A system of quantities from software metrology

International Organization for Standardization (ISO)/International Electrotechnical Commission (IEC) 80000, the International System of Quantities, collects and organizes the most important physical quantities into a coherent system of quantities whose foundation for measurements is the International System of Units (SI). This short communication outlines a report that, in a similar fashion, collects and organizes the most important quantities used in measurements performed on software artifacts, focusing on software as a product rather than its development process.

How to Define the Units of the Revised SI Starting from Seven Constants with Fixed Numerical Values

As part of a revision to the International System of Units (SI) approved in 2018 and to take effect in May 2019, the seven base units will be defined by giving fixed numerical values to seven defining constants. This article shows how the definitions of all seven base units can be derived efficiently from the defining constants, with the result appearing as a table. The table's form makes evident a number of connections between the defining constants and the base units. Appendices show how the same methodology could have been used to define the same base units in the present SI, as well as the mathematics that underpins the methodology. Since the base units are now defined in terms of constants, then all units in the SI are now defined in terms of those constants.

Quantity Calculus, Fundamental Constants, and SI Units

A revised International System of Units (SI) is expected to be established by the 26th General Conference on Weights and Measures when it convenes in November 2018 and to be put into practice starting on 20 May 2019, World Metrology Day. In consequence, the article published in this journal in 2011, "The Current SI Seen from the Perspective of the Proposed New SI," is updated in this paper, which provides an opportunity to again demonstrate the usefulness of the quantity calculus in dealing with quantities and units. The quantity calculus and the seven defining constants of the current and revised SI are reviewed, and expressions for the seven current and revised SI base units are given. Relationships between the magnitudes of revised and current SI units and expressions for the numerical values of current SI defining constants expressed in revised SI units are also obtained using the quantity calculus.

Electromagnetic Units, the Giorgi System, and the Revised International System of Units

The centimeter-gram-second system of electromagnetic units (EMU) has been used in magnetism since the latter part of the 19th century. The International System of Units (SI), a successor to Giorgi's 1901 rationalized four-dimensional meter-kilogram-second system, was adopted by the General Conference on Weights and Measures in 1960 with the ampere as the fourth base unit. However, EMU remains in common use for the expression of magnetic data. The forthcoming revision of the SI will accentuate its differences with EMU. The permeability of vacuum will no longer be a fixed constant, which recalls the Giorgi system and prompts a review of historical arguments on the concepts of magnetic flux density and magnetic field strength in vacuum. The redefinition of the ampere in terms of the fixed numerical values of two defining constants could allow for independent experimental measurements of the permeability of vacuum, i.e., determination of the magnetic constant.

The Permeability of Vacuum and the Revised International System of Units

The International System of Units (SI) is expected to be revised such that all seven base units, including the kilogram, will be defined in terms of fixed numerical values of seven defining constants. The revised SI will include a redefinition of the ampere. One consequence is that the permeability of vacuum will not have a fixed numerical value but will become, in principle, a measurable quantity. The constitutive relation among magnetic flux density, magnetic field strength, and magnetization will not change. However, its expression in the centimeter-gram-second system of electromagnetic units (EMU), where the permeability of vacuum is unity, will no longer be ontologically equivalent, and quantities will not be exactly convertible to the SI. Already contrary to international convention, the still common EMU system will become obsolete.

The kelvin redefinition and its mise en pratique

In 2018, it is expected that there will be a major revision of the International System of Units (SI) which will result in all of the seven base units being defined by fixing the values of certain atomic or fundamental constants. As part of this revision, the kelvin, unit of thermodynamic temperature, will be redefined by assigning a value to the Boltzmann constant k. This explicit-constant definition will define the kelvin in terms of the SI derived unit of energy, the joule. It is sufficiently wide to encompass any form of thermometry. The planned redefinition has motivated the creation of an extended mise en pratique ('practical realization') of the definition of the kelvin (MeP-K), which describes how the new definition can be put into practice. The MeP-K incorporates both of the defined International Temperature Scales (ITS-90 and PLTS-2000) in current use and approved primary-thermometry methods for determining thermodynamic temperature values. The MeP-K is a guide that provides or makes reference to the information needed to perform measurements of temperature in accord with the SI at the highest level. In this article, the background and the content of the extended second version of the MeP-K are presented.

Traceable Quantitative Raman Microscopy and X-ray Fluorescence Analysis as Nondestructive Methods for the Characterization of Cu(In,Ga)Se2 Absorber Films

The traceability of measured quantities is an essential condition when linking process control parameters to guaranteed physical properties of a product. Using Raman spectroscopy as an analytical tool for monitoring the production of Cu(In1-xGax)Se2 thin-film solar cells, proper calibration with regard to chemical composition and lateral dimensions is a key prerequisite. This study shows how the multiple requirements of calibration in Raman microscopy might be addressed. The surface elemental composition as well as the integral elemental composition of the samples is traced back by reference-free X-ray fluorescence analysis. Reference Raman spectra are then generated for the relevant Cu(In1-xGax)Se2 related compounds. The lateral dimensions are calibrated with the help of a novel dimensional standard whose regular structures have been traced back to the International System of Units by metrological scanning force microscopy. On this basis, an approach for the quantitative determination of surface coverage values from lateral Raman mappings is developed together with a complete uncertainty budget. Raman and X-ray spectrometry have here been proven as complementary nondestructive methods combining surface sensitivity and in-depth information on elemental and species distribution for the reliable quality control of Cu(In1-xGax)Se2 absorbers and Cu(In1-xGax)3Se5 surface layer formation.

The Current SI Seen From the Perspective of the Proposed New SI

A revised International System of Units (SI) proposed by the International Committee for Weights and Measures is under consideration by the General Conference on Weights and Measures for eventual adoption. Widely recognized as a significant advance for both metrology and science, it is defined via statements that explicitly fix the numerical values of a selected set of seven reference constants when the values of these constants are expressed in certain specified units. At first sight this approach to defining a system of units appears to be quite different from that used to define the current SI. However, by showing how the definitions of the seven base units of the current SI also fix the numerical values of a set of seven reference constants (broadly interpreted) when the values of these constants are expressed in their coherent SI units, and how the definition of the current SI can be recast into the same form as that of the revised SI under consideration, we show that the revision is not as radical a departure from the current SI as it might initially seem.

Special Report on Electrical Standards: New Internationally Adopted Reference Standards of Voltage and Resistance

This report provides the background for and summarizes the main results of the 18th meeting of the Consultative Committee on Electricity (CCE) of the International Committee of Weights and Measures (CIPM) held in September 1988. Also included are the most important implications of these results. The principal recommendations originating from the meeting, which were subsequently adopted by the CIPM, establish new international reference standards of voltage and resistance based on the Josephson effect and the quantum Hall effect, respectively. The new standards, which are to come into effect starting January 1, 1990, will result in improved uniformity of electrical measurements worldwide and their consistency with the International System of Units or SI. To implement the CIPM recommendations in the U.S. requires that, on January 1, 1990, the value of the U.S. representation of the volt be increased by about 9.26 parts per million (ppm) and the value of the U.S. representation of the ohm be increased by about 1.69 ppm. The resulting increases in the U.S. representations of the ampere and watt will be about 7.57 ppm and 16.84 ppm, respectively. The CCE also recommended a particular method, affirmed by the CIPM, of reporting calibration results obtained with the new reference standards that is to be used by all national standards laboratories.

Recalibration of the U.S. National Prototype Kilogram

The U.S. national prototype kilogram, K20, and its check standard, K4, were recalibrated at the Bureau International des Poids et Mesures (BIPM). Both these kilograms are made of platinum-iridium alloy. Two additional kilograms, made of different alloys of stainless steel, were also included in the calibrations. The mass of K20 in 1889 was certified as being 1 kg-0.039 mg. Prior to the work reported below, K20 was most recently recalibrated at the BIPM in 1948 and certified as having a mass of 1 kg-0.019 mg. K4 had never been recalibrated. Its initial certification in 1889 stated its mass as 1 kg-0.075 mg. The work reported below establishes the new mass value of K20 as 1 kg-0.022 mg and that of K4 as 1 kg-0.106 mg. The new results are discussed in detail and an attempt is made to assess the long-term stability of the standards involved with a view toward assigning a realistic uncertainty to the measurements.

Comparison of Solid Density Standards Between IMGC and NBS

Solid-object density standards developed independently by the Istituto di Metrologia "G. Colonnetti" (IMGC) and NBS, and traceable to SI units of length and mass, have been compared using a silicon transfer standard. Results agree to approximately 1×10-6, which is conistent with the uncertainties assigned by the two laboratories.