Metrologia

In the last 30 days

• Open/close Special issue on Statistical and Probabilistic Methods for Metrology

  Walter Bich and Maurice G Cox 2006 Metrologia 43 Tag this article

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  This special issue of Metrologia is the first that is not devoted to units, or constants, or measurement techniques in some specific field of metrology, but to the generic topic of statistical and probabilistic methods for metrology. The number of papers on this subject in measurement journals, and in Metrologia in particular, has continued to increase over the years, driven by the publication of the Guide to the Expression of Uncertainty in Measurement (GUM) [1] and the Mutual Recognition Arrangement (MRA) of the CIPM [2]. The former stimulated metrologists to think in greater depth about the appropriate modelling of their measurements, in order to provide uncertainty evaluations associated with measurement results. The latter obliged the metrological community to investigate reliable measures for assessing the calibration and measurement capabilities declared by the national metrology institutes (NMIs).

  Furthermore, statistical analysis of measurement data became even more important than hitherto, with the need, on the one hand, to treat the greater quantities of data provided by sophisticated measurement systems, and, on the other, to deal appropriately with relatively small sets of data that are difficult or expensive to obtain.

  The importance of supporting the GUM and extending its provisions was recognized by the formation in the year 2000 of Working Group 1, Measurement uncertainty, of the Joint Committee for Guides in Metrology. The need to provide guidance on key comparison data evaluation was recognized by the formation in the year 2001 of the BIPM Director's Advisory Group on Uncertainty. A further international initiative was the revision, in the year 2004, of the remit and title of a working group of ISO/TC 69, Application of Statistical Methods, to reflect the need to concentrate more on statistical methods to support measurement uncertainty evaluation.

  These international activities are supplemented by national programmes such as the Software Support for Metrology programme in the UK, which includes within its main themes generic items related to modelling, uncertainty evaluation and key comparisons. There are also teams concentrating on statistics within a metrology environment, the largest of which is the Statistical Engineering Division at NIST. There are, however, key pockets of mathematical and statistical expertise at all major and many of the smaller NMIs. Academia also makes considerable input to metrological thinking. The papers in this special issue reflect the above considerations—and more.

  There are several offerings relating to the GUM: (a) the manner in which the GUM is evolving, especially through Supplements to the GUM, (b) a comparison of the GUM, the GUM Supplement concerned with the propagation of distributions and Bayesian statistics, in the context of linear calibration, (c) theoretical and practical aspects of the use of a Monte Carlo method for propagating distributions, (d) the use of a generalization of the sensitivity coefficients in the GUM to correlated quantities, and (e) considerations on obtaining best estimates when the model is non-linear.

  At a more fundamental level, a systematic and versatile approach to developing the model of measurement, on which uncertainty evaluation is of course based, is presented, and a paper is included on principles of probability and statistics that promote sound decision-making.

  The evaluation of key comparison data is represented in terms of contributions relating to (a) models of key comparisons, with measures of operability and interoperability, (b) a Bayesian procedure for providing PDFs from which the measures required by the MRA can be extracted, (c) an extension of the E _n measure familiar to many metrologists, and (d) the use of the median and weighted median as the key comparison reference value in the presence of discrepant measurement results.

  The remaining contributions concern the analysis of measurement data, including spectral analysis. Covered are (a) a comparison of conventional and Bayesian approaches to the evaluation of data subject only to random effects, (b) element-wise weighted least squares and its comparison with conventionally weighted and total least squares, (c) the generalized weighted mean of correlated quantities (with an application to key comparisons), (d) the uncertainty associated with the average of autocorrelated quantities, (e) the fitting of three-dimensional geometric elements to coordinate data, (f) the fitting of calibration curves from data having general uncertainty structure, (g) the estimation of the power spectrum of clock noise, (h) Kalman filtering, also in the presence of clock noise, and (i) an improved Allan deviation-like statistic.

  The realization of such a rich issue involved considerable efforts from many contributors. Thanks are due to the former Editor, Peter Martin, who first conceived the idea of this issue, to Jeffrey Williams, the present Editor, for his support to its realization, to the authors for their contributions, and to the referees who gave their time to review and comment on the papers.

  References

  [1] BIPM, IEC, IFCC, ISO, IUPAC, IUPAP and OIML 1995 Guide to the Expression of Uncertainty in Measurement (Geneva, Switzerland: International Organisation for Standardisation) ISBN 92-67-10188-9

  [2] BIPM 1999 Mutual Recognition of National Measurement Standards and of Calibration and Measurement Certificates Issued by National Metrology Institutes (Sèvres, France: Bureau International des Poids et Mesures)

• Open/close The mole, amount of substance and primary methods

  Martin J T Milton 2013 Metrologia 50 158 Tag this article

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  This paper is an introduction to the principles developed for the application of metrology to the field of chemistry and particularly to analytical chemistry. It starts with a discussion of the mole, the base unit of the SI that is most relevant to analytical chemistry. The mole has become the subject of particular discussion recently, since the publication of proposals to re-define it along with three other base units of the SI. This discussion has also generated interest in the origin of the term ‘amount of substance’ used as the quantity for which the mole is the unit. This paper reviews the origin of this term and explains why it is not sufficient to replace it with an alternative such as a ‘number of entities’. The paper concludes with some discussion of how the mole is realized through the use of primary methods of measurement.

• Open/close The watt-balance operation: magnetic force and induced electric potential on a conductor in a magnetic field

  C P Sasso et al 2013 Metrologia 50 164 Tag this article

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  In a watt-balance experiment, separate measurements of magnetic force and induced electric potential in a conductor in a magnetic field allow for a virtual comparison between mechanical and electrical powers, which leads to an accurate measurement of the Planck constant. In this paper, the macroscopic equations for the magnetic force and the induced electric potential are re-examined from a microscopic point of view and the corrective terms due to a non-uniform density of the conduction electrons induced by their interaction with the magnetic field are investigated. The results indicate that these corrections are irrelevant to the watt-balance operation.

• Open/close A new model of fluid flow to determine pressure balance characteristics

  P Wongthep et al 2013 Metrologia 50 153 Tag this article

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  Some projects such as the EUROMET project 463 have underlined the lack of agreement between experimental measurements and calculations by the finite element method (FEM), used to determine the piston fall rate of a high-pressure balance used in primary standards. This is significant because the piston fall rate is an essential parameter to characterize experimentally the mean gap between the piston and the cylinder and to determine the effective area ( A _p) at each pressure ( p) point. By improving the method used to estimate the piston fall rate it is possible to improve the determination of the gap, the effective area and consequently the pressure distortion coefficient. One possible cause of the lack of agreement between the calculated and measured piston fall rates could be inappropriate modelling of the fluid flow. In fact, the former quasi-1D Stokes model assimilates the gap between the piston and the cylinder as formed by two parallel walls, which is an approximation. In addition, the velocity of the piston wall was neglected. In order to evaluate the influence of this model, the equations of the fluid flow are modified and are presented in this paper. Equations that were defined in a parallel-plane model are defined in an annular gap model. In addition to this, corrections due to the velocity of the piston wall are inserted. This research work is applied on a Desgranges et Huot DH 7594 piston–cylinder unit of PTB with a pressure up to 1 GPa, in the continuity of the EUROMET project 463 in order to quantify the influence of each correction that has been inserted in the new equations. This is carried out using the FEM. This analysis will allow us to evaluate the improvement of our knowledge of the behaviour of piston gauges and consequently to better evaluate the uncertainties due to the models.

• Open/close Watt balance experiments for the determination of the Planck constant and the redefinition of the kilogram

  M Stock 2013 Metrologia 50 R1 Tag this article

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  Since 1889 the international prototype of the kilogram has served as the definition of the unit of mass in the International System of Units (SI). It is the last material artefact to define a base unit of the SI, and it influences several other base units. This situation is no longer acceptable in a time of ever increasing measurement precision.

  It is therefore planned to redefine the unit of mass by fixing the numerical value of the Planck constant. At the same time three other base units, the ampere, the kelvin and the mole, will be redefined. As a first step, the kilogram redefinition requires a highly accurate determination of the Planck constant in the present SI system, with a relative uncertainty of the order of 1 part in 10 ⁸.

  The most promising experiment for this purpose, and for the future realization of the kilogram, is the watt balance. It compares mechanical and electrical power and makes use of two macroscopic quantum effects, thus creating a relationship between a macroscopic mass and the Planck constant.

  In this paper the background for the choice of the Planck constant for the kilogram redefinition is discussed and the role of the Planck constant in physics is briefly reviewed. The operating principle of watt balance experiments is explained and the existing experiments are reviewed. An overview is given of all presently available experimental determinations of the Planck constant, and it is shown that further investigation is needed before the redefinition of the kilogram can take place.

• Open/close The Refractive Index of Air

  Bengt Edlén 1966 Metrologia 2 71 Tag this article

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  Present knowledge of the refractive index of air is reviewed. Regarding the absolute values there are as yet no definite indications that the standard adopted in 1953 on the basis of Barrell and Sears' measurements should be changed, but new experiments aiming at reducing the present uncertainty of about ± 5 × 10 ^-8 would be desirable.

  Several recent investigations have contributed important new information on the dispersion of air, which has made it possible to derive an improved dispersion formula for standard air, ( n − 1) _s × 10 ⁸ = 8342.13 + 2406030 (130 − σ ²) ^-1 + 15997 (38.9 − σ ²) ⁻¹, where σ is the vacuum wave-number in μm ^-1. The deviations from the 1953 formula are small and practically negligible in most spectroscopic work.

  An equation for the dependence of refractivity on temperature and pressure based on theoretical considerations has been derived. For the range of atmospheric conditions normally found in a laboratory the equation can be approximated by the formula ( n − 1) _tp = ( n − 1) _s × 0.00138823 p/(1 + 0.003671 t), with p in torr, t in °C, and ( n − 1) _s given by the dispersion formula for standard air.

  The effect of carbon dioxide and water vapour is discussed. From Erickson's dispersion data for water vapour, combined with Barrell and Sears' absolute measurements, one obtains the equation n _tpf – n _tp = −f (5.722 − 0.0457 σ ²) × 10 ^-8 for the difference in refractive index of moist air, containing f torr of water vapour, and dry air at equal temperature and total pressure. The equation is valid for visible radiations and normal atmospheric conditions.

• Open/close Towards the redefinition of the kilogram: a measurement of the Planck constant using the NPL Mark II watt balance

  I A Robinson 2012 Metrologia 49 113 Tag this article

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  After the elimination of significant mechanical problems, the NPL Mark II moving-coil watt balance made an initial series of measurements in the period from October 2006 to March 2007. Incremental improvements were made to the apparatus in the period from June 2007 to November 2008 and measurements of the Planck constant h were made up to June 2009, with the aim of providing further information to the ongoing efforts to redefine the SI kilogram in terms of a fixed value of the Planck constant. The apparatus was sold to NRC-INMS in early 2009 and was dismantled and shipped to Canada in the period between June and August 2009.

  In June 2009, just prior to the shipment, a possible source of significant type-B uncertainty in the mass/force exchange was discovered. There was insufficient time to fully investigate and correct the effect so a component has been added to the uncertainty budget to account for its estimated magnitude. The standard uncertainty of the apparatus, without allowance for the mass/force exchange problem, is estimated to be 36 nW W ⁻¹, which represents an improvement of almost a factor of two from the previously reported uncertainty of 66 nW W ⁻¹, but, allowing for the problem, the uncertainty increases to 200 nW W ⁻¹. Further work, once the apparatus is rebuilt in Canada, should eliminate the source of the added uncertainty. The value of h calculated from the measurements made from 2006 to 2009 is 6.626 071 23(133) × 10 ⁻³⁴ J s, which represents a change of 43 nW W ⁻¹ from the value reported in 2007. The corresponding value of the Avogadro constant, N _A, is 6.022 139 78(120) × 10 ²³ mol ⁻¹.

• Open/close Temperature dependence of cavity ionization chamber response

  Chul-Young Yi and Hyun-Moon Kim 2013 Metrologia 50 146 Tag this article

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  The temperature dependence of the cavity ion chamber response was measured at room temperature in the range 17 °C to 27 °C. By analysing the variation of the ionization current with temperature produced in the cavity chamber, the temperature coefficient of the cavity chamber response was evaluated. The values were 4.1 × 10 ⁻⁴ °C ⁻¹, 4.3 × 10 ⁻⁴ °C ⁻¹ and 2 × 10 ⁻⁵ °C ⁻¹ for chambers made of C552 air equivalent plastic, polyoxymethylene and graphite, respectively.

• Open/close Dissemination of time and RF frequency via a stabilized fibre optic link over a distance of 420 km

  Łukasz Śliwczyński et al 2013 Metrologia 50 133 Tag this article

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  In this paper we present the results of our work concerning the long-distance fibre optic dissemination of time (1 PPS) and frequency (10 MHz) signals generated by atomic sources, such as caesium clocks, hydrogen masers or caesium fountains. For these purposes we developed dedicated hardware (a fibre optic system with active stabilization of the propagation delay and bidirectional fibre optic amplifiers) together with a procedure to enable calibration of the time transfer. Our laboratory measurements performed over fibre lengths of up to 480 km showed an Allan deviation of the order of 4 × 10 ⁻¹⁷, time deviation below 1 ps (both at one-day averaging) and the possibility of calibration with picosecond accuracy even for the longest from evaluated links. After successful laboratory evaluation the system was next installed on a 421.4 km long route between the Central Office of Measures (GUM) in Warsaw, Poland, and the Astrogeodynamic Observatory (AOS) in Borowiec near Poznań, Poland. Experiments comparing the UTC(PL) and UTC(AOS) atomic timescales using the fibre optic link and TTS-4 dual-frequency GNSS time transfer receivers showed that the consistency of the results is within the calibration accuracy of the GPS receivers and with much better noise performance. The field operation of the system proved its full functionality and confirmed our previous laboratory evaluation to the maximum extent possible using the methods for comparing distant clocks available at GUM and AOS.

• Open/close Phase sensitivity uncertainty in microphone pressure reciprocity calibration

  R J Jackett and R G Barham 2013 Metrologia 50 170 Tag this article

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  The calibration of laboratory standard microphones by the pressure reciprocity method, as specified in IEC 61094-2, is used throughout the world as the basis for primary measurement standards for sound pressure. While the method has long been used to determine the magnitude of the pressure sensitivity of the microphone, the phase sensitivity has until recently been overlooked, and is notable by its absence in BIPM's database of CMCs. A new BIPM key comparison is therefore addressing this by including phase calibration within its scope, and is the incentive for a systematic evaluation of the associated measurement uncertainty. The analysis presented is based on the requirements of IEC 61094-2 and makes use of modelling and experimentation to determine uncertainty in phase pressure sensitivity for type LS1 and type LS2 microphones. Linearity of phase measurement and stray capacitance are the dominant electrical components, both acting independently of frequency. The most significant acoustic components are the uncertainty in thermal diffusivity at low frequencies and microphone parameter uncertainty at high frequencies. Measurement repeatability is below the level of the type B evaluation for most of the frequency range, but at low frequencies it dominates for both microphone types. For both types of microphone the overall measurement uncertainty is estimated to be below 0.5° over the central frequency range.