Table of contents

In March 2009, the Consultative Committee for Electricity and Magnetism (CCEM) reviewed and re-endorsed its recommendations originally proposed during its 25th meeting (April 2007) for changes in the SI electrical units (Recommendation E-1). Among its considerations, the document stated that the representation of the volt using the Josephson effect and the conventional value of the Josephson constant, K_J−90, has provided practical, accessible, reproducible, low noise and highly linear references worldwide since 1990. We summarize the measurement results of comparisons between Josephson voltage standards that help support this statement, especially concerning the accuracy and the simplicity of the Josephson relationship between voltage and frequency. We also detail a list of influence parameters and the ranges over which the Josephson relationship has been tested.

Supplement 1 to the Guide to the Expression of Uncertainty in Measurement states that if a best estimate and associated standard uncertainty are the only information available regarding a certain quantity, then, according to the principle of maximum entropy, a Gaussian probability distribution with support on the real line should be assigned to that quantity. This recommendation holds true if one does not know the range of the possible values of the quantity. However, usually such a range will also be known. It is shown that in this case a Gaussian distribution supported on (−∞, ∞) can be used, but only if the standard uncertainty is sufficiently small. Otherwise, the parameters of the distribution have to be computed numerically.

The ISO TS21748:2003 statement that the laboratory component of 'bias' included in the model and indicated by B in ISO 5725-2:1994 has "zero expectation" is evaluated critically. It is found that this condition should apply not to the B_k of each laboratory modelled in ISO 5725-2:1994, but to the expectation of the distribution of the B_k in a comparison when the method of choosing the participant laboratories supports the hypothesis that it becomes a 'random effect'. A few related inconsistencies are also discussed.

This paper addresses the international humidity community's need for standardization of methods for propagation of uncertainty associated with humidity generators and for handling uncertainty associated with the reference water vapour-pressure and enhancement-factor equations. The paper outlines uncertainty calculations for the mixing ratio, dew-point temperature and relative humidity output from humidity generators, and in particular considers controlling equations for a theoretical hybrid humidity generator combining single-pressure (1-P), two-pressure (2-P) and two-flow (2-F) principles. Also considered is the case where the humidity generator is used as a stable source with traceability derived from a reference hygrometer, i.e. a dew-point meter, a relative humidity meter or a wet-bulb psychrometer. Most humidity generators in use at national metrology institutes can be considered to be special cases of those considered here and sensitivity coefficients for particular types may be extracted. The ability to account for correlations between input variables and between different instances of the evaluation of the reference equations is discussed. The uncertainty calculation examples presented here are representative of most humidity calculations.

It has been argued that the probability associated with a coverage interval calculated following the procedure proposed in Supplement 1 to the GUM should be about equal to the proportion of independent intervals reckoned over time that contain the measurand (Willink 2006 Metrologia43 L39–42, Hall 2008 Metrologia45 L5–8, Possolo et al2009 Metrologia46 L1–7). The opposite point of view maintains that a coverage probability can only be interpreted as the degree of belief in the quoted interval containing the unknown value of the measurand (Lira 2008 Metrologia45 L21–3). In this paper, two simple examples are presented to reinforce the latter interpretation.

Since the quantum Hall resistance (QHR) measured with alternating current (ac) has reached the state of an excellent quantum standard of impedance, we have realized a quadrature bridge with two ac QHRs to accurately calibrate capacitance standards in terms of the SI value of the von-Klitzing constant, without the need for any calculable artefact. The advantages of the realized measuring chain, experimental tests of the coaxial ac bridges involved and the achieved relative uncertainty of 6 × 10⁻⁹ (k = 1) are discussed.

Caesium-fountain frequency standards realize the second in the International System of Units with a relative uncertainty approaching 10⁻¹⁶. Among the main contributions to the accuracy budget, cold collisions play an important role because of the atomic density shift of the reference atomic transition. This paper describes an application of the Bayesian analysis of the clock frequency to estimate the density shift and describes how the Bayes theorem allows the a priori knowledge of the sign of the collisional coefficient to be rigorously embedded into the analysis. As an application, data from the INRIM caesium fountain are used and the Bayesian and orthodox analyses are compared. The Bayes theorem allows the orthodox uncertainty to be reduced by 28% and demonstrates that it is an important tool in primary frequency metrology.

This paper describes the uncertainty contribution of nine different phase-shifting algorithms (PSAs) to a gauge block calibration evaluated using a Monte Carlo method. The phase map and its standard deviation, codified in the output distribution obtained with each PSA, are used as input parameters in the exact fractions method for the final calculation of the gauge block length. Results obtained show the behaviour of each PSA versus different types of error sources. Uncertainty evaluation fits well to a Gaussian distribution for all algorithms tested with more than 10⁴ trials and the central limit theorem is satisfied. As expected, the Symmetric 5 + 1 PSA shows the best behaviour with the lower uncertainty contribution and appears among PSAs used as the best algorithm for this technical application. As the selected PSAs are representative for the main PSA families, the protocol employed can be used for any other specifically tailored algorithm.

The paper presents modifications of the sine-approximation method (SAM) specified in ISO 16063-11:1998, focusing on two of the various well-established versions: (i) SAM version using heterodyne quadrature signals (HQS) and (ii) SAM version using time interval analysis (TIA), and their implementation in the national medium-frequency vibration standard of NIM, China. For the HQS version, modified techniques and procedures have been introduced applicable to suppress disturbing effects from frequency instability of the carrier signal and from displacement drift. For the TIA version, a new algorithm has been developed for which the frequency demodulation is based on the estimation of time intervals between neighbouring peaks and valleys of the laser Doppler interferometer instead of successive positive or negative zero crossings. A spline approximation has been implemented allowing relatively slow sampling rates (e.g. 5 MS s⁻¹) to be applied. The low requirements on hardware techniques allow primary vibration calibrations with high accuracy to be performed efficiently and cost effectively. Some results of investigations of the modified versions of SAM are demonstrated. The results achieved by these modified SAM versions are compared with each other and with PTB results measured within the complementary key comparison CCAUV.V-K1.1 piloted by PTB from 2006 to 2007.

In this paper, the aspects of gas-operated pressure balances that affect their performance are discussed. These aspects include both the features that make gas-operated pressure balances suitable for use as pressure standards and the factors that must be managed to achieve good performance. As key features, gas-operated pressure balances are pressure generators, have excellent relative short-term stability (∼5 × 10⁻⁹) and long-term stability (∼1 × 10⁻⁶), and can be used as primary standards. Factors to manage include harmonic oscillation of the piston in the cylinder, pressure balance temperature and operating height, and geometric imperfections. Three applications are used to illustrate the performance aspects of gas-operated pressure balances: a primary standard, a standard for differential pressure from <1 Pa to >1000 Pa and a standard for absolute pressure from <10 Pa to 10 kPa.

When identical readings are independently obtained under low instrument resolution d, so that a reading x implies an actual value between x − (d/2) and x + (d/2), the method of fiducial inference yields the result that the commonly assumed standard uncertainty applies only to the case where the input standard deviation is known to be very low, ≈ 0.03d or less. The standard uncertainty is the standard deviation of a rectangular distribution whose base is of length d. If there is little knowledge of the input standard deviation, the standard uncertainty is closer to . The standard uncertainty is the standard deviation of a symmetrical (isosceles) triangular distribution whose base is of length d. This latter standard uncertainty increases above as the number of identical independent readings decreases.

Considerations have been made to derive a correction for the diameter measurements of a sphere by means of a special sphere interferometer. This correction is caused by the finite diameter of the light source acting as the entrance 'pinhole' aperture in the light collimating system. The finite diameter has the effect that the wave which is incident on the sphere is a superposition of spherical waves which are slightly inclined with respect to each other. The resulting correction is essential for high accuracy dimensional measurements of silicon spheres to determine the Avogadro constant—a new determination of which is a contribution to a new definition of the kilogram.

At the angle metrology laboratory of the Istituto Nazionale di Ricerca Metrologica (INRiM, formerly IMGC), an instrument to generate very small angles has been recently developed. It is a sine-bar angle generator based on an elastic hinge and a piezocapacitive device. The facility can be used to calibrate precise angle measuring instruments (levels, autocollimators, etc) in a range of 120 µrad with an uncertainty of about 20 nrad and a sensitivity of fractions of a nanoradian. The working principle and metrological characterization are presented.

Harmonized sample pre-treatment is an essential first step in ensuring quality of measurements as regards repeatability, interlaboratory reproducibility and commutability. The development of standard preparation methods for single-wall carbon nanotube (SWCNT) samples is therefore essential to progress in their investigation and eventual commercialization. Here, descriptions of sample preparation and pre-treatment for the physicochemical characterization of SWCNTs are provided. Analytical methods of these protocols include scanning electron microscopy (dry, wet), transmission electron microscopy (dry, wet), atomic force microscopy, inductively coupled plasma mass spectrometry, neutron activation analysis, Raman spectroscopy (dry, wet), UV–Vis–NIR absorption and photoluminescence spectroscopy, manometric isothermal gas adsorption and thermogravimetric analysis. Although sample preparation refers to these specific methods, application to other methods for measurement and characterization of SWCNTs can be envisioned.

This paper presents a prototype real-time clock ensemble system that utilizes a Kalman filter-based ensemble algorithm to combine remote clocks linked via a real-time GPS carrier-phase time transfer network. The calculated ensemble clock is realized by the use of an optimal control technique, where emphasis is placed on seeking a balance between the short-term stability of a hydrogen maser clock and the long-term stability of the ensemble clock. The performance of the system is investigated by conducting a five-month long ensemble experiment based on local realizations of UTC from four timing laboratories, and the frequency stability of the real-time ensemble time scale as well as its realizations are assessed with reference to UTC.

A measurement bench for colorimetric parameters (chromaticity coordinates, correlated colour temperature and colour rendering indices) of LED lightings is described. The analysis of uncertainty sources on relative spectral measurements is exposed. Calculation results of uncertainties, by Monte Carlo simulations, for spectral measurements as well as colorimetric parameters are presented.

In table 2 of this paper, the values of the normal effective emissivity are presented, instead of values of the hemispherical effective emissivity for an isothermal cavity with β = 30°. Here, we present the corrected portion of table 2. Also, in figure 5 (right-side plot) and figure 6 (left column, second row), instead of a cavity with β = 58°, the plots for a cavity with slightly different geometric parameters are shown. We show here the corrected map of reflections and a three-dimensional plot of the distribution of the local normal effective emissivity.

The corrected portions of table 2, figure 5 and figure 6 are given in the pdf file.

The PDF file provided contains web links to all articles in this volume.