Metrology, Volume 5, Issue 4 (December 2025) – 10 articles

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in high-value sectors such as aerospace, transportation, and energy, where technical documentation is often missing or outdated.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