Metrology, Volume 5, Issue 4 (December 2025) – 22 articles

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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 m_s = ±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. Full article

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). Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article