Metrologia

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.

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.

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.

This article presents an interlaboratory comparison (ILC) on Raman spectroscopy as a technique for relative quantification of the two most common polymorphs of titanium dioxide (TiO₂)—anatase and rutile—in binary mixtures. Some standard methods are currently employed internationally for the determination of TiO₂ content in samples (ISO 591-1, ASTM D3720-90), but require extensive sample preparation, do not distinguish between the two polymorphs or are accurate only for small fractions of either polymorph. Raman spectroscopy is a well-suited characterization technique for measuring and differentiating TiO₂ in a fast, non-invasive way, while requiring no particular reagent or sample preparation. Eleven international participants conducted the study under the framework of Versailles Project on Advanced Materials and Standards. The collected data was analyzed by means of partial least squares regression after spectral preprocessing. The resulting models all show discrepancies of lower than 2% from the nominal values in the quantitative analysis over the concentration range of 5%–95% mixture fractions, with many datasets showing substantial improvement margins on this figure. The results of this ILC provide validation of Raman spectroscopy as a reliable method for quantification of TiO₂ phases.

Nuclear counting is affected by pulse pileup and system dead time, which induce rate-related count loss and alter the statistical properties of the counting process. Fundamental equations are presented to predict deviations from Poisson statistics due to non-random count loss in nuclear counters and spectrometers. Throughput and dispersion of counts are studied for systems with pileup, extending and non-extending dead time, before and also after compensation for count loss. Equations are provided for random fractions of the output events, applicable to spectrometry applications. Methods for loss compensation are discussed, including inversion of the throughput equation, live-time counting and loss-free counting. Secondary effects in live-time counting are addressed: residual interference from pileup in systems with imposed dead times and errors due to varying count rate when measuring short-lived radionuclides.

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.

The redefinition of the SI unit of mass in terms of a fixed value of the Planck constant has been made possible by the Kibble balance, previously known as the watt balance. Once the new definition has been adopted, the Kibble balance technique will permit the realisation of the mass unit over a range from milligrams to kilograms. We describe the theory underlying the Kibble balance and practical techniques required to construct such an instrument to relate a macroscopic physical mass to the Planck constant with an uncertainty, which is achievable at present, in the region of 2 parts in 10⁸. A number of Kibble balances have either been built or are under construction and we compare the principal features of these balances.

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.

We revisit the Kibble–Robinson theory, first proposed in 2014 by Kibble and Robinson. This theory significantly simplifies the construction and operation of Kibble balances. We conducted a theoretical investigation of the theory's assumptions, using a corner cube as the optical target in the interferometer for velocity measurement. We find that it is advantageous to build a mechanism whose output has minimal rotation and horizontal motion. For balances with relative uncertainty targets below $1\times10^{-6}$, the mass pan and the optical target should be suspended from a common gimbal so they have the same vertical velocity and no rotation. In this case, the measurement bias due to Abbe offset is minimized, and the bias due to corner loading is repeatable.

This report presents the results of the EURAMET key comparison EURAMET.M.P-K4.2020 (EURAMET Project No. 1494), performed in the range of 1 Pa to 15 kPa of absolute and gauge pressure. Five National Metrology Institutes (NMIs), Physikalisch-Technische Bundesanstalt (PTB), Český Metrologický Institut (CMI), Institut za Kovinske Materiale in Tehnologije (IMT), Ulusal Metroloji Enstitüsü (UME), and RISE Research Institutes of Sweden AB (RISE), participated in the comparison. The comparison was realised as a direct comparison of the PTB, IMT, UME, and RISE standards with the CMI standard, transported to CMI and operated in the CMI premises. The measurements were performed in the period from September 2019 to April 2022. All participants' results obtained for absolute and gauge pressure are equivalent with the reference value of the present comparison and with each other. Being linked to the respective CCM key comparison, CCM.P-K4.2012, some results at some pressures show bigger deviations than their uncertainties, which presumably deals with the uncertainty of the link.

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).

A Regional Metrology Organization (RMO) Key Comparison of dew/frost point temperatures was carried out by the The Federal State Unitary Enterprise "All-Russian Scientific Research Institute of Physical, Technical and Radio Engineering Measurements" (VNIIFTRI, Russia) and the RSE "Kazakhstan Institute of Standardization and Metrology" (KazStandard, Kazakhstan) between September, 2024 and February, 2025. The results of this comparison are reported here, along with descriptions of the humidity laboratory standards for VNIIFTRI and KazStandard and the uncertainty budget for these standards. This report also describes the protocol for the comparison and presents the data acquired. The results are analyzed, determining degree of equivalence between the dew/frost-point standards of VNIIFTRI and KazStandard.

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

Platinum based thermocouples are widely used to provide traceability to accredited laboratories for high temperature contact thermometry (up to 1560 °C). Different NMI's have adopted a very diverse range of methods to calibrate these thermocouples, such as gold and palladium (Au and Pd) 'melt wire' techniques (in both air and argon), mini fixed point of copper, cobalt-carbon eutectic and palladium-carbon eutectic points, and comparison with reference thermocouples or radiation thermometers.

Although a successful comparison, APMP.T-S1-04, up to 1100 °C was performed in 2005-2006, no equivalent comparison has so far been made over the higher temperature range to 1560 °C. The study here fills this gap: 9 NMI's from the APMP region participated in an inverted-star comparison using their normal calibration procedures. The impact of reversible hysteresis was minimised by specifying the thermocouple annealing state, and the impact of irreversible heat treatment minimised using the inhomogeneity analysis methods developed in APMP.T-S1-04, based on detailed knowledge of the participants' furnace temperature profiles.

Despite the wide variation in calibration techniques used by the participants, comparison reference values with uncertainties comparable to that of ITS-90 itself could be achieved: ± 0.06 °C ( k = 2) at Cu point (1084.62 °C), ± 0.19 °C (k = 2) at Co-C point (1324 °C), and ± 0.15 °C (k = 2) at Pd point (1554.8 °C). This resulted in calculated of degrees-of-equivalence comparable to participants claimed uncertainties. The results also showed En ratios <1 at all comparison temperatures for all participants, supporting the equivalence between the wide range of calibration references and methods adopted.

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

The introduction over the last decade of radionuclide therapy based on ²²³Ra and ²²⁷Th has reawakened interest in the radionuclides of the ²³⁵U decay series (the 4n+3 decay chain). This has coincided with a requirement for improved accuracy in dating of long-lived radionuclides for nuclear forensic and for geological purposes. Thus, ²³¹Pa has become the subject of revived interest in recent years.

The short-term ingrowth of the decay progeny is of interest to nuclear forensic science since it enables the direct calculation of the separation age of enriched ²³⁵U^[1]; separation times based on the ²³⁴U-²³⁰Th chain may also be calculated, but are more complex due to the reliance on the ²³⁸U-²³⁴Th-^234mPa-²³⁴U-²³⁰Th decay family. Furthermore, since protactinium fluorides are non-volatile at ordinary temperature, the build-up of ²³¹Pa in fuel enrichment facilities may provide information on throughput of separation units as well as the whole plant.

In the longer term, the characterisation of sedimentation rates is facilitated by a range of natural nuclear chronometers that include ²³¹Pa/²³⁵U to provide information concerning sediment formation, and the measurement of ²³¹Pa:²³⁰Th mass ratios (as well as ²³¹Pa:²³⁵U and ²³⁰Th:²³⁴U mass ratios) may also provide information of global temperature trends over the 100-200 ka range^[2].

This report summarises the results of an international comparison of the activity per unit mass of the same ²³¹Pa solution along with a new half-life determination^[3].

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

The supplementary comparison EURAMET.M.FF-S20 was organized for the purpose of determination of the degree of equivalence of the testing facilities for low-pressure gas flow measurement over the range (50 to 1000) m³/h. A rotary displacement gas meter IRM-3-DUO G650 was used as a transfer standard. The measurements were provided at prescribed reference conditions. Participants were nine laboratories from EURAMET: PTB, Germany; CMI, Czech Republic; FORCE TECHNOLOGY, Denmark; VSL, Netherlands; BEV, Austria; GUM, Poland; LEI, Lithuania; RISE, Sweden; METAS, Switzerland. All participants reported their traceability chains to the SI. Relevant results were used in the determination of the key comparison reference value (KCRV) and the uncertainty of the KCRV. The reference value was determined at each flow separately following procedure A presented by M G Cox. The degrees of equivalence with the KCRV were calculated. All reported results were consistent with the KCRV.

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).

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 medical use of radionuclides depends on the accurate measurement of activity (Bq) for regulatory compliance, patient safety, and effective treatment or image quality. In turn, these measurements rely on the realization of primary standards of activity by national metrology institutes, with uncertainties that are fit for purpose. This article reviews the current status of primary standards of activity for radionuclides used in medical imaging and therapy applications. Results from international key comparisons carried out through the International Bureau of Weights and Measures transfer instruments (SIR and SIRTI) are used to verify that standards for a variety of radionuclides are consistent and conform with practitioners' expectations.

The definition of the kilogram is presently based on the Planck constant h. It is therefore possible to establish a mass standard by realizing the kilogram using any method that relates h to mass. On the basis of this principle, we realized the kilogram by the x-ray crystal density (XRCD) method using a silicon sphere with a nominal mass of 1 kg. For the realization, the silicon core volume of the sphere excluding the surface layer was measured using a laser interferometer to determine the number of silicon atoms in the core. The mass of the silicon core m_core was determined from the number of silicon atoms and the mass of a single silicon atom calculated from h. To evaluate the mass of the surface layer m_SL, the surface of the sphere was characterized by x-ray photoelectron spectroscopy and ellipsometry. The sphere mass m_sphere was determined from m_core and m_SL, and the standard uncertainty of the kilogram realization was estimated to be 23 μg. To statistically evaluate the long-term reproducibility of this realization, the realization result was compared with previous realization results in 2016 and 2019. The standard deviation of m_sphere in the three realizations over five years was estimated to be as small as 2.4 μg, corresponding to 2.4 × 10⁻⁹ in relative terms for 1 kg. This is only 10 % of the standard uncertainty of the kilogram realization. The standard deviations of m_core and m_SL over five years were also estimated to be 3.9 μg and 1.9 μg, respectively. On the basis of these statistical evaluations, the strategy for the kilogram realization by the XRCD method to establish the primary mass standard in the future is discussed.

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 σ_y(τ)=1.5×10^-13/√τ, 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 σ_B=2.2×10^-16.

The Planck-Balance (PB) is a compact Kibble balance, designed for the realization of the unit of mass at values much smaller than 1 kg across multiple orders of magnitude. Recent advancements enable the PB at PTB to measure mass with uncertainties equivalent to calibration accuracy classes E1 (up to 5 g), E2 (up to 50 g), and F1 (up to 100 g), while operating in air. Type B uncertainties limit the relative combined standard uncertainty for a mass of 100 g to the minimum achievable value of $4.5\cdot10^{-7}$. A measurement campaign was conducted using six mass standards (1 mg, 10 mg, 100 mg, 1 g, 10 g, and 100 g), yielding results consistent with the values specified in their E1 calibration certificates. The presented results demonstrate the feasibility of metrologically traceable small mass measurements without reliance on mass standards. Unique design features of the PB will be discussed, including a rigidly mounted coil that minimizes geometrical alignment requirements, and an oscillatory velocity mode that achieves a high signal-to-noise ratio, even with a movement range of less than 0.2 mm. This approach could offer an alternative to calibration and dissemination using mass comparators.

The German national metrology institute Physikalisch-Technische Bundesanstalt is developing a new primary standard for the realization of the quantity air kerma free-in-air in the x-ray energy range up to 50 keV. National metrology institutes use free-air ionization chambers (FACs) for this purpose. FACs with various geometrical dimensions are used for low-energy x-rays. This study aims to (1) determine the optimum air path length of a FAC, which is the most critical geometric parameter for the low-energy x-ray range, and (2) to evaluate the limitations of averaging monoenergetic correction factors, a method that many institutes use to enable time-saving calculation of spectral correction factors for a larger number of radiation qualities. Monte Carlo simulations were performed to compute monoenergetic and spectral correction factors for air attenuation, photon scattering, inadequate charged particle equilibrium, and diaphragm effects. In addition, spectral correction factors were calculated by averaging the monoenergetic correction factors with different x-ray spectra. The results show that for low-energy FACs the predominant correction is the correction for air attenuation. Thus, it is preferable to have a minimized air path length. The minimization of the air path length is limited by the impact of electrons created by diaphragm interactions and the loss of charged particle equilibrium. If the air attenuation between the aperture and the collecting volume is considered for a 10 kV x-ray spectrum, the averaged and simulated spectral correction factors agree within less than 0.1%.

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 σ_y(τ)=1.5×10^-13/√τ, 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 σ_B=2.2×10^-16.

We revisit the Kibble–Robinson theory, first proposed in 2014 by Kibble and Robinson. This theory significantly simplifies the construction and operation of Kibble balances. We conducted a theoretical investigation of the theory's assumptions, using a corner cube as the optical target in the interferometer for velocity measurement. We find that it is advantageous to build a mechanism whose output has minimal rotation and horizontal motion. For balances with relative uncertainty targets below $1\times10^{-6}$, the mass pan and the optical target should be suspended from a common gimbal so they have the same vertical velocity and no rotation. In this case, the measurement bias due to Abbe offset is minimized, and the bias due to corner loading is repeatable.

We recently overhauled the calibration service for the frequency dependence of four-terminal pair (4TP) air capacitors provided by the National Institute of Standards and Technology to its customers. In the past, the calibration was performed with a dual-channel vector network analyzer, requiring nine different connections to the standard with a rigid 7 mm microwave line. The new method streamlines the measurement, as each standard can be measured by simply connecting four coaxial lines between it and a four-channel network analyzer. Here, we discuss the uncertainty budget of this new procedure. Due to the 4TP definition, the measurements are much less dependent on the connectors and the uncertainty in individual scattering parameters than other S parameter measurements.

Quantitative MRI uses conventional clinical MRI hardware to make measurements of physical quantities. It also offers the opportunity to benchmark scanners in specific applications by characterising their measurement performance. This allows independent assessment of different scanners, products and services. Quantitation requires evaluation of the uncertainty and bias in the measurement process and as such requires a metrological framework. This process can be supported by the use of a reference object (phantom) that contains clinically relevant MRI quantities that are traceable to primary standards. Currently, there are very few traceable MRI standards available, and none cover all the forms of quantitative MRI that are being deployed clinically. The objective of this paper is to provide a metrological framework to build on and support the standardisation of qMRI through the provision of improved reference standards that are compatible with quantitative approaches. Here, we describe the design, construction, characterisation and measurement uncertainty of a traceable and metrologically quantified phantom. The phantom design is modular and comprises 30 distinct vials containing well-characterised, traceable solutions with reported uncertainty for the following MRI measurands: T₁, T₂, iron content and fat fraction.

We demonstrate a simple interferometric method for calibrating the length of an uncoated Fabry-Pérot etalon, using a rotary analog of phase-stepping interferometry. The interferometric method is designed to realize nearly the same measurand as a subsequent measurement in a tactile instrument. The estimated expanded uncertainty of 4 nm for the optical calibration, together with the well-matched measurands, make the etalon a promising transfer standard for the calibration of bidirectional corrections in tactile probing systems.

This paper addresses the problem of uncertainty estimation for measurements made with computationally expensive numerical models, which are increasingly applied today. Typically, the Monte Carlo method (MCM) is used for uncertainty propagation in these cases. However, due to its stochastic nature, the MCM is inefficient, requiring a large number of model evaluations and thus resulting in long computation times. In this paper, an efficient alternative to the MCM is introduced. By using systematic samples of the influence quantities which are individually propagated through the measurement model, the overall number of required model evaluations can by drastically reduced. Additionally, the new method offers the possibility to simplify the measurement model for further reduced computational effort. The distributions of the propagated samples are reconstructed using a method specifically designed for systematic samples and combined to the uncertainty distribution of the measurand using convolution. The new method does not only offer increased computational efficiency but also a high information yield, as it estimates the uncertainty distribution of the measurand and the uncertainty contribution of individual influence quantities.

We describe a hydrostatic comparator optimized for the determination of the density (or equivalently volume) of the sinkers used in magnetic suspension densimeters. The hydrostatic comparator is a modification of the traditional hydrostatic weighing technique for the determination of the density of solid objects: by weighing a density standard as well as the unknown object (with both immersed in a fluid) the density information of the standard is transferred to the unknown, and the density of the hydrostatic bath fluid need not be known. Our instrument makes use of two density standards of single-crystal silicon and a high-density, fluorinated-ether bath fluid; it can weigh objects as large as 100 g four-at-a-time (one or more standards and up to three unknowns). We discuss weighing designs and demonstrate a new method that employs an additional standard to eliminate the need for the usual empty-pan weighings. Uncertainties are reduced by the use of compensation and sensitivity masses. As a demonstration of the instrument's capabilities, results are presented for a set of 12 objects with masses from 33 g to 99 g and densities from 2.33 g⋅cm^–3–16.7 g⋅cm^–3. The expanded (k = 2) uncertainty in volume averaged 0.000 041 cm^–3, with relative uncertainties ranging from 1.1 × 10^–6 for a 99 g/42.3 cm³ silicon object to 7.5 × 10^–6 for a 60 g/7.5 cm³ gold-plated stainless steel object.