In the last 30 days

• Open/close Bayesian uncertainty analysis for a regression model versus application of GUM Supplement 1 to the least-squares estimate

  Clemens Elster and Blaza Toman 2011 Metrologia 48 233 Tag this article

  Article References Full text PDF (347 KB)

  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.

• Open/close Final report on the Seventh International Comparison of Absolute Gravimeters (ICAG 2005)

  Z Jiang et al 2011 Metrologia 48 246 Tag this article

  Article References Full text PDF (2.44 MB)

  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.

• Open/close Measurement and testing of the acoustic properties of materials: a review

  Bajram Zeqiri et al 2010 Metrologia 47 S156 Tag this article

  Article References Full text PDF (776 KB)

  A review is presented of methods of measurement for a range of key acoustic properties of materials, spanning three application areas: airborne sound, underwater acoustics and ultrasound. The acoustic properties considered, primarily transmission loss (damping) and echo-reduction, are specifically important to the end application of any material. The state-of-the-art in measurement and likely future challenges are described in detail.

• Open/close A compact tensor algebra expression of the law of propagation of uncertainty

  C Bouchot et al 2011 Metrologia 48 L22 Tag this article

  Article References Full text PDF (365 KB)

  Compact expressions for the GUM's 'law of propagation of uncertainty' and its extensions, including the possible effects of corrections for non-linearity and including the effects of correlation in the variables, are obtained in terms of simple manipulations on three basic tensors: the gradient, the Hessian and the third order third derivative tensor of the measurement function. These formulae are an alternative to those involving mixed matrix and differential algebra. They provide a systematic and reproducible way to arrange the terms provided by the derivatives of various orders of a measurement function. The proposed formulae, which appear mathematically complicated, are surprisingly easy to implement in spreadsheet programs and interpreted matrix oriented programming languages. This is illustrated by means of an example of the propagation of uncertainty for the ratio of two normal and correlated variables.

• Open/close Towards a better definition of the kilogram

  Theodore P Hill et al 2011 Metrologia 48 83 Tag this article

  Article References Full text PDF (77 KB)

  It is widely accepted that improvement of the current International System of Units (SI) is necessary, and that central to this problem is redefinition of the kilogram. This paper compares the relative advantages of two main proposals for a modern scientific definition of the kilogram: an 'electronic kilogram' based on a fixed value of Planck's constant, and an 'atomic kilogram' based on a fixed value for Avogadro's number. A concrete and straightforward atomic definition of the kilogram is proposed. This definition is argued to be more experimentally neutral than the electronic kilogram, more realizable by school and university laboratories than the electronic kilogram, and more readily comprehensible than the electronic kilogram.

• Open/close International determination of the Avogadro constant

  Enrico Massa and Arnold Nicolaus 2011 Metrologia 48 Tag this article

  Article References Full text PDF (35 KB)

  This issue of Metrologia collects papers about the results of an international research project aimed at the determination of the Avogadro constant, N _A, by counting the atoms in a silicon crystal highly enriched with the isotope ²⁸Si. Fifty years ago, Egidi [1] thought about realizing an atomic mass standard. In 1965, Bonse and Hart [2] operated the first x-ray interferometer, thus paving the way to the achievement of Egidi's dream, and soon Deslattes et al [3] completed the first counting of the atoms in a natural silicon crystal.

  The present project, outlined by Zosi [4] in 1983, began in 2004 by combining the experiences and capabilities of the BIPM, INRIM, IRMM, NIST, NPL, NMIA, NMIJ and PTB. The start signal, ratified by a memorandum of understanding, was a contract for the production of a silicon crystal highly enriched with ²⁸Si. The enrichment process was undertaken by the Central Design Bureau of Machine Building in St Petersburg. Subsequently, a polycrystal was grown in the Institute of Chemistry of High-Purity Substances of the Russian Academy of Sciences in Nizhny Novgorod and a ²⁸Si boule was grown and purified by the Leibniz-Institut für Kristallzüchtung in Berlin. Isotope enrichment made it possible to apply isotope dilution mass spectroscopy, to determine the Avogadro constant with unprecedented accuracy, and to fulfil Egidi's dream.

  To convey Egidi's 'fantasy' into practice, two ²⁸Si kilogram prototypes shaped as quasi-perfect spheres were manufactured by the Australian Centre for Precision Optics; their isotopic composition, molar mass, mass, volume, density and lattice parameter were accurately determined and their surfaces were chemically and physically characterized at the atomic scale. The paper by Andreas et al reviews the work carried out; it collates all the findings and illustrates how Avogadro's constant was obtained. Impurity concentration and gradients in the enriched crystal were measured by infrared spectroscopy and taken into account; Zakel et al relate these measurements in detail. Next, Pramann et al illustrate how the molar mass of the enriched crystal was measured by exploiting isotopic enrichment and isotope dilution mass spectrometry. Valkiers et al report about remeasurement of the molar mass of a natural Si crystal, a measurement prompted by the exigency of clarifying the origin of the discrepancy between the N _A value given in the present issue and the value obtained using natural Si crystals. A consistency analysis of the different isotopic-composition determinations is illustrated in the paper by Bulska et al. As reported in two papers by Massa et al, to determine the lattice parameter an x-ray interferometer was manufactured from the material between the already mentioned spheres. The measurement result was combined with lattice comparisons between different crystal samples and with the impurity gradient to extrapolate the sphere's lattice-parameter. Ferroglio et al's contribution analyzes the self-weight deformation of the x-ray interferometer. Fujimoto et al report about the lattice-perfection investigations carried out by a novel self-referencing diffractometer at the National Laboratory for High-Energy Physics (KEK) in Japan. A really great effort was made to characterize the sphere surfaces and to correct for the oxide layer and the contaminating atoms. The results of these investigations are given by Busch et al. The sphere diameter and topography were measured by optical interferometry to nanometer accuracy; the papers of Bartl et al and Kuramoto et al describe how the sphere volumes were determined. Andreas et al's paper describes the calculation of phase corrections for the diameter measurements. The results of mass comparisons against the Pt–Ir standards of the BIPM, NMIJ and PTB are given by Picard et al.

  The results reported in the present issue need to be completed. One of the necessary activities is to relate the mass of the ²⁸Si atom to its Compton wavelength to test the mass–energy–frequency equivalence. Another effort is to monitor the stability of the Pt–Ir prototype: the technologies described in the present issue can be refined and finalized to calculate the mass variation of 1 kg ²⁸Si spheres by monitoring the surface evolution without weighing them on a balance. The last activity is the determination of the mass of a ²⁸Si sphere by electrical measurements using a watt balance and without any reference to the Pt–Ir prototype. In this framework, it will be necessary to demonstrate the mutual consistency and the stability of both the electrical and crystal mise en pratique of a kilogram definition based on a conventional value of the Planck constant. A related issue is to develop suitable procedures and protocols to disseminate the unit of mass from the new realizations.

  Since the molar Planck constant is well known via the measurement of the Rydberg constant, the accurate measurement of N _A also provides an accurate and independent determination of the Planck constant, h. A comparison of the values of the Planck constant obtained via the watt-balance experiment and the N _A determination tests quantum mechanics. In fact, the watt-balance value of h depends on solid state physics through the theories of Josephson and quantum Hall effects, whereas the value of h derived from N _A depends on atomic physics through the energy level differences in hydrogen and deuterium, whose associated transition frequencies yield information on the Rydberg constant.

  Grateful thanks are addressed to H-J Pohl for his outstanding project management in Russia, to A K Kaliteevski and his colleagues of the Central Design Bureau of Machine Building and the Institute of Chemistry of High-Purity Substances for their dedication and the punctual delivery of the enriched material, to H Riemann and his staff of the Institut für Kristallzüchtung for the crystal growth, to our directors for their advice and financial support, and to our colleagues for their daily work.

  Special thanks are addressed to Peter Becker, to whom this issue is dedicated on the occasion of his retirement from work at the Physikalisch-Technische Bundesanstalt. In 1974, young Peter joined the PTB's Avogadro group which, under the direction of Peter Seyfried, followed Bonse's work and improved the measurements of the lattice parameter and the Avogadro constant [5, 6]. In 2004, Peter proposed and backed this project by taking on his shoulders the risks, the management burden and the coordination of the many relevant activities.

  References

  [1] Egidi C 1963 Phantasies on a natural unity of mass Nature 200 61–2

  [2] Bonse U and Hart M 1965 An x-ray interferometer Appl. Phys. Lett. 6 155–6

  [3] Deslattes R D et al 1974 Determination of the Avogadro constant Phys. Rev. Lett. 33 463–6

  [4] Zosi G 1983 A neo-Pythagorean approach towards an atomic mass standard Lett. Nuovo Cimento 38 577–80

  [5] Becker P et al 1981 Absolute measurement of the (220) lattice plane spacing in a silicon crystal Phys. Rev. Lett. 46 1540–3

  [6] Seyfried P et al 1992 A determination of the Avogadro constant Z. Phys. B 87 289–98

• Open/close Investigations at INRIM on a Pd–C cell manufactured by NPL

  M Battuello et al 2011 Metrologia 48 241 Tag this article

  Article References Full text PDF (191 KB)

  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.

• Open/close Measurement of the optical to electrical detection delay in the detector for ground-to-space laser time transfer

  Ivan Prochazka et al 2011 Metrologia 48 L13 Tag this article

  Article References Full text PDF (499 KB)

  We present a new type of measurement and the first results of determination of the optical to electrical delay of a photon counting detector. This type of measurement has not been reported for photon counting. The absolute value of the time interval between the time of arrival of the signal photon onto the detector input aperture and the time when the electrical output signal exceeds the pre-defined level must be determined. The optical to electrical delay value is required for ground-to-space laser time transfer with picosecond accuracy. The laser time transfer link is under construction for the European Space Agency for its application in the experiment Atomic Clock Ensemble in Space. We have developed the measurement technique and have measured the detection delay of the solid state photon counter. The experiment is described along with the first results.

• Open/close Techniques for measuring the microwave dielectric properties of materials

  Udo Kaatze 2010 Metrologia 47 S91 Tag this article

  Article References Full text PDF (1003 KB)

  This review gives a brief introduction to the principles of microwave measurements of the complex permittivity of materials. The fundamentals of reflection, transmission and resonant methods are summarized and examples of sample cell design and measurement systems are presented for each category. The frequency domain and the fast response time domain methods are discussed in view of their merits and limitations. Accuracy aspects and reference materials for calibration procedures are mentioned briefly. Selected examples of applications indicate the diverse usability spectrum of microwave dielectric measurements in basic research and in the characterization of materials in manufacturing processes as well as monitoring and control routines.

• Open/close Revised formula for the density of moist air (CIPM-2007)

  A Picard et al 2008 Metrologia 45 149 Tag this article

  Article References Full text PDF (136 KB)

  Measurements of air density determined gravimetrically and by using the CIPM-81/91 formula, an equation of state, have a relative deviation of 6.4 × 10 ⁻⁵.

  This difference is consistent with a new determination of the mole fraction of argon x _Ar carried out in 2002 by the Korea Research Institute of Standards and Science (KRISS) and with recently published results from the LNE. The CIPM equation is based on the molar mass of dry air, which is dependent on the contents of the atmospheric gases, including the concentration of argon. We accept the new argon value as definitive and amend the CIPM-81/91 formula accordingly. The KRISS results also provide a test of certain assumptions concerning the mole fractions of oxygen and carbon dioxide in air. An updated value of the molar gas constant R is available and has been incorporated in the CIPM-2007 equation. In making these changes, we have also calculated the uncertainty of the CIPM-2007 equation itself in conformance with the Guide to the Expression of Uncertainty in Measurement, which was not the case for previous versions of this equation. The 96th CIPM meeting has accepted these changes.