Abstract Digital data pipelines routinely discard information that authors intend to convey through the number of significant figures and trailing zeros in a reported value. This paper examines when that loss matters and when it does not. It separates three concepts that are often conflated in discussions of digital precision: measurement uncertainty as defined in the Guide to the Expression of Uncertainty in Measurement (GUM), the reporting convention of significant figures, and the mechanics of numerical representation in computing systems. Building on this separation, the paper proposes a taxonomy of digital precision loss with three distinct mechanisms and three distinct remedies: storage-layer loss of trailing zeros in schemas that use native numeric types, computation layer artifacts introduced by IEEE 754 floating-point arithmetic, and display layer formatting failures such as fixed decimal truncation of small probabilities. The paper argues that trailing zero notation retains a legitimate, limited role as a redundant, human-readable check on precision even where explicit uncertainty metadata are present, and that this role is largest for legacy data, provisional readings, and manually reported values that lack a formal uncertainty budget. Case studies from dimensional metrology, optical frequency metrology, interferometric length measurement, and X-ray diffraction lattice parameter measurement illustrate where each failure mode has practical consequences. Recommendations are offered for schema design, software validation, and editorial practice, framed as extensions of existing infrastructure.
Abstract We report an improved absolute frequency measurement of a 176 Lu + ( 3 D 1 ) optical frequency standard, operated at the National University of Singapore (NUS), evaluated via a remote link to the NRC-FCs2 caesium fountain primary frequency standard. Operating a single ion clock with 94.2% uptime over 10 days, and using an ambiguity-resolved precise point positioning (PPP-AR) link over the Global Positioning System (GPS), we determine an absolute frequency of 353 638 794 073 800.332(91) Hz at a fractional uncertainty of 2.6×10 -16 . This agrees with our previous result, which underpins the CIPM recommended frequency value, and reduces the uncertainty by a factor of 3.6.
Abstract This paper describes recent updates to the SI Brochure, the authoritative document describing the International System of Units (SI), the only globally agreed system of units. The changes implemented in the most recent version of the 9th edition of the SI Brochure—version 4.01, published in June 2026—are explained, along with the rationale for making these updates. The revisions have been to the section on non-SI units and to the informative marginal notes. The new section on non-SI units responds to feedback from stakeholders and removes ambiguous and incomplete rules concerning non-SI units. It also makes clear, for the first time since the SI was formalised, that non-SI units no longer have any special status within the SI. The update also incorporates the informative notes, that previously appeared in the margins of the SI Brochure, into the main body of the text with the aim of aiding the digitalisation of the SI Brochure. The explanation of these changes provides for end users increased transparency and a better understanding of the ongoing development of metrology’s essential document.
Abstract We propose a method to assign a statement of measurement uncertainty to the ISO 14999-4:2026 surface form metrics, specifically the peak-to-valley (PV) value, clipped PV (PV%), robust PV (PVr) and the root mean square (RMS) value. We process surface form measurement data with a Monte Carlo simulation method to observe the variations in those metrics in dependence of the known instrument uncertainty and alignment errors. We found, that considering the use case of null testing Fizeau interferometry with a cropped subaperture, the measurement uncertainty significantly varies with lateral displacement errors and surface topography. The expanded uncertainty Utopo = 11 nm (with coverage factor kp = 2) of the instrument in topography height values causes a PV value uncertainty estimate of UPV ≈ 7 nm, UPVr ≈ 1 nm and UPV% ≈ 1 nm. Adding the new model for lateral displacement uncertainty Ulateral = 0.5 mm proposed in this work results in uncertainty estimates of UPV ≈ 20 nm, UPVr ≈ 3 nm and UPV% ≈ 15 nm. The increase in uncertainty is linked to the sample’s surface form deviations. We conclude that it is possible to assign a measurement uncertainty to ISO 14999-4:2026 metrics and it is mandatory to consider the instrument uncertainty, lateral displacement uncertainty and surface form deviations to get a feasible estimate of measurement uncertainty in these metrics. This is a new model to assign a statement of uncertainty to the clipped PV (PV%) and robust PV (PVr) value and a novel attempt to include the instrument uncertainty together with the lateral displacement uncertainty and surface form deviation. Therefore, this article offers a more complete, instrument and sample-specific description of the measurement uncertainty in peak to valley (PV) value, clipped PV (PV%), robust PV (PVr) and the root mean square (RMS) value as represented by the state-of-the-art.
Abstract Two-way satellite time and frequency transfer (TWSTFT) is among the most accurate techniques for comparing clocks over (inter)continental baselines, exchanging bidirectional signals through a geostationary satellite—but the cost and complexity of an active (Tx & Rx) terminal restrict it to a handful of Coordinated Universal Time (UTC)(k) laboratories. We show that a passive, receive-only user can reach those same laboratories by reducing a one-way pseudorange for the satellite-motion, atmospheric, and equipment delays. Using active-network observations over 130 d, the satellite ephemeris is reconstructed by orbit determination (OD). A portable terminal—a commercial TV dish and a software-defined-radio receiver—was calibrated in common-clock mode at INRiM and deployed to the Côte d”Azur Observatory (OCA). Over a 40 d campaign, time transfer to three UTC(k) laboratories agreed with independent GNSS and active-TWSTFT links at the nanosecond level; despite larger short-term noise from solar-radiation-pressure and wet-tropospheric mismodelling, the overlapping Allan deviation reaches ≈ 10 − 14 at one day, matching GNSS performance. The accuracy is bounded by an ≈ 7 ns ( 1 σ ) budget, and an INRiM–OCA–INRiM closure sequence confirmed robustness to relocation and traceability to UTC(k). Passive TWSTFT thus offers a scalable, interference-resilient, and low-cost route to UTC(k) dissemination, with future work targeting automated OD for quasi-real-time operation.
Abstract A primary standard has been developed for the calibration of hygrometers in a range of gases, and at above-atmospheric pressures. The core element of this humidity generation facility is a precision saturator of gas at defined temperature and pressure, providing a primary realisation of dew-and frost-point temperature in the range from −60 °C to +15 °C. This system is used in a number of modes. In single-pressure mode, gas is supplied at nominally the saturator pressure in the range from atmospheric pressure to 3 MPa, providing defined values of dew point or frost point with an expanded uncertainty of 0.12 °C. Additionally, the system can be used in two-pressure mode with the saturator operated at an elevated pressure and humid gas expanded to a lower pressure at the point of use. Thirdly, in flow-mixing mode, the humidified gas can be blended with dry gas to give a chosen water content. In all of these modes of operation, the generation system is used with a variety of inert gases and mixtures, either by direct saturation of gas or by blending gas streams. The combination of these modes of use provides a versatile primary standard for generating dew point and other humidity quantities in a range of gases (air, nitrogen, hydrogen, methane) and gas mixtures at pressures up to 3 MPa. The facility enables the testing and traceable calibration of hygrometers in a range of pressures and gases. Since some hygrometer types are sensitive to the pressure or species of the background gas, the National Physical Laboratory (NPL) facility provides an important capability to calibrate hygrometers in conditions relevant to real-world use, and to assess hygrometer sensitivity to gas species and pressure. The humidity generator is described, and details are given of the characterisation of aspects of its performance, leading to an evaluation of uncertainty in generated values of humidity quantities.
This work presents the results of evaluating and measuring the dc leakage effects associated with programmable Josephson voltage standards (PJVSs) caused by unintended currents flowing in the circuit. Two types of leakage error can occur in PJVS systems: (1) involves leakage currents to Earth ground, which typically result from the finite resistance of cable insulation and the bias electronics, and (2) leakage paths on the precision output leads giving rise to a voltage divider effect between the leads and the load impedance. Both effects impact the PJVS's measurement accuracy and must be monitored regularly. We have developed assessment methods, including both manual and automated measurements, that should be applied to any disseminated PJVS systems currently in use. If these recommended techniques are followed and the leakage current to Earth ground remains below 150 pA when the PJVS array is biased at 10 V, the resulting voltage error at the room-temperature terminals will be less than 0.2 nV.
The triple points of carbon dioxide (TP CO2) and sulfur hexafluoride (TP SF6) have been studied over the last decade as alternative fixed points to the triple point of mercury (TP Hg, 234.3156 K) on the International Temperature Scale of 1990 (ITS-90). NIST has been developing TP CO2 and TP SF6 cells to be employed as drop-in replacements for TP Hg cells for calibrations of standard platinum resistance thermometers (SPRTs). This work presents the results of the assessment of new immersion-type CO2 and SF6 triple point cells built at NIST and the results of their use in ITS-90 calibrations of long-stem SPRTs. It was demonstrated that a very well-controlled realization technique can result in measurements of the triple points of CO2 and SF6 within 25 μK and 75 μK of reproducibility, respectively, with estimated temperatures of 216.591 21(15) K and 223.556 22(33) K for F= 1, respectively. The large volume expansion of CO2 and SF6 upon melting in large immersion cells is responsible for a progressive head correction that increases the realization slopes of the triple points of CO2 and SF6 by 0.1 mK and 0.46 mK, respectively. Calibrations of two SPRTs on different ITS-90 subranges using either TP Hg, TP CO2 or TP SF6 cells showed that the interpolated temperatures using either triple point agreed within their realization uncertainties. These results demonstrate that both fixed points can be used as alternatives for the Hg TP in a future revision of the ITS-90.
Abstract In order to fulfill its mission to ensure and promote the global comparability of measurements, the BIPM operates laboratories in the fields of physical metrology, ionizing radiation, chemistry and time. These laboratories act as centers for scientific and technical collaboration between Member States providing capabilities for international measurement comparisons on a shared cost basis. They coordinate international comparisons of national measurement standards agreed to be of the highest priority, and they establish and maintain appropriate reference standards for use as the foundation of key international comparisons at the highest level and provide selected calibrations from them. In the following sections, we provide highlights of the work the laboratories have undertaken during 2025.
Abstract The redefinition of the System of Unit (SI) second is expected in the near future due to progress in time and frequency metrology. One promising option is to use several transitions to define the SI second. However, the proposed definitions use a ‘constant’ that is unnecessary for such a definition, is not a constant in value between possible redefinitions and has no physical meaning, which may be controversial properties. Therefore, this paper proposes alternative wording for the definition of the SI second that does not directly use such a constant, in order to improve a possible definition based on several transitions.
Abstract We report the first replication of a high-precision measurement of the gravitational constant, G . The experiment employed the torsion balance originally designed and constructed at the International Bureau of Weights and Measures (BIPM) approximately three decades ago. Using the same apparatus and geometry, with several modifications documented in this work, we determined G = ( 6.67387 ± 0.00038 ) × 10 − 11 m 3 kg − 1 s − 2 , corresponding to a relative standard uncertainty of 5.7 × 10 − 5 . The result is lower by 2.5 × 10 − 4 relative to the BIPM determination. This replication provides an independent verification of one of the most precise torsion-balance determinations of G and contributes to assessing the reproducibility limits of current experimental techniques in measurements of the gravitational constant.
This companion guide revises and expands upon the established technical guidelines for reliable direct current measurements of the quantized Hall resistance, adapting them to the unique characteristics of epitaxial graphene. Graphene has emerged as a viable alternative to traditional Gallium Arsenide heterostructures for metrological applications due to its relaxed operating conditions. These less demanding requirements facilitate the use of low-cost, compact cryomagnet platforms, which is expected to broaden the deployment of primary resistance standards to National Metrology Institutes and other laboratories with limited resources. The guide explores the specific challenges and considerations of epitaxial graphene devices, including aspects of device choice, cooling and handling, contact resistance, conditions of quantization, and general measurements of the quantized Hall resistance. The presented details should assist those seeking to conduct rigorous characterization procedures to verify device integrity, ultimately contributing to a global effort to formally accept graphene-based devices as reliable primary resistance standards.
Abstract Acoustic pressure determined in water is a critical parameter for many applications of underwater acoustics (UW) and ultrasonics (US). These areas cover diverse drivers, from the need to measure ocean acoustics in support of noise pollution regulation, to the acoustic output of diagnostic and therapeutic medical equipment to ensure safe clinical exposure levels. Within the metrology community, one of the lowest uncertainty primary realisations of the relevant unit, the acoustic pascal, has been through optical interferometry. Here, an optical interferometer was used to probe picometre displacements of a thin, quasi-acoustically transparent, membrane suspended within acoustic fields to measure the acoustic pascal at a specific spatial location. At the UK National Physical Laboratory, this SI unit is realised and disseminated to the user community through secondary calibration of user hydrophones. This manuscript describes a new realisation of the acoustic pascal built around a commercial optical heterodyne-type vibrometer which allows limitations of the previous homodyne realisations to be overcome. These limitations included: sensitivity to external vibration, limited linear dynamic range and the need to individually calibrate multiple onboard electronics, including frequency response of the photodiodes. We demonstrate continuity in the realisation of the acoustic pascal and hydrophone calibrations, with good agreement over a variety of hydrophone types. The new interferometer has shown good agreement with the previous optical primary standards, with free-field reciprocity, current secondary standard disseminations, and the key comparison reference values derived for hydrophones used in CIPM key comparisons spanning both UW and US frequency ranges. A novel aspect of the work is the improvement in hydrophone calibration uncertainties at high frequencies through the application of spatially broad acoustic fields using acoustic signals generated by finite amplitude distortion. Hydrophone calibration uncertainty budgets are presented demonstrating uncertainties which vary from 9.41% at 100 kHz to 14.03% at 60 MHz (k=2).
The SI units of plane angle (radian) and solid angle (steradian) have been the subject of much international debate and discussion, stretching back over several decades. This letter presents the viewpoint from practising dimensional metrologists for whom the realisation of angular units is their responsibility.
We report improved performance of the 171Yb optical lattice clocks at East China Normal University (ECNU), achieving a total uncertainty of 4.4×10-18 for the Yb2 clock through high-precision synchronous frequency comparisons with the similar Yb1 clock. A 578-nm laser for the 1S0 - 3P0 clock transition is cavity-stabilized using a newly developed ultra-stable laser system, featuring a reduced thermal-noise limit compared to its predecessor. Through systematic optimization, including suppression of technical noise in the laser system and detailed evaluation of frequency shifts, such as collision, blackbody radiation, lattice, and Zeeman shifts, we achieved stable clock-transition spectra for the mF = ±1/2 spin states using 400-ms interrogation pulses, obtaining a Fourier-limited linewidth of 2 Hz. Based on these optimizations, synchronous comparisons between two 171Yb clocks enable a fractional frequency instability for each clock to average at a rate of 2.0×10-16/ √τ, reaching ×10-18 at 8000 s, which provides the resolution necessary for high-precision systematic evaluation. Furthermore, a complementary asynchronous comparison accounting for the Dick noise yields an instability of 4.0×10-18 at 8000 s. The combination of these high-precision comparisons and rigorous frequency shift evaluations validates the total systematic uncertainty below 5×10-18.
This paper is an introduction to the Metrologia Focus on the Challenges in Time and Frequency (TF) Metrology. It presents the main consultative committee for time and frequency (CCTF) activities in different fields of TF metrology: primary and SFS, TF transfer techniques, and atomic time scales. This includes cross-cutting 'hot topics' that deserve special attention such as: redefinition of the international system of units second, continuous UTC and leap seconds, mutual benefits between UTC and global navigation satellite system. The CCTF aims to ensure the best services to the TF community, including focused training based on resource sharing to improve national and international timekeeping.
The measurand for line scales is currently defined as the distance between mark centres for prescribed portions of two marks when the scale is at 20 degrees C, the ambient pressure is 101.3 kPa, and with specified support conditions. This definition does not specify a method for determining the mark centre, and differences between methods are a potential source of uncertainty. We present a quantitative study of this uncertainty, comparing results obtained by a range of centre-finding methods modelled on those published in the literature and in key comparison reports, including methods applicable to photoelectric sensors and cameras. In addition, the influence on the centre-finding algorithms of lighting conditions, defects in the artefact, defocus, and the use of reversal measurements have all been investigated. We have built a simple numerical model of a microscope system in order to understand the causes of the method-dependence. Alignment of the light source as well as comatic and spherical aberrations in the microscope system account for the algorithm-dependent focus sensitivity observed in experiments.
Gravimetric preparation is internationally recognized as the primary method for producing calibration gas mixtures, and its uncertainty is commonly evaluated using the law of propagation of uncertainty within the GUM uncertainty framework (GUF). For impurities in parent gases with amount fractions close to or below the limit of detection, ISO 19229 indicates that symmetric distributional assumptions may yield unphysical results and requires the use of asymmetric probability density functions, such as the beta distribution. However, the quantitative impact of such assumptions in gravimetric gas mixture preparation has not yet been systematically reported. In this work, a Monte Carlo method (MCM) was implemented to propagate asymmetric input distributions in accordance with ISO 19229. A representative multi-stage gravimetric dilution case study was designed, including major components, significant impurities and trace impurities, to systematically compare the uncertainty evaluation results obtained using the GUF and the MCM. The results show that, for target gas mixtures prepared through three dilution stages, the GUF and the MCM yield highly consistent results, with deviations between the estimates below 0.02% and relative differences in standard uncertainties below 0.2% for most components, increasing to about 6% for 1,3-butadiene due to the limited purity of the parent gas. By contrast, for intermediate mixtures prepared through at most two dilution stages, components dominated by beta-distributed uncertainty contributions exhibit asymmetric output distributions. In these cases, differences between mean-based and mode-based estimates exceed 40%, and differences in standard uncertainties exceed 8%. The MCM further provides asymmetric coverage intervals and additional statistical descriptors such as skewness and kurtosis. These results demonstrate the MCM as a practical approach for complying with ISO 19229 in gravimetric preparation. Furthermore, this framework holds broader significance for uncertainty evaluation in trace-level monitoring tasks characterized by asymmetric distributional assumptions.
Microwave frequency transfer over optical fiber is an enabling technology for disseminating frequency standards from atomic clocks to remote users. We report a continental-scale fiber-optic microwave frequency transfer system deployed on installed telecommunication fibers between Xi'an and Beijing. In the stabilized two-way noise-compensation configuration, the round-trip path is implemented using two fibers within the same cable: the signal travels 1571 km along one fiber and returns via the other, yielding a total round-trip length of 3143 km. By adopting a cascaded architecture with multiple regeneration nodes and a simplified integer frequency conversion scheme, we achieve a fractional frequency instability of 2.73 & times; 10-17 at 105 s. The system performance is validated over nearly one year of continuous operation, demonstrating robustness in real-world environments (urban and rural segments, seasonal temperature variations, and operational perturbations). Bidirectional wavelength-division multiplexing on deployed fibers and active phase noise compensation suppress fiber-induced phase fluctuations, and the added single-sideband phase noise of the transferred signal is maintained below -60 dBc Hz-1 at 1 Hz offset (normalized to 3.6 GHz), with an integrated timing jitter of similar to 1.2 ps (1 Hz-1 MHz). These results indicate that continental-scale dissemination of microwave frequency references can meet the stability requirements of modern cesium fountain clocks and support emerging applications in navigation, telecommunications, radio astronomy, and fundamental physics.
