Table of contents

We briefly review the recent experimental results on possible variations of the fine structure constant α on the cosmological time scale and its position dependence. We outline the theoretical grounds for the assumption that α might be variable, mention some phenomenological models incorporating a variable α into the context of modern cosmology and discuss the significance of possible α variations for theoretical and practical metrology.

Fotowicz (2006 Metrologia43 42–5) presented an approximation for computing the coverage interval of the convolution of two Student's t distributions. This approximation appeared to perform well for a limited range of values of the degrees of freedom. In this letter, we provide an eight-line program for exact computation of the coverage interval with no limitations. Several advantages of our approach are noted.

WC–C, Cr₃C₂–C and Mn₇C₃–C peritectic systems were investigated for their potential of serving as high-temperature reference points in thermometry. Mixtures of high-purity graphite powder with W, Cr and Mn powder of 99.99%, 99.9% and 99.95% purity by mass, respectively, were placed in graphite blackbody crucibles and melting/freezing plateaus were observed by means of a radiation thermometer. The observed melting temperatures were 2749 °C (WC–C), 1826 °C (Cr₃C₂–C) and 1331 °C (Mn₇C₃–C), with a repeatability—in each case—of 0.02 K. The melting range for WC–C and Cr₃C₂–C peritectics was roughly 0.1 K. WC–C showed a flat freezing plateau that agreed with the melting plateau within the repeatability. The three fixed points are possible candidates, like the metal (carbide)–carbon eutectic fixed points, in the realization of an improved high-temperature scale above the copper point.

Measurement of the thickness of SiO₂ films on crystalline Si substrates was the subject of the key comparison (K-32) of the Surface Analysis Working Group of the Consultative Committee for Amount of Substance. X-ray photoelectron spectroscopy (XPS) gave the most reproducible results that are consistent with other reflectivity based methods. In addition, XPS is free from surface contamination effects. However, the emission angle of photoelectrons is one of the main sources of the uncertainty in the measured thickness. In this report, we propose a simple and reliable procedure to determine the surface normal for accurate control of the emission angle using an amorphous SiO₂ overlayer on an amorphous Si substrate. The surface normal can be accurately determined from the condition that the estimated thickness of a SiO₂ overlayer on an amorphous Si substrate measured must be the same for different emission angles. With the proposed calibration procedure, the surface normal can be determined precisely and the uncertainty of the electron emission angle can be evaluated.

Calibrated standard platinum resistance thermometers (SPRTs) are used to realize the International Temperature Scale of 1990 (ITS-90) from 13.8033 K to 1234.93 K. The SPRTs are calibrated at a series of fixed points, each assigned a temperature on the ITS90, by measuring the ratios of the SPRT resistances at those temperatures to that at the triple point of water (TPW). For realizing the scale with a calibrated SPRT, a user measures the resistance ratio at the unknown temperature and uses ITS-90-defined equations to interpolate between fixed points. The uncertainty of the SPRT temperature is therefore largely influenced by the propagation of fixed-point resistance-ratio uncertainties. In this paper, we rigorously derive the equations for calculating these uncertainties for a variety of circumstances and we use software tools written by us to perform these calculations using realistic uncertainties for fixed points and other input parameters. For properly calculating the standard uncertainty for SPRT realization of the ITS-90, correlations between the input quantities must be considered, in particular those involving measurement of the TPW resistance. The proper calculation depends on three factors involving SPRT use and calibration. The different combinations of these factors result in six different equations for calculating the realization uncertainty. We derive these six equations, specify the conditions of their use and discuss the relevant uncertainty components for each of them. We also compare the results of these equations with those of two approximations that may be used for calculating the standard uncertainty and explain the conditions under which the simpler approximations agree with the more detailed calculations. Because these calculations are complicated, we are making our software tools available upon request to the user community.

We have performed calculations to study ITS-90 non-uniqueness from subrange inconsistencies over the range 24.5561 K to 273.16 K, where the scale is defined by an interpolating platinum resistance thermometer (PRT) that is calibrated via sets of defined fixed points. For this work, subrange inconsistency calculations have been performed on eighteen PRTs; fourteen are standard PRTs and four are miniature PRTs. The inconsistency uncertainties, which result from propagation of fixed-point uncertainties, have also been calculated. The calculations show that PRT subrange inconsistencies in the temperature region studied can be as large as 1 mK. We have also studied possible correlations between PRT subrange inconsistencies and other PRT properties/parameters that are simpler to determine; these studies show that there is a correlation between the average magnitude of the inconsistencies and the value of a certain calibration coefficient. Finally, for the range studied we have used a statistical analysis on the inconsistencies of the PRT ensemble to calculate a standard uncertainty to the ITS-90 temperature T₉₀ due to the inconsistencies. Over the temperature intervals 25 K ⩽ T₉₀ ⩽ 50 K and 100 K ⩽ T₉₀ ⩽ 200 K, this uncertainty dominates those propagated from fixed-point uncertainties.

'The present system design' summarizes the theoretical model, the physical realization and the operational analysis of the automatic cavity frequency stabilization system based upon square wave modulation of the resonance frequency of the cavity in the atomic hydrogen maser. The effect produced on the maser output frequency by various perturbations of the cavity frequency is calculated and the theoretical results are compared with the experimental measurements. 'Possible improvements' describes an improved design of the cavity frequency control system. An analysis of the new servo response to cavity frequency perturbations is given and the improvement expected in hydrogen maser frequency stability compared with previous maser performance is discussed.

A non-contact technique associated with a circle least-squares method allows one to determine the areas of the apertures used in radiometric and photometric measurements. Uncertainty evaluation in these non-contact aperture area measurements is presented.

We present a determination of Planck's constant from radiometric measurements using an optical detector operating in photon counting mode and two absolute radiometric methods: a source of correlated photons and an electric substitution radiometer. This measurement allows one to demonstrate the consistency of the two radiometric methods.

For high-purity metal fixed points the sum of individual estimates (SIE) and the overall maximum estimate (OME) have been introduced as tools to estimate the uncertainty in the correction for the effect of impurities. In this paper we investigate the feasibility of applying these tools to metal–carbon (M–C) eutectics as well on the basis of material collected for the eutectics Fe–C and Co–C. This would be of interest since it would obviate the need for modelling the full freezing or melting curve, which requires detailed knowledge of the material properties involved. For SIE we need only the liquidus slopes pertinent to the detected impurities, whereas for OME under certain conditions detailed knowledge of the impurity parameters would not be needed at all.

In attempting to develop a capacitance standard based on the charge of the electron, one question which has been open for many years is the frequency dependence of the vacuum-gap cryogenic capacitor; the crucial difficulty has been: How do we measure frequency dependence down to 0.01 Hz? In this paper, we succeed in putting an upper bound on the frequency dependence, from 0.01 Hz to 1 kHz, of about 2 × 10⁻⁷. We do this by considering a model for the dispersion in the surface insulating films on the surface of the Cu electrodes; the crucial prediction of this model is that the dispersion falls to very low values at low temperatures. By measuring the frequency dependence over a restricted range of frequencies, we have verified this prediction, and thus provide adequate support to conclude that the model is correct. We also point out that, independent of the capacitance standard, this cryogenic capacitor provides a frequency-independent standard for measurements in fields such as the low-temperature dynamics of amorphous materials.

Motivated by emerging needs for accurate force measurements in the nanotechnology and biophysics areas, we present an atomic force microscope (AFM) cantilever calibration system, the 'nano force calibrator' (NFC), consisting of a microbalance and a precision translation stage. Calibration using the NFC has proved to be a reliable and accurate method through a series of experiments with a commercial piezoresistive AFM cantilever. In these experiments, linearity, repeatability and reproducibility of measurements were investigated along with the effects of calibration conditions, such as orientation of the cantilever and temperature. Uncertainty analysis shows that the stiffness and force sensitivity are determined to be 3.385 N m⁻¹ and 0.6490 µN Ω⁻¹, which are traceable to the Système International d'Unités (SI units). The relative standard uncertainties of both the stiffness and sensitivity are approximately 0.4% or conservatively 0.5%.

We made an analysis of uncertainty propagation in parameter estimation when the cost function minimization leads to a set of non-linear equations. In our study, which concerns an uncertainty-propagation law independent of any specific minimization algorithm, we review the relationship between the Hessian of the cost function and the estimate uncertainty, as well as the reasons supporting their identification. We show that the uncertainty expressed on this basis could lead to accuracy overestimation.

Uncertainties in the distribution temperature (DT) and correlated colour temperature are estimated for common sources and typical measurement uncertainties of a spectral transfer from a reference lamp. Uncertainty sensitivity coefficients for both parameters in terms of measured values of spectral irradiance are derived using a generalized matrix inverse. The uncertainty values are compared with differences in the source temperature parameters. DT is calculated using the CIE definition; shifts in DT due to the alternative of a direct fit of Planck's distribution, and to including weights in the process, are compared with the estimated uncertainties.

In this paper, it is shown that a quantum Hall resistor (QHR) which exhibits a proportionality relationship between the deviation of the Hall resistance from R_K/i and the ac dissipation in the system, represented by ρ_xx, can be used as a primary standard of ac resistance. As an example, a calculable quadrifilar resistor was calibrated against the QHR at kilohertz frequencies. The agreement between the calibration using the QHR and the calculated frequency dependence of the quadrifilar resistor is better than 4 parts in 10⁸ at 1 kHz. This result is achieved despite the frequency and current dependence of the ac-QHR. The most important criterion to achieve accurate measurements using an ac-QHR standard is to extrapolate the value of the Hall resistance to zero dissipation.

The set standard deviation, repeatability and offset of absolute gravimeter A10-008 were assessed at the Walferdange Underground Laboratory for Geodynamics (WULG) in Luxembourg. Analysis of the data indicates that the instrument performed within the specifications of the manufacturer. For A10-008, the average set standard deviation was (1.6 ± 0.6) µGal (1Gal ≡ 1 cm s⁻²), the average repeatability was (2.9 ± 1.5) µGal, and the average offset compared to absolute gravimeter FG5-216 was (3.2 ± 3.5) µGal.

This paper discusses the issue of repeated versus non-repeated measurements on standards. Starting from the general issue of replication of measurement operations, we consider the consequences of the differences that these two types of measurements entail in the comparison of standards. We look at MRA key comparisons (KCs) as a specific case. Recent developments seem to have somewhat obscured the fact that the replication and combination of observations is the everyday task of NMIs. Therefore, this paper first recalls the many facets of intra-laboratory measurements on standards, some not very different from the inter-laboratory exercises. The meaning of the replicated observations is analysed starting from this context. Then the issue is examined in the context of inter-laboratory comparisons, namely, in the case of KCs. Some of the consequences for the statistical treatment of repeated and non-repeated measurement data are illustrated and solutions proposed.

The ubiquitous technology of magnetic force compensation of gravitational forces acting on artifacts on the pans of modern balances and comparators has brought with it the problem of magnetic leakage from the compensation coils. Leaking magnetic fields, as well as those due to the surroundings of the balance, can interact with the artifact whose mass is to be determined, causing erroneous values to be observed. For this reason, and to comply with normative standards, it has become important for mass metrologists to evaluate the magnetic susceptibility and any remanent magnetization that mass standards may possess. This paper describes a comparison of measurements of these parameters among seventeen national metrology institutes. The measurements are made on three transfer standards whose magnetic parameters span the range that might be encountered in stainless steel mass standards.

We present accurate measurements of the triple point of nitrogen. The quality of this triple point is once more confirmed, and its temperature value is found to be T₉₀ = 63.1526 K (expanded uncertainty U = 0.30 mK, reproducibility better than 0.1 mK). This is the first direct determination of this point on ITS-90 since the introduction of the scale. This point is useful as a non-uniqueness checkpoint.

Sources of bias in the National Institute of Standards and Technology ozone Standard Reference Photometer (SRP) maintained by the Bureau International des Poids et Mesures have been investigated. A relative bias of −0.4% in the ozone mole fraction measurement caused by a temperature gradient in the gas cells of the instrument was characterized and corrected for in a modified version of the instrument. A second relative bias of +0.5% due to the multiple reflections of light within the gas cells was also corrected. The Guide to the Expression of Uncertainty in Measurement approach was used to develop an uncertainty budget for the modified SRP, including a relative value for the ozone absorption cross-section uncertainty of 2.1% (k = 2). The measurement uncertainty for the bias-corrected SRPs is enlarged compared with earlier studies, but their comparability improved.

GPS is already a main method of positioning measurement in geodesy and is applied widely in many fields. In order to maintain and ensure the accuracy of positioning, an accurate and efficient system for calibrating the GPS receivers must be established. A highly accurate GPS calibration network, tied to the ITRF coordinates of IGS stations, can be effectively used to evaluate the performance of GPS receivers. This study addresses the feasibility of establishing a system for calibrating GPS receivers and the system's traceability in metrology. Uncertainties of the GPS calibration networks were established and maintained by NML (National Measurement Laboratory, Taiwan). Furthermore, the networks are evaluated based on the method suggested by the ISO (International Organization for Standardization). The uncertainties of NML network coordinates are obtained and used as a basis for calibration. The results of the slope distances between pillars measured by the GPS processing units and the precise EDM units are discussed. Analytical results indicate that the 3D expanded uncertainty of the main station TNML of the network in the ITRF system is around 33.2 mm at the 95% confidence level. The 3D expanded uncertainties of the calibration points of the ultra-short distance network and the short distance network are evaluated to be about 2.2 mm and 3.4 mm, respectively in relation to the main station TNML at the 95% confidence level. The precision of the NML network coordinates suffices to calibrate the geodetic and navigational GPS receivers of regional users and is available through the Internet.

Eleven platinum resistance thermometers (PRT) were compared at the Al–Cu eutectic point (548.2 °C) in order to measure the non-uniqueness of ITS-90 roughly half-way between the Zn and the Al points. It turned out that the cubic deviation function describes this set of PRTs within ±0.6 mK in this temperature interval.

In addition, the measured data were used to determine the non-uniqueness and the sub-range inconsistency, using cubic and quadratic deviation functions, at the In point (156.6 °C). The non-uniqueness was found to be ± 0.26 mK, and the sub-range inconsistency ± 0.12 mK.

This paper deals with the problem of establishing degrees of equivalence for national measurement standards participating in regional key comparisons (RMO KC), with respect to a key comparison reference value (KCRV), using measurement results obtained by linking national metrology institutes (NMIs). Two types of key comparisons are considered, which differ in applying either a material measure or a measuring instrument as a travelling measurement standard.

The results obtained by linking NMIs are used to determine transformation procedures for measurement results of the RMO KC so that the transformed results can be compared directly with CIPM KC results.

Formulae are given for evaluating the degrees of equivalence of the national measurement standards of laboratories participating in the RMO KC, with respect to the KCRV, taking into account possible correlations between measurement results.