Metrologia

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.

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.

Alpha-particle spectrometry is routinely performed with the aim of measuring absolute activities, activity ratios between different alpha-emitting nuclides or decay data such as branching factors, alpha emission probabilities and relative half-lives. It is most commonly performed with ion-implanted silicon detectors. Strong features of the technique are the low background levels that can be achieved due to low sensitivity to other types of radiation, the intrinsic efficiency close to 1 which reduces the efficiency calculations to a geometrical problem and the uniqueness of the energy spectra for each α-decaying nuclide. The main challenge is the limitation to the attainable energy resolution, even with thin and homogenous sources, which causes alpha energy peaks to be partially unresolved due to their width and low-energy tailing. The spectral deconvolution often requires fitting of analytical functions to each peak in the alpha spectrum. True coincidence effects between alpha particles and subsequently emitted conversion electrons cause distortions of the alpha spectra which lead to significant changes in the apparent peak area ratios. Optimum energy resolution can only be achieved on very thin sources, which puts constraints on the source preparation techniques. Radiochemical separations may be needed to extract the alpha emitters from voluminous matrices and efficiency tracing is performed by adding in another isotope by known amounts. Typical uncertainty components are discussed by means of some hypothetical examples.

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.

A primary force standard is implemented to realize the watt through Planck's constant by means of radiation pressure at the kilowatt level. The high amplification laser-pressure optic, or HALO, is a multiple reflection radiation pressure apparatus used for absolute radiometry of high-power lasers. In this work, a primary standard electrostatic force balance is used to measure the reflection-enhanced optical forces. With this configuration, the HALO is used to measure laser powers in the range of 100 W–5000 W from a 1070 nm fiber laser. The expanded uncertainty of the 5 kW measurement is 0.12%, which is both the lowest uncertainty multi-kW measurement and radiation pressure-based measurement to-date. The HALO result was validated against a thermal primary standard using a calibrated transfer standard at 2 kW. The degree of equivalence was 0.78% ± 1.12%, which demonstrates agreement within the uncertainties of these two primary standards.

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.

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 present improvements in dual-mode calibration of predictable quantum efficient detectors and demonstrate the importance of calculating absolute uncertainties instead of relative uncertainties. We have implemented a new uncertainty component for the thermal fluctuations in the temperature signal which results in a propagated Type A uncertainty, matching the observed standard deviation. A new thermal drift correction method exploiting a monitor thermistor on the heat sink is relaxing the need for thermal stabilisation of the experimental set-up. With beam position uncertainty ±0.25 mm and background electrical power varying from 10 μW to 900 μW, the measured internal quantum deficiency (IQD) is in average 0.00% ± 0.03% (k = 2). The IQD exhibits clear systematic effects of beam position and background power, showing the need for improved design of dual-mode modules to further improve the uncertainty.

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.

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.

Upgrades to the vacuum wavelength calibration service at the National Institute of Standards and Technology are reported. The instrumentation centerpiece is an optical frequency comb stabilized to a GPS-disciplined oscillator, thereby providing direct traceability to the SI second. Historically, the service has covered lasers at the popular interferometry wavelengths red and green. Recently, capability has been added for calibrating wavemeters at multiple telecom wavelengths in the range $(1520 \lt \lambda \lt 1570)\ \textrm{nm}$. For most commercially available wavemeters, the test uncertainty ratio is about 10⁴.

For a single radionuclide being measured in an ionisation chamber, a calibration factor can be established that relates the ionisation current to the source activity. The same applies to a decay chain in secular equilibrium, for which the calibration factor comprises the ionisation current produced by the parent and progeny nuclei combined. The calibration of an ionisation chamber for non-equilibrated parent–progeny decay poses a problem because the activity ratio of the parent and progeny nuclei varies with time. This study examines cases in which the half-lives of the parent and only one of the progenies in the decay series are significantly long. Thus, two calibration factors are involved, which combine differently as a function of time. By means of nuclear dating of the material, the parent–progeny activity ratio can be determined, and the respective contributions to the ionisation current can be unambiguously distinguished. Once the ionisation chamber is calibrated, two measurements taken at different times are sufficient to determine the activity and age of the parent–progeny mixture. This study presents equations for calculating the calibration factors and propagating uncertainties, illustrated with a case study focusing on the ²²⁷Th/²²³Ra decay chain used in alpha-immunotherapy.

Exact-matching double isotope dilution inductively coupled plasma mass spectrometry (ID-ICP/MS) is widely used to characterize reference materials (RMs) in elemental analysis. In this technique, achieving exactly matching isotope ratios for the sample and calibration blends is regarded as an important prerequisite for obtaining accurate measurement results. However, meeting this condition requires multiple time-consuming iterative measurements. In the current study, an alternative approach that can avoid lengthy iterative procedures while maintaining the accuracy of the ID-ICP/MS results was successfully investigated. We examined the effects of an extensively wide range of inexact-matching isotope ratios (approximately 75%–130%) in double ID-ICP/MS for elements with a wide mass range. Our experimental study, using gravimetrically prepared samples of Ca, Cd, Cu, Fe, Hg, Mg, Ni, Pb, and Zn, demonstrated that, despite deliberately introducing mismatching of isotope ratios, the accuracy of the ID-ICP/MS results remained consistent with relative measurement bias of typically less than 0.5%. The absence of a systematic bias due to deviations in the sample blend isotope ratios from the target ratios of the calibration blends revealed that the variability due to an isotope ratio mismatch was sufficiently compensated for. Furthermore, the expanded measurement uncertainties were sufficiently small with negligible variations observed across the different matching ratios. Typically, they were less than 1%, except for Fe, Hg, Pb, and Zn which were less than 2%. This assertion is also supported by theoretically calculated error magnification factors. Consequently, it is feasible to directly utilize the marginally estimated mass fraction of the analyte of interest without extensive iterative measurements. The findings of this study provide robust data for ID-ICP/MS, allowing to circumvent lengthy iterative procedures while maintaining the accuracy and precision of the measurement results, particularly in the characterization of RMs for elemental analysis.

This supplementary comparison was about the calibration of platinum resistance thermometers in the range of -70 °C to 250 °C. Four laboratories participated in the comparison: Emirates Metrology Institute (EMI) from United Arab Emirates, SASO-NMCC from Saudi Arabia, QGOSM from Qatar and Tubitak UME from Türkiye. These Institutes are full or associated (Tubitak UME) members of the GULFMET Regional Metrology Organization.

The pilot institute was Emirates Metrology Institute, who also provided the two transfer platinum resistance thermometers and monitor their stability during the comparison.

The measurements of the comparison were performed between April 2019 and February 2021 and the circulation of the instruments was without problems, except for a delay of four months between the laboratories QGOSM and EMI due to the Coronavirus pandemic.

The weighted mean of the measurements from all laboratories was used to produce the W ratios and R_0.01 reference values of the thermometers and no laboratory was excluded from this weighted mean. Note that this comparison is an RMO supplementary comparison, so the weighted mean values generated are used only as a baseline for reporting the results, and they have no particular meaning of reference values in the sense of the key comparisons.

The results show a satisfactory agreement between the participating laboratories (|E_n| <1), except for two set-points: -35 °C and 100 °C, for one of the two transfer thermometers, for one of the laboratories. Combined expanded uncertainties for R_0.01 were equivalent to about 0.004 °C for the laboratories using water triple point cells as a reference, and 0.010 °C for QGOSM laboratory using ice point as reference. For the other measurement points, R values, were having equivalent combined expanded uncertainties ranging from 0.0060 °C to 0.010 °C for UME, 0.008 °C to 0.016 °C for EMI, 0.012 °C to 0.024 °C for SASO-NMCC and 0.014 °C to 0.054 °C for QGOSM. The mentioned uncertainties refer to the most stable of the transfer thermometers used in the comparison.

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).

We present improvements in dual-mode calibration of predictable quantum efficient detectors and demonstrate the importance of calculating absolute uncertainties instead of relative uncertainties. We have implemented a new uncertainty component for the thermal fluctuations in the temperature signal which results in a propagated Type A uncertainty, matching the observed standard deviation. A new thermal drift correction method exploiting a monitor thermistor on the heat sink is relaxing the need for thermal stabilisation of the experimental set-up. With beam position uncertainty ±0.25 mm and background electrical power varying from 10 μW to 900 μW, the measured internal quantum deficiency (IQD) is in average 0.00% ± 0.03% (k = 2). The IQD exhibits clear systematic effects of beam position and background power, showing the need for improved design of dual-mode modules to further improve the uncertainty.

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.

We present the results of a finite element analysis of the electro-optical non-equivalence of planar electrical substitution radiometers with vertically aligned carbon nanotube absorbers, operating at either room or cryogenic temperature. These detectors are the basis of the new room temperature standards of the Laboratory for Atmospheric and Space Physics' (LASP) Total solar irradiance Radiometer Facility (TRF) and the Spectral solar irradiance Radiometer Facility (SRF), and the NIST Boulder open beam cryogenic radiometer facility.&#xD;We show that the detector of our cryogenic electrical substitution radiometer has no significant electro-optical non-equivalence. Further, we also show that with careful detector design, the non-equivalence can be minimized at room temperature. It was found that in general the non-equivalence cannot be deduced from the temperature mismatch between the electrical and the optical states without considering the conductance mismatch and optical power input. The results are regarded as being precise rather than absolute to account for potentially unknown modelling errors. The numerical accuracy is typically less than 5 ppm.&#xD;

We present an optical scheme to simultaneously characterize the cross-axis and rota- tional parasitic motions of a long-stroke shaker. By leveraging the geometric properties of a corner cube retroreflector mounted on the shaker load table, we independently sample pitch, yaw, and horizontal and vertical displacements with sampling rates above 10 kHz. We have applied our optical apparatus to a 400-mm-stroke shaker operated from 0.1 Hz to 100 Hz and present two forms of analysis: (A) Frequency-domain data for the four measured parasitic degrees of freedom, with the resulting implications for accelerometer calibration uncertainties, and (B) extracted trajectories of the shaker table, allowing visualization of the bowed linear guide below 0.5 Hz and higher harmonics and hysteresis above 10 Hz. Our findings demonstrate our optical measurement scheme to be an effective tool for the characterization of parasitic motion for long-stroke shakers. As an example, we determine the "gravity error" in accelerometer calibration with our shaker to be (1.3 ± 0.1) % times the acceleration amplitude at 0.1 Hz, providing a correction to reduce uncertainty from this effect by an order of magnitude.

This work describes improvements to our Single Pressure Refractive-Index Gas Thermometry (SPRIGT) system [Metrologia 57 (2020) 065006], where a new experimental procedure for Constant Refractive-Index Gas Thermometry (CRIGT) was proposed and implemented, and after 2.5 years new values of T–T₉₀ obtained in the temperature range from 5 K to 25 K. Comparison results indicate that our SPRIGT system is robust with excellent repeatability, reliability, and stability. Not only is the uncertainty in thermodynamic temperature T still below 0.17 mK, but also good reproducibility of T₉₀ (temperature of the 1990 International Temperature Scale), T and T—T₉₀ is observed with values of 21 μK, 28 μK and 35 μK, respectively. Furthermore, we have implemented direct dissemination of thermodynamic temperature T by establishing our own thermodynamic temperature wire scale under the new International System of Units (SI) from 5 K to 25 K. The remarkable agreement further enhances our confidence on SPRIGT for implementing the redefined kelvin below 25 K, disseminating thermodynamic temperature T, and ultimately partaking in an international comparison of thermodynamic temperature via highly stable resistance thermometers.

We present the results of a finite element analysis of the electro-optical non-equivalence of planar electrical substitution radiometers with vertically aligned carbon nanotube absorbers, operating at either room or cryogenic temperature. These detectors are the basis of the new room temperature standards of the Laboratory for Atmospheric and Space Physics' (LASP) Total solar irradiance Radiometer Facility (TRF) and the Spectral solar irradiance Radiometer Facility (SRF), and the NIST Boulder open beam cryogenic radiometer facility.&#xD;We show that the detector of our cryogenic electrical substitution radiometer has no significant electro-optical non-equivalence. Further, we also show that with careful detector design, the non-equivalence can be minimized at room temperature. It was found that in general the non-equivalence cannot be deduced from the temperature mismatch between the electrical and the optical states without considering the conductance mismatch and optical power input. The results are regarded as being precise rather than absolute to account for potentially unknown modelling errors. The numerical accuracy is typically less than 5 ppm.&#xD;

For a single radionuclide being measured in an ionisation chamber, a calibration factor can be established that relates the ionisation current to the source activity. The same applies to a decay chain in secular equilibrium, for which the calibration factor comprises the ionisation current produced by the parent and progeny nuclei combined. The calibration of an ionisation chamber for non-equilibrated parent–progeny decay poses a problem because the activity ratio of the parent and progeny nuclei varies with time. This study examines cases in which the half-lives of the parent and only one of the progenies in the decay series are significantly long. Thus, two calibration factors are involved, which combine differently as a function of time. By means of nuclear dating of the material, the parent–progeny activity ratio can be determined, and the respective contributions to the ionisation current can be unambiguously distinguished. Once the ionisation chamber is calibrated, two measurements taken at different times are sufficient to determine the activity and age of the parent–progeny mixture. This study presents equations for calculating the calibration factors and propagating uncertainties, illustrated with a case study focusing on the ²²⁷Th/²²³Ra decay chain used in alpha-immunotherapy.

Exact-matching double isotope dilution inductively coupled plasma mass spectrometry (ID-ICP/MS) is widely used to characterize reference materials (RMs) in elemental analysis. In this technique, achieving exactly matching isotope ratios for the sample and calibration blends is regarded as an important prerequisite for obtaining accurate measurement results. However, meeting this condition requires multiple time-consuming iterative measurements. In the current study, an alternative approach that can avoid lengthy iterative procedures while maintaining the accuracy of the ID-ICP/MS results was successfully investigated. We examined the effects of an extensively wide range of inexact-matching isotope ratios (approximately 75%–130%) in double ID-ICP/MS for elements with a wide mass range. Our experimental study, using gravimetrically prepared samples of Ca, Cd, Cu, Fe, Hg, Mg, Ni, Pb, and Zn, demonstrated that, despite deliberately introducing mismatching of isotope ratios, the accuracy of the ID-ICP/MS results remained consistent with relative measurement bias of typically less than 0.5%. The absence of a systematic bias due to deviations in the sample blend isotope ratios from the target ratios of the calibration blends revealed that the variability due to an isotope ratio mismatch was sufficiently compensated for. Furthermore, the expanded measurement uncertainties were sufficiently small with negligible variations observed across the different matching ratios. Typically, they were less than 1%, except for Fe, Hg, Pb, and Zn which were less than 2%. This assertion is also supported by theoretically calculated error magnification factors. Consequently, it is feasible to directly utilize the marginally estimated mass fraction of the analyte of interest without extensive iterative measurements. The findings of this study provide robust data for ID-ICP/MS, allowing to circumvent lengthy iterative procedures while maintaining the accuracy and precision of the measurement results, particularly in the characterization of RMs for elemental analysis.

We present improvements in dual-mode calibration of predictable quantum efficient detectors and demonstrate the importance of calculating absolute uncertainties instead of relative uncertainties. We have implemented a new uncertainty component for the thermal fluctuations in the temperature signal which results in a propagated Type A uncertainty, matching the observed standard deviation. A new thermal drift correction method exploiting a monitor thermistor on the heat sink is relaxing the need for thermal stabilisation of the experimental set-up. With beam position uncertainty ±0.25 mm and background electrical power varying from 10 μW to 900 μW, the measured internal quantum deficiency (IQD) is in average 0.00% ± 0.03% (k = 2). The IQD exhibits clear systematic effects of beam position and background power, showing the need for improved design of dual-mode modules to further improve the uncertainty.

A primary force standard is implemented to realize the watt through Planck's constant by means of radiation pressure at the kilowatt level. The high amplification laser-pressure optic, or HALO, is a multiple reflection radiation pressure apparatus used for absolute radiometry of high-power lasers. In this work, a primary standard electrostatic force balance is used to measure the reflection-enhanced optical forces. With this configuration, the HALO is used to measure laser powers in the range of 100 W–5000 W from a 1070 nm fiber laser. The expanded uncertainty of the 5 kW measurement is 0.12%, which is both the lowest uncertainty multi-kW measurement and radiation pressure-based measurement to-date. The HALO result was validated against a thermal primary standard using a calibrated transfer standard at 2 kW. The degree of equivalence was 0.78% ± 1.12%, which demonstrates agreement within the uncertainties of these two primary standards.

In this paper, we show that the SPARK software of the Natural Resources Canada (NRCan) with their DCR (Decoupled Clock Rapid) products can be used to generate the PPP-AR continuous batch clock solutions of multiple days, which we use to build frequency transfer links between two remotely located GPS receivers. The reliability and confidence in forming the long-term frequency transfer links have been improved compared to Jian et al (2023 Metrologia60 065002). We compare the SPARK PPP-AR links to an optical fiber and TWSTFT links for hundreds of days. The ~500-day-long comparisons with TWSTFT show no frequency bias for continental and cross-continental links. Frequency transfer links formed using the SPARK solutions have uncertainty of $1\times10^{-15}/\mathrm{T}$, where T is in days, without reaching the noise floor, a critical requirement for comparing optical frequency standards and for the redefinition of the SI second. The short latency of the NRCan DCR products enables the quick availability of the PPP-AR links presented in this paper marking it particularly relevant for time sensitive applications.

The calibration of current broadband seismometers with the aim to provide traceability to the International System of Units (SI) is an active topic in the vibration metrology community. As it turns out, this exercise has its specific challenges at very low frequencies. A major problem faced at that end of the applicable frequency range, is the influence of tilt as a disturbance on the measured motion component of the sensor. In the presented work, the roles of the quantities are swapped. Tilt is used as a means of excitation of a seismometer and the rectilinear motion is considered as a disturbance, which is, however, well defined by the facilitated set-up. As it is demonstrated, this approach can be very beneficial for very low frequency calibration, and if applied correctly, it can provide a reliable link to base units of the SI.

We have built and demonstrated a digital four-arm bridge for the comparison of resistance with capacitance. The digital four-arm bridge mimics the classical quad bridge in the digital domain with three balances: the source balance, the detector balance, as well as the main balance. Due to correlation, the required precision of the source voltages is only of the order of the square root of the ultimate bridge precision. For the comparison of a 100 kΩ resistor with a 1 nF capacitor near 1592 Hz, the combined standard uncertainty $(k = 1)$ is $5 \times 10^{-9}$.

The detection of single photons plays an essential role in advancing single-photon science and technologies. Yet, within the visible/near-infrared spectral region, accurate fibre-based optical power measurements at the few-photon level are not yet well-established. In this study, we report on a fibre-based setup, enabling traceable optical power measurements at the few-photon level in this spectral region. The setup was used to calibrate the detection efficiency (DE) of four single-photon avalanche diode (SPAD) detectors. The relative standard uncertainties on the mean DE values obtained from repeat fibre-to-detector couplings ranged from 0.67% to 0.81% (k = 2). However, the relative standard deviation of DE values, which ranged from 1.38% to 3.20% (k = 2), poses a challenge for the metrology of these devices and applications that require high accuracy and repeatability. We investigated the source of these variations by spatially mapping the response of a detector's fibre connector port, using a focused free-space beam, allowing us to estimate the detector's spatial non-uniformity. In addition, we realise a novel calibration approach for fibre-coupled SPADs in a free-space configuration, enabling a direct comparison between the fibre-based setup and the National Physical Laboratory's established free-space facility using a single SPAD. Finally, we investigated alternative coupling methods, testing the repeatability of different fibre-to-fibre connectors in addition to direct fibre-to-detector couplings: SPADs from three manufacturers were tested, with both single-mode and multi-mode fibre.