Metrologia

A full evaluation of the uncertainty budget for the ytterbium ion optical clock at the National Physical Laboratory (NPL) was performed on the electric octupole (E3) $^2\mathrm{S}_{1/2}\,\rightarrow\, ^2\mathrm{F}_{7/2}$ transition. The total systematic frequency shift was measured with a fractional standard systematic uncertainty of $2.2\times 10^{-18}$. Furthermore, the absolute frequency of the E3 transition of the ¹⁷¹Yb⁺ ion was measured between 2019 and 2023 via a link to International Atomic Time (TAI) and against the local caesium fountain NPL-CsF2. The absolute frequencies were measured with fractional standard uncertainties between $3.7 \times 10^{-16}$ and $1.1 \times 10^{-15}$, and all were in agreement with the 2021 BIPM recommended frequency.

This paper outlines the roadmap towards the redefinition of the second, which was recently updated by the CCTF Task Force created by the CCTF in 2020. The main achievements of optical frequency standards (OFS) call for reflection on the redefinition of the second, but open new challenges related to the performance of the OFS, their contribution to time scales and UTC, the possibility of their comparison, and the knowledge of the Earth’s gravitational potential to ensure a robust and accurate capacity to realize a new definition at the level of 10⁻¹⁸ uncertainty. The mandatory criteria to be achieved before redefinition have been defined and their current fulfilment level is estimated showing the fields that still needed improvement. The possibility to base the redefinition on a single or on a set of transitions has also been evaluated. The roadmap indicates the steps to be followed in the next years to be ready for a sound and successful redefinition.

The virial coefficients of cryogenic gases, especially helium-4 and helium-3, are playing an ever more critical role in the establishment of primary reference standards for temperature after the redefinition of the kelvin in the SI. Thus, the reliability of the values and uncertainties of these coefficients, especially those of the second, third, and even fourth density virial coefficients (B, C and D), has become more significant. To check the accuracy of these coefficients for helium-4 from ab initio calculations, the refractive-index gas thermometry (RIGT) method was developed, allowing for the simultaneous determination of thermodynamic temperatures and density virial coefficients. Using this technique, highly accurate experimental values of B, C and D for helium-4, as well as T–T₉₀ values, were obtained for the range 5 K–25 K. Direct comparisons with the ab initio calculation density virial coefficients for helium-4 were conducted, revealing excellent agreement. Furthermore, good agreements of thermodynamic temperatures T between absolute RIGT and our previous single pressure RIGT (Gao et al 2021 Metrologia 58 059501) were achieved at temperatures from 5 K to 25 K, with differences within each standard uncertainty. This further strengthens our confidence in the comparisons made in this work. It is foreseeable that the rigorously verified ab initio calculations of the density virial coefficients for helium-4 will continue to be used to improve the measurement accuracy of helium-based primary reference standards for temperature and pressure.

Coordinated Universal Time (UTC) has considerably changed in recent years. The evolution of UTC follows the scientific and industrial progress by developing appropriate models, more adapted calculation algorithms, more efficient and rapid dissemination processes and a well defined traceability chain. The enormous technical progress worldwide has resulted in an impressive number of atomic clocks now available for UTC calculation. The refined time and frequency transfer techniques are approaching the accuracy requested for the new definition of the SI second. The more regular operation of primary frequency standards (PFS) increases the accuracy of UTC and opens a possible new development for time scale algorithms. From the metrological point of view all the ingredients are available for major improvements to UTC. Dissemination of UTC is done by the monthly publication of results in BIPM Circular T. This document makes a quality evaluation of local representations of UTC, named UTC(k), in national institutes, and other organizations, by giving the evolution of their offsets relative to UTC and their respective uncertainties. The clock models adopted and the time transfer techniques have progressively improved over the years, assuring the long-term stability of UTC. Each computation of UTC processes data over one month with five-day sampling and publication. A rapid solution of UTC (UTCr) has existed since 2013, and consists of the processing of daily sampled data over four consecutive weeks, computed and published weekly. It gives quick access to UTC, and allows participating laboratories to better monitor the offsets of their realizations to the reference UTC. The traditional monthly publication, containing results of all the laboratories contributing data to the BIPM for the computation of UTC was complemented after the establishment of the Mutual Recognition Arrangement of the International Committee on Weights and Measures (CIPM MRA). This time comparison, which has been the responsibility of the BIPM since 1988, added as a complement the key comparison on time defined by the Consultative Committee for Time and Frequency (CCTF) in 2006 as CCTF-K001.UTC, where the results published are those of national metrology institutes (NMIs) signatories of the CIPM MRA, or designated institutes (DIs). The traceability issues are formalized in the framework of the CIPM MRA. The development of time metrology activities in the different metrology regions, supports the actions of the BIPM time department to improve the accuracy of [UTC–UTC(k)], where the coordination with the Regional Metrology Organizations (RMOs) has a key role. This paper presents an overview of UTC.

Half-life measurements of radionuclides are undeservedly perceived as ‘easy’ and the experimental uncertainties are commonly underestimated. Data evaluators, scanning the literature, are faced with bad documentation, lack of traceability, incomplete uncertainty budgets and discrepant results. Poor control of uncertainties has its implications for the end-user community, varying from limitations to the accuracy and reliability of nuclear-based analytical techniques to the fundamental question whether half-lives are invariable or not. This paper addresses some issues from the viewpoints of the user community and of the decay data provider. It addresses the propagation of the uncertainty of the half-life in activity measurements and discusses different types of half-life measurements, typical parameters influencing their uncertainty, a tool to propagate the uncertainties and suggestions for a more complete reporting style. Problems and solutions are illustrated with striking examples from literature.

The letter provides a short comment on a recent paper in Metrologia, explaining the reasons why the Avogadro constant must be the defining constant of the mole in the International System of Units.

This work describes the apparatus for NIST-F4, an updated cesium atomic fountain at the National Institute of Standards and Technology (NIST), and presents an accuracy evaluation of the fountain as a primary frequency standard. The fountain uses optical molasses to laser cool a cloud of cesium atoms and launch it vertically in a fountain geometry. In high-density mode, the fractional frequency stability of NIST-F4 is $\sigma_y(\tau) = 1.5\times10^{-13}/\sqrt{\tau}$, where τ is the measurement time in seconds. The short-term stability is limited by quantum projection noise and by phase noise from the local oscillator, an oven-controlled crystal oscillator operating at 5 MHz. Systematic frequency shifts and their uncertainties have been evaluated, resulting in a systematic (type B) fractional frequency uncertainty $\sigma_\mathrm{B} = 2.2\times10^{-16}$.

On 16 November 2018 a revision of the International System of Units (the SI) was agreed by the General Conference on Weights and Measures. The definitions of the base units were presented in a new format that highlighted the link between each unit and a defined value of an associated constant. The physical concepts underlying the definitions of the kilogram, the ampere, the kelvin and the mole have been changed. The new definition of the kilogram is of particular importance because it eliminated the last definition referring to an artefact. In this way, the new definitions use the rules of nature to create the rules of measurement and tie measurements at the atomic and quantum scales to those at the macroscopic level. The new definitions do not prescribe particular realization methods and hence will allow the development of new and more accurate measurement techniques.

The International System of Units (SI) is supposed to be coherent. That is, when a combination of units is replaced by an equivalent unit, there is no additional numerical factor. Here we consider dimensionless units as defined in the SI, e.g. angular units like radians or steradians and counting units like radioactive decays or molecules. We show that an incoherence may arise when different units of this type are replaced by a single dimensionless unit, the unit ‘one’, and suggest how to properly include such units into the SI in order to remove the incoherence. In particular, we argue that the radian is the appropriate coherent unit for angles and that hertz is not a coherent unit in the SI. We also discuss how including angular and counting units affects the fundamental constants.

The current definition of the System of unit second based on the Cs ground state hyperfine transition is expected to be replaced by a new definition based on optical frequency standards in the next decade. Several options are currently under consideration for the new definition, including a definition based on the weighted geometric mean of several transitions. In this paper, we review several properties of this option, and most notably introduce a quantitative method to set the weights of transitions, and a graphical representation of the unit that make the distinction between the definition and the realisation of the unit easier to understand.

We performed lattice comparison measurements between ²⁸Si-enriched crystals using a self-referenced lattice comparator (SRLC). The relative lattice spacing difference between two crystals sectioned from the same ingot were measured, showing agreement with values calculated from impurity and vacancy corrections, as well as with those obtained by other measurement techniques. Further comparison involving crystals from different ingots enabled an independent determination of the {220} lattice-plane spacing of a ²⁸Si enriched crystal as 192.014 712 91(55) nm, confirming previously reported values. When applied to the realization of the kilogram via the x-ray crystal density method, the uncertainty contribution from the SRLC measurement corresponds to 8.4 μg uncertainty in the mass of a 1 kg silicon sphere, supporting its role in the accurate realization of the kilogram.

This report gives the result of the bilateral comparison of resistances of 10 kΩ between UME (National Metrology Institute of Türkiye/TÜBITAK Ulusal Metroloji Enstitüsü) and the BIPM carried out from October 2024 to April 2025, as part of the ongoing BIPM key comparison BIPM.EM-K13.b. Two 10 kΩ travelling standards belonging to the BIPM were used. The comparison was carried out with an A-B-A pattern of measurements; the standards were first measured at the BIPM for about one month, then at UME for about three months, and finally again at the BIPM for about one month. The measurand was the 4-terminal DC resistance at low power. The BIPM was the pilot laboratory and the key comparison reference value is the BIPM value.

The results from TÜBİTAK UME and the BIPM were found to be in good agreement, with a difference D smaller than the relative expanded uncertainty U_c (considering the degrees of freedom for BIPM and TÜBİTAK UME respectively, the expansion factors at 95.45% confidence level are t_pBIPM(v) = 2.025 and t_pUME(v) = 2.37) giving D = 0.017 × 10^-6, U_c = 0.050 × 10^-6 for 10 kΩ.

To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database https://www.bipm.org/kcdb/.

The final report has been peer-reviewed and approved for publication by the CCEM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Measurement tapes are a classic and widely used measuring tool in dimensional metrology. High volume commercial tapes play an important role in business transactions and official measurements. In addition, there are also extremely high-quality measurement tapes acting as transfer standards for the dissemination of the SI unit metre. The calibration of such transfer standards or measuring instruments with the lowest possible measurement uncertainties is a standard task for NMIs with a high economic relevance. The EURAMET.L-S2.3.n01 supplementary comparison on measurement of steel tapes of 10 m and 50 m was carried out between 2018 and 2025 with 20 participants. The Physikalisch-Technische Bundesanstalt (PTB) acted as pilot laboratory. National metrology institutes (NMIs) and designated institutes (DIs) from four regional metrology organisations (RMOs) participated: fourteen institutes from EURAMET were joined by three institutes from APMP, one from GULFMET and one from SIM.

The comparison results generally supported the measurement capabilities of the international dimensional metrology community in the field of tape calibration for high quality tapes. Especially in case of commercial grade tapes, the comparison results clearly show that the scale marker quality must be carefully assessed, individually for each tape. Besides, a small, but systematic and persistent change of the artefact properties due to the repeated mechanical elongation was observed, even for standards of decades of age. The pilot control measurements could be successfully used to mitigate this typical challenge for a round robin.

To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database https://www.bipm.org/kcdb/.

The final report has been peer-reviewed and approved for publication by the CCL, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

To establish robust calibration and measurement capabilities (CMCs) for atmospheric methane (CH₄) stable isotope ratios, National Metrology Institutes (NMIs) and Designated Institutes (DIs) need a comprehensive understanding of the underlying measurement techniques, reference materials (RMs), calibration hierarchies, value assignment, uncertainty evaluation, and inter-laboratory comparison activities. This review, developed by the CH₄ Task Team within the Consultative Committee for Amount of Substance: Metrology in Chemistry and Biology (CCQM) Gas Analysis Working Group (GAWG) and the Isotope Ratio Working Group (IRWG), provides key insights for developing these capabilities at NMIs/DIs. The World Meteorological Organization (WMO) recommended network compatibility goals for atmospheric methane stable isotope ratio monitoring, expressed as isotope delta values, are 0.02‰ for the stable carbon isotope delta (δ¹³C) value and 1‰ for the stable hydrogen isotope delta (δ²H) value, with extended targets of 0.2‰ for δ¹³C and 5‰ for δ²H. Global inter-laboratory comparisons have revealed offsets of up to 0.5‰ for δ¹³C and 13‰ for δ²H measurements, substantially exceeding the WMO targets. To address these discrepancies, steady progress is being made, particularly by expert isotope laboratories, with increasing engagement from NMIs/DIs. Improved measurement techniques and the use of common RMs are bringing measurements closer to the WMO goals. This overview not only reviews the components necessary for establishing NMI/DI CMCs but also provides actionable recommendations to further align global measurements, including the development of standardized protocols, adoption of the VPDB carbon isotope delta scale for atmospheric data harmonization, and international comparison studies to support NMI/DIs in their CMC claims. These actions are critical for achieving long-term consistency and advancing global standards for atmospheric methane stable isotope ratio measurements.

Johnson noise thermometry (JNT) is a purely electronic method of thermodynamic thermometry. In primary JNT, the temperature is inferred from a comparison of the Johnson noise voltage of a resistor at the unknown temperature with a pseudo-random noise synthesized by a quantum-based voltage-noise source (QVNS). The advantages of the method are that it relies entirely on electronic measurements, and it can be used over a wide range of temperatures due to the ability of the QVNS to generate programmable, scalable, and accurate reference signals. The disadvantages are the requirement of cryogenic operation of the QVNS, the need to match the frequency responses of the leads of the sense resistor and the QVNS, and long measurement times. This review collates advice on current best practice for a primary JNT based on the switched correlator and QVNS. The method achieves an uncertainty of about 1 mK near 300 K and is suited to operation between 4 K and 1000 K.

This paper outlines the roadmap towards the redefinition of the second, which was recently updated by the CCTF Task Force created by the CCTF in 2020. The main achievements of optical frequency standards (OFS) call for reflection on the redefinition of the second, but open new challenges related to the performance of the OFS, their contribution to time scales and UTC, the possibility of their comparison, and the knowledge of the Earth’s gravitational potential to ensure a robust and accurate capacity to realize a new definition at the level of 10⁻¹⁸ uncertainty. The mandatory criteria to be achieved before redefinition have been defined and their current fulfilment level is estimated showing the fields that still needed improvement. The possibility to base the redefinition on a single or on a set of transitions has also been evaluated. The roadmap indicates the steps to be followed in the next years to be ready for a sound and successful redefinition.

Bayesian statistical methods are being used increasingly often in measurement science, similarly to how they now pervade all the sciences, from astrophysics to climatology, and from genetics to social sciences. Within metrology, the use of Bayesian methods is documented in peer-reviewed publications that describe the development of certified reference materials or the characterization of CIPM key comparison reference values and the associated degrees of equivalence. This contribution reviews Bayesian concepts and methods, and provides guidance for how they can be used in measurement science, illustrated with realistic examples of application. In the process, this review also provides compelling evidence to the effect that the Bayesian approach offers unparalleled means to exploit all the information available that is relevant to rigorous and reliable measurement. The Bayesian outlook streamlines the interpretation of uncertainty evaluations, aligning their meaning with how they are perceived intuitively: not as promises about performance in the long run, but as expressions of documented and justified degrees of belief about the truth of specific conclusions supported by empirical evidence. This review also demonstrates that the Bayesian approach is practicable using currently available modeling and computational techniques, and, most importantly, that measurement results obtained using Bayesian methods, and predictions based on Bayesian models, including the establishment of metrological traceability, are amenable to empirical validation, no less than when classical statistical methods are used for the same purposes. Our goal is not to suggest that everything in metrology should be done in a Bayesian way. Instead, we aim to highlight applications and kinds of metrological problems where Bayesian methods shine brighter than the classical alternatives, and deliver results that any classical approach would be hard-pressed to match.

The CIPM Mutual Recognition Arrangement (CIPM MRA) provides a technical framework to the measurement community for comparability of measurement results and international recognition of metrological capabilities declared by the national metrology institutes throughout the globe. Since its founding in 1999, the participating institutes have now published more than 25 700 peer-reviewed calibration and measurement capabilities (CMCs) in the CIPM MRA database (Key Comparison Database (KCDB)). It is these capabilities and the technical evidence behind them that underpin the international acceptance of measurements around the world. The success and wide adoption of the CIPM MRA indicate the maturity of the arrangement, however, the accompanying increased workload for the participants motivated a review of the practices with the aim to increase the efficiency while maintaining the technical rigor. This review identified a number of key factors that formed the basis of the revision of the modus operandi, including the procedures and the database. The review resulted in recommendations for the CIPM Consultative Committees (CCs), regional metrology organizations (RMOs), participating institutes, as well as the BIPM. The revamped KCDB incorporated the whole lifecycle of CMCs, familiarizing with the new system being supported by the Capacity Building and Knowledge Transfer Programme of the BIPM. The result was an improvement in not only efficiency of the CIPM MRA, but also its effectiveness. For example, the time required for the Joint Committee of the RMOs and the BIPM (JCRB) review of CMCs has dropped by more than 50% to 59 d (median) in 2022, and the number of uncompleted key comparisons (KCs) have been reduced by a factor of three to a total of 38 in March 2023, representing now less than 3% of the total KCs. In this paper we look at the key factors through the various metrological areas addressing practices by each CCs.

We present a double-beam method using a spectrophotometer to measure total luminous transmittance and haze. We derived analytical formulas to describe the measurements, which showed the dependence of haze on the exit angle and the reflectance of an integrating sphere. The use of double beams effectively cancels out multiplier factors caused by multiple reflections in the integrating sphere. In contrast, when employing single-beam methods recommended in ASTM (ISO) standards [1-3], the multiplier factors remain present in haze and luminous transmittance measurements. We evaluated measurement uncertainties by propagating the uncertainties of spectral transmittance to those of luminous transmittance and haze. We conducted experiments using two spectrophotometers with different exit angles, which led to different results. For one of the spectrophotometers, which was closer in exit angle to a hazemeter, we compared the experimental results with those obtained from the hazemeter reported in [4,5]. The difference in haze from the ASTM (ISO) method was 1.3 % (0.2 %) in the haze unit, and total luminous transmittances agreed with each other within their uncertainties. These comparison results were consistent with the theoretical predictions. Additionally, we calculated haze changes with varying exit angles to interpret the observed differences between the two spectrophotometers.

After the redefinition of the kelvin in 2019, several start-of-the-art primary gas thermometry techniques were successfully implemented at low-temperature regions. To further make a direct and reliable international comparison of thermodynamic temperature T, we have developed an ultra-stable cryogenic international temperature comparator (CITC) working from 4 K to 25 K. Based on our design and developed temperature control methods, ultra-high stable temperature was achieved with stabilities (standard deviation) better than 10 μK from 4 K to 25 K. The long-term temperature instability is 6.1 μK@4 K, 6.7 μK@5 K, 7.8 μK@13.8 K and 7.4 μK@24.6 K with a sampling time of 33.6 s. Moreover, multibridge, especially four-bridges, comparison and calibration methods were proposed to realize temperature measurements in a more precise and efficient way. The feasibility was demonstrated by using one AC bridge and three super-thermometers. The performance of CITC and the proposed methods in this work showed their great superiority to be used for temperature comparison and calibration.

In 1993 the Guide to the Expression of Uncertainty in Measurement (GUM) defined measurement uncertainty as a parameter, and therefore a mathematical entity. In the following thirty years this definition has been maintained as a reference, though increasingly proven to be too narrow in its scope. In 2023 the Introduction to the Guide to the Expression of Uncertainty in Measurement (GUM-1) introduced a different definition, which implied three radical changes to the well established and widely adopted conceptual framework of the GUM, as adopted by the International Vocabulary of Metrology (VIM). These involved treating measurement uncertainty as (i) a psychological entity, instead of a mathematical one, (ii) related to the doubt about a theoretical true value, instead of to an operational dispersion of measured values, and (iii) only applicable to single-valued measurands, instead of the more general and more useful case of measurands with non-zero definitional uncertainty. Since the same changes are now proposed for inclusion in the next edition of the VIM, it is appropriate to carefully analyze them. Our conclusion is that there are no sufficient reasons for radically changing the fundamental concept of measurement uncertainty. Instead, the definition should rather be generalized to make it more widely applicable.

The authors wish to report the following corrections to the above-mentioned article, which have come to our attention since its publication. These corrections do not affect the main conclusions of the study.

Kibble balances are complex electromechanical instruments that enable the determination of mass within the SI by linking it to the Planck constant h, the defining constant of the mass unit. The LNE has been developing its own Kibble balance since 2002, with the most recent improvements focusing on the implementation of a contactless linear motor for the dynamic phase and the fine adjustment of the beam’s orientation with respect to the horizontal plane for the static phase. In 2024, two mass calibration campaigns were carried out using the LNE Kibble balance: first with an iridium standard (DB1), and then with a platinum-iridium standard (W1). Both artefacts have a nominal mass of 500 g, and their masses were determined with relative standard uncertainties of 3.1·10⁻⁸ and 3.5·10⁻⁸ respectively (k = 1).

We present a double-beam method using a spectrophotometer to measure total luminous transmittance and haze. We derived analytical formulas to describe the measurements, which showed the dependence of haze on the exit angle and the reflectance of an integrating sphere. The use of double beams effectively cancels out multiplier factors caused by multiple reflections in the integrating sphere. In contrast, when employing single-beam methods recommended in ASTM (ISO) standards [1-3], the multiplier factors remain present in haze and luminous transmittance measurements. We evaluated measurement uncertainties by propagating the uncertainties of spectral transmittance to those of luminous transmittance and haze. We conducted experiments using two spectrophotometers with different exit angles, which led to different results. For one of the spectrophotometers, which was closer in exit angle to a hazemeter, we compared the experimental results with those obtained from the hazemeter reported in [4,5]. The difference in haze from the ASTM (ISO) method was 1.3 % (0.2 %) in the haze unit, and total luminous transmittances agreed with each other within their uncertainties. These comparison results were consistent with the theoretical predictions. Additionally, we calculated haze changes with varying exit angles to interpret the observed differences between the two spectrophotometers.

The current definition of the System of unit second based on the Cs ground state hyperfine transition is expected to be replaced by a new definition based on optical frequency standards in the next decade. Several options are currently under consideration for the new definition, including a definition based on the weighted geometric mean of several transitions. In this paper, we review several properties of this option, and most notably introduce a quantitative method to set the weights of transitions, and a graphical representation of the unit that make the distinction between the definition and the realisation of the unit easier to understand.

After the redefinition of the kelvin in 2019, several start-of-the-art primary gas thermometry techniques were successfully implemented at low-temperature regions. To further make a direct and reliable international comparison of thermodynamic temperature T, we have developed an ultra-stable cryogenic international temperature comparator (CITC) working from 4 K to 25 K. Based on our design and developed temperature control methods, ultra-high stable temperature was achieved with stabilities (standard deviation) better than 10 μK from 4 K to 25 K. The long-term temperature instability is 6.1 μK@4 K, 6.7 μK@5 K, 7.8 μK@13.8 K and 7.4 μK@24.6 K with a sampling time of 33.6 s. Moreover, multibridge, especially four-bridges, comparison and calibration methods were proposed to realize temperature measurements in a more precise and efficient way. The feasibility was demonstrated by using one AC bridge and three super-thermometers. The performance of CITC and the proposed methods in this work showed their great superiority to be used for temperature comparison and calibration.

In 1993 the Guide to the Expression of Uncertainty in Measurement (GUM) defined measurement uncertainty as a parameter, and therefore a mathematical entity. In the following thirty years this definition has been maintained as a reference, though increasingly proven to be too narrow in its scope. In 2023 the Introduction to the Guide to the Expression of Uncertainty in Measurement (GUM-1) introduced a different definition, which implied three radical changes to the well established and widely adopted conceptual framework of the GUM, as adopted by the International Vocabulary of Metrology (VIM). These involved treating measurement uncertainty as (i) a psychological entity, instead of a mathematical one, (ii) related to the doubt about a theoretical true value, instead of to an operational dispersion of measured values, and (iii) only applicable to single-valued measurands, instead of the more general and more useful case of measurands with non-zero definitional uncertainty. Since the same changes are now proposed for inclusion in the next edition of the VIM, it is appropriate to carefully analyze them. Our conclusion is that there are no sufficient reasons for radically changing the fundamental concept of measurement uncertainty. Instead, the definition should rather be generalized to make it more widely applicable.

The authors wish to report the following corrections to the above-mentioned article, which have come to our attention since its publication. These corrections do not affect the main conclusions of the study.

The realisation of the kilogram at PTB is based on the established x-ray crystal density method (XRCD). This method is based on a high-precision characterisation of spheres of isotope-enriched ²⁸Si. The crystal and material parameters are considered constant and do not need to be re-determined when the realisation of the kilogram is updated. Therefore, the re-determination is primarily based on new measurements of the volume and the mass of the surface layers of the ²⁸Si spheres. This paper presents new insights in the XRF analysis method used in the XRCD method by PTB and its effects on the volume and mass of ²⁸Si spheres used as primary mass standards, which provides a basis for participation in the key comparison CCM.M-K8.2024. In the key comparisons CCM.M-K8 from 2019, 2021 and 2024, the definition of the kilogram was realised using the AVO28-S8c and Si28kg01a spheres, as outlined in this document. When applying the new model for the spectral components of the XRF spectrum, realisation results of both spheres show an average mass increase of 13.5 µg.

Machine learning (ML) classification models are increasingly being used in a wide range of applications where it is important that predictions are accompanied by uncertainties, including in climate and earth observation, medical diagnosis and bioaerosol monitoring. The output of an ML classification model is a type of categorical variable known as a nominal property in the International Vocabulary of Metrology (VIM). However, concepts related to uncertainty evaluation for nominal properties are not defined in the VIM, nor is such evaluation addressed by the Guide to the Expression of Uncertainty in Measurement (GUM). In this paper we propose a metrological conceptual uncertainty evaluation framework for nominal properties. This framework is based on probability mass functions and summary statistics thereof, and it is applicable to ML classification. We also illustrate its use in the context of two applications that exemplify the issues and have significant societal impact, namely, climate and earth observation and medical diagnosis. Our framework would enable an extension of the GUM to uncertainty for nominal properties, which would make both applicable to ML classification models.

Background/Purpose: Radiopharmaceutical therapy (RPT) with alpha-emitting radionuclides, such as 225Ac, offers highly localized dose delivery due to its short particle range and high linear energy transfer (LET). However, unlike external beam radiotherapy (EBRT) and brachytherapy, which have traceable absorbed dose standards, RPT currently lacks a standardized absorbed dose measurement framework. This study aims to quantify the absorbed dose to air from a 225Ac source using an extrapolation chamber, supported by Monte Carlo (MC) simulations, to establish a robust methodology for dose validation of computational methods.
Methods: An extrapolation chamber was used to measure the absorbed dose to air from a drop casted 225Ac source, with source activity determined using a Low-Energy Germanium (LEGe) detector. High-resolution 2D imaging characterized the spatial distribution of deposited activity, enabling precise source geometry modeling for MC simulations. Self-attenuation effects were quantified using alpha spectrometry, and automated voltage control improved measurement repeatability of the extrapolation chamber. Absorbed dose calculations were compared between experimental and MC results across multiple air gaps.
Results: Experimental and simulated absorbed dose values were in strong agreement, with experimental measurements consistently 1–2% higher than MC predictions across all air gaps. The ionizing-radiation Quantum Imaging Detector (iQID) system provided activity mapping for source characterization, reducing uncertainties in MC modeling. The integration of automated chamber voltage control enhanced measurement precision, while uncertainty analyses highlighted activity determination and alignment as key contributors to variability.
Conclusions: This study establishes a validated methodology for quantifying 225Ac absorbed dose using extrapolation chamber measurements. The findings support the development of traceable absorbed dose standards for RPT and highlight the need for further refinement in alignment protocols and activity quantification. Future work should explore comparisons with time-integrated activity (TIA)-based absorbed dose calculations to align experimental methodologies with clinical RPT dosimetry practices.

The virial coefficients of cryogenic gases, especially helium-4 and helium-3, are playing an ever more critical role in the establishment of primary reference standards for temperature after the redefinition of the kelvin in the SI. Thus, the reliability of the values and uncertainties of these coefficients, especially those of the second, third, and even fourth density virial coefficients (B, C and D), has become more significant. To check the accuracy of these coefficients for helium-4 from ab initio calculations, the refractive-index gas thermometry (RIGT) method was developed, allowing for the simultaneous determination of thermodynamic temperatures and density virial coefficients. Using this technique, highly accurate experimental values of B, C and D for helium-4, as well as T–T₉₀ values, were obtained for the range 5 K–25 K. Direct comparisons with the ab initio calculation density virial coefficients for helium-4 were conducted, revealing excellent agreement. Furthermore, good agreements of thermodynamic temperatures T between absolute RIGT and our previous single pressure RIGT (Gao et al 2021 Metrologia58 059501) were achieved at temperatures from 5 K to 25 K, with differences within each standard uncertainty. This further strengthens our confidence in the comparisons made in this work. It is foreseeable that the rigorously verified ab initio calculations of the density virial coefficients for helium-4 will continue to be used to improve the measurement accuracy of helium-based primary reference standards for temperature and pressure.

We have built an atom interferometer that can measure g, the local acceleration due to gravity, with a resolution of Δg/g = 2 × 10⁻⁸ after a single 1.3 s measurement cycle, 3 × 10⁻⁹ after 1 min and 1 × 10⁻¹⁰ after two days of integration time. The difference between our value for g and one obtained by a falling corner-cube optical interferometer is (7 ± 7) × 10⁻⁹ g. The atom interferometer uses velocity-selective stimulated Raman transitions and laser-cooled caesium atoms in an atomic fountain. We extend previous methods of analysing the interferometer to include the effects of a gravitational gradient. We also present detailed experimental and theoretical studies of potential systematic errors and noise sources.

This paper outlines the roadmap towards the redefinition of the second, which was recently updated by the CCTF Task Force created by the CCTF in 2020. The main achievements of optical frequency standards (OFS) call for reflection on the redefinition of the second, but open new challenges related to the performance of the OFS, their contribution to time scales and UTC, the possibility of their comparison, and the knowledge of the Earth’s gravitational potential to ensure a robust and accurate capacity to realize a new definition at the level of 10⁻¹⁸ uncertainty. The mandatory criteria to be achieved before redefinition have been defined and their current fulfilment level is estimated showing the fields that still needed improvement. The possibility to base the redefinition on a single or on a set of transitions has also been evaluated. The roadmap indicates the steps to be followed in the next years to be ready for a sound and successful redefinition.

We report on an improved systematic evaluation of the JILA SrI optical lattice clock, achieving a nearly identical uncertainty compared to the previous strontium record set by the JILA SrII optical lattice clock at . This improves upon the previous evaluation of the JILA SrI optical lattice clock in 2013, and we achieve a more than twenty-fold reduction in systematic uncertainty to . A seven-fold improvement in clock stability, reaching for an averaging time in seconds, allows the clock to average to its systematic uncertainty in under 10 min. We improve the systematic uncertainty budget in several important ways. This includes a novel scheme for taming blackbody radiation-induced frequency shifts through active stabilization and characterization of the thermal environment, inclusion of higher-order terms in the lattice light shift, and updated atomic coefficients. Along with careful control of other systematic effects, we achieve low temporal drift of systematic offsets and high uptime of the clock. We additionally present an improved evaluation of the second order Zeeman coefficient that is applicable to all Sr optical lattice clocks. These improvements in performance have enabled several important studies including frequency ratio measurements through the boulder area clock optical network (BACON), a high precision comparison with the JILA 3D lattice clock, a demonstration of a new all-optical time scale combining SrI and a cryogenic silicon cavity, and a high sensitivity search for ultralight scalar dark matter.

Experimental results from four recent research reports on the determination of the density/temperature relationship of Standard Mean Ocean Water (SMOW) under a pressure of 101 325 Pa are analysed and a new formula is recommended for metrological applications. This paper determines the formulae of density and relative density, with their uncertainties, in the temperature range 0 °C to 40 °C. The uncertainty estimation of one of the reports included in the analysis has been re-evaluated. Effects on water density due to isotopic mixtures other than SMOW, ambient pressures different from 101 325 Pa, and the presence of dissolved air, are also reviewed.

Liquid scintillation counting (LSC) techniques can be used for radionuclide standardization when the calculation of detection efficiency is possible. This is done using a model of the physicochemical processes involved in light emission and also of the statistics of photon emission: the free parameter model. This model can then be applied in two ways: by deducing the free parameter from the measurement of a tracer (the CIEMAT/NIST method) or by calculating this free parameter from coincidence ratio in a specific LS counter (the TDCR method). The purpose of this paper is to describe both these models and some practical issues that need to be addressed if LSC is to be effectively used in radionuclide metrology.

For many years, the time community has been using the precise point positioning (PPP) technique which uses GPS phase and code observations to compute time and frequency links. However, progress in atomic clocks implies that the performance of PPP frequency comparisons is a limiting factor in comparing the best frequency standards. We show that a PPP technique where the integer nature of phase ambiguities is preserved consitutes significant improvement of the classical use of floating ambiguities. We demonstrate that this integer-PPP technique allows frequency comparisons with 1  ×  10⁻¹⁶ accuracy in a few days and can be readily operated with existing products.

Measurements of air density determined gravimetrically and by using the CIPM-81/91 formula, an equation of state, have a relative deviation of 6.4 × 10⁻⁵.

This difference is consistent with a new determination of the mole fraction of argon x_Ar carried out in 2002 by the Korea Research Institute of Standards and Science (KRISS) and with recently published results from the LNE. The CIPM equation is based on the molar mass of dry air, which is dependent on the contents of the atmospheric gases, including the concentration of argon. We accept the new argon value as definitive and amend the CIPM-81/91 formula accordingly. The KRISS results also provide a test of certain assumptions concerning the mole fractions of oxygen and carbon dioxide in air. An updated value of the molar gas constant R is available and has been incorporated in the CIPM-2007 equation. In making these changes, we have also calculated the uncertainty of the CIPM-2007 equation itself in conformance with the Guide to the Expression of Uncertainty in Measurement, which was not the case for previous versions of this equation. The 96th CIPM meeting has accepted these changes.

We report the realization of the closed-loop operation of an optical lattice clock based on ⁸⁷Sr atoms. A cavity-stabilized 698 nm laser is used to probe the $^{1}S_{0}\!\rightarrow\!^{3}P_{0}$ clock transition of strontium atoms trapped in optical lattices. Therein, we obtain a Fourier-limited Rabi spectrum with 0.6 Hz linewidth. The two transitions from $m_\mathrm{F}\! = \! \pm 9/2$ ground states are alternatively interrogated to realize the closed-loop operation of the clock, and the clock laser light is frequency-stabilized to the center of the two transitions. Based on the interleaved measurement, the frequency instability of a single optical clock is optimized for the Dick effect, which is demonstrated to be $4.5\!\times\! 10^{-16}/\sqrt{\tau}$, with τ being the averaging time for measurement. Further, we build another similar setup of the strontium lattice clock, which is used for the asynchronous comparison between the two clocks, where the stability is measured as $2.1\!\times\! 10^{-18}$ at 47 000 s. Moreover, we carefully calibrate the systematic effects of the Sr1 optical clock, and the total uncertainty is evaluated as $4.4 \!\times\! 10^{-18}$.

On 16 November 2018 a revision of the International System of Units (the SI) was agreed by the General Conference on Weights and Measures. The definitions of the base units were presented in a new format that highlighted the link between each unit and a defined value of an associated constant. The physical concepts underlying the definitions of the kilogram, the ampere, the kelvin and the mole have been changed. The new definition of the kilogram is of particular importance because it eliminated the last definition referring to an artefact. In this way, the new definitions use the rules of nature to create the rules of measurement and tie measurements at the atomic and quantum scales to those at the macroscopic level. The new definitions do not prescribe particular realization methods and hence will allow the development of new and more accurate measurement techniques.