposed. This alternative is referred to in the literature as Maxwell’s formalism. It is noted that, in this case, there is a consistent possibility of treating the observed relaxation time, τc, as impedance time τrc(τc→τrc=RC). Here, R is the resistance of the dilute electrolyte part of the cell, and C is the electrolytic capacitance of the same cell. This capacitance does not coincide with the traditional geometric one, C0<<C, and has to be calculated self-consistently. Examples of the successful application of RC-consistent ac diagnostics are discussed. This refers to the numerous instances in which the effective conductivity of various colloidal media deviates from the predictions of Maxwell’s well-known theory and to the correct interpretation of these anomalies in the RC representation.

Metrology doi: 10.3390/metrology6010004

Authors: Bo Shi Hongli Liu Emanuele Zappa

To achieve low-cost and flexible wheel angles measurement, we propose a novel strategy that integrates wheel segmentation network with 3D vision. In this framework, a semantic segmentation network is first employed to extract the wheel rim, followed by angle estimation through ICP-based point cloud registration. Since wheel rim extraction is closely tied to angle computation accuracy, we introduce APCS-SwinUnet, a segmentation network built on the SwinUnet architecture and enhanced with ASPP, CBAM, and a hybrid loss function. Compared with traditional image processing methods in wheel alignment, APCS-SwinUnet delivers more accurate and refined segmentation, especially at wheel boundaries. Moreover, it demonstrates strong adaptability across diverse tire types and lighting conditions. Based on the segmented mask, the wheel rim point cloud is extracted, and an iterative closest point algorithm is then employed to register the target point cloud with a reference one. Taking the zero-angle condition as the reference, the rotation and translation matrices are obtained through point cloud registration. These matrices are subsequently converted into toe and camber angles via matrix-to-angle transformation. Experimental results verify that the proposed solution enables accurate angle measurement in a cost-effective, simple, and flexible manner. Furthermore, repeated experiments further validate its robustness and stability.

Metrology doi: 10.3390/metrology6010003

Authors: Mishraim Sanchez-Torres Ismael Hernández-Capuchin Cristina Ramírez-Fernández Eddie Clemente José Luis Javier Sánchez-González Alan López-Martínez

Digital fringe projection profilometry (DFPP) is a widely used technique for full-field, non-contact 3D surface measurement, offering precision from the sub-micrometer-to-millimeter scale depending on system geometry and fringe design. This review provides a consolidated synthesis of advances reported between 2022 and 2025, covering projection and imaging architectures, phase formation and unwrapping strategies, calibration approaches, high-speed implementations, and learning-based reconstruction methods. A central contribution of this review is the integration of these developments within a metrological perspective, explicitly relating phase–height transformation, fringe parameters, system geometry, and calibration to dominant uncertainty sources and error propagation. Recent progress highlights trade-offs between sensitivity, robustness, computational complexity, and applicability to non-ideal surfaces, while learning-based and hybrid optical–computational approaches demonstrate substantial improvements in reconstruction reliability under challenging conditions. Remaining challenges include measurements on reflective or transparent surfaces, dynamic scenes, environmental instability, and real-time operation. The review outlines emerging research directions such as physics-informed learning, digital twins, programmable optics, and autonomous calibration, providing guidance for the development of next-generation DFPP systems for precision metrology.

Metrology doi: 10.3390/metrology6010002

Authors: Haider Ali Hasan Ali Noori Abdulrasool Hadeel Raad Mahdi Bashar Alsadik

This paper introduces a constraint-aware optimization framework for designing spherical multi-camera rigs that achieve complete panorama coverage while adhering to physical and field-of-view limitations. The approach assesses coverage using solid-angle geometry and calculates the sampling density in pixels per steradian, providing a measurable, traceable basis for panoramic optical measurement. By viewing panoramic imaging as a directional measurement challenge, the framework aligns with principles of optical metrology and guarantees uniform, non-contact optical sensing around the sphere. The optimization process includes capsule-based collision constraints, soft coverage losses, and field-of-view intersection modeling to produce physically feasible rig configurations. Experiments show that the optimized rigs provide improved coverage uniformity and less redundancy, with validation through Blender-generated synthetic panoramas confirming the practical performance of the designed optical systems. The proposed approach allows for systematic, measurement-driven design of spherical camera rigs for use in immersive imaging, robotic perception, and structural inspection.

Metrology doi: 10.3390/metrology6010001

Authors: Hening Huang

Many fields or disciplines (e.g., uncertainty analysis in measurement science) require a combination of probability distributions. This technical note examines three methods for combining probability distributions: weighted linear pooling, geometric pooling, and the law of combination of distributions (LCD). Although these methods have been discussed in the literature, a systematic comparison of them appears insufficient. In particular, there is no discussion in the literature regarding the potential information loss that these methods may cause. This technical note aims to fill this gap. It provides insights into these three methods under the normality assumption. It shows that the weighted linear pooling method preserves all the variability (including heterogeneity) information in the original distributions; neither the geometric pooling method nor the LCD method preserves all the variability information, leading to information loss. We propose an index for measuring the information loss of a method with respect to the weighted linear pooling method. This technical note also shows that the weighted linear pooling method can be used as an alternative to the traditional random-effects meta-analysis. Three examples are presented: the combination of two normal distributions, the combination of three discrete distributions, and the determination of the Newtonian constant of gravitation.

Metrology doi: 10.3390/metrology5040079

Authors: Haruka Tsuboi Taichi Kaizuka Katsuaki Shirai

Photoacoustic (PA) velocimetry offers a promising solution to the limitations of conventional techniques for measuring blood flow velocity. Given its moderate penetration depth and high spatial resolution, PA imaging is considered suitable for measuring low-velocity blood flow in capillaries located at moderate depths. High-resolution measurements based on PA signals from individual blood cells can be achieved using a high-frequency transducer. However, high-frequency signals attenuate rapidly within biological tissue, restricting the measurable depth. Consequently, low-frequency transducers are required for deeper measurements. To date, PA flow velocimetry employing low-frequency transducers remains insufficiently explored. In this study, we investigated the effect of the concentration of particles that mimic blood cells within vessels under low-concentration conditions. The performance of flow velocity measurement was evaluated using an ultrasonic transducer (UST) with a center frequency of 10 MHz. The volume fraction of particles in the solution was systematically varied, and the spatially averaged flow velocity was assessed using two different distinct analysis methods. One method employed a time-shift approach based on cross-correlation analysis. Flow velocity was estimated from PA signal redpairs generated by particles dispersed in the fluid, using consecutive pulsed laser irradiations at fixed time intervals. The other method employed a pulsed Doppler method in the frequency domain, widely applied in ultrasound Doppler measurements. In this method, flow velocity redwas estimated from the Doppler-shifted frequency between the transmitted and received signals of the UST. For the initial analysis, numerical simulations were performed, followed by experiments based on displacement measurements equivalent to velocity measurements. The target was a capillary tube filled with an aqueous solution containing particles at different concentration levels. The time–domain method tended to underestimate flow velocity as particle concentration increased, whereas the pulsed Doppler method yielded estimates consistent with theoretical values, demonstrating its potential for measurements at high concentrations.

Metrology doi: 10.3390/metrology5040078

Authors: Amna Qayyum Joël Bachmann David Eugen Grimm

Rapid advancements in surveying technology have necessitated the development of more accurate and efficient tools. Leica Geosystems AG (Heerbrugg, Switzerland), a leading provider of measurement and surveying solutions, has initiated a study to enhance the capabilities of its GNSS INS-based surveying systems. This research focuses on integrating the Leica GS18 I GNSS receiver and the AP20 AutoPole with a Time of Flight (ToF) camera through sensor fusion. The primary objective is to leverage the unique strengths of each device to improve accuracy, efficiency, and usability in challenging surveying environments. Results indicate that the fused AP20 configuration achieves decimetre-level accuracy (2.7–4.4 cm on signalized points; 5.2–20.0 cm on natural features). In contrast, the GS18 I fused configuration shows significantly higher errors (17.5–26.6 cm on signalized points; 16.1–69.4 cm on natural features), suggesting suboptimal spatio-temporal fusion. These findings confirm that the fused AP20 configuration demonstrates superior accuracy in challenging GNSS conditions compared to the GS18 I setup with deviations within acceptable limits for most practical applications, while highlighting the need for further refinement of the GS18 I configuration.

Metrology doi: 10.3390/metrology5040077

Authors: Ondrej Benko Marek Fraštia

The calibration of levelling staff is a key prerequisite for achieving high-precision levelling. Traditionally, this process is carried out using laser interferometric systems, which provide the required accuracy but are demanding in terms of operation, maintenance, and measurement conditions. This paper focuses on verifying the applicability of the convergent photogrammetry method for levelling staff calibration with a target accuracy of 0.010 mm. An experimental prototype of a photogrammetric calibration system (without real scale) was developed and tested using three different lenses, two processing software packages (Photomodeler and Agisoft Metashape), and two different approaches to camera calibration (self-calibration and field calibration). The repeatability of measurements was evaluated based on mutual lengths between selected checkpoints and the accuracy of determining the 3D positions of these points. The results showed that the Nikon AF-S NIKKOR 35 mm f/1.8G ED lens achieved the best repeatability and met the target accuracy requirement, while Photomodeler yielded smaller standard deviations in the determination of control point positions compared to Agisoft Metashape. The findings indicate that convergent photogrammetry, when applied under optimal conditions, has the potential to achieve the accuracy required for high-precision measurements in metrology, and may even offer an alternative to laser interferometric calibration systems in certain applications.

Metrology doi: 10.3390/metrology5040076

Authors: Siddhant Shah Minfei Liang Eugene Pinsky

The concept of dynamic symmetry in art and extensive measurements on Greek vases suggest that a vase and its parts can be inscribed into similar rectangles, with all rectangles having the same ratio of lengths of their side. Such an observation is often used in describing self-similarity and fractal geometry. This work proposes a hypothesis that a logarithmic spiral describes the equation of the cross-section of a Greek vase. From extensive measurements, the parameters of such spirals are computed, and explicit formulae are derived for volume based on a few size measurements. The exact formula is quite complex and cannot be easily used, certainly not in antiquity. Therefore, a simple approximation formula is proposed for amphorae, the most important type of vase. This formula expresses the volume of the vase in terms of its diameter and the height of the corresponding solid. The approximation is compared with some exact volume computation results reported for amphorae, and it is shown that the proposed approximation is fairly close to the exact value. The simplicity of the proposed formula suggests an efficient method of calculating volume that was probably known in antiquity.

Metrology doi: 10.3390/metrology5040075

Authors: Adriana Palos Ismael Caballero Daniel de Mercado Yolanda Álvarez David Peral Javier Díaz de Aguilar

Centro Español de Metrología (CEM) is developing a quantum frequency standard based on trapped calcium ions, marking its entry into the landscape of the second quantum revolution. Optical frequency standards offer unprecedented precision by referencing atomic transitions that are fundamentally stable and immune to environmental drift. However, the challenge of developing such a system from scratch is unaffordable for a medium-sized National Metrology Institute (NMI), which seems to limit the ability of an institute such as CEM to contribute to this field of research. To overcome this, CEM has adopted a hybrid strategy, combining commercially available components with custom integration to accelerate deployment. This paper defines and implements an architecture adapted to the constraints of a medium-size NMI, where the main contribution is the systematic design, selection, and interconnection of the subsystems required to realize this standard. The rationale behind the system design is presented, detailing the integration of key elements for ion trapping, laser stabilization, frequency measurement, and system control. Current progress, ongoing developments, and future research directions are outlined, establishing the foundation for spectroscopic measurements and uncertainty evaluation. The project represents a strategic step toward strengthening national capabilities in quantum metrology for a medium-sized NMI.

Metrology doi: 10.3390/metrology5040074

Authors: Patrice Salzenstein Thomas Y. Wu Ekaterina Pavlyuchenko

International comparisons play a critical role in ensuring precision, accuracy, consistency, and trust in the global metrology system. The Comité International des Poids et Mesures (CIPM) established the Mutual Recognition Arrangement (MRA) in 1999 to facilitate global trade. This paper gives an overview of the critical role of international comparisons to National Metrology Institutes (NMIs), industrial calibration laboratories, and research laboratories in fostering global measurement equivalence and the CIPM MRA. NMIs rely on Key and Supplementary Comparisons to ensure the mutual recognition of calibration and reference material certificates, vital for global trade and regulatory compliance. Industrial calibration laboratories participate in inter-laboratory or international comparisons to validate their calibration and measurement capability (CMC) and balance their risk management. Research laboratories push the frontiers of measurement science and validate their measurement result via international comparisons. Through some examples of comparisons, the paper illustrates how measurement result discrepancies uncovered in comparisons drive technical improvements, uncertainty component identification, and measurement technique refinement. International comparisons enhance scientific credibility, build public trust, support industrial innovation, and drive evolution in measurement science. As technological demands grow, fostering broader participation in international comparisons by various metrology and research laboratories remains crucial to maintain a robust and reliable global metrology system.

Metrology doi: 10.3390/metrology5040073

Authors: So Ito Daichi Inukai Takehiro Tomioka Yasutomo Sugisawa Kenta Matsumoto Kazuhide Kamiya

In three-dimensional measurement using a microprobing system with a micrometric spherical tip, a deviation in the diameter of the probe tip sphere causes measurement errors. In a typical probing system calibration, the effective diameter of the probe tip sphere is estimated based on the probing coordinates obtained on a calibration artifact with guaranteed dimensional accuracy. On the other hand, the calibration results of the effective diameter of the probe tip include uncertainty sources derived from errors inherent to the calibration artifacts and probing system itself, which cannot be eliminated. In this study, a micro-stylus with a tip sphere having a diameter less than 25 μm was fabricated. The actual diameter of its tip sphere was measured based on the contour form obtained along with the high-precision plane. The effective diameter of the same microprobe tip sphere was also measured by probing inside the precision micro-slit constructed with three gauge blocks. The measurement uncertainties of the actual and effective diameters were calculated and compared to each other. The measurement uncertainty of the actual diameter of the microprobe tip sphere based on the contour form measurement was confirmed to be smaller than that of the effective diameter measurement uncertainty, as it did not include errors inherent in the probing system. Furthermore, because the difference between the actual and effective diameters was smaller than that of the measurement uncertainties, the effectiveness of measuring actual diameter in microprobe calibration has been demonstrated.

Metrology doi: 10.3390/metrology5040072

Authors: Markus Zeier Michael Wollensack Johannes Hoffmann Peter Morrissey Juerg Ruefenacht Daniel Stalder

This paper presents METAS VNA Tools Version 2.9.0, a metrology software suite designed to support the digital traceability chain in vector network analyzer measurements. Built on the METAS UncLib Version 2.9.0 uncertainty engine, the software enables rigorous modeling of the entire measurement process and comprehensive uncertainty evaluation. By encapsulating values, dependencies, and sensitivities in structured uncertainty objects, the software ensures that traceability and correlation information are preserved and propagated throughout complex calibration chains. This approach allows for seamless, modular uncertainty evaluation and supports the generation of digitally signed calibration certificates with embedded calibration data. The methodology enhances transparency, reproducibility, and interoperability, aligning with the goals of digital transformation in metrology. VNA Tools thus provides a robust foundation for implementing traceable, data-driven workflows across all levels of the metrological infrastructure.

Metrology doi: 10.3390/metrology5040071

Authors: Hongliang Zhou Yanchu Liu Yunxiao Wu

The cross-correlation algorithm, widely used for transit-time determination in ultrasonic gas flowmeters, becomes susceptible to significant errors under high flow rates. Fluid disturbances and noise distort ultrasonic waveforms, causing cycle-skipping errors that result in large, integer-period miscalculations of time-of-flight. To overcome these limitations, this study introduces a novel similarity-symmetry method. First, a similarity-based technique is proposed that exploits the stable rising-edge profile of the signal envelope, which remains consistent across flow rates, to accurately pinpoint the arrival time and mitigate cycle-skipping. Second, for multi-path flowmeters, the inherent physical symmetry between upstream and downstream transit times in each channel provides a basis for cross-validation. Any significant asymmetry flags potential cycle-skip events for correction. By integrating these two principles, our hybrid method enhances robustness. Experimental results on a six-path gas flowmeter rig demonstrate that the proposed approach reduces average flow rate errors by 75% compared to the standard cross-correlation method and maintains the maximum relative error below 1% when the flow rate is above 71.78 m3/h. This work provides a reliable solution for high-precision gas flow measurement in demanding conditions, with direct relevance to applications such as natural gas custody transfer and industrial process control where measurement accuracy is critical.

Metrology doi: 10.3390/metrology5040070

Authors: Sascha Eichstädt Jens Niederhausen

Data spaces are digital realms of data and information shared between stakeholders and peer groups. They underpin several developments in sectors ranging from the automotive industry, through social sciences, to governmental networks. Digital traceability of information in data spaces is needed to validate statements about metadata, data quality, and data features. In many cases, this also directly translates to metrological traceability of measurements to the SI. The concept and development of Digital Product Passports bring these traceability aspects together to form a tool for a digital quality infrastructure. This paper outlines the general principles of digital metrological traceability based on digital certificates, a digital international system of units, and Digital Product Passports.

Metrology doi: 10.3390/metrology5040069

Authors: André Bülau Daniela Walter Magnus Kofoed Florian Janek Volker Kible Karl-Peter Fritz

Optically detected magnetic resonance (ODMR) of nitrogen-vacancy centers in diamonds, in addition to optical excitation with green light, requires microwave excitation and thus a microwave structure. While many different microwave structures including microwave resonators have been presented in the past, none of them fulfilled the need to fit inside the miniaturized quantum magnetometer with limited space used in this work. This is why a novel microwave resonator design using commercially available printed circuit board technology is proposed. It is demonstrated that this design is of small form factor, highly power efficient and low-cost, with very good reproducibility, and in addition, it can be fabricated as a flexible printed circuit board to be bent and thus fit into the miniaturized sensor used in this work. The design choices made for the resonator and the way in which it was trimmed and optimized geometrically are presented and ODMR spectra made with a miniaturized quantum sensor in combination with such a resonator, which was fed by a microwave generator set to different microwave powers, are shown. These measurements revealed that a microwave power of −4 dBm is sufficient to excite the ms = ±1 states of the nitrogen-vacancy centers, while exceeding −1 dBm already introduces sidebands in the ODMR spectrum. This underlines the efficiency of the resonator in exciting the nitrogen-vacancies of the diamond in the sensor platform used and can lead to development of low-power quantum sensors in the future.

Metrology doi: 10.3390/metrology5040068

Authors: Kate Pexman Stuart Robson Hannah Corcoran

Measurement systems such as laser trackers and 3D imaging systems are being increasingly adopted across the manufacturing industry. These metrology technologies can allow for live, high-precision measurement in a digital system, enabling the spatial component of the digital manufacturing twin. In aircraft wing manufacturing, drilling and fastening operations must be guided by precise measurements from a digital design model. With thousands of fasteners on each aircraft wing, even small errors in alignment of surface covers to wing ribs and spars can impact component longevity due to aerodynamic drag. Determining surface conformance of airstream-facing surfaces is currently largely performed though manual gauge checking by human operators. In order to capture the surface details and reverse engineer components to assure tolerance has been achieved, laser scanners could be utilised alongside a precise registration strategy. This work explores the quality of the aerostructure surface in a captured point cloud and the subsequent accuracy of surface normal determination from planar fastener heads. These point clouds were captured with a reference hand-held laser scanner and two terrestrial laser scanners. This study assesses whether terrestrial laser scanners can achieve <0.5° surface normal accuracy for aerospace fastener alignment. Accuracy of the surface normals was achieved with a nominal mean discrepancy of 0.42 degrees with the Leica RTC360 3D Laser Scanner (Leica Geosystems AG, Heerbrugg, Switzerland) and 0.27 degrees with the Surphaser 80HSX Ultra Short Range (Basis Software Inc., Redmond, WA, USA).

Metrology doi: 10.3390/metrology5040067

Authors: Atilla Barna Vandra Ágota Drégelyi-Kiss

This study presents a novel error model that distinguishes between constant and variable components of systematic error (bias) in measurement systems, particularly within clinical laboratory settings. Traditional approaches often conflict with these components, resulting in miscalculations of total error and measurement uncertainty. Through mathematical deduction and computer simulations, the authors demonstrate that the standard deviation derived from long-term quality control (QC) data includes both random error and the variable bias component, challenging its use as a sole estimator of random error. The proposed model defines the constant component of systematic error (CCSE) as a correctable term, while the variable component (VCSE(t)) behaves as a time-dependent function that cannot be efficiently corrected. The study further reveals that long-term QC data are not normally distributed, contradicting prevailing assumptions in metrology. It advocates for revised definitions in the International Vocabulary of Metrology (VIM3), emphasizing the need to distinguish between bias types determined under different measurement conditions. By applying this refined model, laboratories can enhance decision-making accuracy and more accurately estimate measurement error and uncertainty. The findings have implications beyond clinical laboratories, suggesting a paradigm shift in how systematic error is conceptualized and managed across all domains of metrology.

Metrology doi: 10.3390/metrology5040066

Authors: Binoy Debnath Zahra Pourfarash Bhairavsingh Ghorpade Shivakumar Raman

Reverse engineering (RE) is increasingly recognized as a vital methodology for reconstructing mechanical components, particularly in high-value sectors such as aerospace, transportation, and energy, where technical documentation is often missing or outdated. This study presents a systematic review that investigates the application, challenges, and future directions of RE in mechanical component reconstruction. Adopting the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) framework, 68 peer-reviewed studies were identified, screened, and synthesized. The review highlights RE applications in restoration, redesign, internal geometry modeling, and simulation-driven performance assessment, leveraging technologies such as 3D scanning, CAD modeling, and finite element analysis. However, persistent challenges remain across five domains: product complexity, tolerance and dimensional variations, scanning limitations, integration barriers, and human-material-process dependencies, which hinder automation, accuracy, and manufacturability. Future research opportunities include the automated conversion of point cloud data into editable boundary representation (B-rep) models and AI-driven approaches for feature recognition, geometry reconstruction, and the generation of simulation-ready models. Additionally, advancements in scanning techniques to capture hidden or internal features more effectively are crucial. Overall, this review provides a comprehensive synthesis of current practices and challenges while proposing pathways to advance RE in industrial applications, fostering greater automation, accuracy, and integration in digital manufacturing workflows.

Metrology doi: 10.3390/metrology5040065

Authors: Christopher R. Schwarze Anthony D. Manni David S. Simon Abdoulaye Ndao Alexander V. Sergienko

Measurement technology employing optical interference phenomena such as a fringe pattern or frequency shift has been evolving for more than a century. Systems are being designed better, and their components are being built better. However, the major components themselves hardly change. Most modern interferometers rely on the same conventional set of components to separate the electromagnetic field into multiple beams, such as plate optics and beam splitters. This naturally limits the design scope and thus the potential applicability and performance. However, recent investigations suggest that incorporating novel, higher-dimensional linear optical splitters in interferometer design can lead to several improvements. In this work, we review the underlying theory of these novel optical scatterers and some demonstrated configurations with enhanced resolution. The basic principles of optical interference and optical phase sensing are discussed in tandem. Emphasis is placed on both familiar and unfamiliar scatterers, such as the maximally symmetric Grover multiport, whose actions are left unchanged by certain gauge transformations. These higher-dimensional, gauge-invariant multiports embody a new class of building blocks that can tailor optical interference to metrology in unconventional ways.

Metrology doi: 10.3390/metrology5040064

Authors: Ilias Chouridis Gabriel Mansour Vasileios Papageorgiou Michel Theodor Mansour Apostolos Tsagaris

Conducting measurements is a daily and time-consuming process that is critical to the manufacturing industry. The most widespread way to carry out the measuring process is using a Coordinate Measuring Machine (CMM). In this paper, a methodology is presented to accelerate the measuring procedure by optimally programming a CMM. The proposed methodology utilizes the information from a computer-aided design (CAD) file and the capabilities of CMMs in order to optimize the measurement process. An improved artificial fish swarm algorithm was modified to meet the requirements of the measurement process and the capabilities of the CMMs. In addition, the ant colony optimization method is applied to extract the optimal sequence of measurements throughout the multiple areas on the component. The resulting optimal path also utilizes the free areas between the different manufactured features of the component. Finally, the resulting path is collision-free, ensuring the integrity and the safety of the CMM. The proposed methodology is verified through real-world experiments.

Metrology doi: 10.3390/metrology5040063

Authors: Stylianos-Vasileios Kontomaris Anna Malamou Gamal M. Ismail Anna Katsiki Andreas Stylianou

The Hertz equation is the most widely used equation for data processing in AFM nanoindentation experiments on soft samples when using spherical indenters. Although valid only for small indentation depths relative to the tip radius, it is usually preferred because it directly relates applied force to indentation depth. Sneddon derived accurate equations relating force and contact radius to indentation depth for shallow and deep indentations, but they are rarely used in practice. This paper presents analytical approaches to solving Sneddon’s nonlinear system. Using Taylor series expansions and a simple equation linking applied force, average contact radius, and indentation depth, we derive a two-term equation that directly relates force to indentation depth. This expression is accurate for h ≤ 1.5 R, where h is the indentation depth and R is the indenter radius, making it applicable to most practical AFM measurements on soft materials. It should be used instead of the Hertzian model for extracting Young’s modulus, thereby enhancing measurement accuracy without increasing the complexity of data processing. In addition, the results are generalized to produce a series solution that is valid for large indentation depths. The newly derived equations proposed in this paper are tested on both simulated and experimental data from cells, demonstrating excellent accuracy.

Metrology doi: 10.3390/metrology5040062

Authors: Friedrich Bleicher Benjamin Raumauf Günther Poszvek

The growing demand for automated production systems is driving continuous innovation in smart and data-driven manufacturing technologies. In the field of production metrology, the trend is shifting from using measurement laboratories to integrating measurement systems directly into production processes. This has led the Institute of Manufacturing Technology at TU Vienna together with its partners to develop a roughness measurement device that can be directly integrated into machine tools. Building on this foundation, this study tries to find applications beyond mere surface roughness assessment and demonstrates how the device could be applied in broader contexts of manufacturing process monitoring. By linking surface measurements with tool wear monitoring, the study establishes a correlation between surface roughness and wear progression of indexable inserts in milling. It demonstrates how in situ data can support predictive maintenance and the real-time adjustment of cutting parameters. This represents a first step toward integrating in situ metrology into closed-loop control in machining. The experimental setup followed ISO 8688-1 guidelines for tool life testing. Indexable inserts were operated throughout their entire service life while surface roughness was continuously recorded. In parallel, cutting edge conditions were documented at defined intervals using focus variation microscopy. The results show a consistent three-phase pattern: initially stable roughness, followed by a steady increase due to flank wear, and an abrupt decrease in roughness linked to edge chipping. These findings confirm the potential of integrated roughness measurement for condition-based monitoring and the development of adaptive machining strategies.

Metrology doi: 10.3390/metrology5040061

Authors: Elena Serea Codrin Donciu Marinel Costel Temneanu

Lighting measurements and calculation is an old and widespread process, evolving with the variety of technologies that use light or operate efficiently depending on the natural or artificial light conditions in the ambient environment. The complexity of human activities gives rise to different techniques and approaches to lighting effect analysis, and this paper aims to clarify which type of units, photometric or radiometric, are appropriate, and which light measurement and calculation techniques are optimal for evaluating the environmental microclimate intended for an activity. Quantitative lighting analysis is common and accessible through the measuring devices, calculation formulas, and simulation software available. In contrast, qualitative analysis remains less prevalent, partly due to its complexity and the need to consider human perception as a central component in assessing lighting impact, as emphasized by the human-centric lighting paradigm. Current evaluation frameworks distinguish between the quantitative and qualitative approaches, with actinic calculations addressing biologically relevant aspects of lighting in specific environmental contexts.

Metrology doi: 10.3390/metrology5040060

Authors: Bong Gyu Jeong Sang-Hoon Park Deuk-Hoon Goh Bong-Jae Lee

In this study, we propose a simple and effective method for gas analysis by establishing a correlation between residual gas analyzer (RGA) intensity and gas concentration. To achieve this, we focused on CF4 and NF3, two high-global warming potential (GWP) gases commonly used in industrial applications. The experiment was conducted in four key steps: identifying gas species using optical emission spectroscopy (OES), calibrating RGA with a quadrupole mass spectrometer (QMS), constructing a five-point calibration graph to correlate RGA and Fourier-transform infrared spectroscopy (FT-IR) data, and estimating the concentration of unknown samples using the calibration graph. The results under plasma-on conditions demonstrated correlation and accuracy, confirming the reliability of our approach. In other words, the method effectively captured the relationship between RGA intensity and gas concentration, providing valuable insights into concentration trends. Thus, our approach serves as a useful tool for estimating gas concentrations and understanding the correlation between RGA intensity and gas composition.

Metrology doi: 10.3390/metrology5040059

Authors: Gertjan Kok Marcel van Dijk

Virtual experiments (VE) can be used to assess the measurement uncertainty of complex measurements. The typical calculation procedure implemented in such a VE, called VE-DA in this paper, is based on a Monte Carlo method involving simulating possible measurement errors and possible measurement data based on extensive modeling of the measurement instrument, followed by applying a data analysis function (DA) to evaluate the measurement data. This procedure is similar to the propagation of distributions using a Monte Carlo method (PoD) procedure presented in the written standard JCGM-101, in which the Monte Carlo method is applied to an explicit mathematical model for the measurand involving simulating and applying possible corrections to the observed measurement data. However, in this paper, we show that the uncertainty provided by the VE-DA procedure can be both larger and smaller than the uncertainty evaluated based on applying the PoD to the correct measurement model, when available. This is important to realize by users of the VE-DA procedure when claiming conformity of an uncertainty evaluation with JCGM-101.

Metrology doi: 10.3390/metrology5040058

Authors: Fernando Lopez-Medina José A. Núñez-López Oleg Sergiyenko Dennis Molina-Quiroz Cesar Sepulveda-Valdez Jesús R. Herrera-García Vera Tyrsa Ruben Alaniz-Plata

Some laser scanners utilize stepper motor-driven optomechanical assemblies to position the laser beam precisely during triangulation. In laser scanners such as the presented Technical Vision System (TVS), to enhance motion resolution, gear transmissions are implemented between the motor and the optical assembly. However, due to the customized nature of the mechanical design, errors in manufacturing or insufficient mechanical characterization can introduce deviations in the computed 3D coordinates. In this work, we present a novel method for estimating the degrees-per-step ratio at the output of the laser positioner’s transmission mechanism using a stereovision system. Experimental results demonstrate the effectiveness of the proposed method, which reduces the need for manual metrological instruments and simplifies the calibration procedure through vision-assisted measurements. The method yielded estimated angular resolutions of approximately 0.06° and 0.07° per motor step in the horizontal and vertical axes, respectively, key parameters that define the minimal resolvable displacement of the projected beam in dynamic triangulation.

Metrology doi: 10.3390/metrology5030057

Authors: Martin Straka Christian Höhne Christian Koglin Bernhard Funck Thomas Eichler

Most flow metering methods used in industrial applications produce results sensitive to the local velocity profile. In response, manufacturers often implement correction algorithms; however, these are rarely supported by rigorous uncertainty evaluations. This paper presents a Reynolds number-dependent velocity profile correction, applicable under fully developed flow conditions and for the Reynolds-dependent part of the correction in disturbed flows, demonstrated on the example of an ultrasonic clamp-on flow meter. Measurement uncertainties are evaluated and propagated through a regression model using Monte Carlo simulation, in compliance with the Guide to the Expression of Uncertainty in Measurement (GUM). Special care is taken to assess the validity range and impact of assuming fully developed flow conditions at the test rig. A validation case demonstrates the reliability of the correction algorithm and its associated uncertainty within the tested conditions. The proposed approach is applicable to other meter types and can be extended to corrections for specific flow disturbances.

Metrology doi: 10.3390/metrology5030056

Authors: Mike Dohmen Andreas Heinrich Cornelius Neumann

Droplet-based microlens fabrication using Ultra Violet (UV) curable polymers demands the precise measurement of three-dimensional geometries, especially for non-axisymmetric shapes influenced by electric field deformation. In this work, we present a polar coordinate-based contour fitting method combined with Hermite interpolation to reconstruct 3D droplet geometries from two orthogonal shadowgraphy images. The image segmentation process integrates superpixel clustering with active contours to extract the droplet boundary, which is then approximated using a spline-based polar fitting approach. The two resulting contours are merged using a polar Hermite interpolation algorithm, enabling the reconstruction of freeform droplet shapes. We validate the method against both synthetic Computer-Aided Design (CAD) data and precision-machined reference objects, achieving volume deviations below 1% for axisymmetric shapes and approximately 3.5% for non-axisymmetric cases. The influence of focus, calibration, and alignment errors is quantitatively assessed through Monte Carlo simulations and empirical tests. Finally, the method is applied to real electrically deformed droplets, with volume deviations remaining within the experimental uncertainty range. This demonstrates the method’s robustness and suitability for metrology tasks involving complex droplet geometries.

Metrology doi: 10.3390/metrology5030055

Authors: Marco Tarabini

Integrating optical metrology into steelmaking and metalworking processes faces challenges not only from harsh conditions but also from a limited understanding of metrology concepts. The literature often overlooks distinctions between different uncertainty sources. This paper proposes a model for the quantification of uncertainty in dimensional measurements of open-die forged components, addressing the different uncertainty sources related to the measurand variability, to the instrumental uncertainty and to the definitional uncertainty. Guidelines for their evaluation are provided, and two case-studies related to measurement of forged shafts are presented and discussed.

Metrology doi: 10.3390/metrology5030054

Authors: Sonja Schmelter Ines Fortmeier Daniel Heißelmann

In the course of digitalization, the importance of modeling and simulating real-world processes in a computer is rapidly increasing. Simulations are now in everyday use in many areas. For example, simulations are used to gain a better understanding of the real experiment, to plan new experiments, or to analyze existing experiments. Simulations are now also increasingly being used as an essential component of a real measurement, usually as part of an inverse problem. To ensure confidence in the results of such virtual measurements, traceability and methods for evaluating uncertainty are needed. In this paper, the challenges and benefits inherent to virtual metrology techniques are shown using three examples from different metrological fields: the virtual coordinate measuring machine, the tilted-wave interferometer, and the virtual flow meter.

Metrology doi: 10.3390/metrology5030053

Authors: Cameron Kenneth Baribeau

Particle accelerator laboratories, which enable world-class research across many scientific fields, depend on the magnets used to manipulate their particle beams for successful operation. The community employs various techniques, typically based on Hall probes and induction sensors/coils, to verify the performance of these accelerator magnets. When the transverse access around a magnet is restricted, conventional Hall probe systems cannot be deployed or require significant modification, while moving wire/coil systems tend to provide information only on the magnetic field’s integral. This research builds upon a vibrating wire setup first commissioned to locate the magnetic center of quadrupole magnets. Scans up to the n = 200 wire harmonic (∼10 kHz drive frequency) were measured to reconstruct the magnetic field across a wire strung through a test magnet. New software was developed to systematically process the many frequency response scans needed for a detailed field reconstruction. This research investigated the speed and precision of the measurement, identifying limitations due to both instrumentation and nonlinear wire behavior. The vibrating wire data agreed with a reference Hall probe scan on the order of 6%; roughly 0.7% RMS error persisted after calibrating the vibrating wire data to the reference scan via scaling factor.

Metrology doi: 10.3390/metrology5030052

Authors: Ryan M. White

This paper proposes using provenance information to describe processes in metrology. The PROV data model is used as an example to showcase a conceptual analysis about how to improve quality, reliability, and overall interoperability within cross-domain applications that require communicating measurement data and traceability information. The analysis considers various metrological processes and outputs that support traceability. The conceptual analysis will be used as a foundation for further contributions to the topic of improving the documentation of metrological traceability with provenance data models. Several use cases illustrate how provenance information can provide context for traceability claims, especially when the measurement result is the focal object of interest. The PROV family of specifications provides machine-actionable metadata and semantic interoperability when communicating measurement information in traceability chains. PROV supports various perspectives that arise in the context of metrological traceability.

Metrology doi: 10.3390/metrology5030051

Authors: Aleksandr Shikhov Kirill Gogolinskii Darya Kopytina Anna Vinogradova Aleksei Zubarev

This article investigates the acoustic properties of artificial discontinuities in reference specimens for the ultrasonic testing of welded joints in polyethylene pipes. An analysis is conducted on the reflectivity of various materials (air, sand, heat-resistant silicate-based sealant, and aluminum foil) and their correspondence to real defects occurring in weld seams. A theoretical analysis of reflection coefficients is performed, along with laboratory studies using digital radiography and ultrasonic testing. The results demonstrate that heat-resistant silicate sealant is the most suitable material for simulating defects, as its acoustic properties closely match those of real inclusions, and its geometric parameters remain stable during the welding process. The use of such specimens enhances the reliability of ultrasonic testing and reduces the likelihood of errors in defect classification.

Metrology doi: 10.3390/metrology5030050

Authors: István Sztankovics

Accurate characterization of 3D surface topography is essential for assessing the quality of machined components. This study investigates the influence of measurement area selection on the evaluation of roughness parameters in high-feed tangential turning of 42CrMo4 alloy steel. Cylindrical surfaces were machined using different process parameters, and their surface topography was analyzed by varying the size of the areal measurement region. Key roughness parameters were examined to determine the impact on the reliability and consistency of surface characterization. The results highlight how different measurement areas influence roughness values and their variations. The findings contribute to improved metrological practices in tangential turning, and they are particularly relevant for precision machining applications where surface integrity plays a critical role. The area width of the measurement area was shown to play a critical role in data reliability. The results showed that Sa and Sk stabilized after 5.5–6.0 mm, while Ssk and Sku stabilized earlier, at approximately 5.0 mm. Spk and Svk required the longest evaluation area widths, up to 6.0 mm, to achieve consistent values.

Metrology doi: 10.3390/metrology5030049

Authors: Fernando Martin-Rivera Darío Rodrigo-Mallorca Luis M. Franco-Grau Jose Vidal-Vidal Angel Saez-Berlanga Iván Chulvi-Medrano

Background: Velocity-based training (VBT) requires precise measurement devices to monitor neuromuscular performance. PowerTrackTM is a novel optoelectronic device designed to assess movement velocity in resistance training. This study aimed to evaluate the validity and reliability of PowerTrackTM during the Smith machine back squat. Methods: Twenty experienced-trained men performed three repetitions at three submaximal loads (20, 50, and 70 kg) across two sessions. Velocity metrics—mean velocity (MV), mean propulsive velocity (MPV), and maximum velocity (Vmax)—were simultaneously recorded by PowerTrackTM and the criterion device (MuscleLabTM). Validity was assessed via ordinary least products (OLP) regression, Lin’s concordance correlation coefficient (CCC), and Bland–Altman plots. Reliability was determined using intraclass correlation coefficients (ICCs), standard error of measurement (SEM), coefficient of variation (CV), and minimum detectable change (MDC). Results: PowerTrack showed high agreement with MuscleLabTM for MPV and Vmax (slope ≈ 1.00; CCC = 0.95–0.97), while MV presented a proportional bias (slope = 0.83). ICCs ranged from 0.78 to 0.91 across loads, and SEM remained <0.09 m/s for all metrics, indicating excellent relative reliability and acceptable absolute precision. Conclusion: Despite a slight underestimation of MV at light loads, PowerTrackTM proved to be a valid and reliable device for velocity monitoring in VBT contexts.

Metrology doi: 10.3390/metrology5030048

Authors: Helena Paula Nierwinski Arthur Miguel Pereira Gabardo Ricardo José Pfitscher Rafael Piton Ezequias Oliveira Marieli Biondo

Cone Penetration Tests with pore pressure measurements (CPTu) are widely used in geotechnical site investigations due to their high-resolution profiling capabilities. However, traditional interpretation methods—such as the Soil Behavior Type Index (Ic)—often fail to capture the internal heterogeneity typical of mining tailings deposits. This study presents a machine learning-based approach to enhance stratigraphic interpretation from CPTu data. Four unsupervised clustering algorithms—k-means, DBSCAN, MeanShift, and Affinity Propagation—were evaluated using a dataset of 12 CPTu soundings collected over a 19-year period from an iron tailings dam in Brazil. Clustering performance was assessed through visual inspection, stratigraphic consistency, and comparison with Ic-based profiles. k-means and MeanShift produced the most consistent stratigraphic segmentation, clearly delineating depositional layers, consolidated zones, and transitions linked to dam raising. In contrast, DBSCAN and Affinity Propagation either over-fragmented or failed to identify meaningful structures. The results demonstrate that clustering methods can reveal behavioral trends not detected by Ic alone, offering a complementary perspective for understanding depositional and mechanical evolution in tailings. Integrating clustering outputs with conventional geotechnical indices improves the interpretability of CPTu profiles, supporting more informed geomechanical modeling, dam monitoring, and design. The approach provides a replicable methodology for data-rich environments with high spatial and temporal variability.

Metrology doi: 10.3390/metrology5030047

Authors: Rigoberto Juarez-Salazar Sofia Esquivel-Hernandez Victor H. Diaz-Ramirez

Optical fringe projection is an outstanding technology that significantly enhances three-dimensional (3D) metrology in numerous applications in science and engineering. Although the complexity of fringe projection systems may be overwhelming, current scientific advances bring improved models and methods that simplify the design and calibration of these systems, making 3D metrology less complicated. This paper provides an overview of the fundamentals of fringe projection profilometry, including imaging, stereo systems, phase demodulation, triangulation, and calibration. Some applications are described to highlight the usefulness and accuracy of modern optical fringe projection profilometers, impacting 3D metrology in different fields of science and engineering.

Metrology doi: 10.3390/metrology5030046

Authors: Samuel Heikens Degang Chen

Thermal management is an area of study in electronics focused on managing temperature to improve reliability and efficiency. When temperatures are too high, cooling systems are activated to prevent overheating, which can lead to reliability issues. To monitor the temperatures, sensors are often placed on-chip near hotspot locations. These sensors should be very small to allow them to be placed among compact, high-activity circuits. Often, they are connected to a central control circuit located far away from the hot spot locations where more area is available. This paper proposes sensing units for a novel temperature sensing architecture in the TSMC 180 nm process. This architecture functions by approximating the current through the sensing unit at a reference voltage, which is used to approximate the temperature in the digital back end using fitting functions. Sensing units are selected based on how well its temperature–current relationship can be modeled, sensing unit area, and power consumption. Many sensing units will be experimented with at different reference voltages. These temperature–current curves will be modeled with various fitting functions. The sensing unit selected is a diode-connected p-type MOSFET (Metal Oxide Semiconductor Field Effect Transistor) with a size of W = 400 nm, L = 180 nm. This sensing unit is exceptionally small compared to existing work because it does not rely on multiple devices at the sensing unit location to generate a PTAT or IPTAT signal like most work in this area. The temperature–current relationship of this device can also be modeled using a 2nd order polynomial, requiring a minimal number of trim temperatures. Its temperature error is small, and the power consumption is low. The range of currents for this sensing unit could be reasonably made on an IDAC.

Metrology doi: 10.3390/metrology5030045

Authors: Vendula Samelova Jana Pekarova Frantisek Bradac Jan Vetiska Matej Samel Robert Jankovych

Articulated arm coordinate measuring machines are designed for in situ use directly in manufacturing environments, enabling efficient dimensional control outside of climate-controlled laboratories. This study investigates the influence of ambient temperature variation on the accuracy of length measurements performed with the Hexagon Absolute Arm 8312. The experiment was carried out in a laboratory setting simulating typical shop floor conditions through controlled temperature changes in the range of approximately 20–31 °C. A calibrated steel gauge block was used as a reference standard, allowing separation of the influence of the measuring system from that of the measured object. The results showed that the gauge block length changed in line with the expected thermal expansion, while the articulated arm coordinate measuring machine exhibited only a minor residual thermal drift and stable performance. The experiment also revealed a constant measurement offset of approximately 22 µm, likely due to calibration deviation. As part of the study, an uncertainty budget was developed, taking into account all relevant sources of influence and enabling a more realistic estimation of accuracy under operational conditions. The study confirms that modern carbon composite articulated arm coordinate measuring machines with integrated compensation can maintain stable measurement behavior even under fluctuating temperatures in controlled environments.

Metrology doi: 10.3390/metrology5030044

Authors: Olga Kozlova Rémy Braive Tristan Briant Stéphan Briaudeau Paulina Castro Rodríguez Guochun Du Tufan Erdoğan René Eisermann Emile Ferreux Dario Imbraguglio Judith Elena Jordan Stephan Krenek Graham Machin Igor P. Marko Théo Martel Maria Jose Martin Richard A. Norte Laurent Pitre Sara Pourjamal Marco Queisser Israel Rebolledo-Salgado Iago Sanchez Daniel Schmid Cliona Shakespeare Fernando Sparasci Peter G. Steeneken Tatiana Steshchenko Stephen J. Sweeney Shahin Tabandeh Georg Winzer Anoma Yamsiri Alethea Vanessa Zamora Gómez Martin Zelan Lars Zimmermann

Current temperature sensors require regular recalibration to maintain reliable temperature measurement. Photonic/quantum-based approaches have the potential to radically change the practice of thermometry through provision of in situ traceability, potentially through practical primary thermometry, without the need for sensor recalibration. This article gives an overview of the European Partnership in Metrology (EPM) project: Photonic and quantum sensors for practical integrated primary thermometry (PhoQuS-T), which aims to develop sensors based on photonic ring resonators and optomechanical resonators for robust, small-scale, integrated, and wide-range temperature measurement. The different phases of the project will be presented. The development of the integrated optical practical primary thermometer operating from 4 K to 500 K will be reached by a combination of different sensing techniques: with the optomechanical sensor, quantum thermometry below 10 K will provide a quantum reference for the optical noise thermometry (operating in the range 4 K to 300 K), whilst using the high-resolution photonic (ring resonator) sensor the temperature range to be extended from 80 K to 500 K. The important issues of robust fibre-to-chip coupling will be addressed, and application case studies of the developed sensors in ion-trap monitoring and quantum-based pressure standards will be discussed.

Metrology doi: 10.3390/metrology5030043

Authors: Neil Sutherland Stuart Marsh Fabio Remondino Giulio Perda Paul Bryan Jon Mills

The determination of precise and reliable interior (IO) and relative (RO) orientation parameters for thermal infrared (TIR) cameras is critical for their subsequent use in photogrammetric processes. Although 2D calibration boards have become the predominant approach for TIR geometric calibration, these targets are susceptible to projective coupling and often introduce error through manual construction methods, necessitating the development of 3D targets tailored to TIR geometric calibration. Therefore, this paper evaluates TIR geometric calibration results obtained from 2D board and 3D field calibration approaches, documenting the construction, observation, and calculation of IO and RO parameters. This includes a comparative analysis of values derived from three popular commercial software packages commonly used for geometric calibration: MathWorks’ MATLAB, Agisoft Metashape, and Photometrix’s Australis. Furthermore, to assess the validity of derived parameters, two InfraRed Thermography 3D-Data Fusion (IRT-3DDF) methods are developed to model historic building façades and medieval frescoes. The results demonstrate the success of the proposed 3D field calibration targets for the calculation of both IO and RO parameters tailored to photogrammetric data fusion. Additionally, a novel combined TIR-RGB bundle block adjustment approach demonstrates the success of applying ‘out-of-the-box’ deep-learning neural networks for multi-modal image matching and thermal modelling. Considerations for the development of TIR geometric calibration approaches and the evolution of proposed IRT-3DDF methods are provided for future work.

Metrology doi: 10.3390/metrology5030042

Authors: Akira Ono

The rapid advancement of materials science is driving the development of emerging advanced materials, such as nanomaterials, composites, biomaterials, and high-performance metals. These materials possess unique properties and offer significant potential for innovative applications across industries. Standardization plays a crucial role in ensuring the reliability, consistency, and comparability of material quality assessments. Although typical material specification standards, which rigidly define allowable characteristic ranges, are well-suited for established materials like steel, they may not be directly applicable to emerging advanced materials due to their novelty and evolving nature. To address this challenge, a distinct approach is required—flexible yet robust testing standards for assessing material quality. This paper introduces scenario-based methodologies, a structured approach to developing such standards, with a particular focus on metrological aspects of measurement methods and procedures. Additionally, self-assessment processes aimed at verifying measurement reliability are integrated into the methodology. These methodologies involve defining target materials and their applications, identifying critical material characteristics, specifying appropriate measurement methods and procedures, and promoting adaptable yet reliable guidelines. To maintain relevance with metrological advancements and evolving market demands, these quality testing standards should undergo periodic review and updates. This approach enhances industrial confidence and facilitates market integration.

Metrology doi: 10.3390/metrology5030041

Authors: Daniela Walter André Bülau Sebastian Bengsch Kerstin Gläser André Zimmermann

Thermal mass flow sensors (TMFS) are used to detect the flow rates of gases. TMFS elements are available in different technologies and, depending on the one used, the material choice of substrate, heater, and temperature sensors can limit their performance. In this work, a sensor element based on the Ensinger Microsystems Technology (EMST) is presented that uses PEEK as the substrate, nickel-chromium as the heater, and nickel as the temperature sensor material. The fabrication process of the element is described, the completion to a flow sensor with a control and readout circuit based on discharge time measurement with picosecond resolution is presented, and measurement results are shown, which are compared to sensors with a commercially available element based on thin film technology on ceramic and an element built with discrete components, all using the same electronics. It is shown that the operation of all sensor elements with the proposed readout circuit was successful, flow-dependent signals were achieved, and the performance of TMFS in EMST improved. Its heater shows better results compared to the commercial element due to material choice with a smaller temperature coefficient of resistance. In its current state, the TMFS in EMST is suitable to detect flow rates > 20 SLPM. The performance needs to be improved further, since the temperature sensors still differ too much from another.

Metrology doi: 10.3390/metrology5030040

Authors: Minol Jayawickrema Madhubhashitha Herath Nandita Hettiarachchi Harsha Sooriyaarachchi Sourish Banerjee Jayantha Epaarachchi B. Gangadhara Prusty

Access to significant amounts of data is typically required to develop structural health monitoring (SHM) systems. In this study, a novel SHM approach was evaluated, with all training data collected solely from a validated finite element analysis (FEA) of a reinforced concrete (RC) beam and the structural health based on the tension side of a rebar under flexural loading. The developed SHM system was verified by four-point bending experiments on three RC beams cast in the dimensions of 4000 mm × 200 mm × 400 mm. Distributed optical fibre sensors (DOFS) were mounted on the concrete surface and on the bottom rebar to maximise sample points and investigate the reliability of the strain data. The FEA model was validated using a single beam and subsequently used to generate labelled SHM strain data by altering the dilation angle and rebar sizes. The generated strain data were then used to train an artificial neural network (ANN) classifier using deep learning (DL). Training and validation accuracy greater than 98.75% were recorded, and the model was trained to predict the tension state up to 90% of the steel yield limit. The developed model predicts the health condition with the input of strain data acquired from the concrete surface of reinforced concrete beams under various loading regimes. The model predictions were accurate for the experimental DOFS data acquired from the tested beams.

Metrology doi: 10.3390/metrology5030039

Authors: Rafał Szostak-Staropiętka Wojciech Presz Roksana Pawlic Anna Dziubińska Katarzyna Kołacz

Over recent years, ultrasonic atomization, especially with regard to liquid metals, has become an object of increased interest, mainly from industry, for additive manufacturing, but also from investigators, for research purposes. A strong correlation between the average particle size, distribution of particle sizes, and other process parameters like frequency and vibration amplitude was noted based on the analysis of available theoretical studies, simulations and experiments. The influence of parameters of the atomized fluid-like viscosity and surface tension on process parameters was also mentioned. The objective of this study is further research on the feasibility of using ultrasonic atomization to examine the properties of liquids, especially metals in liquid state. It attempts to close a gap in existing knowledge in searching for a new, possibly simple and cost-effective method to study the properties of liquid metals and further clarify the relationship between ultrasonic atomization parameters (amplitude, frequency, characteristics of metal being spilled on a vibrating surface) and obtained atomization results meant by average particle size and atomization time. Using numerical modeling (finite element method and computational fluid dynamics) as a methodology, combined with tests of using ultrasonic atomization as an instrument to determine properties of liquid metals, was considered as an introduction to a series of experiments. These tests were followed by real experiments that are also presented. At the first stage, numerical modeling was applied to a case of a specific liquid being spilled over a vibrating surface of different angles of inclination and specified, constant frequency and amplitude. The results of the simulation are in line with the current state of knowledge about ultrasonic atomization. Moreover, they can provide some more information on scalability, thus easing the comparison of the results of other experiments presented in the available literature. As a result, the relationship between fluid properties and the average size of atomized particles was demonstrated independently of the surface inclination angle. In the same way, the dependence of successful atomization on a sufficiently thin layer of a liquid was demonstrated. Thirdly, a correlation between the aforementioned layer thickness and the value of vibration amplitude has also been shown. Taking all the above into consideration, ultrasonic atomization can also be considered a research method and can be applied to study the properties of liquid metals. Further research, simulations and experimentation will be conducted to verify, develop and describe this method in full.

Metrology doi: 10.3390/metrology5030038

Authors: Parisa Esmaili Federico Cavedo Michele Norgia

Slight changes in the local properties of a transmission line, dipped in a liquid, can be used to estimate its level through two different determination techniques, involving the capacitance and electromagnetic wave speed, measured by the time of flight. Indeed, the overall capacitance of a transmission line varies linearly with the liquid level, as well as the time of flight of the electromagnetic wave. Both quantities can be estimated via the measurement of a phase shift at radio frequencies, and the simultaneous measurements can be realized using a compact and low-cost design working at a few megahertz. This paper presents a further improvement in sensitivity to challenge the performance of this kind of level sensor, dealing with liquids with low dielectric constants. To better describe this effect, a study on the overall capacitance of different transmission path segments was conducted in COMSOL Multiphysics. The level measurement was performed experimentally on the realized prototype while considering the measured phase shift as a function of the liquid level, for both an unshielded twisted-pair and magnet wires. As the results showed, with the magnet wires the sensitivity was improved by a factor of about 4, consistently aligning with the simulation results and providing a predictable phase shift response with increasing liquid levels. Consequently, magnet wire is a good choice for precise level measurements through RF phase shifts, especially in the case of low relative permittivity liquids.

Metrology doi: 10.3390/metrology5020037

Authors: Pawel Kosek Anthony Beaumont Melvin Liebsch

In particle physics experiments, fragment separators utilize dipole magnets to distinguish and isolate specific isotopes based on their mass-to-charge ratio as particles traverse the dipole’s magnetic field. Accurate fragment selection relies on precise knowledge of the magnetic field generated by the dipole magnets, necessitating dedicated measurement instrumentation to characterize the field in the constructed magnets. This study presents measurements of the two first-of-series dipole magnets (Type II—11 degrees bending angle—and Type III—9.5 degrees bending angle) for the Superconducting Fragment Separator that is being built in Darmstadt, Germany. Stringent field quality requirements necessitated a novel measurement system—the so-called translating fluxmeter. It is based on a PCB coil array installed on a moving trolley that scans the field while passing through the magnet aperture. While previous publications have discussed the design of the moving fluxmeter and the characterization of its components, this article presents the results of a measurement campaign conducted using the new system. The testing campaign was supplemented with conventional methods, including integral field measurements using a single stretched wire system and three-dimensional field mapping with a Hall probe. We provide an overview of the working principle of the translating fluxmeter system and validate its performance by comparing the results with those obtained using conventional magnetic measurement methods.

Metrology doi: 10.3390/metrology5020036

Authors: Reinoud Wolffenbuttel David Bilby Jaco Visser

The proper usage of a bandwidth-limited imaging bolometer for the measurement of the lateral temperature profile of microstructures in Silicon-Carbide (SiC) is analyzed. The SiC spectral emissivity, ϵSiC(λ), has a dip at λ∼12μm, which is in the band of a typical commercially available instrument and complicates the selection of the value of the equivalent emissivity, ϵeq,SiC, in the instrument settings. The impact is analyzed by deduction using simulation, and by experimental validation. Membranes of 3C-SiC of 1000 μm diameter and 3 μm thickness have been fabricated on Si wafers, with integrated poly-SiC resistors for both membrane heating and on-membrane temperature measurement for calibration purposes. The optimum setting was found as ϵeq,SiC = 0.705 ± 0.025 by deduction and as ϵeq,SiC = 0.66 ± 0.06 by experimental validation in the temperature range 120 °C to 400 °C. The apparent temperature coefficient of emissivity, TCE< 2 × 10−4 °C−1 is due to the shift of the Wien peak wavelength relative to the instrument’s sensitivity band.

Metrology doi: 10.3390/metrology5020035

Authors: Gabriela R. Piazzetta Thomas M. Zeller Juan M. Hernandez-Otalvaro Giuseppe Pintaude

Predicting the wear of disc cutters in Tunnel Boring Machines (TBMs) is a complex challenge due to the large scale of the machinery and the numerous operational variables involved. Laboratory-scale tests offer a controlled approach to isolating and analyzing specific wear mechanisms. However, the extremely low wear rates observed in such simulations pose challenges for conventional characterization methods, as gravimetric and profilometric techniques often lack the precision and accuracy needed to measure low wear patterns with an uneven morphology. To address this, this study revisited a methodology for quantifying low wear rates in a reciprocating wear test using AISI H13 tool steel disc cutters. This approach integrates spherical indentation marks as reference points with 3D white-light interferometry, enabling high-precision material loss measurements. Eighteen disc samples were subjected to wear testing, with 3 indentations analyzed per sample, for a total of 54 indentations. The statistical validation confirmed the method’s reproducibility and reliability. The proposed approach provides a robust alternative to existing techniques, addressing a critical gap regarding the accurate quantification of low wear rates in controlled laboratory settings.

Metrology doi: 10.3390/metrology5020034

Authors: So Ito Takumi Yamagishi Kimihisa Matsumoto Kazuhide Kamiya

An Abramson-type oblique-incident interferometer was used for the surface-form measurement of hand-scraped marks consisting of rough surfaces. Although the Abramson interferometer could measure the rough surface of hand-scraped marks under noncontact conditions, the inconsistency in the measurement results was caused by the differences in the incident direction of the measuring light. This study investigated the inconsistency in the measurement results of the Abramson interferometer caused by the oblique incidence of the measuring light. The reproducibility of inconsistencies due to the difference in the incident direction of the measuring light was confirmed, and the relationship between the inconsistency of the measurement results and the incident angle of the measuring light was investigated. Consequently, it was confirmed that the inconsistency of the measurement results due to the difference in the incident direction of the measuring light could be reduced by decreasing the incident angle of the measuring light. To avoid the overcrowding of the interference fringes caused by the reduction in the incident angle of the measuring light, an oblique-incident interferometer with a near-infrared laser was constructed. The validity of the developed oblique-incident interferometer was evaluated by comparison with a commercially available contour measurement instrument. The surface form obtained by the developed oblique-incident interferometer was confirmed to be consistent with the envelope of the cross-sectional profile measured by the contour measurement instrument.

Metrology doi: 10.3390/metrology5020033

Authors: Abbass Walid Matthias Eifler

More and more surfaces are required to fulfill functional characteristics that are embodied by their surface topography. In the process of measuring and characterizing the corresponding surfaces, many research activities have been conducted, and a broad variety of measuring principles and evaluation strategies have been developed. However, in industrial practice, there is still a lack of experience and a significant unhinged potential in this field. To predict which techniques will most likely be transferred more commonly into industrial applications, a study to identify the most frequently used measurement principles, methods, and surface texture parameters for characterizing functional surfaces through a systematic literature review of scientific research studies is conducted here. It can be shown that optical measuring instruments have emerged significantly, whereas the analysis is mostly performed using traditional and simple amplitude-based surface texture parameters. Based on the results, untapped potential in functional analysis can be revealed and the use of, e.g., function-oriented parameters or a direct measurement of the angular distribution can be recommended for a wider range of applications.

Metrology doi: 10.3390/metrology5020032

Authors: Shahrokh Hatefi Farouk Smith Kayla Auld Stefan Van Aardt

In Maxillofacial Reconstruction Applications (MRA), nonunion is one of the critical complications after the reconstruction process and fracture treatment, including bone grafts and vascularized flap. Nonunion describes the failure of a fractured bone to heal and mend after an extended period. Different systems and methods have been developed to monitor bone regeneration and fracture healing during and after the treatment. However, the developed systems have limitations and are yet to be used in MRA. The proposed smart reconstruction plate is a microdevice that could be used in MRA for wireless monitoring of fracture healing by measuring the forces applied to the reconstruction plate. The device is wireless and can transmit the acquired data to a human–machine interface or an application. The designed system is small and suitable for use in MRA. The results of finite element analysis, as well as experimental verification, showed the functionality of the proposed system in measuring small changes on the surface strain of the reconstruction plate and determining the corresponding load. By using the proposed system, continuous monitoring of bone regeneration and fracture healing in oral and maxillofacial areas is possible.

Metrology doi: 10.3390/metrology5020031

Authors: Christopher Dunn Jonathan Scott Marcus Wilson Michael Mucalo Michael Cree

Incremental capacity analysis (ICA), where incremental charge (Q) movements associated with changes in potential are tracked, and cyclic voltammetry (CV), where current response to a linear voltage sweep is recorded, are used to investigate the properties of electrochemical systems. Electrochemical impedance spectroscopy (EIS), on the other hand, is a powerful, non-destructive technique that can be used to determine small-signal AC impedance over a wide frequency range. It is frequently used to design battery equivalent-circuit models. This manuscript explores the relationships between ICA, CV and EIS and demonstrates how sweep rate in CV is related to charging (C) rate in ICA. In addition, it shows the connection between observations linked to rate of charge movement in CV and ICA and intermittent, irregular behavior seen in EIS when performed on a battery. It also explains the use of an additional DC stimulus during EIS to ensure reliability of battery impedance data and to facilitate equivalent-circuit modeling, and suggests a method for obtaining data analogous to CV from a whole battery without risking its destruction.

Metrology doi: 10.3390/metrology5020030

Authors: Allen Love Omar Alejandro Valdez Pastrana Saeed Behseresht Young Ho Park

Metal additive manufacturing (AM) techniques such Direct Energy Deposition (DED), Powder Bed Fusion (PBF), and Wire Arc Additive Manufacturing (WAAM) enable the production of complex metal components built at rapid rates. Because of the complexity of the process, including high thermal gradients, residual stress, and parameter optimization, these techniques pose significant challenges necessitating the need for advanced computational modeling. A powerful technique to reduce or, in some cases, eliminate these challenges at a much lower cost compared to trial-and-error experiments, is Finite Element Analysis (FEA). This study provides a comprehensive review of the FEA techniques being used and developed to model metal AM processes focusing on the thermal, mechanical, and coupled thermo-mechanical models in DED, PBF, and WAAM. Key topics include heat transfer, residual stress and distortion prediction, microstructure evolution and parameter optimization. Recent advancements in FEA have improved the accuracy of AM process simulations, reducing the need for costly experimental testing, though there is still room for improvement and further development of FEA in metal AM. This review serves as a foundation for future work in the metal AM modeling field, enabling the development of optimized process parameters, defect reduction strategies and improved computational methodologies for high-fidelity simulations.

Metrology doi: 10.3390/metrology5020029

Authors: Mohamed Ouameur Emmanuel Patois

This paper presents a Maxwell–Wien bridge for use in the calibration of standard inductances with values between 100 µH and 10 H and frequencies from 20 Hz to 20 kHz. The inductances are measured by comparison with a variable standard capacitor, in parallel association with a variable standard resistor, on the bridge modified by a Wagner balance. The variable standards are calibrated after the bridge balance. The other resistors in the bridge are standard resistors, pre-calibrated in AC using an automatic Wheatstone bridge and in DC after the bridge has been balanced using a comparison bridge with standard resistors traceable to the quantum Hall effect standards. PXI modules are used to supply the bridge with two voltages controllable in amplitude and phase. Design details and the uncertainty budget are discussed. For an inductance of 100 mH characterized by an internal resistance of 83 Ω, the expanded uncertainties are less than 6 µH on the inductance and 20 mΩ on the internal resistance. For inductances from 100 µH to 10 H, the relative uncertainties are less than 0.02% of the inductance and 0.2% of the internal resistance from 20 Hz to 20 kHz.

Metrology doi: 10.3390/metrology5020028

Authors: Alexander Hinton Alexander Bainbridge Olli Tarvainen

Boundary Element Methods (BEMs) can be applied to determine the value of the magnetic field at any point within a domain if the magnetic field components are measured on the surface of the domain. For large magnetic volumes, BEMs provide an attractive alternative to fine three-dimensional Hall probe scans for determining the local shape of the field as the fields can be evaluated inside the volume with an arbitrary position and with a reduced measurement time. BEMs have been applied to the field data measured on the boundary of three-dimensional Hall probe scans for two example magnets, which have been measured at STFC Daresbury Laboratory, UK. The fields reconstructed using BEMs are compared to the fields directly measured during the Hall probe scans. The reconstructed fields can be calculated to within 1 mT rms of the directly measured fields. For the transverse field components greater than 1 mT, the fields can be reconstructed to within 5% rms of the directly measured fields.

Metrology doi: 10.3390/metrology5020027

Authors: Richard J. C. Brown Paul J. Brewer

Metrology, the science of measurement, is an essential underpinning technology—an infratechnology. The correct functioning of the international measurement system that metrology supports is a prerequisite for the development of technology and wider progress in science. Metrology and the measurement system are at risk of being underappreciated. They potentially face a ‘no-win’ environment: their consistent success, a testament to their effectiveness, ironically leads to invisibility. The public and media tend only to pay attention when things go wrong, resulting in negative headlines. Furthermore, metrology’s emphasis on gradual, incremental improvements, crucial for maintaining long-term stability and safety, is incompatible with the short-term focus of the media. This leaves metrology perpetually struggling to gain recognition for its vital contributions and can lead to a danger that metrology will not receive the recognition or resources that it needs to continue delivering benefits. A different way of explaining the indispensability of metrology is therefore needed. This work takes a novel approach to explaining the benefits of metrology by considering the counterfactual argument—examining the consequences if the international measurement system was to fail. It concludes that a balanced argument demonstrating what benefits metrology provides, challenged with the counterfactual of what would happen if it did not, is likely to be the most effective mechanism to ensure the work of metrology and the indispensability of the international measurement system are properly appreciated.

Metrology doi: 10.3390/metrology5020026

Authors: Efi-Maria Papia Vassilios Constantoudis Youmin Hou Prexa Shah Michael Kappl Evangelos Gogolides

Several materials widely used in scientific research and industrial applications, including nano-filters and neuromorphic circuits, consist of fiber structures. Despite the fundamental structural similarity, the key feature that should be considered depends on the specific application. In the case of membranes and filters, the main concern has been on the pores among fibers, whereas in neuromorphic networks the main functionality is performed through the junctions of nanowires simulating neuron synapses for information dissemination. Precise metrological characterization of these structural features, along with methods for their effective control and replication, is essential for optimizing performance across various applications. This paper presents a comprehensive metrological framework for characterizing the spatial point patterns formed by pores or junctions within fibrous materials. The aim is to probe the influence of fiber randomness on both the point patterns of intersections (ppi) and pores (ppp). Our findings indicate a strong tendency of ppi toward aggregation, contrasting with a tendency of ppp toward periodicity and consequent pore uniformity. Both patterns are characterized by peculiarities related to collinearity effects on neighboring points that cannot be captured by the conventional anisotropy analysis of point patterns. To characterize local collinearity, we develop a method that counts the number of collinear triplets of nearest neighbor points in a pattern and designs an appropriate parameter to quantify them, also applied to scanning electron microscopy (SEM) images of membranes, demonstrating consistency with simulated data.

Metrology doi: 10.3390/metrology5020025

Authors: Blair D. Hall

Metrological traceability is essential for ensuring the accuracy of measurement results and enabling a comparison of results to support decision-making in society. This paper explores a structured approach to modelling traceability chains, focusing on the role of residual measurement errors and their impact on measurement accuracy. This work emphasises a scientific description of these errors as physical quantities. By adopting a simple modelling framework grounded in physical principles, the paper offers a formal way to account for the effects of errors through an entire traceability chain, from primary reference standards to end users. Real-world examples from microwave and optical metrology highlight the effectiveness of this rigorous modelling approach. Additionally, to further advance digital systems development in metrology, the paper advocates a formal semantic structure for modelling, based on principles of Model-Driven Architecture. This architectural approach will enhance the clarity of metrological practices and support ongoing efforts toward the digital transformation of international metrology infrastructure.

Metrology doi: 10.3390/metrology5020024

Authors: Leo Miyashita Satoshi Tabata Masatoshi Ishikawa

Three-dimensional measurement technologies based on computer vision have been developed with the aim of achieving perceptual speeds equivalent to humans (30 fps). However, in a highly mechanized society, there is no need for computers and robots to work slowly to match the speed of human perception. From this kind of circumstance, high-speed 3D vision with speeds far beyond that of humans, such as 1000 fps, has emerged. High-speed 3D measurement has great applicability not only for accurately recognizing a moving and deforming target but also for enabling real-time feedback, such as manipulation of the dynamic targets based on the measurement. In order to accelerate 3D vision and control the dynamic targets in real time, high-speed vision devices and high-speed image processing algorithms are essential. In this review, we revisit the basic strategy, triangulation as a suitable measurement principle for high-speed 3D vision, and introduce state-of-the-art 3D measurement methods based on high-speed vision devices and high-speed image processing utilizing structured light patterns. In addition, we introduce recent applications using high-speed 3D measurement and show that high-speed 3D measurement is one of the key technologies for real-time feedback in various fields such as robotics, mobility, security, interface, and XR.

Metrology doi: 10.3390/metrology5020023

Authors: Mihai Raul Gherase Vega Mahajan

Blood concentrations of essential trace elements can be used to diagnose conditions and diseases associated with excess or deficiency of these elements. Inductively coupled plasma mass spectrometry (ICP-MS), inductively coupled plasma atomic emission spectroscopy (ICP-AES), and graphite furnace atomic absorption spectrometry (GF-AAS) have been employed for such measurements, but maintenance and operation costs are high. X-ray fluorescence (XRF) detectability in cutaneous blood of iron (Fe), copper (Cu), zinc (Zn), and selenium (Se) was assessed as an alternative to ICP-MS. Three phantoms were made up of two polyoxymethylene (POM) plastic cylindrical cups of 0.6 mm and 1.0 mm thick walls and a 5.3 mm diameter POM cylindrical insert. Six aqueous solutions of Fe in 0 to 500 mg/L and Cu, Zn, and Se in 0 to 50 mg/L concentrations were poured into the phantoms to simulate X-ray attenuation of skin. Measurements using an integrated X-ray tube and polycapillary X-ray lens unit generated 24 calibration lines. Detection limit intervals in mg/L were (36–100), (14–40), (3.7–10), and (2.1–3.4) for Fe, Cu, Zn, and Se, respectively. Fe was the only element with detection limits lower than its 480 mg/L median human blood concentration. The estimated radiation dose and equivalent dose to skin were below those of common radiological procedures. Applications will require further instrumental development and finding a calibration method.

Metrology doi: 10.3390/metrology5020022

Authors: Xiang Zhang Zidi Wu Li’an Jin Jing Yang Xianjin Ou Dongsheng Ni Yue Cheng Lixia Zhao Yujin Tong Weigang Dong Beimin Wu Guohong Li Qinggao Yao

The High-Intensity Heavy-Ion Accelerator Facility (HIAF) is a significant national science and technology infrastructure project, constructed by the Institute of Modern Physics, Chinese Academy of Sciences (IMP, CAS). It is designed to provide intense proton, heavy ion beams, and target-produced radioactive ion beams for nuclear physics and related research. Large-aperture, high-precision, room-temperature, and superconducting dipole magnets are extensively used to achieve high-intensity beams. However, for large-scale magnets (particularly superconducting magnets), the traditional Hall probe mapping measurement platform encounters several limitations: a long preparation time, high cost, low testing efficiency, and positional inaccuracies caused by repeated magnet disassembly. This paper presents a new magnetic field mapping measurement system incorporating ultrasonic motors operable in strong magnetic fields (≥7 T), enabling portable, highly efficient, and high-precision magnetic field measurements. After system integration and commissioning, the prototype dipole magnet for the high-precision spectrometer ring (SRing) was measured. The measurement system demonstrated superior accuracy and efficiency compared with traditional Hall probe mapping systems. On this basis, the magnetic field distribution and integral excitation curve of all 11 warm-iron superconducting dipole magnets and 3 anti-irradiation dipole magnets in the HIAF fragment separator (HFRS) were measured. Each magnet took less than 1 day to measure, and all magnetic field measurement results met the physical specifications.

Metrology doi: 10.3390/metrology5020021

Authors: Gilad Orr Moshe Azoulay Gady Golan Arnold Burger

GaN High-Electron-Mobility Transistors have gained some foothold in the power-electronics industry. This is due to wide frequency bandwidth and power handling. Gallium Nitride offers a wide bandgap and higher critical field strength compared to most wide-bandgap semiconductors, resulting in better radiation resistance. Theoretically, it supports higher speeds as the device dimensions could be reduced without suffering voltage breakdown. The simulation and experimental results illustrate the superior performance of the Gallium Nitride High-Electron-Mobility Transistors in an amplifying circuit. Using a spice model for commercially available Gallium Nitride High-Electron-Mobility Transistors, non-distorted output to an input signal of 200 ps was displayed. Real-world measurements underscore the fast response of the Gallium Nitride High-Electron-Mobility Transistors with its measured slew rate at approximately 3000 V/μs, a result only 17% lower than the result obtained from the simulation. This fast response, coupled with the amplifier radiation resistance, shows promise for designing improved detection and imaging circuits with long Mean Time Between Failure required, for example, by next-generation industrial-process gamma transmission-computed tomography.

Metrology doi: 10.3390/metrology5020019

Authors: Ingo Ortlepp Simon Eisele Kevin Treptow Josias Rühle Christof Pruß Tobias Haist Stephan Reichelt Oliver Sawodny Eberhard Manske Thomas Kissinger

Quantitative determination of the uncertainty of a measurement result is the key to assessing the quality and reliability of a measurement process and its result. The comparability of measurement results is ensured by the method for evaluating and expressing uncertainty defined by the Joint Committee for Guides in Metrology, where the model of the measurement process—which expresses the causal relationship of the measurand and the input quantities—is fundamental for the uncertainty evaluation. Setting up this model is very specific to the particular measurement setup and process, as well as the required level of detail. In this contribution, a vectorial method is presented which has been developed to assist users in modelling complex relationships, based on basic physical effects and their combination. Using a hierarchical approach, the method aims to be flexible, extensible and adaptable to a wide range of applications.

Metrology doi: 10.3390/metrology5020020

Authors: Ziyang Yan Nazanin Padkan Paweł Trybała Elisa Mariarosaria Farella Fabio Remondino

Non-collaborative (i.e., reflective, transparent, metallic, etc.) surfaces are common in industrial production processes, where 3D reconstruction methods are applied for quantitative quality control inspections. Although the use or combination of photogrammetry and photometric stereo performs well for well-textured or partially textured objects, it usually produces unsatisfactory 3D reconstruction results on non-collaborative surfaces. To improve 3D inspection performances, this paper investigates emerging learning-based surface reconstruction methods, such as Neural Radiance Fields (NeRF), Multi-View Stereo (MVS), Monocular Depth Estimation (MDE), Gaussian Splatting (GS) and image-to-3D generative AI as potential alternatives for industrial inspections. A comprehensive evaluation dataset with several common industrial objects was used to assess methods and gain deeper insights into the applicability of the examined approaches for inspections in industrial scenarios. In the experimental evaluation, geometric comparisons were carried out between the reference data and learning-based reconstructions. The results indicate that no method can outperform all the others across all evaluations.

Metrology doi: 10.3390/metrology5010018

Authors: Marco Pradella

Medical laboratories are perhaps the largest measurement industry in the world. The metrology terminology is relevant for effective and efficient communication, particularly where metrology activities are carried out by operators with different metrology skills. The World Association of Societies of Pathology and Laboratory Medicine (WASPaLM) and SIPMeL have had some opportunities to propose changes to the documents in preparation for the Clinical and Laboratory Standards Institute (CLSI) and the ISO/TC 212 in order to harmonize the terminology with the Metrology Vocabulary (VIM) of the Joint Committee for Guides in Metrology (JCGM). Many proposals have been accepted. Here, we summarize some particularly critical points for metrological terms. The main terms discussed are the following: measuring, measuring range, examination, pre-examination, post-examination, manufacturer, measuring instrument, quantitative, qualitative, semi-quantitative, processing, measurement error, maximum permissible error of measurement, total error of measurement, monitoring, variability, performance, reliability, influence, interference, selectivity, sensitivity, detection limit, reliability, comparability, compatibility, control material. Despite all the efforts to coordinate terminologies, it is inevitable that overlapping and inconsistent terminologies will continue to be used because documents and policies are produced in different contexts. In some ISO/TC 212 and CLSI documents, the phenomenon of magnetic attraction toward common words (such as “analysis” and derivatives), without any consideration of the true metrological meaning, is noted. The ISO/TC 212 and CLSI working groups show, alongside moments of openness, phenomena of true self-referential conservatism.

Metrology doi: 10.3390/metrology5010017

Authors: Jacopo Bongiorno Sahil Bhagat

The testing of rolling stock for the assessment of disturbance in signalling circuits is considered with a focus on the measurement process and the selection of operating conditions. The definition of interference limits is briefly reviewed, but they are considered an external input. The spectral behavior of acquired signals and the evaluation of repeatability are instead discussed with the help of three different real test cases, considering correspondence between similar operating points and differences as rolling stock operation evolves during a test run. Repeatability evaluated as standard deviation is in the order of 3% to 5% in the harmonic and audio frequency range for the different systems, slightly lower for AC railways; above about 10–15 kHz it increases to 30%. Uncorrelated components (with much lower amplitudes) may show much higher dispersion.

Metrology doi: 10.3390/metrology5010016

Authors: Eslam Deef-Allah Magdy Abdelrahman

Assessing the binder performance of thermal characterization is critical for quality control. This is pertinent for recovered binders from mixtures, which may not be in adequate quantities to evaluate their performance, particularly in mixtures containing reclaimed asphalt pavement (RAP). The present study deployed a thermogravimetric analyzer to evaluate compositional changes in recovered binders from RAP-containing mixtures, focusing on thermograph and derivative of thermograph (DTG) characteristics and correlating the results to rheological features. Incorporating RAP in mixtures influenced recovered binders’ DTG shapes, reducing low-combusted components (%LCC) and increasing residues (%R). The recovered binder from the zero-RAP-containing mixture showed a 4.36% increase in %LCC and a 1.97% decrease in %R compared to the short-term aged original binder. Binders recovered from RAP-containing mixtures exhibited greater stiffness than the short-term aged original binders. The %LCC dropped from 7.22% to 25.52%, while the %R increased from 20.69% to 33.06%. Uncertainty analyses showed that the DTG area and %R had the least uncertainty and that the %LCC had greater uncertainty. Analysis through regression revealed that DTG area and %R can predict G*/sinδ well, showing a correlation between better thermal stability and binder stiffness. This research puts a number on the correlation between thermal and rheological properties, which helps to improve quality control for binders.

Metrology doi: 10.3390/metrology5010014

Authors: Seif Ben-Hassine Jean-Marie Lerat Jimmy Dubard Pierre Betis Dominique Renoux

This paper introduces a method for calibrating radar sensors in a multi-sensor cinemometer system using a reference cinemometer based on CW Doppler radar. The method involves synchronizing sensors, pairing data with reference measurements, and performing polynomial corrections. Tests conducted on various traffic sites demonstrate the accuracy and reliability of the calibration process. Results show low uncertainties compared to regulatory standards. Validation against a calibrated lidar system confirms accuracy. This method ensures precise speed measurements, surpassing regulatory requirements, and demonstrating practical applicability in real-world scenarios.

Metrology doi: 10.3390/metrology5010015

Authors: Alexander Bainbridge Alexander Hinton Clive Hill Thomas Smith Ben Pine Neil Thompson

We present the design, construction, measurement, and troubleshooting of a prototype hybrid Halbach quadrupole magnet. This magnet was significantly under-strength due to local demagnetization in the permanent magnet material. We discuss how this effect was uncovered, how it was verified by performing Hall probe measurements of the individual magnet blocks, and how the effect was reconstructed in simulations.

Metrology doi: 10.3390/metrology5010013

Authors: Ben Sargeant Pablo Puerto Charles Richards Ibai Leizea Asier Garcia Stuart Robson

The capability of low-cost photogrammetric systems to provide live six degrees of freedom (6DoF) tracking of multiple objects offers great value in providing high-quality and consistent part production by automated manufacturing systems. However, monitoring of high-speed components, such as cutting heads, presents several unique challenges that existing systems struggle to meet. The solution given here uses a small number of short-exposure imaging sensors coupled with high-intensity lighting and retrorefective markers to allow for high-speed capture. The use of an initial characterization process carried out using IDEKO’s VSET© system is followed by live object tracking in bespoke image processing software running on a consumer-grade computer. Once this system is in use, it can simultaneously capture images of multiple markers in less than 0.1 milliseconds and use these to determine the 6DoF of the objects that the markers define. 6DoF recalculation of all objects within each measurement instance makes the system resilient to large movements, object occlusion, and sensor relocation. Feasibility tests of a four-camera system as a machine characterization tool tracking a cutting tool spinning at up to 3000 rpm across a volume of 1 m3 achieved a mean reference marker agreement between tool poses of 2.5 µm with markers moving at up to 17.5 ms−1. Given good photogrammetric geometry, 6DoF parameters of the spinning tool were determined to standard deviations of 37.7 µm and 0.086°.