Table of contents

With the redefinition of the international system of units, the value of the Planck constant was fixed, similarly to the values of the unperturbed ground state hyperfine transition frequency of the ¹³³Cs atom and speed of light in vacuum. Theoretically and differently from the past, the kilogram is now explicitly defined as the unit of inertial mass. Experimentally, the kilogram is realized by atom count or the Kibble balance. We show that only the former method measures the inertial mass without assuming the universality of free fall. Under ordinary circumstances, the results obtained by the Kibble balance require the equivalence of inertial and gravitational mass. Therefore, the agreement between the two measures can be interpreted as a test of the equivalence principle.

The overall aim of this study is to enable the traceable to International System of Units (SI) determination of column-integrated aerosol optical depth (AOD) retrieved from the passive remote sensing of the atmosphere using SI-traceable direct solar spectral irradiance measurements. A precision filter radiometer that measures direct solar spectral irradiance for the retrieval of AOD has been characterized and calibrated at the state-of-the-art calibration facilities of Physikalisch-Technische Bundesanstalt. The measured SI-traceable solar irradiances together with three state-of-the-art top-of-the-atmosphere (TOA) solar spectra have been used for retrieving AODs, which were validated against the reference AOD instruments of the World Aerosol Optical Depth Calibration Centre of the World Meteorological Organization (WMO). Calibration factors agreed within ±0.57% (3σ) using all three TOA spectra except for 368 nm (−1.1%) and 862 nm (1.8%) channels for one out of the three TOA spectra. Application of these results to the AOD retrieval showed AOD differences with the current reference methods/instruments well within the recommended WMO limits. The work provides a first step to opening a new era of AOD measurements traceability, providing a link to the SI through a laboratory-based approach, with the main advantages being the low uncertainty, the possibility of enhancing global AOD homogenization efforts and the chance to avoid calibration activities based on instrument relocations.

We have developed generalized methods for electrical substitution optical measurements, as well as cryogenic detectors which can be used to implement them. The new methods detailed here enable measurement of arbitrary periodic waveforms by an electrical substitution radiometer (ESR), which means that spectral and dynamic optical power can be absolutely calibrated directly by a primary standard detector. Cryogenic ESRs are not often used directly by researchers for optical calibrations due to their slow response times and cumbersome operation. We describe two types of ESRs with fast response times, including newly developed cryogenic bolometers with carbon nanotube absorbers, which are manufacturable by standard microfabrication techniques. These detectors have response times near 10 ms, spectral coverage from the ultraviolet to far-infrared, and are ideal for use with generalized electrical substitution. In our first tests of the generalized electrical substitution method with FTS, we have achieved uncertainty in detector response of 0.13% (k = 1) and total measurement uncertainty of 1.1% (k = 1) in the mid-infrared for spectral detector responsivity calibrations. The generalized method and fast detectors greatly expand the range of optical power calibrations which can be made using a wideband primary standard detector, which can shorten calibration chains and improve uncertainties.

X-ray computed tomography (XCT) is increasingly used for dimensional metrology, where it can offer accurate measurements of internal features that are not accessible with other techniques. However, XCT scanning can be relatively slow, which often prevents routine uptake for many applications. This paper explores the feasibility of improving the speed of XCT measurements while maintaining the quality of the dimensional measurements derived from reconstructed volumes. In particular, we compare two approaches to fast XCT acquisition, the use of fewer XCT projections as well as the use of shortened x-ray exposure times for each projection. The study shows that the additional Poisson noise produced by reducing the exposure for each projection has significantly less impact on dimensional measurements compared to the artefacts associated with strategies that take fewer projection images, leading to about half the measurement error variability. Advanced reconstruction algorithms such as the conjugate gradient least squares method or total variation constrained approaches, are shown to allow further improvements in measurement speed, though this can come at the cost of increased measurement bias (e.g. 2.8% increase in relative error in one example) and variance (e.g. 25% in the same example).

A current focus of the international metrology community is the digitalisation of documents, certificates and services in response to initiatives underway throughout industry and to the requirement to follow the principles of data being Findable, Accessible, Interoperable, and Reusable. We propose the key elements of a digital framework for the SI metre, at the point of realisation, showing how it may be implemented in practice. We give examples of direct benefits of this approach, which may be extended to other SI units.

In an absolute gravimeter based on optical interferometry, the rotation of a falling body leads to inaccurate gravity measurement. By arranging the center of mass (COM) of the falling body together with its optical center (OC), the rotation error can be minimized rapidly. An optical measurement system with a two-stage pendulum structure is proposed to measure the distance between the COM and the OC of the falling body. The displacement of the OC is measured by an orthogonal interferometer while the falling body twists around the torsion wire, and the rotation angle of the falling body is measured synchronously by a photoelectric autocollimator. It is proved that a twist of the falling body by 2.4 degrees leads to a significant offset of about 0.2 nm along the direction of the laser beam. This results in a limit error of the measurement of the distance between the OC and the COM less than 1 μm. Thus, the rotation error in absolute gravity measurement is reduced to 0.07 μGal.

A model for errors-in-variables regression is described that can be used to overcome the challenge posed by mutually inconsistent calibration data. The model and its implementation are illustrated in applications to the measurement of the amount fraction of oxygen in nitrogen from key comparison CCQM-K53, and of carbon isotope delta values in steroids from human urine. These two examples clearly demonstrate that inconsistencies in measurement results can be addressed similarly to how laboratory effects are often invoked to deal with mutually inconsistent results from interlaboratory studies involving scalar measurands. Bayesian versions of errors-in-variables regression, fitted via Markov Chain Monte Carlo sampling, are employed, which yield estimates of the key comparison reference function in one example, and of the analysis function in the other. The fitting procedures also characterize the uncertainty associated with these functions, while quantifying and propagating the 'excess' dispersion that was unrecognized in the uncertainty budgets for the individual measurements, and that therefore is missing from the reported uncertainties. We regard this 'excess' dispersion as an expression of dark uncertainty, which we take into account in the context of calibrations that involve regression models. In one variant of the model the estimate of dark uncertainty is the same for all the participants in the comparison, while in another variant different amounts of dark uncertainty are assigned to different participants. We compare these models with the conventional errors-in-variables model underlying the procedure that ISO 6143 recommends for building analysis functions. Applications of this procedure are often preceded by the selection of a subset of the measurement results deemed to be mutually consistent, while the more discrepant ones are set aside. This new model is more inclusive than the conventional model, in that it easily accommodates measurement results that are mutually inconsistent. It produces results that take into account contributions from all apparent sources of uncertainty, regardless of whether these sources are already understood and their contributions have been included in the reported uncertainties, or still require investigation after they will have been detected and quantified.

The Canadian air-kerma primary standard for ⁶⁰Co beams is updated according to ICRU report 90 (ICRU-90) recommendations. The effect of these recommendations and a more detailed chamber model on the primary standard is investigated. Dosimetric quantities and corrections required for the realization of air kerma are calculated using the EGSnrc Monte Carlo (MC) simulation system. The validity of Spencer–Attix (SA) cavity theory as function of Δ, the secondary particle production threshold energy, is investigated to assess the accuracy of its current selection criterion. Although individual changes in some correction factors are statistically non-negligible, the overall effect amounts to only a 0.04% increase of the standard. The mean restricted mass electronic stopping power ratio graphite to air, ${\bar{S}}_{{\Delta},\mathrm{g},\mathrm{a}}$ decreases from the previous value of 1.0010 to a value of 0.9949. If this value is used with the recommended W_air value of 33.97 eV, the effect on the standard is a reduction of 0.613%. When the recommended ${W}_{\text{air}}{\bar{S}}_{\text{g,}\;\text{a}}$ value of 33.72 eV is used instead, the change results in a 0.835% reduction in K_air. Using SA cavity theory to obtain K_air with a Δ value of 20 keV, corresponding to the cavity's mean chord length, reproduces a direct MC calculation at the 0.03% level. Type B uncertainties due to uncertainty in the photon and electron cross sections for the largest corrections K_wall and K_comp are estimated to be 0.01% and 0.10%, respectively. No statistically significant effect on the standard is observed due to changes in the correction factors. Fano tests and comparison to single scattering calculations demonstrate EGSnrc's electron transport algorithm accuracy to be within 0.03% relative to its own cross sections. The latter also validates the criterion for selecting Δ based on the average chord length of the chamber's cavity. A 0.2% difference in the restricted stopping power ratio obtained in this work and the value resulting from ICRU-90 recommendations has the potential for affecting standards relying on the absolute value of W_air, thus further investigation is granted. The current update results in a 0.8% decrease of the Canadian ⁶⁰Co air-kerma primary standard with a reduced uncertainty of 0.2%. This change is in excellent agreement with the reported change to the BIPM ⁶⁰Co air-kerma standard.

Carbon dioxide emissions made up from fossil fuel is a weighted contribution to the total carbon dioxide emissions in Korea. To keep on track of the long-term mitigation pathway, the new solution for enhancing the emission flow measurements more accurately in industrial smokestacks is urgent. Thus, along with the popular instrument, an S-type pitot tube, three-dimensional (3D) pitot tubes have been introduced to determine the emission flow in smokestacks by international standards and Korean regulations. To comply with the regulations mandated in Korea, the Korea Research Institute of Standards and Science established the 3D pitot tube calibration system for stack flow measurements assembled to the airspeed standard system. This calibration system can produce accurate pitch and velocity calibration curves for 3D pitot tubes in the range of testing pitch angle within ±30°, and have an expanded uncertainty attributed to the calibration curves (0.005–0.086) and (1.3–2.9)% for the prism pitot tube and (0.008–0.175) and (1.6–3.1)% for the spherical pitot tube.

In this paper, optimization of acceptance interval in conformity assessment using the expression of the revenue that we showed in part 1 of this study is proposed under the condition of a systematic effect component being present in the measurement uncertainty. Systematic effect components are caused by unknown biases. Using the distribution based on the uncertainty information of the bias, we can develop the distribution of the revenue. Our idea is to set a percentile of the revenue distribution as the target of the maximization to reflect the systematic effect component in the optimization of the acceptance interval. We provide an equation for the optimum acceptance interval that can be numerically solved with little burden. We found that the choice of the probability for the percentile is an essential task in the optimization. Our proposed method incorporating the systematic effect seems to be sufficiently practical to be applied to actual processes.

In inspections for conformity assessment, an acceptance interval smaller than the tolerance interval is often determined in order to reduce the risk of consumers obtaining non-conforming items in the market. The presence of non-conforming items in the market impairs the evaluation of items by customers and may have an impact on revenue by decreasing prices. However, setting too small an acceptance interval reduces the revenue from the process by decreasing the number of the items available in the market. We thus propose a method to determine the optimum acceptance interval in conformity assessment by means of maximization of the revenue from processes. For this purpose, we give a mathematical model for the price of an item and its cost in the production process. Through theoretical analysis and simulations, it is shown that a parameter in the price model is the key in the optimization. In this paper we report a method for processes where no systematic effect component of measurement uncertainty exists, and in part 2 of this series we will report an extended method in which systematic effects are taken into consideration.

The technique of precise point positioning with integer ambiguity resolution (IPPP) has been developed for many years and has been shown to significantly improve the long-term performance of time and frequency transfer with respect to other GNSS-based techniques. In this paper, we present results of GPS IPPP links over a period of 22 months for a dozen time laboratories participating to UTC. We show that continuous links, in which the continuity of the GPS phase measurements is preserved, can be maintained for periods exceeding one year and further extended if data from two receivers per station are available. We quantify the frequency transfer uncertainty of IPPP by comparison to optical links and show how IPPP could improve UTC links to below 1 × 10⁻¹⁶ relative frequency uncertainty over averaging times of up to one month, i.e. the characteristic period of UTC publication. Comparisons of primary and secondary frequency standards reported for TAI indicate that IPPP could somewhat improve the accuracy of TAI/UTC. Comparisons of IPPP to two-way time transfer techniques reveal very long-term ns-size instabilities which must be further studied. Use of IPPP for UTC links is possible only if integer GNSS satellite products become available with a short delay and we report on such experimental products. Finally, we discuss the practical implications of using IPPP link in UTC and describe how the necessary steps could be implemented.

Accurate density measurement of molten refractory metals over 3000 K is very challenging, and difficult to achieve with conventional methods. Although containerless techniques have been the most effective and well-established methods to measure the density of molten metals at such high temperatures, a large discrepancy in the containerlessly measured density values has been reported. Here, we identify the uncertainty factors of the density measurement and their influence on the measured density of molten refractory metals over 3000 K using an electrostatic levitator (ESL). We find that intensely focused laser beams can cause rotation-induced deformation of a levitated droplet and thus the large uncertainty in the measured density. Moreover, the combination of sample rotation and precession seriously affects the measurements of density and temperature dependence of density (i.e., volume thermal expansion). By minimizing such rotation and precession, we successfully measure the density and volume expansion coefficient of refractory liquids (tantalum, molybdenum, and niobium) with significantly improved reproducibility and accuracy, and evaluate the uncertainties associated with the density measurement using ESL.

We investigate temperature uncertainty of Coulomb blockade thermometer (CBT) arising from inevitable non-uniformities in tunnel junction arrays. The corrections are proportional to the junction resistance variance in the linear operation regime and this result holds approximately also beyond this originally studied high temperature range. We present both analytical and numerical results, and discuss briefly their implications on achievable uniformity based on state-of-the-art fabrication of sensors.

In this paper we propose an approach for performing fault detection and identification in clock ensembles based on the generalized likelihood ratio test. We show that by applying a set of purposefully-designed statistical tests, one can successfully detect faults occurring in a clock of the ensemble, and identify which measurement in the ensemble is most likely to have triggered the detection. We first develop the theoretical framework for the characterization of the detectors and their performance, and validate the derivations via Monte Carlo simulations. Then, we apply the statistical tests to an ensemble of cesium clocks, aiming at detecting and identifying three types of non-nominal behaviors. The faulty conditions are obtained by injecting a pattern of phase steps, a phase and frequency drift, and an oscillatory phase component.

This paper describes the NRC measurement set-up and the preparatory work for the CCT-K7.2021 key comparison (KC) of triple-point-of-water (TPW) cells. The preparatory work at NRC (charged with piloting the KC) included a comprehensive testing of the measurement set-up, the definition of the new NRC national standard for the TPW temperature, and the evaluation of the uncertainty budgets relevant for this KC. The new NRC TPW national standard is composed of an ensemble of ten fused silica TPW cells, characterized in both their isotopic composition and impurity content. Three uncertainty budgets were evaluated, corresponding to three different cases involved in the measurements at the pilot laboratory: (a) the temperature difference between two TPW cells, which amounted to 26 μK (k = 2), (b) the temperature difference between a TPW cell and NRC national reference, which amounted to 35 μK (k = 2) and (c) the temperature difference between a comparison participant's transfer cell and the comparison reference, composed of the average of two NRC national reference cells, which amounted to 19 μK (k = 2).

We present a method to determine the internal quantum deficiency (IQD) of a predictable quantum efficient detector (PQED) based on measured photocurrent dependence on bias voltage and a 3D simulation model of charge carrier recombination losses. The simulation model of silicon photodiodes includes wafer doping concentration, fixed charge of SiO₂ layer, bulk lifetime of charge carriers and surface recombination velocity as the fitted parameters. With only one set of physical photodiode defining parameters, the simulation shows excellent agreement with experimental data at power levels from 100 μW to 1000 μW with variation in illumination beam size. We could also predict the dependence of IQD on bias voltage at the wavelength of 476 nm using photodiode parameters determined independently at 647 nm wavelength. The fitted values of doping concentration and fixed charge extracted from the simulation model are in close agreement with the expected parameter values determined earlier. At bias voltages larger than 5 V at the wavelength of 476 nm, the internal quantum efficiency of one of the tested PQEDs is measured to be 0.999 970 ± 0.000 027, where the relative expanded uncertainty of 0.000 027 is one of the lowest values ever achieved in spectral responsivity measurement of optical detectors.

Relative humidity (RH) is a fundamental quantity used in many fields of engineering and science, and in particular in meteorology and climate research. Relative fugacity (RF) and, equivalently, relative activity of water vapour in humid air have recently been proposed as a physically well-founded, unambiguous common metrological reference quantity for several conventional but mutually inconsistent definitions of RH. The RF definition is valid is valid under real-gas conditions and above boiling and sublimation temperatures. While differences between RH and RF mostly remain within uncertainties of typical present-day RH measurements, such systematic discrepancies are expected to be of substantial climatological relevance. Consequently, interdisciplinary harmonisation of RH definitions is overdue within the SI framework. Dew-point and frost-point temperatures are preferred measurands in humidity metrology using, for example, chilled-mirror hygrometers. Here, relations are presented for estimating RF from those temperatures, based on equations of state of the 2011 IUGG 6 standard TEOS-10, the 'international thermodynamic equation of seawater—2010'. Recommendations are given for numerically computing RF using the open-source TEOS-10 SIA library⁶. The asymptotic limiting laws of RF for nearly saturated humid air exhibit the familiar form of Clausius–Clapeyron-like equations, despite departing from ideal-gas assumptions. Under various practical conditions, these simple equations may cover the full humidity range with only minor residuals compared to the full numerical TEOS-10 solution for RF.

We demonstrate operation of a constant-pressure flowmeter capable of generating and accurately measuring flows as low as 2 × 10⁻¹³ mol s⁻¹. Generation of such small flows is accomplished by using a small conductance element with C ≈ 50 nl s⁻¹. Accurate measurement then requires both low outgassing materials ($< 1\times 1{0}^{-15}$ mol s⁻¹) and small volume changes ($\approx 70$ μl). We outline the present flowmeter's construction, detail its operation, and quantify its uncertainty. The type-B uncertainty is $< 0.2$% (k = 1) over the entire operating range. In particular, we present an analysis of its hydraulic system, and quantify the shift and uncertainty due to the slightly compressible oil. Finally, we compare our flowmeter against a NIST standard flowmeter, and find agreement to within 0.5% (k = 2).

The fixed points adopted in the international temperature scale of 1990 have generally been used to calibrate contact thermometers, such as thermocouples, to get the highest accuracy. The fixed point for Pd is located at the upper limit range of the Pt/Rh noble metal thermocouple calibration. However, the high price of Pd itself restricts its wide use in calibration laboratories. To overcome this difficulty, this study develops an alternative fixed point having a close transition temperature to the Pd freezing temperature of 1554.8 °C. The alternative is pure Fe with a quoted melting temperature of 1538 °C. To make a thermometric cell, an alumina crucible was used to contain the molten liquid and it was found to be robust enough to last for more than 60 cycles of melting and freezing tests without any chemical and mechanical damage. Two cells were fabricated, and their melting and freezing behaviors were studied using type B thermocouples. By considering the advantage and disadvantages of melting and freezing, the melting temperature was selected as a thermometric transition point for the calibration of thermocouples because of its easy operational processes and acceptable uncertainty level. Using a reference thermocouple that had been calibrated versus a standard radiation thermometer, the average melting temperature of the two Fe cells was 1534.0 °C with an uncertainty of 1.2 °C (k = 2). From the studies, an Fe cell made in an alumina crucible can successfully replace the Pd fixed point.

The primary reference measurement procedure is a method to realize the definition of the quantity without relation to a reference standard of the same quantity. This paper presents a candidate primary reference measurement procedure for the measurement of the amount-of-substance of a complexing agent expressed as ethylenediaminetetraacetic acid (EDTA) based on coulometric titration. Herein, mercury (Hg) was used as the anode because it does not undergo spontaneous oxidation. Furthermore, a 1:1 complex is formed between the electrogenerated Hg²⁺ ions and EDTA (in the form of Y⁴⁻). Although the electrochemical oxidation of Hg may generate Hg₂²⁺ ion, Hg₂²⁺ undergoes disproportionation in the presence of EDTA, thereby forming the desired Hg²⁺ species. The equivalence point occurs at the maximum of the derivative of the theoretical titration curve. As such, the measurement results were obtained by assuming that the maximum of the derivative of the experimental titration curve was the end point. The developed procedure was employed for the measurement of the amount-of-substance content of the complexing agent in EDTA reference material certified at the Slovak Institute of Metrology. The experimental measurements agreed well with the certified value for the reference material within the measurement uncertainty. The candidate procedure will be useful in certifying EDTA reference material and establishing international equivalence of amount content of the complexing agent.