Metrology, Volume 6, Issue 1 (March 2026) – 21 articles

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 T_ref 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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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 $R^2=0.9992$, 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 $\mid S_{21}\mid$ 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. Full article

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. Full article

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. Full article

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 pH_T values achieved expanded uncertainties ($U_{{\mathrm{p}\mathrm{H}}_{\mathrm{T}}}$ ≤ 0.006), meeting Global Ocean Acidification Observing Network (GOA-ON) “climate” quality standards. Absolute salinity (S_A) 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 pH_T 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 pH_T calibration under climate-relevant high-salinity environments at different temperature conditions, offering a practical tool for high-accuracy calibration in variable marine conditions. Full article

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 $n_d$. It is shown that the requirement of linearity on $n_d$ 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, ${\tau }_c$, as impedance time ${\tau }_{rc}({\tau }_c\to {\tau }_{rc}=RC)$. 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, $C_0<<C$, 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. Full article

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. Full article

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. Full article

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. Full article

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. Full article