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.
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The International Bureau of Weights and Measures (BIPM) was set up by the Metre Convention and has its headquarters near Paris, France. It is financed jointly by its Member States and operates under the exclusive supervision of the CIPM.
Its mandate is to provide the basis for a single, coherent system of measurements throughout the world, traceable to the International System of Units (SI). This task takes many forms, from direct dissemination of units (as in the case of mass and time) to coordination through international comparisons of national measurement standards (as in electricity and ionizing radiation).
The BIPM has an international staff of over 70 and its status vis-à-vis the French Government is similar to that of other intergovernmental organizations based in Paris.
ISSN: 1681-7575
The leading international journal in pure and applied metrology, published by IOP Publishing on behalf of Bureau International des Poids et Mesures (BIPM).
N Dimarcq et al 2024 Metrologia 61 012001
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A Tofful et al 2024 Metrologia 61 045001
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) transition. The total systematic frequency shift was measured with a fractional standard systematic uncertainty of
. 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
and
, and all were in agreement with the 2021 BIPM recommended frequency.
G Panfilo and F Arias 2019 Metrologia 56 042001
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.
D B Newell et al 2018 Metrologia 55 L13
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 NA 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.
Michael Stock et al 2019 Metrologia 56 022001
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.
S Pommé 2015 Metrologia 52 S51
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.
Peter J Mohr and William D Phillips 2015 Metrologia 52 40
The International System of Units (SI) is supposed to be coherent. That is, when a combination of units is replaced by an equivalent unit, there is no additional numerical factor. Here we consider dimensionless units as defined in the SI, e.g. angular units like radians or steradians and counting units like radioactive decays or molecules. We show that an incoherence may arise when different units of this type are replaced by a single dimensionless unit, the unit 'one', and suggest how to properly include such units into the SI in order to remove the incoherence. In particular, we argue that the radian is the appropriate coherent unit for angles and that hertz is not a coherent unit in the SI. We also discuss how including angular and counting units affects the fundamental constants.
Lorenz Keck et al 2024 Metrologia 61 045006
We studied the anelastic aftereffect of a flexure being used in a Kibble balance, where the flexure is subjected to a large excursion in velocity mode after which a high-precision force comparison is performed. We investigated the effect of a constant and a sinusoidal excursion on the force comparison. We explored theoretically and experimentally a simple erasing procedure, i.e. bending the flexure in the opposite direction for a given amplitude and time. We found that the erasing procedure reduced the time-dependent force by about 30%. The investigation was performed with an analytical model and verified experimentally with our new Kibble balance at the National Institute of Standards and Technology employing flexures made from precipitation-hardened Copper Beryllium alloy C17200. Our experimental determination of the modulus defect of the flexure yields . This result is about a factor of two higher than previously reported from experiments. We additionally found a static shift of the flexure's internal equilibrium after a change in the stress and strain state. These static shifts, although measurable, are small and deemed uncritical for our Kibble balance application at present. During this investigation, we discovered magic flexures that promise to have very little anelastic relaxation. In these magic flexures, the mechanism causing anelastic relaxation is compensated for by properly shaping and loading a flexure with a non-constant cross-section in the region of bending.
John Lehman et al 2024 Metrologia 61 033001
In this letter we examine the organization of the traditional base units and defining constants established in the 2019 redefinition of the international system of units (SI). For the next redefinition of the SI, which will accompany the anticipated redefinition of the second, we propose an organizational change to improve clarity while maintaining practicality. We propose three distinct categories of units: The first category comprises the four base-measurement units: The second, meter, kilogram, and ampere. The second contains physiologically-relevant derived units. The third category contains the remaining units derived from the base units.
Tobias Dietl et al 2024 Metrologia 61 045007
We report comprehensive and accurate measurements of the speed of sound in neon. These measurements were carried out by a double-path-length pulse-echo technique and cover the temperature range between 200 K and 420 K with pressures up to 100 MPa. The standard uncertainties are 1.9 mK in temperature, 22 parts in 106 in pressure and 35 parts in 106 in speed of sound. The third and fourth acoustic virial coefficients of neon were derived from the speed of sound data in the temperature range of the measurements by fitting a fourth-order acoustic virial expansion in pressure with the second acoustic virial coefficient constrained from first-principles calculations. To support our claimed uncertainty, we determined the ratio between the molar mass M and the ideal-gas heat capacity ratio
of the neon sample with a relative standard uncertainty of 7.7 parts in 106 by additional speed of sound measurements using a spherical resonator at 273.16 K.
Seungjin Yoon et al 2024 Metrologia 61 055001
We propose a quantum plasmonic sensor using Hong–Ou–Mandel (HOM) interferometry that measures the refractive index of an analyte, embedded in a plasmonic beam splitter composed of a dual-Kretschmann configuration, which serves as a frustrated total internal reflection beamsplitter (BS). The sensing performance of the HOM interferometry, combined with single-photon detectors, is evaluated through Fisher information for estimation of the refractive index of the analyte. This is subsequently compared with the classical benchmark that considers the injection of a coherent state of light into the plasmonic BS. By varying the wavelength of the single photons and the refractive index of the analyte, we identify a wide range where a 50% quantum enhancement is achieved and discuss the observed behaviors in comparison with the classical benchmark. We expect this study to provide a useful insight into the advancement of quantum-enhanced sensing technologies, with direct implications for a wide range of nanophotonic BS structures.
D Bhattacharjee et al 2024 Metrologia 61 054002
Current gravitational wave (GW) observatories rely on photon calibrators that use laser radiation pressure to generate displacement fiducials used to calibrate detector output signals. Reducing calibration uncertainty enables optimal extraction of astrophysical information such as source distance and sky position from detected signals. For the ongoing O4 observing run that started on 24 May 2023, the global GW detector network is employing a new calibration scheme with transfer standards calibrated at both the National Institute of Standards and Technology (NIST) and the Physikalisch-Technische Bundesanstalt (PTB). These transfer standards will circulate between the observatories and the metrology institutes to provide laser power calibration traceable to the International System of Units (SI) and enable assessment and reduction of relative calibration errors for the observatory network. The Laser Interferometer Gravitational-Wave Observatory (LIGO) project and the Virgo project are currently participating in the new calibration scheme. The Large-scale Cryogenic Gravitational-wave Telescope project (KAGRA) is expected to join in 2024, with the LIGO Aundha Observatory in India joining later. Before implementing this new scheme, a NIST-PTB bilateral comparison was conducted. It validated the scale representation by both laboratories, with a degree of equivalence of −0.2% and an associated expanded uncertainty of 0.32% (k = 2) which is significantly lower than previous studies. We describe the transfer of power sensor calibration, including detailed uncertainty estimates, from the transfer standards calibrated by NIST and PTB to the sensors operating continuously at the interferometer end stations. Finally, we discuss the ongoing calibration of Pcal-induced displacement fiducials for the O4 observing run. Achieved combined standard uncertainty levels as low as 0.3% facilitate calibrating the interferometer output signals with sub-percent accuracy.
Richard J C Brown 2024 Metrologia 61 053001
This letter considers the potential for confusion in the presentation and interpretation of measurement results caused by the existence of upper- and lower-case letter pairs for SI prefix symbols, an example of this being the newest prefix symbols Q & q and R & r, adopted at the 27th Meeting of the General Conference on Weights and Measures in November 2022. The requirements of digitalisation and machine readability, when making choices for new unit and prefix symbols, are also examined.
Hristina Georgieva et al 2024 Metrologia 61 054001
We present a comprehensive metrological characterization of a commercial single-photon source with high photon flux emission for use in radiometry. The source is based on an InGaAs quantum dot in a micropillar. A comparative analysis of two excitation schemes—phonon-assisted excitation and two-photon excitation—explores differences in excitation power dependence, temporal stability and single-photon purity. The commercial source exhibits excellent properties for the field of quantum radiometry, achieving simultaneously a photon flux of (17.19 ± 0.09) million photons/s for a pulse repetition rate of 79.4 MHz, and a single-photon purity of 98%. Its optical power of (3.68 ± 0.02) pW is directly determined with a traceably calibrated low-noise photodiode. The ability to directly compare the photocurrent in a low-noise photodiode with the count rate at a single-photon avalanche detector allows for a seamless transition between the classical and quantum realizations of optical power. Therefore, we were able to build another bridge between classical and quantum radiometry by using a deterministic single-photon source.
Jinglin Fu et al 2024 Metrologia 61 044001
To perform accurate, high-quality and traceable measurement of optical diffuse transmission, which is quantified using the bidirectional transmittance distribution function (BTDF), a new primary facility has been developed at the Physikalisch–Technische Bundesanstalt (PTB), the German metrology institute. This newly developed reference facility will complement the available calibration services and research facilities at PTB for regular reflectance and transmittance and diffuse reflectance. The performance of the new BTDF setup has been investigated in an internal comparison, where consistency of the results was achieved. A thorough uncertainty analysis results in a minimum combined standard (k=1) uncertainty of about 0.8 %. Research on the accurate characterisation of the BTDF of samples with non-negligible lateral scattering is being carried out on this new setup. Some first results have shown that the measured BTDF value depends on the applied irradiation area size. An empirical model has been found to describe the diffuse transmission of such translucent samples with different scattering parameters.
Samuel P Benz et al 2024 Metrologia 61 022001
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.
N Dimarcq et al 2024 Metrologia 61 012001
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.
Juris Meija et al 2023 Metrologia 60 052001
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.
Olav Werhahn et al 2023 Metrologia 60 042001
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.
S M Judge et al 2023 Metrologia 60 012001
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.
Leroux et al
We derive an estimator for the step size in phase-shifting interferometry. Using a minimum of five samples, it avoids the occasional indeterminate results that afflict the traditional Carré step-size estimate. The estimator can be understood as a generalization of the modified-covariance frequency estimator for a real-valued sinusoid with an unknown mean. We describe its use in the NRC Gauge
Block Interferometer for monitoring the motion of a phase-shifting mirror mount.
Levine
The definition of Coordinated Universal Time (UTC) in 1972 balanced the needs of the time and frequency community for a universal time scale that was traceable to the definition of frequency in the SI system of units with the needs of the astronomical community for a time scale that was closely linked to UT1, a time scale related to the rotation of Earth. The balance between these two considerations has changed very significantly since 1972, and there is widespread agreement that the method of relating UTC to UT1 should be changed by increasing the maximum tolerance between the two scales to more than the current limit of 0.9 s. We propose to realize this decision by means of an algorithmic adjustment process based on the variation in the length of the day over the previous centuries. We use these historical data to extrapolate the length of the day for a century into the future, and to compute a periodic rate adjustment to UTC based on this extrapolation. The adjustment process will not use time steps. The magnitude of the periodic rate adjustment will be re-considered every century, but the basic adjustment algorithm will not change. We suggest a maximum tolerance between UT1 and UTC that is large enough to absorb the irregular and unpredictable variations in the length of the day with respect to the long-term average increase in this value but plays no role in determining the parameters of the adjustment process that is proposed. We also propose that the adjustment be implemented at 12 UTC on 1 January or on another date that is close to a universal holiday in all time zones.

Dury et al
We have assessed the absolute spectral responsivities of three-element trap detectors calibrated against the NPL primary standard cryogenic radiometer at eight krypton ion laser emission wavelengths over an approximate period of twenty-years. As expected, we observed that the absolute spectral responsivities decrease with time. Additionally, we found that as the wavelength decreases, the ageing rate increases. At 356.4 nm, an average responsivity decrease of around -1800 ppm/year is reported. While at longer wavelengths, the slowest rate of ageing, approximately 40 ppm/year, occurs at 799.3 nm. Interestingly, the year-on-year changes exhibit a relatively linear trend, allowing us to predict the future performance of the trap detectors. It is important to note, however, that predicted performance cannot be guaranteed and regular recalibration against a primary standard is essential, especially if low calibration uncertainties are required.
Aschan et al
This work characterizes a facility for bidirectional transmittance distribution function (BTDF) measurements in the visible and near-infrared wavelength range. The facility includes an absolute reference gonioreflectometer, with an extended capability for BTDF measurements, and a commercial instrument, Cary 7000, using a goniometer extension, Universal Measurement Accessory. The facility characterization includes measurements of two quasi-Lambertian diffusers for their BTDF. The diffuser samples include a piece of porous polytetrafluoroethylene (PTFE) and a piece of fused synthetic silica, HOD-500. The samples are measured for their spectral BTDF in the wavelength range from 450 nm to 1650 nm in 50 nm steps, and in the viewing zenith angle range from -35° to 35° in 5° steps. Measurements are performed in-plane, using an incident zenith angle of 0°, while rotating the samples around their surface normal from 0° to 180° in 90° steps. Rotation of the sample serves the dual purpose of checking the sample rotational symmetry in azimuth angles and for averaging the measurement results. The characterization results show that both samples exhibit Lambertian characteristics across the visible and near-infrared wavelength range. Furthermore, both samples show a smooth increase in their spectral BTDF as a function of wavelength. Notably, the PTFE sample demonstrates a steeper slope in its spectral BTDF and a higher signal above 650 nm. The facility capability for measurements of spectral BTDF is validated by a rigorous uncertainty analysis and by comparing the difference in measurement results between the absolute gonioreflectometer and the commercial instrument. Characterization results indicate that the absolute reference gonioreflectometer has a standard uncertainty ranging from 0.29 % to 0.42 %, dependent on the BTDF measurement wavelength. Experimental results show that the devices of the facility deviate in their BTDF within their combined expanded uncertainty, affirming the capability and reliability of the facility for BTDF measurements.
Hristina Georgieva et al 2024 Metrologia 61 054001
We present a comprehensive metrological characterization of a commercial single-photon source with high photon flux emission for use in radiometry. The source is based on an InGaAs quantum dot in a micropillar. A comparative analysis of two excitation schemes—phonon-assisted excitation and two-photon excitation—explores differences in excitation power dependence, temporal stability and single-photon purity. The commercial source exhibits excellent properties for the field of quantum radiometry, achieving simultaneously a photon flux of (17.19 ± 0.09) million photons/s for a pulse repetition rate of 79.4 MHz, and a single-photon purity of 98%. Its optical power of (3.68 ± 0.02) pW is directly determined with a traceably calibrated low-noise photodiode. The ability to directly compare the photocurrent in a low-noise photodiode with the count rate at a single-photon avalanche detector allows for a seamless transition between the classical and quantum realizations of optical power. Therefore, we were able to build another bridge between classical and quantum radiometry by using a deterministic single-photon source.
Jinglin Fu et al 2024 Metrologia 61 044001
To perform accurate, high-quality and traceable measurement of optical diffuse transmission, which is quantified using the bidirectional transmittance distribution function (BTDF), a new primary facility has been developed at the Physikalisch–Technische Bundesanstalt (PTB), the German metrology institute. This newly developed reference facility will complement the available calibration services and research facilities at PTB for regular reflectance and transmittance and diffuse reflectance. The performance of the new BTDF setup has been investigated in an internal comparison, where consistency of the results was achieved. A thorough uncertainty analysis results in a minimum combined standard (k=1) uncertainty of about 0.8 %. Research on the accurate characterisation of the BTDF of samples with non-negligible lateral scattering is being carried out on this new setup. Some first results have shown that the measured BTDF value depends on the applied irradiation area size. An empirical model has been found to describe the diffuse transmission of such translucent samples with different scattering parameters.
Ian Daniel Leroux and Brian J Eves 2024 Metrologia
We derive an estimator for the step size in phase-shifting interferometry. Using a minimum of five samples, it avoids the occasional indeterminate results that afflict the traditional Carré step-size estimate. The estimator can be understood as a generalization of the modified-covariance frequency estimator for a real-valued sinusoid with an unknown mean. We describe its use in the NRC Gauge
Block Interferometer for monitoring the motion of a phase-shifting mirror mount.
Tobias Dietl et al 2024 Metrologia 61 045007
We report comprehensive and accurate measurements of the speed of sound in neon. These measurements were carried out by a double-path-length pulse-echo technique and cover the temperature range between 200 K and 420 K with pressures up to 100 MPa. The standard uncertainties are 1.9 mK in temperature, 22 parts in 106 in pressure and 35 parts in 106 in speed of sound. The third and fourth acoustic virial coefficients of neon were derived from the speed of sound data in the temperature range of the measurements by fitting a fourth-order acoustic virial expansion in pressure with the second acoustic virial coefficient constrained from first-principles calculations. To support our claimed uncertainty, we determined the ratio between the molar mass M and the ideal-gas heat capacity ratio
of the neon sample with a relative standard uncertainty of 7.7 parts in 106 by additional speed of sound measurements using a spherical resonator at 273.16 K.
Robin Erik Aschan et al 2024 Metrologia
This work characterizes a facility for bidirectional transmittance distribution function (BTDF) measurements in the visible and near-infrared wavelength range. The facility includes an absolute reference gonioreflectometer, with an extended capability for BTDF measurements, and a commercial instrument, Cary 7000, using a goniometer extension, Universal Measurement Accessory. The facility characterization includes measurements of two quasi-Lambertian diffusers for their BTDF. The diffuser samples include a piece of porous polytetrafluoroethylene (PTFE) and a piece of fused synthetic silica, HOD-500. The samples are measured for their spectral BTDF in the wavelength range from 450 nm to 1650 nm in 50 nm steps, and in the viewing zenith angle range from -35° to 35° in 5° steps. Measurements are performed in-plane, using an incident zenith angle of 0°, while rotating the samples around their surface normal from 0° to 180° in 90° steps. Rotation of the sample serves the dual purpose of checking the sample rotational symmetry in azimuth angles and for averaging the measurement results. The characterization results show that both samples exhibit Lambertian characteristics across the visible and near-infrared wavelength range. Furthermore, both samples show a smooth increase in their spectral BTDF as a function of wavelength. Notably, the PTFE sample demonstrates a steeper slope in its spectral BTDF and a higher signal above 650 nm. The facility capability for measurements of spectral BTDF is validated by a rigorous uncertainty analysis and by comparing the difference in measurement results between the absolute gonioreflectometer and the commercial instrument. Characterization results indicate that the absolute reference gonioreflectometer has a standard uncertainty ranging from 0.29 % to 0.42 %, dependent on the BTDF measurement wavelength. Experimental results show that the devices of the facility deviate in their BTDF within their combined expanded uncertainty, affirming the capability and reliability of the facility for BTDF measurements.
Lorenz Keck et al 2024 Metrologia 61 045006
We studied the anelastic aftereffect of a flexure being used in a Kibble balance, where the flexure is subjected to a large excursion in velocity mode after which a high-precision force comparison is performed. We investigated the effect of a constant and a sinusoidal excursion on the force comparison. We explored theoretically and experimentally a simple erasing procedure, i.e. bending the flexure in the opposite direction for a given amplitude and time. We found that the erasing procedure reduced the time-dependent force by about 30%. The investigation was performed with an analytical model and verified experimentally with our new Kibble balance at the National Institute of Standards and Technology employing flexures made from precipitation-hardened Copper Beryllium alloy C17200. Our experimental determination of the modulus defect of the flexure yields . This result is about a factor of two higher than previously reported from experiments. We additionally found a static shift of the flexure's internal equilibrium after a change in the stress and strain state. These static shifts, although measurable, are small and deemed uncritical for our Kibble balance application at present. During this investigation, we discovered magic flexures that promise to have very little anelastic relaxation. In these magic flexures, the mechanism causing anelastic relaxation is compensated for by properly shaping and loading a flexure with a non-constant cross-section in the region of bending.
Rugiada Cuccaro et al 2024 Metrologia 61 045003
A low frost-point generator (INRIM 03) able to operate at sub-atmospheric pressure has been recently designed, constructed, and assessed at the Istituto Nazionale di Ricerca Metrologica (INRiM) with the aim of providing the metrological traceability both to instruments developed for the measurement of humidity in atmosphere and to sensors and analysers used in industry for controlling and measuring the amount of water vapour in manufacturing processes. The humidity generator operates in a single temperature single pressure mode, letting the carrier gas (nitrogen) achieve saturation in a single passage through an isothermal saturator. Its working range encompasses a frost-point temperature range from −100 °C to −20 °C, in a pressure range between 200 and 1100 hPa, corresponding to an amount of water fraction range from 13 · 10−9 mol·mol−1 to 6.2 · 10−3 mol·mol−1. In a previous work its performance was assessed in the frost-point temperature range from −75 °C to −20 °C (Cuccaro et al 2018 Meas. Sci. Technol.29 054002). In this work, a comprehensive set of tests for its characterisation and performance evaluation between −75 °C and −100 °C is presented. A detailed uncertainty analysis in the above temperature range is reported, taking into account all the sources of uncertainty that affect the humid gas generation. An expanded uncertainty (k= 2) of 0.07 °C was found for frost-point temperature measurements between −75 °C and −95 °C, while an expanded uncertainty of 0.26 °C resulted at a frost-point temperature of −100 °C. The relative expanded uncertainty (k = 2) associated with water vapour amount fraction measurements was estimated equal to or better than 1.2% between 35 · 10−9 mol·mol−1 and 6.1 · 10−3 mol·mol−1, increasing up to 6.5% at 1310−9 mol·mol−1.
John Lehman et al 2024 Metrologia 61 049501
In this corrigendum, we correct several typographical or typesetting errors and small but meaningful errors in tables 1, A.1 and A.3 found in the original manuscript. We emphasize as a correction that the Avogadro constant is not a dimensionless number. The corrections are placed according to the original organization: section 2, references, and appendix.
M G White et al 2024 Metrologia 61 045002
We have developed a technique to determine the electrical substitution power of a cryogenic optical radiant power detector, that directly implements a frequency-programmable Josephson voltage standard (FPJVS), thus reducing the traceability chain. The optical power detector and the Josephson voltage reference are combined inside a common cryogenic environment. We demonstrate the practicality of the technique by using a FPJVS to apply a known voltage across the resistive heater of a standard NIST cryogenic planar radiometric detector. The power applied to the detector heater is calculated from a measurement of the heater resistance and the known applied voltage. The FPJVS dc bias current source supplies dc current to the resistive heater. In this demonstration, the standard uncertainty of the substituted electrical power is limited by the uncertainty of the electrical heater four-wire resistance measurement at 4 K. The uncertainty due to the resistance measurement is 1 part in 105 out of a total uncertainty of 1 part in 104 (k = 2) on the 1 mW optical power measurement. We aim to develop the technique, to provide traceability to the International System of Units for the picowatt power measurement of single-photon emitters such as quantum dot sources.
![$2.2\times 10^{-18}$](https://content.cld.iop.org/journals/0026-1394/61/4/045001/revision3/metad53cdieqn1.gif)
A Tofful et al 2024 Metrologia 61 045001
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) transition. The total systematic frequency shift was measured with a fractional standard systematic uncertainty of
. 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
and
, and all were in agreement with the 2021 BIPM recommended frequency.