Metrology

Precise measurement of large mirrors is essential for high-performance space-based optics. Traditionally, laser interferometry provides high accuracy but faces challenges related to the requirements of computer-generated holograms (CGHs) and the transformation of standard wavefronts to match complex test surfaces. This paper presents a proof-of-concept contact-based surface metrology method for large mirrors. To reduce drift errors caused by stylus instability or contact loss, a wavefront-based calibration method was developed to suppress measurement artifacts while preserving intrinsic surface errors. The method was tested on a concave aspherical mirror using a tactile coordinate measuring machine (CMM), and its accuracy was evaluated by comparing deviations between calibrated CMM error maps and laser-based measurements. Experimental results demonstrated that the XENO CMM achieved a global metric accuracy comparable to interferometric systems for relevant geometric parameters. These findings suggest that ultra-precision CMMs combined with focus point calibration can provide practical preliminary surface verification and serve as a flexible alternative to laser interferometry when global geometric accuracy is the primary concern. Future work will enhance robustness by addressing higher-order aberrations. Full article

Biofilm is known to negatively affect the hydraulic performance of open channels by increasing friction and energy losses and, consequently, economic costs. This study proposes a method to accurately quantify the effect of flow reduction caused by biofouling in open channels. The approach is based on Manning’s equation, using the Monte Carlo Method for the propagation of input uncertainties. A case study concerning a trapezoidal concrete open channel of an agricultural irrigation network is presented, showing a relative expanded uncertainty (95% confidence level) of 10% for flow rates ranging from 1 m³·s⁻¹ to 50 m³·s⁻¹. Manning’s roughness coefficient was identified as the dominant contribution to the overall dispersion of flow rate values, being probabilistically modeled by a beta distribution using minimum, expected and maximum reference values. This information was used for conformity assessment of the studied open channel, considering flow reductions due to moderate and severe biofilm effects of 12.5% and 31.3%, respectively. The corresponding standard uncertainties (4.8% and 7.8%), the adopted confidence level (95%), tolerance upper limit (33%) and decision rule led to different conformity assessment outcomes. These results highlight the importance of accurate assessment of flow reduction due to biofouling for management entities. Full article

The need to measure the geometric dimensions of a railway wheel during train motion at a speed of 120–150 km/h with an error below ±0.25 mm and to identify defects on the tread surface and flange is justified. A new optical measurement system that provides this measurement accuracy was developed. The wheel geometric parameters were measured, and defects were identified using square-wave pulsed laser radiation with a plane-parallel wavefront in the form of a 4 mm wide and 280 mm long line, with a pulse duration of 14 μs, formed using a newly designed collimator. A method was developed for selecting the laser pulse duration so that image blur would have an insignificant influence on the measurement results. Under these conditions, the wheel surface could be considered locally flat with respect to the incident laser radiation. The receiving modules were positioned relative to the rail surface so that the CMOS field of view covered a wheel-surface sector of 10°12′ from both sides and recorded the reflected radiation as a point cloud. To reduce stray illumination and reflections, a filter with a 12.6 nm bandwidth centered at 638.2 nm with a transmittance of 0.71 was installed in front of the CMOS matrix. A point-cloud processing algorithm was developed. Of 236 recorded profiles, 232 were processed successfully, corresponding to a successful-processing rate of 98.3%. Defects were detected in seven processed profiles and confirmed by control measurements. The geometric parameters were determined with a calculated error not exceeding 0.25 mm at 150 km/h. Complete wheel monitoring required 36 sequentially installed optical measurement modules developed in this work, approximately 1.4 times fewer than in comparable systems, for which the measurement error at 150 km/h was approximately ±0.6 mm and the reported defect identification reliability was 95%. Full article

Insight into spectrum measurement is provided regarding the possibility of achieving a unified definition of the measurand for important classes of phenomena, including periodic, transitory impulsive, stochastic stationary, and stochastic non-stationary ones. Furthermore, the notion of characterizing the observation window as a key feature of the measurement method is introduced, and the issue of reducing the variability of the results is discussed, with a focus on the key role that can be played by the multi-taper method. Full article

Low-cost air temperature and relative humidity sensors are increasingly deployed in dense urban monitoring networks for the characterization of urban heat islands and heat exposure. However, measurement accuracy strongly depends on the performance of the radiation shield protecting the sensor from solar heating. This study evaluates five low-cost radiation shield designs, including naturally ventilated, forced-ventilated, spherical, and chimney-type configurations, under tropical outdoor conditions on Reunion Island. Five calibrated SHT31 sensors were deployed simultaneously alongside a reference meteorological station over a five-week measurement campaign. Shield performance was assessed using standard metrological indicators, daytime–nighttime analyses, error distributions, and two-dimensional irradiance–wind diagnostics. Temperature RMSE values ranged from 0.68 to 1.18 °C, while relative humidity RMSE ranged from 2.65 to 7.39%. The forced-ventilated shield provided the best overall temperature performance, whereas the chimney-type design exhibited the largest errors. Combined irradiance–wind analyses showed that measurement errors were primarily governed by the balance between radiative forcing and convective cooling, with maximum temperature biases exceeding 2.5 °C under high-irradiance and low-wind-speed conditions. Based on these findings, several correction approaches were evaluated. A physically interpretable semi-empirical model reduced RMSE by 50%, while a Random Forest model achieved reductions of up to 66%. These results suggest that low-cost meteorological measurements can be substantially improved through appropriate shield design and meteorologically informed calibration procedures, particularly under tropical conditions characterized by strong solar radiation and limited precipitation. Full article

This closing editorial summarizes and introduces the Special Issue, Applied Industrial Metrology: Methods, Uncertainties, and Challenges, highlighting recent advances in traceability, uncertainty evaluation, intelligent metrology, sensor technologies, flow measurement, and standardization. The collected contributions demonstrate how digitalization, artificial intelligence, and advanced sensing are transforming industrial measurement while reinforcing the enduring importance of measurement traceability, comparability, and uncertainty for reliable, sustainable industrial applications. Full article

Anisotropic polymers fabricated via additive manufacturing exhibit complex thermal transport profiles that are challenging to characterize using steady-state techniques. We present a transient thermal method utilizing a short rectangular current pulse excitation to determine the directional thermal diffusivity and conductivity of anisotropic materials. The measurement is conducted on finite specimens, where the low diffusivity of the polymer media results in a highly attenuated and dispersed rear-side temperature profile over an extended transient window. Conduction losses to the adjacent coolers are accounted for by solving the one-dimensional heat conduction equation on an asymmetric multi-layer sandwich structure using the implicit Crank–Nicolson method. Because thermal diffusivity and conductivity are not independent quantities ($\lambda =a\rho c$), the inverse problem is deliberately formulated to estimate the diffusivity alone: the volumetric heat capacity is predetermined and held fixed, and the conductivity follows directly as $\lambda =a\rho c$. This removes the ill-conditioning that would otherwise arise from treating $\lambda$ and a as free, independent parameters in the fit. A two-parameter non-linear least-squares fit is applied to the rear-side temperature rise following Savitzky–Golay noise filtering to estimate the directional diffusivity and effective heat flux. The method is validated using an isotropic reference standard to rule out false system anisotropy, and is subsequently applied to additively manufactured polymer specimens to resolve print-induced directionality through sequential, axis-aligned (unidirectional) measurements along the axial and transverse printing directions. The validity of the one-dimensional reduction is confirmed quantitatively by two- and three-dimensional anisotropic simulations of the exact geometry, which bound the lateral-spreading bias below $0.01\%$ even for the highest-anisotropy specimen, and the robustness of the method to sensor thermal response, signal filtering, and effective-flux estimation is quantified. A rigorous evaluation of the expanded metrological uncertainty demonstrates the high accuracy and reliability of this low-energy excitation technique for highly dispersing media, making it a viable and highly accessible alternative for evaluating material anisotropy. Full article

An interlaboratory comparison of RF power measurements using automatic power measurement software was carried out among partners of the European Partnership on Metrology project titled “Development of RF and microwave metrology capability II” (RFMicrowave2). The absolute RF power output of a travelling signal generator was measured at six frequencies between 2 GHz and 18 GHz and at three nominal power levels of −10 dBm, 0 dBm, and 10 dBm. Comparison results were evaluated in terms of comparison reference values, degrees of equivalence, and normalised errors. Uncertainty evaluations were performed using both the Guide to the Expression of Uncertainty in Measurement and Monte Carlo simulation methods. The results demonstrate an acceptable level of agreement among participating laboratories and confirm the applicability of automatic power measurement software for interlaboratory RF power comparisons. Full article

The use of industrial and collaborative robots in tasks requiring high precision places increasing demands on the evaluation of their performance. In practice, parameters such as positioning accuracy, repeatability and stability are typically assessed according to ISO 9283, based on repeated measurements and comparison of commanded and measured positions. This paper presents a measurement and analysis system developed for this purpose. The system combines selected measurement hardware with a software solution that covers the full workflow from data acquisition to result evaluation. A Python-based backend is used to handle communication with measuring devices, data processing and storage, while a web-based interface provides access to system control, real-time monitoring, and visualization of results. The separation of these components allows the system to remain stable even if the user interface is interrupted. Measured data are evaluated using statistical methods based on repeated measurements, with results presented in both numerical and graphical form. This approach simplifies interpretation and reduces the need for additional external tools. The proposed solution provides a practical and extendable framework for evaluating robot performance in laboratory as well as industrial conditions. Based on the obtained data, the robot’s performance can be evaluated in terms of pose accuracy and pose repeatability. In addition, robot parameters can be monitored and evaluated over an extended period, which allows the proposed solution to be used in predictive maintenance. This article primarily focuses on verifying pose accuracy, since these data were required by the robot user, who specified a minimum of 30 measurement repetitions. The maximum allowable deviation was ±0.01 mm. In the case of pose repeatability and drift of pose characteristics, the calculated value obtained from the measured data must not exceed ±0.02 mm, which is the value declared by the robot manufacturer. Full article

Accurate calibration of anisotropic magnetoresistive (AMR) sensors under varying environmental conditions is crucial for reliable magnetic field measurements in geophysics, navigation, and space applications. Traditional physics-based calibration models offer interpretability but are limited in modeling complex nonlinear effects and typically lack trustworthy uncertainty estimation, whereas purely data-driven approaches often suffer from poor physical consistency and uncalibrated uncertainty estimates. This study proposes a hybrid calibration approach that integrates a physics-based analytical model for primary calibration with a neural network used exclusively for residual error correction, together with explicit uncertainty quantification. A temperature-compensated analytical calibration model is first estimated using nonlinear multivariate regression, with physics-based aleatoric uncertainty quantified via Quasi-Monte Carlo sampling and epistemic uncertainty propagated through a combination of parameter sampling and a Jacobian-based covariance approach. Residual errors not captured by the analytical model are learned using heteroscedastic neural networks, while Monte Carlo DropConnect is employed to quantify neural network epistemic uncertainty. The final calibrated output is computed by integrating physics-based predictions with data-driven error corrections and their associated uncertainties. Experimental results and simulation studies exhibit improved calibration accuracy and statistically consistent confidence interval coverage. Full article

A robust evaluation of predictive uncertainty is essential for deploying machine learning models in high-risk sectors. While various techniques such as Gaussian Processes and Bayesian Neural Networks have been considered to address model uncertainty, the measurement uncertainty associated with input data, particularly regarding heteroscedasticity and autocorrelation, is often overlooked. This work introduces the Generalized Least Squares Support Vector Machine (GLS-SVM), a kernel-based regression model designed to integrate the full variance–covariance matrix of the response variable into the training process. A GUM-consistent methodology was developed for evaluating prediction uncertainty, including a correction for model bias. The model’s performance was validated against standard Least Squares Support Vector Machines (LS-SVMs) and Gaussian Processes (GPs) through two case studies: a simulated regression problem with correlated data and the calibration of a mass flow controller. Performance was quantified using a comparability index ($C_{\mathrm{index}}$), defined as the absolute error of the prediction weighted by its expanded uncertainty. Results demonstrated that, in the simulated case study, the GLS-SVM achieved a $C_{\mathrm{index}}$ consistently below 0.65, indicating that its predictions are statistically consistent with the ground truth. In contrast, competing models significantly exceeded unity, with peak values near 8, indicating a failure to provide physically consistent estimations. For the calibration of the mass flow controller, the GP models produced uncertainties one to three orders of magnitude smaller than the measurement uncertainties, whereas GLS-SVM yielded uncertainties that were more physically consistent with the underlying measurement process. Eventually, the proposed approach offers a versatile, metrologically informed framework for data-driven regression tasks where measurement covariance information is available and rigorous uncertainty quantification is required. Full article

Curvature-based descriptors are increasingly used in surface metrology for the characterization of complex geometries. However, their sensitivity to measurement uncertainty remains insufficiently understood, particularly in comparison with conventional deviation-based metrics. This study investigates the propagation of coordinate measurement noise into curvature estimation using a numerical framework combining differential geometry, local quadratic surface fitting, and Monte Carlo simulation. A set of nominal surfaces, including spherical, cylindrical, and free-form geometries, was analyzed under controlled stochastic perturbations. The results show that curvature uncertainty increases nonlinearly with coordinate noise and is significantly more sensitive to measurement errors than point-wise deviations. Even small perturbations in measured coordinates lead to amplified variability in curvature due to its dependence on second-order derivatives. The analysis further reveals the presence of systematic bias in curvature estimation and demonstrates that the resulting distributions deviate from normality, despite Gaussian input noise. This finding highlights the limitations of classical uncertainty evaluation approaches based on linear propagation and normality assumptions. In addition, the study shows that increasing sampling density does not necessarily improve estimation reliability, while the size of the local fitting window plays a key role in stabilizing curvature estimation, acting as an implicit regularization parameter. The comparison with conventional form deviation metrics confirms that curvature-based analysis provides complementary information about local geometric stability, which is not captured by global measures. The proposed simulation-based approach offers a practical framework for evaluating uncertainty in nonlinear geometric measurements and supports the integration of curvature-based descriptors into advanced metrological applications. The proposed framework can support uncertainty-aware evaluation of free-form surfaces in practical measurement tasks, including coordinate measurement of turbine blades and aerodynamic components in the aerospace industry, as well as optical scanning and verification of patient-specific biomedical implants, where accurate curvature characterization is essential for quality assessment. Full article

With the rise of Industry 4.0, digital manufacturing and smart measuring technologies are enabling the development of zero-defect manufacturing strategies, which leads to less material waste and lower energy consumption, moving from off-line metrology and dedicated measuring equipment to in-line measurements and automated inspection systems. This is especially important for the production and manufacturing of large-scale parts, because of the high component cost and long delivery cycle. However, establishing traceability for measurement systems is often complicated due to both the measurement technology and the objects being measured. Traceability of measurement in the manufacturing environment is not ensured yet, and uncertainty evaluation for in-process measurement remains a complex and active research challenge. This work introduces a new uncertainty modelling and evaluation framework for traceable measurement of the large-scale components in ‘shop floor’ conditions. The framework is verified using real data obtained from various instruments for in situ measurement of a large artefact. Experimental results demonstrate that uncertainty evaluation for large-scale metrology is crucial for precision manufacturing on the production floor. The methods can be extended to the evaluation of measurement uncertainty of components with a smaller size and off-line inspection. Full article

This study presents experimental results from high-speed interferometric measurements on a transonic compressor blade cascade, where three of the five blades were torsionally oscillated at various frequencies up to $150\mathrm{Hz}$ and different inter-blade phase angles. The primary research objective is to develop and validate a non-intrusive methodology capable of quantifying unsteady flow fields surrounding aeroelastically unstable components. The resulting flow field images demonstrate the potential of the method. Unlike classical interferometric methods, the proposed approach has less stringent requirements for the optical quality of the test section windows. This advantage allows for the use of organic-glass windows, which are necessary for investigating highly loaded compressor blade cascades. Such windows are required to accommodate the suction slots used to maintain a representative Axial Velocity Density Ratio (AVDR). Unlike the classical schlieren technique, the method provides quantitative results with high spatial and temporal resolution, while the synthetic schlieren images can also be produced. The method proved suitable for measurements in the harsh environment of transonic flow through oscillating blades and is capable of capturing important unsteady flow phenomena. Full article

The work of the laboratories does not end with the measurement or examination results. However, there are significant differences between medical laboratories and testing laboratories in how they handle results. Comparing the two approaches, useful insights can be gained regarding both metrological concepts and the practice of activities. Testing laboratories have always been confronted with the interpretation of measurement results to make decisions, in relation to the intended users of test reports, based on threshold values and measurement uncertainty. In medical laboratories, the approach is quite different. For ISO 15189 accreditation requirements recipients of test results are given interpretive criteria provided by reference intervals, decision limits and differences from previous results. Constantly improving guidelines are available for this. However, critical points emerge that laboratories must take into account, involving both formal and content aspects. Some of these critical issues have been highlighted in the official SIPMeL recommendations. The laboratories can choose different criteria for interpreting test results: either relying primarily on measurement uncertainty or aligning as closely as possible with medical decision-making. Full article

Accurate photovoltaic power forecasting is essential for the reliable integration of solar energy into the electrical grid. This work presents a high-resolution dataset and acquisition framework that integrates electrical measurements, environmental variables, and solar position data into a unified relational database, suitable for PV power prediction across all temporal horizons. Using this dataset, we focus on very-short-term forecasting and propose a comprehensive forecasting framework that combines wavelet-based feature extraction with advanced deep learning techniques. The framework is evaluated across forecasting horizons from 5 to 30 min, achieving nMAE values between 0.73% and 4.64%, nRMSE between 1.65% and 7.98%, and PICP ranging from 62.4% to 74.7%. Robustness is assessed by simulating realistic cloud-induced perturbations in the input data. A hybrid approach that combines the deep learning model with a gradient boosting regressor to correct residual errors reduces the overall nMAE from 4.72% to 3.89% and nRMSE from 9.52% to 6.83%, effectively mitigating large errors caused by abrupt power fluctuations. These results demonstrate the framework’s ability to provide accurate and reliable probabilistic forecasts under both standard and perturbed conditions, offering a solid foundation for future PV prediction research and practical applications. Full article

Deterministic and probabilistic models of measured quantities, processes, and fields in production process control systems, as well as physical and probabilistic measures, enable the formation of measurement results and confer them the properties of objectivity and reliability. The issue of improving and developing models and measures in measurement methodology plays an increasingly important role in achieving high measurement accuracy in control systems and the reliability of decision-making by expert systems in production processes. The measurement result is formed by many factors, most of which are random in nature. The stochastic approach in measurement theory is particularly important for the measurement of probabilistic physical quantities and for the construction of decision rules for expert systems. Probabilistic measures play a key role in both the measurement of physical quantities and the construction of decision rules when using a stochastic approach. The main contribution of this paper is a measure-centred formulation of stochastic measurement and decision support, in which physical and probabilistic measures are treated as an explicit intermediate layer between the model and the algorithm. This is not presented as a new entropy or distance metric, but as a methodological integration that clarifies uncertainty handling, improves traceability of measurement results, and supports decision rules for production-process monitoring. The approach is illustrated on air-quality monitoring data from a real control system. Full article

Emerging materials often face challenges in market adoption due to limited comparability and reliability of measurement-based material information, despite their potential to drive technological innovation. While standardization is widely recognized as an important mechanism for market diffusion, existing approaches provide limited insight into how material specifications facilitate the comparative evaluation of material characteristics and their use in market decision-making. This study introduces a novel perspective, conceptualizing standardization as an institutional infrastructure designed to coordinate the generation, sharing, and evaluation of measurement-based material information across industries, standards development organizations (SDOs), and markets. Within this framework, the study distinguishes between two complementary types of standards for material specifications. Type A standards enable the structured disclosure of measured characteristic values and associated measurement uncertainties, allowing application-specific evaluation without predefined acceptance criteria. In contrast, Type B standards define predefined characteristic values and compliance criteria, providing a basis for conformity assessment, certification, and quality assurance. These two types may be understood as complementary mechanisms that fulfill different functions of comparability and compliance under varying technological and market conditions in emerging material systems. Consequently, they contribute to both innovation-oriented market evaluation and quality-assured market acceptance. Full article