Metrology, Volume 6, Issue 1 (March 2026) – 8 articles

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