Teachers and Students in Science, Technology, Engineering and Mathematics

Information on the practical realizations of the definitions of the SI base units are provided in the mises en pratique prepared by the relevant Consultative Committees (CC) of the International Committee for Weights and Measures (CIPM). They are published on the BIPM website.

According to the CCs, "to realize a unit" means the establishment of the value and associated uncertainty of a quantity of the same kind as the unit that is consistent with the definition of the unit.

The methods stated in the mises en pratique are generally the highest-level experimental methods used for the realization of units using the equations of physics. They are called primary methods and they do not involve reference standards of the same quantity.

 

The SI unit of time, the second s, can be realized by the methods below:

1. Primary frequency standards
   The primary frequency standards can be realized by atomic clocks that produce electric oscillations at a frequency which is related to the transition frequency of the atom of caesium 133, the SI definition of second. In 2017, the best primary standards produce the SI second with a relative standard uncertainty almost approaching one part in 10¹⁶.
2. Secondary representations of the second
   The secondary representations of second include atomic clocks that work on rubidium microwave transition and other optical transitions, including such in neutral atoms and in single trapped ions. Their uncertainties are in the range of parts in low 10¹⁴ – 10¹⁶.
3. Other frequency standards
   Commercial caesium clocks are able to maintain a frequency with a stability better than 1 part in 10¹⁴ over a few months. Hydrogen masers which depend on the 1.4 GHz hyperfine transition in atomic hydrogen have excellent short-term frequency stability which can achieve frequency stability of about 1 part in 10¹⁵ over intervals of less than one day.

 

1. Direct measurement of light travelling time (time of flight measurement)

   Primary realization of the length is performed by direct measurement of time delay between light-wave packets travelling pathways of different lengths before reaching a detector using the following relationship:

   ∫ = c·Δt

   where c = 299 792 458 m/s and Δt is the travelling time of the light along a geometrical path, of length ∫. This method of realization may be achieved directly with high relative accuracy for long range such as the distance from the earth to the moon, but at typical macroscale ranges, indirect travelling time measurement offers better accuracy.

2. Indirect measurement of light travelling time (optical interferometry)

   Optical interferometry is a measurement method based on the superposition (interference) of light. The time delay Δt between monochromatic light-waves travelling pathways of different lengths before reaching a detector is:

   Δt = 1/(2π) * Δφ/ƒ

   where ƒ is the frequency of light and Δφ is the phase difference between two interfering waves. To apply this method, the knowledge of the frequency of the light, ƒ, is an essential requirement. It provides the scaling factor between a measured phase difference and the length that is realized by interferometry. The CCL and CCTF Joint Working Group on Frequency Standards (WGFS) produced and maintains the CIPM List of recommended frequency standard values (LoF). The LoF is a single list of recommended values of standard frequencies for applications including the practical realization of the metre.

 

1. Realization by comparing electrical power to mechanical power

   Watt balances, or more recently called Kibble balances are the accurate instruments to equate the electrical and mechanical power.

   I * U = m * g * v

   Where
   current (I) * voltage (U) is the electrical power where I can be determined using Ohm's law by measuring the voltage drop across a stable resistor which is measured in terms of the Von Klitzing constant. U is measured in terms of the Josephson constant.

   mass (m) * gravity (g) * velocity (v) is the mechanical power. The quantities v and g are measured in the respective SI units, ms^-1 and ms^-2.

2. Realization by the x-ray-crystal-density (XRCD) method

   The mass of a pure substance can be expressed in terms of the number of elementary entities in the substance. The XRCD method is used to measure this number in which the volumes of the unit cell and of a nearly perfect crystal are determined. The macroscopic volume V_s of a crystal is equal to the mean microscopic volume per atom in the unit cell multiplied by the number of atoms in the crystal. For the following, assume that the crystal contains only the isotope ²⁸Si. The number N of atoms in the macroscopic crystal is

   N = 8V_s/a(²⁸Si)³

   where 8 is the number of atoms per unit cell of crystalline silicon and a(²⁸Si)³ is the volume of the unit cell, which is a cube; i.e., Vs/a(²⁸Si)³ is the number of unit cells in the crystal and each unit cell contains eight silicon 28 atoms. To realize the definition of the kilogram, the mass m of the sphere is expressed in terms of the mass of a single atom:

   m = N m(²⁸Si) = h N(m(²⁸Si)/h)

   where XRCD experiment determines N and m(²⁸Si)/h is a constant of nature and h is Planck constant.

 

The SI unit of electric current, the ampere A, can be realized by the methods below:

1. By using Ohm's law, the unit relation A = V/Ω, and using practical realizations of the SI derived units the volt V and the ohm Ω, based on the Josephson and quantum Hall effects respectively.
2. By using a single electron transport (SET) or similar device, the unit relation A = C/s, the value of e given in the definition of the ampere and a practical realization of the SI base unit the second s or
3. By using the relation I = C•dU/dt, the unit relation A = F•V/s, and practical realizations of the SI derived units the volt V and the farad F and of the SI base unit second s.

 

1. Practical realization of the kelvin by applying defined temperature scales

   The CIPM has adopted a series of International Temperature Scales - The International Temperature Scale of 1990 (ITS-90) from 0.65 K upwards and the Provisional Low Temperature Scale from 0.9 mK to 1 K (PLTS-2000). The fixed-point temperatures assigned in an International Temperature Scale are exact with respect to the respective scale temperature (there is no assigned uncertainty) and fixed (the value remains unchanged throughout the life of the scale). As a consequence, the definition of the kelvin in terms of the Boltzmann constant has no effect on the temperature values or realization uncertainties of the International Temperature Scales.

2. Other practical realization of the kelvin by primary thermometry are as follow: -
   • Thermodynamic temperature measurement by acoustic gas thermometry (AGT)
   • Spectral-band radiometric thermometry (1235 K and above)
   • Thermodynamic temperature measurement by polarizing gas thermometry
   • Thermodynamic temperature measurement by Johnson noise thermometry

 

The SI unit of luminous intensity, the candela cd, can be realized by the methods below:

1. Using a reference illuminance meter

   The reference illuminance meter which is a filtered radiometer whose relative spectral responsivity has been designed to be a close match to the spectral characteristics of the desired CIE spectral luminous efficiency function. This filter radiometer is generally used together with a precision aperture A and is calibrated by reference to an absolute radiometer (or so-called cryogenic radiometer) to give a known illuminance responsivity. This calibrated reference illuminance meter can then be used to calibrate a standard lamp in terms of its luminous intensity in a specified direction by means of a photometric bench, which allows the geometrical quantity of distance, r, from the source to the illuminance meter limiting aperture area, A.

2. Using an incandescent source

   An incandescent source which approximates the relative spectral power distribution of CIE standard illuminant A is used as a luminous intensity reference lamp. The spectral radiant intensity in a certain direction of the lamp is typically measured at a sufficiently large distance r using a series of calibrated reference filter-radiometers with limiting aperture area A and known irradiance responsivities at the range from 360 nm to 830 nm. The spectral radiant intensity values then can be multiplied by the desired CIE spectral luminous efficiency function and spectrally integrated to give the corresponding luminous intensity.