Metrologia

In this paper we outline the impact of mixing slotted N-type and slotless N-type connectors during a vector network analyzer calibration. We want to point out that making precise measurements of typical transfer standards, while using both N-type jack connectors is very difficult, because of the reference plane shift. We performed simulations of the two connector jack geometries to estimate the impact on measurements of devices under test with either plug or jack interface. The influence of mixing slotted and slotless connectors is then validated through simple measurements, which can be easily repeated in many labs. The results show that mixing of slotted and slotless jacks adds errors in the same order of magnitude sometimes reported as measurement uncertainties by national metrology institutes.

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.

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.

On July 2, 2025, the Joint Committee for Guides in Metrology (JCGM) organized a widely attended webinar to present and discuss a new definition of measurement uncertainty to be considered as a potential replacement for the current definition in the International Vocabulary of Metrology. The original version of the new definition first appeared in Possolo (2015 Simple Guide for Evaluating and Expressing the Uncertainty of NIST Measurement Results (National Institute of Standards and Technology)) and was adopted by the National Institute of Standards and Technology (NIST) of the United States: ‘Measurement uncertainty is the doubt about the true value of the measurand that remains after making a measurement. Measurement uncertainty is described fully and quantitatively by a probability distribution on the set of the measurand.’ This definition was inspired by an earlier, similar characterization of measurement uncertainty that Stephanie Bell (National Physical Laboratory, United Kingdom) published in 1999 (Bell 1999 A Beginner’s Guide to Uncertainty of Measurement (Measurement Good Practice Guide) vol 11 (National Physical Laboratory)). The present short communication first compares definitions of measurement uncertainty and reviews the ‘error’ and ‘uncertainty’ approaches featured in the introduction to the third edition of the International Vocabulary of Metrology. Next, it explains the principal motivation for the redefinition, which was a critical review of the current definition by Thompson (2011 Accr. Qual. Assur. 17 93–94). The third section discusses the relation between doubt, incomplete knowledge, and uncertainty, and the concern that words like ‘doubt’ and ‘uncertainty’ can cast a negative light upon the science and technology that produce measurement results, in particular in laboratory medicine. A closing Coda highlights the principal benefits of the proposed redefinition.

The performance of a caesium fountain frequency reference for use in precision measurements of trapped antihydrogen in the ALPHA experiment at CERN is evaluated. A description of the fountain is provided together with a characterisation of systematic effects. The impact of the magnetic environment in the Antimatter Factory, where the fountain is installed, on the performance of the fountain is considered and shown to be insignificant. The systematic fractional frequency uncertainty of the fountain is $3.0 \times 10^{-16}$. The short-term frequency stability of the measured frequency from the ALPHA-HM1 maser is $1.5 \times 10^{-13}\tau^{-1/2}$, whereas the fountain itself shows a stability limit of $4.7 \times 10^{-14}\tau^{-1/2}$. We find a fractional frequency difference of (1.0 ± 2.2 (stat.) ± 6.5 (syst.)) $\times 10^{-16}$ in a comparison with Terrestrial Time via a GNSS Common View satellite link between January 2023 and June 2024. The fountain enables a significant increase in frequency precision in antihydrogen spectroscopic measurements, and paves the way for improved limits on matter–antimatter comparisons.

Sufficient progress towards redefining the International System of Units (SI) in terms of exact values of fundamental constants has been achieved. Exact values of the Planck constant h, elementary charge e, Boltzmann constant k, and Avogadro constant N_A from the CODATA 2017 Special Adjustment of the Fundamental Constants are presented here. These values are recommended to the 26th General Conference on Weights and Measures to form the foundation of the revised SI.

We demonstrate a method for radionuclide assay that is spectroscopic with 100% counting efficiency for alpha decay. Advancing both cryogenic decay energy spectrometry (DES) and drop-on-demand inkjet metrology, a solution of Am-241 was assayed for massic activity (of order 100 kBq g⁻¹) with a relative combined standard uncertainty less than 1%. We implement live-timed counting, spectroscopic analysis, validation by liquid scintillation counting, and confirmation of quantitative solution transfer. Experimental DES spectra are well modeled with a Monte Carlo simulation. The model was further used to simulate Pu-238 and Pu-240 impurities, calculate detection limits, and demonstrate the potential for tracer-free multi-nuclide analysis, which will be valuable for new cancer therapeutics based on decay chains, standard reference materials containing impurities, and more widely in nuclear energy, environmental monitoring, security, and forensics.

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 $\sigma_\mathrm{B} = 2.2\times10^{-16}$.

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.

In order to show equivalence in the calibration of 50 kg stainless steel mass standards, this key comparison was organized among eight National Metrology Institutes (NMI) of the Sistema Interamericano de Metrología (SIM).

The aims of this key comparison were to compare the results obtained by NMIs in calibration of 50 kg stainless steel weights and to link the participant results to the key comparison identified as CCM.M-K6, organized by Consultative Committee for Mass and Related Quantities (CCM).

For this key comparison CENAM – Mexico acted as pilot laboratory. CENAM – Mexico and NRC – Canada act as linking laboratories between this comparison and the CCM.M-K6.

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 CCM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Virial coefficients for noble gases calculated from first principles play a key role in gas-based temperature and pressure metrology. They have typically been presented in tabular form, but as smaller uncertainties are achieved the uncertainty introduced by interpolation between tabulated points can become significant. We demonstrate these interpolation errors for the second density and acoustic virial coefficients of ⁴He and for the second density virial coefficients of Ne and Ar. We then offer an alternative approach, using simple scripts along with a data structure containing precalculated phase shifts to generate these coefficients at any temperature of metrological interest. The approach is applied to the state-of-the-art pair potentials for ³He, ⁴He, Ne, and Ar, and the software and data tables are made available for general use.

The absolute responsivity of an optical detector in a trap configuration has been investigated in the interest of high-accuracy fiber-coupled measurements for commercial optical fiber power meters and fiber-coupled single-photon detector calibrations. The highest accuracy measurements of optical power are typically undertaken free space and then disseminated for fiber-coupled measurements with some additional uncertainty. At the lowest uncertainty, the difference between free-space and fiber-coupled optical power measurements can be significant. We present here a complete evaluation of multiple trap detectors consisting of two InGaAs photodiodes and a concave mirror. This evaluation includes fiber-based responsivity at discrete laser wavelengths measured both with cryogenic and room temperature standards (diverging input beam), free-space absolute spectral responsivity over a broad wavelength range (converging beam), free-space responsivity at discrete laser wavelengths (collimated), linearity, and spatial uniformity.

On July 2, 2025, the Joint Committee for Guides in Metrology (JCGM) organized a widely attended webinar to present and discuss a new definition of measurement uncertainty to be considered as a potential replacement for the current definition in the International Vocabulary of Metrology. The original version of the new definition first appeared in Possolo (2015 Simple Guide for Evaluating and Expressing the Uncertainty of NIST Measurement Results (National Institute of Standards and Technology)) and was adopted by the National Institute of Standards and Technology (NIST) of the United States: ‘Measurement uncertainty is the doubt about the true value of the measurand that remains after making a measurement. Measurement uncertainty is described fully and quantitatively by a probability distribution on the set of the measurand.’ This definition was inspired by an earlier, similar characterization of measurement uncertainty that Stephanie Bell (National Physical Laboratory, United Kingdom) published in 1999 (Bell 1999 A Beginner’s Guide to Uncertainty of Measurement (Measurement Good Practice Guide) vol 11 (National Physical Laboratory)). The present short communication first compares definitions of measurement uncertainty and reviews the ‘error’ and ‘uncertainty’ approaches featured in the introduction to the third edition of the International Vocabulary of Metrology. Next, it explains the principal motivation for the redefinition, which was a critical review of the current definition by Thompson (2011 Accr. Qual. Assur.17 93–94). The third section discusses the relation between doubt, incomplete knowledge, and uncertainty, and the concern that words like ‘doubt’ and ‘uncertainty’ can cast a negative light upon the science and technology that produce measurement results, in particular in laboratory medicine. A closing Coda highlights the principal benefits of the proposed redefinition.

In the solar reflective band, the on-board calibration method based on a solar diffuser (SD) is the mainstream calibration method. However, the calibration accuracy is limited by the measurement accuracy of the SD bidirectional reflectance distribution function (BRDF) in the laboratory. The limitations of the light sources and detectors hinder accurate BRDF measurements in the short-wave infrared band, particularly beyond 1700 nm. In this study, the angle integration-band crossing transfer (AIBCT) method is proposed for SD BRDF measurement to avoid the influence of the Fourier spectrometer’s signal processing and detector non-linearity in the absolute measurement. The method utilized the relationship between the BRDF and directional-hemispherical reflectance, and calculated the spectral distribution of the SD BRDF at the standard in-plane geometry with an 0° incidence zenith angle and a 45° reflection zenith angle (0:45) by integration. The absolute measurement result of the 0:45 SD BRDF at 1150 nm was used as the standard for transfer to the short-wave infrared band. The SD BRDF at 0:45 was generalized to other geometries through relative measurements based on the reciprocity theorem. The mean relative error of the results of the AIBCT and absolute measurement methods was less than 0.3% in the range of 1100 nm to 1600 nm. Analysis of the results showed that the AIBCT method’s measurement uncertainty (coverage factor k = 2) of the 0:45 SD BRDF is better than 0.84% at 1100 nm to 2300 nm and 1.05% at 2300 nm to 2500 nm. Furthermore, the AIBCT method was found suitable for the ultraviolet band.

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.

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, 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 to 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 (Metrologia 58 (2021) 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 density virial coefficients for helium-4 will continue to be used to improve the measurement accuracy of primary reference standards for temperature and pressure, based on helium-4.

Virial coefficients for noble gases calculated from first principles play a key role in gas-based temperature and pressure metrology. They have typically been presented in tabular form, but as smaller uncertainties are achieved the uncertainty introduced by interpolation between tabulated points can become significant. We demonstrate these interpolation errors for the second density and acoustic virial coefficients of ⁴He and for the second density virial coefficients of Ne and Ar. We then offer an alternative approach, using simple scripts along with a data structure containing precalculated phase shifts to generate these coefficients at any temperature of metrological interest. The approach is applied to the state-of-the-art pair potentials for ³He, ⁴He, Ne, and Ar, and the software and data tables are made available for general use.

The absolute responsivity of an optical detector in a trap configuration has been investigated in the interest of high-accuracy fiber-coupled measurements for commercial optical fiber power meters and fiber-coupled single-photon detector calibrations. The highest accuracy measurements of optical power are typically undertaken free space and then disseminated for fiber-coupled measurements with some additional uncertainty. At the lowest uncertainty, the difference between free-space and fiber-coupled optical power measurements can be significant. We present here a complete evaluation of multiple trap detectors consisting of two InGaAs photodiodes and a concave mirror. This evaluation includes fiber-based responsivity at discrete laser wavelengths measured both with cryogenic and room temperature standards (diverging input beam), free-space absolute spectral responsivity over a broad wavelength range (converging beam), free-space responsivity at discrete laser wavelengths (collimated), linearity, and spatial uniformity.

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, 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 to 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 (Metrologia 58 (2021) 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 density virial coefficients for helium-4 will continue to be used to improve the measurement accuracy of primary reference standards for temperature and pressure, based on helium-4.

On July 2, 2025, the Joint Committee for Guides in Metrology (JCGM) organized a widely attended webinar to present and discuss a new definition of measurement uncertainty to be considered as a potential replacement for the current definition in the International Vocabulary of Metrology. The original version of the new definition first appeared in Possolo (2015 Simple Guide for Evaluating and Expressing the Uncertainty of NIST Measurement Results (National Institute of Standards and Technology)) and was adopted by the National Institute of Standards and Technology (NIST) of the United States: ‘Measurement uncertainty is the doubt about the true value of the measurand that remains after making a measurement. Measurement uncertainty is described fully and quantitatively by a probability distribution on the set of the measurand.’ This definition was inspired by an earlier, similar characterization of measurement uncertainty that Stephanie Bell (National Physical Laboratory, United Kingdom) published in 1999 (Bell 1999 A Beginner’s Guide to Uncertainty of Measurement (Measurement Good Practice Guide) vol 11 (National Physical Laboratory)). The present short communication first compares definitions of measurement uncertainty and reviews the ‘error’ and ‘uncertainty’ approaches featured in the introduction to the third edition of the International Vocabulary of Metrology. Next, it explains the principal motivation for the redefinition, which was a critical review of the current definition by Thompson (2011 Accr. Qual. Assur.17 93–94). The third section discusses the relation between doubt, incomplete knowledge, and uncertainty, and the concern that words like ‘doubt’ and ‘uncertainty’ can cast a negative light upon the science and technology that produce measurement results, in particular in laboratory medicine. A closing Coda highlights the principal benefits of the proposed redefinition.

In the solar reflective band, the on-board calibration method based on a solar diffuser (SD) is the mainstream calibration method. However, the calibration accuracy is limited by the measurement accuracy of the SD bidirectional reflectance distribution function (BRDF) in the laboratory. The limitations of the light sources and detectors hinder accurate BRDF measurements in the short-wave infrared band, particularly beyond 1700 nm. In this study, the angle integration-band crossing transfer (AIBCT) method is proposed for SD BRDF measurement to avoid the influence of the Fourier spectrometer’s signal processing and detector non-linearity in the absolute measurement. The method utilized the relationship between the BRDF and directional-hemispherical reflectance, and calculated the spectral distribution of the SD BRDF at the standard in-plane geometry with an 0° incidence zenith angle and a 45° reflection zenith angle (0:45) by integration. The absolute measurement result of the 0:45 SD BRDF at 1150 nm was used as the standard for transfer to the short-wave infrared band. The SD BRDF at 0:45 was generalized to other geometries through relative measurements based on the reciprocity theorem. The mean relative error of the results of the AIBCT and absolute measurement methods was less than 0.3% in the range of 1100 nm to 1600 nm. Analysis of the results showed that the AIBCT method’s measurement uncertainty (coverage factor k = 2) of the 0:45 SD BRDF is better than 0.84% at 1100 nm to 2300 nm and 1.05% at 2300 nm to 2500 nm. Furthermore, the AIBCT method was found suitable for the ultraviolet band.

The performance of a caesium fountain frequency reference for use in precision measurements of trapped antihydrogen in the ALPHA experiment at CERN is evaluated. A description of the fountain is provided together with a characterisation of systematic effects. The impact of the magnetic environment in the Antimatter Factory, where the fountain is installed, on the performance of the fountain is considered and shown to be insignificant. The systematic fractional frequency uncertainty of the fountain is $3.0 \times 10^{-16}$. The short-term frequency stability of the measured frequency from the ALPHA-HM1 maser is $1.5 \times 10^{-13}\tau^{-1/2}$, whereas the fountain itself shows a stability limit of $4.7 \times 10^{-14}\tau^{-1/2}$. We find a fractional frequency difference of (1.0 ± 2.2 (stat.) ± 6.5 (syst.)) $\times 10^{-16}$ in a comparison with Terrestrial Time via a GNSS Common View satellite link between January 2023 and June 2024. The fountain enables a significant increase in frequency precision in antihydrogen spectroscopic measurements, and paves the way for improved limits on matter–antimatter comparisons.

At the Physikalisch-Technische Bundesanstalt (PTB), a rotating glass disk serves as the primary velocity standard for calibrating laser Doppler anemometers (LDAs). The interference field within the LDA measurement volume is characterized by single scattering particles adhering to the glass disk’s circumferential surface. As the result of calibration the mean fringe spacing $d_\textrm{mean}$ of the LDA interference field finally represents the velocity-independent LDA calibration factor of PTB’s standard calibration procedure, which is therefore limited to LDA systems providing access to the photodetector signal. PTB’s standard procedure for calibrating LDAs has been verified as part of a CIPM key comparison (CIPM: Comité International des Poids et Mesures) with a degree of equivalence of $E_\textrm{n} = 0.38$ amongst the participants. In this paper, a detailed uncertainty analysis of the LDA calibration facility is presented including a method to investigate the radius deviation of the glass disk in dynamic operation. The relative expanded uncertainty of the facility is $7.2 \times 10^{-4}$ (with a coverage factor of k = 2), whereby the main contribution to the measurement uncertainty results from the dynamic radius deviation, i.e. the eccentricity of the rotating glass disk. This contribution can be significantly reduced by an angular-dependent eccentricity correction of the rotating glass disk leading to a decrease of the overall measurement uncertainty by a factor of about 5. Additionally, an alternative approach is introduced to circumvent the eccentricity of the glass disk using its lateral surface for calibration, including an uncertainty analysis of this so-called difference procedure and results of first example measurements.

We demonstrate a method for radionuclide assay that is spectroscopic with 100% counting efficiency for alpha decay. Advancing both cryogenic decay energy spectrometry (DES) and drop-on-demand inkjet metrology, a solution of Am-241 was assayed for massic activity (of order 100 kBq g⁻¹) with a relative combined standard uncertainty less than 1%. We implement live-timed counting, spectroscopic analysis, validation by liquid scintillation counting, and confirmation of quantitative solution transfer. Experimental DES spectra are well modeled with a Monte Carlo simulation. The model was further used to simulate Pu-238 and Pu-240 impurities, calculate detection limits, and demonstrate the potential for tracer-free multi-nuclide analysis, which will be valuable for new cancer therapeutics based on decay chains, standard reference materials containing impurities, and more widely in nuclear energy, environmental monitoring, security, and forensics.

This paper presents a comparison between the provisional low-temperature scale of 2000 (PLTS-2000) and the magnetic field fluctuation thermometer (MFFT) scales, as realized at LNE-Cnam. The comparison was carried out using three different realizations (i.e. different melting pressure sensors) of PLTS-2000 and a magnetic field fluctuation thermometer operated with a long measurement time (about 3 h) and a more precise power spectral density model of the MFFT response that included an offset term to account for the background noise in the MFFT electronics. The comparison over the range between 8 mK and 1 K shows that the PLTS- 2000 and MFFT scales agree within about 0.2 mK. The results confirm the thermodynamic accuracy of PLTS-2000 at the same level of uncertainty, and show that, under suitable conditions, MFFT measurements can achieve comparable performance. This highlights its potential use in certain practical applications where direct realization of PLTS-2000 is not feasible.

A two-wavelength absolute distance meter operating at 780 nm and 1560 nm has been developed. It measures two optical path lengths simultaneously, the difference of which enables an in-line refractivity compensation. The result is a dispersion-based air-index-compensated distance independent of temperature and pressure along the optical paths. In previous works, the instrumental errors were evaluated and an uncertainty on the measured optical path lengths was assessed. However, the dispersion-based air-index-compensated distance is not traceable to the SI metre, as its calculation requires parameters derived from the air refractive index formula, the dispersion K(λ) and humidity g(λ) terms, which are not always associated with uncertainties nor defined for infrared wavelengths. The current article reviews how the refractive index has been defined by various authors, such as Edlén, Ciddor, or Voronin and Zheltikov. We first show that whatever formula is used, it can be applied to two-wavelength telemetry for refractivity compensation. The equivalences between the formulae, as well as their differences, are highlighted. Secondly, we compare the formulae using experimental measurements at 780 nm and 1560 nm for distances up to 6.5 km. For these wavelengths, the Voronin and Zheltikov equation is the one that compensates best changes in air refractive index when a fixed distance is measured over several days, with standard deviations better than 280 µm over 2.6 km or 5.4 km. When other formulae are used for the same measurements, the standard deviations exceed 500 µm. Furthermore, when distances obtained by our two-wavelength ADM are compared with those of a GNSS-based distance meter, the measurements of the two systems are compatible within their uncertainties only if the Voronin and Zheltikov equation is used. Otherwise, there is a scale error higher than 2 ppm. This article shows that these errors arise mainly from the humidity term g(λ) in the infrared.