This paper outlines the roadmap towards the redefinition of the second, which was recently updated by the CCTF Task Force created by the CCTF in 2020. The main achievements of optical frequency standards (OFS) call for reflection on the redefinition of the second, but open new challenges related to the performance of the OFS, their contribution to time scales and UTC, the possibility of their comparison, and the knowledge of the Earth's gravitational potential to ensure a robust and accurate capacity to realize a new definition at the level of 10−18 uncertainty. The mandatory criteria to be achieved before redefinition have been defined and their current fulfilment level is estimated showing the fields that still needed improvement. The possibility to base the redefinition on a single or on a set of transitions has also been evaluated. The roadmap indicates the steps to be followed in the next years to be ready for a sound and successful redefinition.
The 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
Piotr Morzyński et al 2024 Metrologia 61 045009
We report a remote, intercontinental frequency comparison between 171Yb (NMIJ) and 88Sr (UMK) optical lattice clocks. The frequencies were compared via the Global Positioning System Precise Point Positioning technique over the period from 10 March 2020, 00:00 UTC until 15 March 2020, 00:00 UTC. The comparison of the optical clocks yields results with a relative frequency uncertainty of .
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.
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.
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.
Luke Arabskyj et al 2024 Metrologia 61 055008
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.
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.
Peter Blattner and Richard J C Brown 2024 Metrologia 61 043001
This contribution discusses the direct relationship of any SI unit to the defining constants. For many of the SI derived units the relationships to the defining constants are simpler than to the SI base units. Furthermore, some of the relationships directly reflect the fundamental quantum-physical effects that are exploited in the primary realisation of units. It is not the intention of this article to question the status of the seven SI base units and the distinction between the SI base units and the SI derived units, which have evolved historically and persist for pedagogical reasons, but instead to provide an alternative view of the SI. This alternative view also allows a broader and more modern presentation of metrology in general and demonstrates that, in respect of the ability to be directly realised from the defining constants, there is little practical difference between the SI base units and SI derived units.
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.
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.
Bin Jian and Marina Gertsvolf 2024 Metrologia 61 065001
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 , 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.
Boris Khlevnoy et al 2024 Metrologia 61 055011
Candela, a unit of luminous intensity, was realised with an expanded (k = 2) uncertainty of 0.20% using a fixed-point blackbody based on a molybdenum–carbon (
Th Bruns et al 2024 Metrologia 61 055012
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.
Hamish McPhee et al 2024 Metrologia 61 055010
In this article, the principles of robust estimation are applied to the standard basic time scale equation to obtain a new method of assigning weights to clocks. Specifically, the Student's t-distribution is introduced as a new statistical model for an ensemble of clocks that are experiencing phase jumps, frequency jumps or anomalies in their measurement links. The proposed robust time scale is designed to mitigate the effects of these anomalies without necessarily identifying them, but through applying a method of robust estimation for the parameters of a Student's t-distribution. The proposed time scale algorithm using the Student's t-distribution (ATST) is shown to achieve comparable robustness to phase jumps, frequency jumps, and anomalies in the measurements with respect to the AT1 oracle time scale. The AT1 oracle is a special realization of the AT1 time scale which corrects all anomalies by having prior knowledge of their occurrences. The similar performance of ATST and AT1 oracle suggests that the ATST algorithm is efficient for obtaining robustness with no prior knowledge or detection of the occurrences of anomalies.
Yicheng Wang and Stephan Schlamminger 2024 Metrologia 61 055009
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 k
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.
Yi et al
The average mass attenuation coefficient of air for the KRISS 137Cs gamma-ray irradiation beam was measured using a 30 cm-long vacuum-sealable cylindrical column. Six different models of ionization chambers were employed for the measurement. Under ambient room conditions, the average mass attenuation coefficient was found to be (0.0778 ± 0.0012) cm²/g across the six chambers. This coefficient will be used to adjust the variation in air kerma with air density for the 137Cs gamma-ray irradiation beam.
Pommé
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, since the activity ratio of parent and progeny nuclei varies with time. This paper examines cases in which the half-lives of the parent and only one of the progeny 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 unambiguously distinguished. Once the ionisation chamber is calibrated, two measurements taken at different times are sufficient to determine the activity and age of a parent-progeny mixture. This study presents equations for calculating the calibration factors and propagating uncertainties, illustrated with a case study focussing on the 227Th-223Ra decay chain used in alpha-immunotherapy.
Huang et al
High-precision line intensities are of great value in various applications, such as greenhouse gas metrology, planetary atmospheric analysis, and trace gas detection. 
Here we report simultaneous measurements of cavity-enhanced absorption and dispersion spectroscopy of the prototype molecule $^{12}$C$^{16}$O using the same optical resonant cavity. Nine lines were measured in the R branch of the $v=3-0$ band. The absorption and dispersion spectra were fitted separately with speed-dependent Voigt profiles, and the line intensities obtained by the two methods agree within the experimental uncertainty of about 1\textperthousand. 
The results demonstrate the feasibility of SI-traceable molecular density measurements based on laser spectroscopy.
Solheim et al
We present improvements in dual-mode calibration of predictable quantum efficient detectors (PQED) 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
Egan et al
Recent developments in diameter metrology at NIST have improved the dimensional characterization of piston--cylinder assemblies (PCAs) to unprecedented precision. For the newest generation of PCA, the standard uncertainty on measurement of outer diameter is 12 nm, while uncertainty on measurement of inner diameter is 14 nm. With a high-accuracy dimensional dataset in hand, the task of determining the pressure generated by a specific PCA is reduced to converting diameter (and straightness and roundness) to effective area (and distortion coefficient). Details on how this was done for the artifact PCA2062 are described. PCA2062 was dimensioned in 2017 and 2020; the area repeated within 0.2 \times 10^-6 * A_0. The calculation produced estimates of fall-rate and rotation-decay that agree with experimental observations within 12 %. Fall-rate is proportional to the square of gap-width, so the agreement between calculation and measurement validates the dimensional estimate of gap-width within (36 +/- 42) nm, where the 42 nm standard uncertainty is governed by the present state of flow theory. The piston-gage model is buttressed by three comparison tests against a laser barometer, which support a view that PCA2062 is linear and reproducible within 0.2 uPa/Pa. Finally, an estimate of uncertainty in the effective area of a dimensioned artifact is provided: as expected, diameter measurement is the main culprit, but there are open questions with the flow model that preclude an accurate evaluation of the distortion coefficient. For the 530 kPa operating range of PCA2062, distortion is not a significant problem, but the effect would be dominant in assemblies operating 1 MPa and above.
Bin Jian and Marina Gertsvolf 2024 Metrologia 61 065001
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 , 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.
Stefaan Pommé 2024 Metrologia
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, since the activity ratio of parent and progeny nuclei varies with time. This paper examines cases in which the half-lives of the parent and only one of the progeny 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 unambiguously distinguished. Once the ionisation chamber is calibrated, two measurements taken at different times are sufficient to determine the activity and age of a parent-progeny mixture. This study presents equations for calculating the calibration factors and propagating uncertainties, illustrated with a case study focussing on the 227Th-223Ra decay chain used in alpha-immunotherapy.
Th Bruns et al 2024 Metrologia 61 055012
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.
Johanne Heitmann Solheim et al 2024 Metrologia
We present improvements in dual-mode calibration of predictable quantum efficient detectors (PQED) 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
Yicheng Wang and Stephan Schlamminger 2024 Metrologia 61 055009
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 k
Luke Arabskyj et al 2024 Metrologia 61 055008
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.
Piotr Morzyński et al 2024 Metrologia 61 045009
We report a remote, intercontinental frequency comparison between 171Yb (NMIJ) and 88Sr (UMK) optical lattice clocks. The frequencies were compared via the Global Positioning System Precise Point Positioning technique over the period from 10 March 2020, 00:00 UTC until 15 March 2020, 00:00 UTC. The comparison of the optical clocks yields results with a relative frequency uncertainty of .
Edwin Chen et al 2024 Metrologia 61 055005
Atomic clocks are the most accurate timekeeping instruments in the world and play a crucial role in numerous applications, notably in satellite navigation. Nonetheless, the accuracy of these clock signals is subject to anomalies, highlighting the importance of anomaly characterization and detection. In our study, we identify three types of anomalies in the phase data of atomic clocks—outliers, phase jumps and inflection points, and also frequency jumps in the frequency data, which corresponds to the inflection points. The novelty of our work lies in the application of machine learning methods for atomic clock anomaly detection (AD), as opposed to traditional algorithms. We introduce a variety of unsupervised AD and change point detection (CPD) algorithms from the realms of statistics and machine learning, propose a customized thresholding function for AD, and evaluate AD and CPD algorithms on both synthetic and real-world atomic clock data. Our experiments reveal that the subsequence local outlier factor algorithm achieves excellent performance in detecting outliers and phase jumps, but struggles with inflection points. Crucially, we found that the application of a CPD algorithm specifically for detecting the frequency jumps in frequency data substantially improves performance. Our study adopts unsupervised machine learning methods for AD provides robust detection strategies, thereby contributing an expanded understanding of the use of machine learning for clock data monitoring.
Robin Aschan et al 2024 Metrologia 61 055004
This work characterizes a facility for bidirectional transmittance distribution function (BTDF) measurements in the visible and near-infrared (NIR) 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 NIR 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.
Ian D Leroux and Brian J Eves 2024 Metrologia 61 055003
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.