Metrology, Volume 2, Issue 1 (March 2022) – 9 articles

There is currently interest in the digitalisation of metrology because technologies that can measure, analyse, and make critical decisions autonomously are beginning to emerge. The notions of metrological traceability and measurement uncertainty should be supported, following the recommendations in the Guide to the Expression of Uncertainty in Measurement (GUM). However, GUM offers no specific guidance. Here, we report on a Python package that implements algorithmic data processing using ‘uncertain numbers’, which satisfy the general criteria in GUM for an ideal format to express uncertainty. An uncertain number can represent a physical quantity that has not been determined exactly. Using uncertain numbers, measurement models can be expressed clearly and succinctly in terms of the quantities involved. The algorithms and simple data structures we use provide an example of how metrological traceability can be supported in digital systems. In particular, uncertain numbers provide a format to capture and propagate detailed information about quantities that influence a measurement along the various stages of a traceability chain. More detailed information about influence quantities can be exploited to extract more value from results for users at the end of a traceability chain. Full article

A virtual experiment simulates a real measurement process by means of a numerical model. The numerical model produces virtual data whose properties reflect those of the data observed in the real experiment. In this work, we explore how the results of a virtual experiment can be employed in the context of uncertainty evaluation for a corresponding real experiment. The uncertainty evaluation was based on the Guide to the Expression of Uncertainty in Measurement (GUM), which defines the de facto standard for uncertainty evaluation in metrology. We show that, under specific assumptions about model structure and variance of the data, virtual experiments in combination with a Monte Carlo method lead to an uncertainty evaluation for the real experiment that is in line with Supplement 1 to the GUM. In the general case, a GUM-compliant uncertainty evaluation in the context of a real experiment can no longer be based on a corresponding virtual experiment in a simple way. Nevertheless, virtual experiments are still useful in order to increase the reliability of an uncertainty analysis. Simple generic examples as well the case study of a virtual coordinate measuring machine are presented to illustrate the treatment. Full article

Laser interferometers that operate over a dynamic range exceeding one wavelength are used as compact displacement sensors for gravitational wave detectors and inertial sensors and in a variety of other high-precision applications. A number of approaches are available to extract the phase from such interferometers by implementing so-called phasemeters, algorithms to provide a linearised phase estimate. While many noise sources have to be considered for any given scheme, they are fundamentally limited by additive noise in the readout, such as electronic readout, digitisation, and shot-noise, which manifest as an effective, white phase noise in the phasemeter output. We calculated and compared the Cramer–Rao lower bound for phasemeters of some state-of-the-art two-beam interferometer schemes and derived their noise limitations for sub-fringe operation and for multi-fringe readout schemes. From this, we derived achievable noise performance levels for one of these interferometer techniques, deep-frequency modulation interferometry. We then applied our analysis to optical resonators and show that frequency scanning techniques can in theory benefit from such resonant enhancement, indicating that the sensitivities can be improved in future sensors. Full article

The tilted-wave interferometer (TWI) is a recent and promising technique for optically measuring aspheres and freeform surfaces and combines an elaborate experimental setup with sophisticated data analysis algorithms. There are, however, many parameters that influence its performance, and greater knowledge about the behavior of the TWI is needed before it can be established as a measurement standard. Virtual experiments are an appropriate tool for this purpose, and in this paper we present a digital twin of the TWI that was carefully designed for such experiments. The expensive numerical calculations involved combined with the existence of multiple influencing parameters limit the number of virtual experiments that are feasible, which poses a challenge to researchers. Experimental design is a statistical technique that allows virtual experiments to be planned such as to maximize information gain. We applied experimental design to virtual TWI experiments with the goal of identifying the main sources of uncertainty. The results from this work are presented here. Full article

Layering deposition methodology in metal additive manufacturing (AM) and the influence of different processing parameters, such as energy source level and deposition speed, which can change the melt pool condition, are known to be the important influencing factors on properties of components fabricated via AM. The effect of melt pool conditions and geometry on properties and quality of fabricated AM components has been widely studied through experimental and simulation techniques. There is a need for better understanding the influence of solidified melt pool topography on characteristics of next deposition layer that can be applied to complex surfaces, especially those with sparse topographical features, such as those that occur in AM deposition layers. Topography of deposited layers in metal additive manufacturing is a significant aspect on the bonding condition between the layers and defect generation mechanism. Characterization of the topography features in AM deposition layers offers a new perspective into investigation of defect generation mechanisms and quality evaluation of AM components. In this work, a feature-based topography study is proposed for the assessment of process parameters’ influence on AM deposition layers topography and defect generation mechanism. Titanium alloy (Ti6Al4V) samples deposited on steel substrate, by direct energy deposition (DED) AM technique at different process conditions, were used for the assessment. Topography datasets and analysis of shape and size differences pertaining to the relevant topographic features have been performed. Different AM process parameters were investigated on metallic AM samples manufactured via direct energy deposition (DED) and the potential defect generation mechanism was discussed. The assessment of the topography features was used for correlation study with previously published in-situ monitoring and quality evaluation results, where useful information was obtained through characterization of signature topographic formations and their relation to the in-situ acoustic process monitoring, as the indicators of the manufacturing process behavior and performance. Full article

Micro-coordinate measuring machines (micro-CMMs) for measuring microcomponents require a probe system with a probe tip diameter of several tens to several hundreds of micrometers. Scale effects work for such a small probe tip, i.e., the probe tip tends to stick on the measurement surface via surface adhesion forces. These surface adhesion forces significantly deteriorate probing resolution or repeatability. Therefore, to realize micro-CMMs, many researchers have proposed microprobe systems that use various surface-sensing principles compared with conventional CMM probes. In this review, the surface-sensing principles of microprobe systems were the focus, and the characteristics were reviewed. First, the proposed microprobe systems were summarized, and the probe performance trends were identified. Then, the individual microprobe system with different sensing principles was described to clarify the performance of each sensing principle. By comprehensively summarizing multiple types of probe systems and discussing their characteristics, this study contributed to identifying the performance limitations of the proposed micro-probe system. Accordingly, the future development of micro-CMMs probes is discussed. Full article

Supplement 1 to the ‘Guide to the expression of uncertainty of measurement’ describes a Monte Carlo method as a general numerical approach to uncertainty evaluation. Application of the approach typically delivers a large number of values of the output quantity of interest from which summary information such as an estimate of the quantity, its associated standard uncertainty, and a coverage interval for the quantity can be obtained and reported. This paper considers the use of a Monte Carlo method for uncertainty evaluation in calibration, using two examples to demonstrate how so-called ‘digital calibration certificates’ can allow the complete set of results of a Monte Carlo calculation to be reported. Full article

The article presents the determination of the topographic spatial resolution of an optical point sensor. It is quantified by the lateral period limit $D_{\mathrm{LIM}}$ measured on a type ASG material measure, also called (topographic) Siemens star, with a confocal sensor following both a radial measurement and evaluation, as proposed by ISO 25178-70, and the measurement and subsequent evaluation of two line scans, proposed by the NPL Good Practice Guide. As will be shown, for the latter, an only slightly misidentified target centre of the Siemens star leads to quite significant errors of the determined $D_{\mathrm{LIM}}$. Remarkably, a misidentified target centre does not necessarily result in an overestimation of $D_{\mathrm{LIM}}$, but lower values might also be obtained. Therefore, a modified Good Practice Guide is proposed to determine $D_{\mathrm{LIM}}$ more accurately, as it includes a thorough determination of the centre of the Siemens star as well. While the measurement and evaluation effort is increased slightly compared to the NPL Good Practice Guide, it is still much faster than a complete radial measurement and evaluation. Full article

Each experiment provides new information about the value of some physical quantity. However, not only measured values but also the uncertainties assigned to them are an important part of the results. The metrological guides provide recommendations for the presentation of the uncertainties of the measurement results: statistics and systematic components of the uncertainties should be explained, estimated, and presented separately as the results of the measurements. The experimental set-ups, the models of experiments for the derivation of physical values from primary measured quantities, are the product of human activity, making it a rather subjective field. The Systematic Distortion Factor (SDF) may exist in any experiment. It leads to the bias of the measured value from an unknown “true” value. The SDF appears as a real physical effect if it is not removed with additional measurements or analysis. For a set of measured data with the best evaluated true value, their differences beyond their uncertainties can be explained by the presence of Unrecognized Source of Uncertainties (USU) in these data. We can link the presence of USU in the data with the presence of SDF in the results of measurements. The paper demonstrates the existence of SDF in Prompt Fission Neutron Spectra (PFNS) measurements, measurements of fission cross sections, and measurements of Maxwellian spectrum averaged neutron capture cross sections for astrophysical applications. The paper discusses introducing and accounting for the USU in the data evaluation in cases when SDF cannot be eliminated. As an example, the model case of ²³⁸U(n,f)/²³⁵U(n,f) cross section ratio evaluation is demonstrated. Full article