Table of contents

The most widely used method for the preparation of primary standard gas mixtures involves weighing the individual components into a cylinder. We present a new mathematical description of the method and its uncertainties. We use this to demonstrate how strategies for serial dilution can be identified that minimize the uncertainty in the final mixture and show how they can be implemented practically. We review published reports of high accuracy gravimetry and give examples of relative uncertainties in the composition of standards approaching 1 part-per-million in the best cases and in the range of 100 to 1000 parts-per-million more typically.

Application of least-squares as, for instance, in curve fitting is an important tool of data analysis in metrology. It is tempting to employ the supplement 1 to the GUM (GUM-S1) to evaluate the uncertainty associated with the resulting parameter estimates, although doing so is beyond the specified scope of GUM-S1. We compare the result of such a procedure with a Bayesian uncertainty analysis of the corresponding regression model. It is shown that under certain assumptions both analyses yield the same results but this is not true in general. Some simple examples are given which illustrate the similarities and differences between the two approaches.

One of a set of metal–carbon eutectic cells (a Pd–C cell, 1765 K) manufactured by NPL and used for a previous comparison of temperature scales with NIST has been investigated at INRIM. There it was implemented in two different furnaces, namely a single- and a three-zone, and measured with a standard radiation thermometer operating at 900 nm and 950 nm. Both ITS-90 and thermodynamic melting temperatures of the cell were determined by means of an extrapolation approach. The thermodynamic temperature differs by only −0.31 K from the NIST value whereas the ITS-90 temperature differs by only −0.46 K from the NPL value. The agreements, within the combined expanded uncertainties, are particularly significant, because of the different approach followed at INRIM, namely the extrapolation of multi-fixed-point scales (n = 3 and n = 4), as compared with a direct radiometric method at NIST and an ITS-90 realization traceable to the gold point at NPL.

The Bureau International des Poids et Mesures (BIPM), Sèvres, France, hosted the 7th International Comparison of Absolute Gravimeters (ICAG) and the associated Relative Gravity Campaign (RGC) from August to September 2005.

ICAG 2005 was prepared and performed as a metrological pilot study, which aimed:

(1) To determine the gravity comparison reference values;

(2) To determine the offsets of the absolute gravimeters; and

(3) As a pilot study to accumulate experience for the CIPM Key Comparisons.

This document presents a complete and extensive review of the technical protocol and data processing procedures. The 1st ICAG–RGC comparison was held at the BIPM in 1980–1981 and since then meetings have been organized every 4 years.

In this paper, we present an overview of how the meeting was organized, the conditions of BIPM gravimetric sites, technical specifications, data processing strategy and an analysis of the final results. This 7th ICAG final report supersedes all previously published reports.

Readings were obtained from participating instruments, 19 absolute gravimeters and 15 relative gravimeters. Precise levelling measurements were carried out and all measurements were performed on the BIPM micro-gravity network which was specifically designed for the comparison.

We report on a successful bilateral intercomparison between the Physikalisch-Technische Bundesanstalt (PTB) and the National Institute of Standards and Technology (NIST). In both laboratories deuterium lamps were calibrated using the calculability of synchrotron radiation. However, the methods applied in the two laboratories differed significantly. Whereas the calibrations at PTB were performed in vacuum and led to spectral radiant intensities, the measurements at NIST were done in air and resulted in spectral irradiances. Therefore, for this bilateral comparison we not only proved the equivalence of the two measurement procedures, but also the validity of the conversion between the different spectro-radiometric quantities. This successful comparison re-establishes the usefulness of deuterium lamps as transfer standards in the ultraviolet spectral range.

The expression of uncertainty in the field of metrology is based, since 1993, on the Guide to the Expression of Uncertainty in Measurement. According to this, 'it is assumed that the results of a measurement have been corrected for all recognized significant systematic effects'. Since the International Temperature Scale of 1990 considers the substances used for the realization of the 'fixed points' to be ideally pure, to fully implement the intent of the GUM corrections should be applied for any chemical impurities that affect the value of the measurand. The present paper aims at reviewing an aspect that must be tackled to arrive to reliable and scientifically sound corrections: the use of an appropriate statistical method. In addition to the SIE, OME and hybrid methods recommended by the CCT, two new approaches are proposed in this paper, called one-sided OME and Average Overall Estimate (AOE). They are illustrated and their merits compared with the previous one, by applying them for the correction of the measured values of the triple-point temperature of the four gaseous substances (hydrogen, neon, oxygen and argon) used for the realization of the ITS-90 reference points in the range 13.8 K to 273.16 K. Some suggestions are drawn from the resulting evidence.

An interlaboratory comparison of the melting temperatures of three palladium–carbon (Pd–C) eutectic fixed-point cells of different designs and usable for the calibration of thermocouples was performed at NIM. Two Pt/Pd thermocouples were constructed for this particular purpose. One of the Pd–C eutectic cells is of conventional design and size; the two other cells are miniature fixed-point cells of different designs. The melting temperature of the conventional cell, PdC1-NIM, was slightly higher than the melting temperatures of the miniature cells by about 160 mK (PdCM2 of PTB) and 290 mK (PdC2-NIM). The melting temperatures of the two miniature Pd–C cells agree within their measurement uncertainties for k = 2 of about 135 mK. Furthermore, a new aspect of leakage effects often observed in the use of Pd–C cells is presented.

We evaluate the distributed cavity phase (DCP) and microwave lensing frequency shifts, which were the two largest sources of uncertainty for the NPL-CsF2 caesium fountain clock. We report measurements that confirm a detailed theoretical model of the microwave cavity fields and the frequency shifts of the clock that they produce. The model and measurements significantly reduce the DCP uncertainty to 1.1 × 10⁻¹⁶. We derive the microwave lensing frequency shift for a cylindrical cavity with circular apertures. An analytic result with reasonable approximations is given, in addition to a full calculation that indicates a shift of 6.2 × 10⁻¹⁷. The measurements and theoretical models we report, along with improved evaluations of collisional and microwave leakage induced frequency shifts, reduce the frequency uncertainty of the NPL-CsF2 standard to 2.3 × 10⁻¹⁶, nearly a factor of two lower than its most recent complete evaluation.

An absolute gravimeter allows us to determine the local value of gravity, which makes its accuracy assessment challenging. The instrumental offsets are classically estimated by performing comparisons of the results obtained by a set of instruments measuring at the same location but at different epochs (measuring at the same place and epoch is physically impossible). Such intercomparison campaigns have been done a few times since 1980. In this paper, we discuss the method of data processing used for those comparisons. We demonstrate that one of the methods used is inadequate, as it underestimates the dispersion of the instrumental offsets, which is the only reliable quantity that can be obtained from such a comparison. We also propose a new criterion, based on the minimization of the L1 norm of the offsets, for fixing the constant of the ill-conditioned problem, which we show to be statistically more precise than the one classically used.

We present a numerical method, based on a FEM simulation, for the determination of the gravitational field generated by massive objects, whatever geometry and space mass density they have. The method was applied for the determination of the self-gravity effect of an absolute cold atom gravimeter which aims at a relative uncertainty of 10⁻⁹. The deduced bias, calculated with a perturbative treatment, is finally presented. The perturbation reaches (1.3 ± 0.1) × 10⁻⁹ of the Earth's gravitational field.

We have analysed the uncertainty of measured electron density using a phase-resolved wave cutoff probe and compared it with a previous cutoff probe. To determine the cutoff frequency (i.e. plasma frequency), we used the phase difference between two antennas of the cutoff probe and its slow time modulation instead of the transmittance used in the previous cutoff method. The phase-resolved cutoff method gives remarkable results under wide discharge conditions. The uncertainty of the phase-resolved cutoff method is much better than the previous cutoff method.

Over the last 15 years, research in ac Josephson voltage metrology has focused on two fundamentally different systems: the programmable and the pulse-driven Josephson voltage standards (JVSs). This paper reports the first high precision comparison between the two types of JVS. The METAS programmable voltage standard was moved from Switzerland to the Netherlands to be compared with the Dutch pulse-driven system during four days in November 2010. After a careful investigation of the systematic sources of errors, the comparison was made at a frequency of 500 Hz and an rms amplitude of 104 mV. At that level, the voltage difference measured between the fundamental frequency components of the two standards was −0.18 ± 0.26 µV V⁻¹ (k = 2), showing an excellent agreement between the two systems.

An intercomparison of the absorbed dose rate in tissue, , at radiation protection levels for beta dosimetry was performed between two national metrology institutes, the D I Mendeleyev Institute for Metrology (VNIIM) in St Petersburg (Russia) and the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig (Germany), from 2009 to 2010. For this comparison, radiation sources of both institutes were calibrated using the primary standard measuring devices (extrapolation chambers) of both institutes, i.e. no transfer instrument was used as both primary standards were directly compared. The values of the absorbed dose rates in tissue agree within 1.2% for two different ⁹⁰Sr/⁹⁰Y sources, within 1.0% for one ⁸⁵Kr source and within 1.5% and 4.2% for two different ¹⁴⁷Pm sources. All these deviations are within 1 to 2 times the corresponding standard deviations.

Simple expressions are obtained for the measurement uncertainty of complex quantities when no information about phase is available. Three different cases are considered: a known magnitude, an upper bound on the magnitude and an estimate of the magnitude with an associated uncertainty. An expression is also given for the uncertainty of a product when there is no information about the phase of the factors. These results are applied to simple examples of power, attenuation and impedance measurements. The performance of uncertainty calculations is checked by observing the coverage of uncertainty statements achieved under simulated measurement conditions.

Supplement 1 to the GUM (GUM-S1) produces an arbitrarily large sample from a probability distribution for the measurand which is used for the calculation of an estimate and its associated uncertainty. In the presence of Gaussian observations on one or several input quantities this distribution is equivalent to the Bayesian posterior obtained for a particular choice of a non-informative prior. Recently, a reference prior under partial information was proposed as an alternative non-informative prior in this context. Since for non-linear problems different results are obtained with this prior than by application of GUM-S1, the question arises whether GUM-S1 should actually be recommended for non-linear problems.

We address this question by comparing the properties of the GUM-S1 distribution and the posterior distribution obtained by the proposed alternative prior. The comparison is supplemented by also considering a hybrid prior which assigns a constant prior for the measurand. We specify the conditions when the same results are reached. While the GUM-S1 distribution is always proper, we show that the proposed reference prior under partial information and the hybrid prior can fail to yield a proper posterior. On the basis of this (most important) criterion we can already recommend application of GUM-S1. Finally, we show that the prior underlying GUM-S1 can be derived as a (conditional) data-translated likelihood prior that exploits the symmetry and invariance of the considered likelihood function.

The effects of different working conditions and specifically of different velocity profiles on the output of a commercial cup anemometer were analysed experimentally. A simple mathematical model is also presented and provides results in line with the experiments. Results show that a cup anemometer with certain geometrical features can be calibrated through a rotating drag rig by correcting for the bias on the instrument output. The increase in uncertainty caused by this systematic correction was evaluated and applied to the results. The correction was validated by checking the compatibility of calibrations of a cup anemometer at the rotating rig and in a wind tunnel.

Deformational characteristics of a controlled-clearance piston-cylinder (CCPC) have been evaluated to precisely estimate the pressure dependence of its effective area. Among the experimentally accessible characteristics, the jacket pressure coefficient d, which denotes the relative change in the effective area due to applied jacket pressure p_j, is examined in this paper. Two methods for precisely determining d at pressures up to 1 GPa are proposed. One is a comparative method that uses a set of a pressure balance and a multiplier as the tare gauge. The other is a new method that uses precise pressure transducers as monitoring devices. Both p_j and weights loaded on the CCPC are changed so that the pressure generated by the CCPC remains constant, which is monitored by the transducers. d is estimated by the relative change in the weights loaded on the CCPC itself. Using the two methods, d for a 1 MPa kg⁻¹ CCPC is measured at pressures up to 1 GPa. At each system pressure, d obtained by each method is approximated by a linear function of p_j. The consistency of the fit values of d by the two methods is confirmed. The method using pressure transducers as monitoring devices is advantageous in terms of efficiency and operability especially at higher pressures.

The throughput performance of a ten-element transmission trap detector has been investigated at the laser wavelength 647.1 nm. The input beam of 1/e² diameter 1.9 mm was studied at the output of the device in both s and p polarization states. The beam diameter was measured to change by less than 0.1 mm after undergoing ten internal reflections within the transmission trap detector for both polarization states of the incoming beam. The transmitted beam was observed to maintain a Gaussian distribution profile of the optical power intensity along the propagation direction, when compared with that of the input beam.

An Elekta Synergy clinical linac facility is now in routine use at the National Physical Laboratory (NPL). For the purpose of therapy-level dosimetry, this has replaced the NPL research linac, which is over 40 years old, and in which the NPL absorbed dose primary standard for high-energy photons was established. This standard has been disseminated to clinical beams by interpolation of the calibration factor as a function of tissue phantom ratio TPR_20/10. In this work the absorbed dose standard has been commissioned in all the beams produced by the Elekta Synergy linac. Reference standard ionization chambers have been calibrated in terms of absorbed dose to graphite and this calibration has been converted to one in terms of absorbed dose to water. The results have been combined with the calibration in ⁶⁰Co γ-rays to obtain measured values for the quality-dependent correction, k_Q, for these reference standard chambers used in the Elekta beams. The resulting data are consistent with the interpolated k_Q to within 0.4%, which is less than the combined standard uncertainty of k_Q, 0.56%.

An intercomparison of the melting temperatures of four Pd–C eutectic fixed-point cells was performed using four Pt/Pd thermocouples. The cells are designed for the calibration of thermocouples and were constructed in the participating laboratories of NPL, LNE, NMIJ and PTB. The measurements were performed in four different high-temperature furnaces but by applying the same measurement procedure. In spite of slightly different cell designs and different material sources, the melting temperatures of three of the four Pd–C cells (NPL, LNE and NMIJ) agreed very well within their expanded uncertainties of k = 2.

Within an international project directed to the new definition of the base unit kelvin, the Boltzmann constant k has been determined by dielectric-constant gas thermometry at PTB. In the pressure range from about 1 MPa to 7 MPa, 11 helium isotherms have been measured at the triple point of water (TPW) by applying a new special experimental setup consisting of a large-volume thermostat, a vacuum-isolated measuring system, stainless-steel 10 pF cylindrical capacitors, an autotransformer ratio capacitance bridge, a high-purity gas-handling system including a mass spectrometer, and traceably calibrated special pressure balances with piston–cylinder assemblies having effective areas of 2 cm². The value of k has been deduced from the linear, ideal-gas term of an appropriate virial expansion fitted to the combined isotherms. A detailed uncertainty budget has been established by performing Monte Carlo simulations. The main uncertainty components result from the measurement of pressure and capacitance as well as the influence of the effective compressibility of the measuring capacitor and impurities contained in the helium gas. The combination of the results obtained at the TPW (k_TPW = 1.380 654 × 10⁻²³ J K⁻¹, relative standard uncertainty 9.2 parts per million) with data measured earlier at low temperatures (21 K to 27 K, k_LT = 1.380 657 × 10⁻²³ J K⁻¹, 15.9 parts per million) has yielded a value of k = 1.380 655 × 10⁻²³ J K⁻¹ with uncertainty of 7.9 parts per million.

This paper reports on work to improve mass stability when transferring platinum/iridium, stainless steel and silicon artefacts between air and vacuum using inert gas (argon) as a transfer/storage medium. Work is underway to redefine the kilogram in terms of a fundamental constant of nature and this will involve realizing a kilogram in vacuum. The development of an effective traceability link to this kilogram in vacuum is therefore essential for dissemination of the mass scale in the future. The work reported here investigates the effect of cycling artefacts between air and vacuum compared with cycling artefacts between argon and vacuum. Additionally, the effect of transferring artefacts between short-term storage in air compared with short term-storage in argon is investigated. The results presented demonstrate improved stability in the artefacts that are transferred between storage in argon and vacuum compared with those that are transferred between storage in air and vacuum.

With ⁸⁷Sr atoms confined in a one-dimensional optical lattice, the frequency of the optical clock transition 5s²¹S₀–5s5p ³P₀ has been determined to be 429 228 004 229 872.9(5) Hz. The transition frequency was measured with the help of a femtosecond-frequency comb against one of Physikalisch-Technische Bundesanstalt (PTB's) H-masers whose frequency was measured simultaneously by the PTB Cs-fountain clock CSF1. The Sr optical frequency standard contributes with a fractional uncertainty of 1.5 × 10⁻¹⁶ to the total uncertainty. The agreement of the measured transition frequency with previous measurements at other institutes supports the status of this transition as the secondary representation of the second with the currently smallest uncertainty.

As they are light, thin, rollable, break-resistant, and have fewer limitations on space, flexible components, especially flexible displays, are highly attractive for next generation electronic products. Curved is the most common shape for current flexible products. Two methods for measuring the luminance distribution of curved surface sources are investigated in this paper, including the theoretical analysis, numerical simulation, experiment and uncertainty analysis. The luminance measurement results of flexible sources not only depend on the photometric characteristics of the sources themselves, but also depend on the measurement method, such as the setting of the measuring instrument and the measurement position. The results of numerical simulation show that the more the source is unlike a Lambertian source or the smaller the curvature of the source, the greater the effect of the measurement method on the measurement results. Theoretically, the luminance distribution from one measurement method can be estimated from the other method by multiplying by conversion factors. An experiment is performed to verify the possibility of converting and also verify the correction of the theoretical analysis. For precise luminance measurement, position alignment is the key factor to reduce the uncertainty. Unlike with flat surface sources, the luminance measurement result for a curved surface source is strongly dependent on the measurement conditions. The currently documented standards for evaluating the optical performance of a flat surface source may not be appropriate for a flexible surface source. It is necessary to refine a new measurement provision to help the manufacturers utilize the appropriate metrology.

One of the standard methods used to measure the size of nanoparticles in aqueous solutions in situ is dynamic light scattering (DLS). The principle of this technique used to measure the real size of nanoparticles in a solution is the use of a procedure that extrapolates the apparent diffusion coefficients at different scattering angles and the sample concentration to infinite conditions. The uncertainty in the measurement is related to the extrapolating procedure used, and we have evaluated this for nanoparticles with diameters in the range 20 nm to 100 nm using the methods described in the ISO Guide to the Expression of Uncertainty in Measurement. The size of nanoparticles measured using DLS was compared with that obtained using a microscopic method, a cryo-transmission electron microscope, to check the reliability of the results obtained from the DLS measurements, which showed good agreement within the uncertainty levels evaluated.

Measurement of nanometre-sized aerosol particles is based on particle number concentration measurements. The commonly used method for providing traceability for these measurements involves charging and electrical counting of aerosol particles. This method requires that the particles are singly charged or that the average charge is exactly known, neither of which is easy to ensure. In the device called a single charged aerosol reference (SCAR), the fraction of multiply charged particles is minimal due to the novel operating principle of electrical charging and subsequent growth. In this study the SCAR was validated as a primary particle number concentration standard. The average charge of the output aerosol was evaluated for the whole operational particle size range. For this, the effect of the size distribution of the primary nanoaerosol and the output number concentration on the fraction of doubly charged and neutral particles was measured. It was found that the uncertainty caused by assuming singly charged particles is only 0.16%. A full uncertainty analysis was carried out for a condensation particle counter (CPC) calibration. According to the results, the relative expanded uncertainty of calibration was 3.0%. This represents a typical uncertainty level achieved in CPC calibrations performed with SCAR. As a result of this study, SCAR was validated as a particle number concentration standard suitable for traceable calibration of particle counting instruments in the particle size range from 10 nm to 500 nm.

In the paper by Rothleitner and Francis (2011 Metrologia48 187–95) the correction due to the finite speed of light in absolute gravimeters is analysed from the viewpoint of special relativity. The relativistic concepts eventually lead to the two classical approaches to the problem: analysis of the beat frequency, and introduction of the retarded times. In the first approach, an additional time delay has to be assumed, because the frequency of the beam bounced from the accelerated reflector differs at the point of reflection from that at the point of interference. The retarded times formalism is equivalent to a single Doppler shift, but results in the same correction as the beat frequency approach, even though the latter explicitly combines two Doppler shifts. In our comments we discuss these and other problems we found with the suggested treatment of the correction.

In reply to the comment by Nagornyi et al we show that the introduction of a time delay after the application of a relativistic Doppler shift, as proposed by the authors, is equivalent to an introduction of a time dilation into the reference beam. This would partly cancel the effect of the Doppler shifts. We conclude that the introduction of such an additional time delay is incorrect.

We discuss the treatment of distributed cavity phase, microwave lensing and microwave leakage in the paper by Ovchinnikov and Marra (2011 Metrologia48 87–100). The paper neglects the potential distributed cavity phase shifts from linear phase gradients and quadrupolar phase variations. Only azimuthally symmetric phase variations were analysed and an incorrect model was used for these. The paper also omits an uncertainty due to microwave lensing, which must be included. Finally, we describe additional measurements that could clarify the model used to analyse the frequency shifts due to microwave leakage.