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ACTA IMEKO 
May 2014, Volume 3, Number 1, 23 – 31 
www.imeko.org 

 

ACTA IMEKO | www.imeko.org May 2014 | Volume 3 | Number 1 | 23 

Theoretical, physical and metrological problems of further 
development of measurement techniques and 
instrumentation in science and technology 
D. Hofmann, Y.V. Tarbeyev 

Friedrich -Schiller- University, 32 Ernst-Thälmannring, 69 Jena, GDR 

 

 

Section: RESEARCH PAPER  

Keywords: metrology, measurement technology, measurement theory, standards, fundamental physical constants, uniformity of measurements 

Citation: D. Hofmann, Y.V. Tarbeyev, Theoretical, physical and metrological problems of further development of measurement techniques and 
instrumentation in science and technology, Acta IMEKO, vol. 3, no. 1, article 7, May 2014, identifier: IMEKO-ACTA-03 (2014)-01-07 

Editor: Luca Mari, Università Carlo Cattaneo 

Received May 1st, 2014; In final form May 1st, 2014; Published May 2014 

Copyright: © 2014 IMEKO. This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 License, which permits 
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited 

 
 

1. INTRODUCTION 
The conversion of science into a major productive force is 

inevitably accompanied with growing interest in increasing 
measurement accuracy. Many objective studies of reality are 
reduced to measurements. At the same time the results of 
scientific research serve as a basis for the further development 
of this reality. 

Experimenters in science and practical engineers are 
interested in higher measurement accuracy, in technical 
improvement of measuring instrumentation and in higher 
reliability of measurements. These aspects make up the object 
of metrology. 

The task of meeting the urgent requirements of science and 
technology is the motive force for the progress of metrology 
and improvement of systems of units and standards which in 
the long run should provide for an optimum metrological 
assurance. This capacious concept includes not only the 
establishment of standards per se but also the development of 
most efficient methods of dissemination of the values of units 
and metrological supervision of the correctness of 
measurements as well as the development of up-to-date 
measuring transducers, fast automatic measuring systems that 
require minimum metrological supervision [1]. 

Metrology is a science, whose scope of knowledge is 
extremely polytechnical. 

It should embrace a wide range of electromagnetic, optical, 
mechanical, physical and chemical, nuclear and many other 
phenomena and incorporate an immense number of measuring 
problems that cover measurement transformations, estimation 
of measurement results and uncertainties, realization of the 
units of physical quantities and their dissemination. Therefore, 
it is not difficult to foresee that the task of establishing 
metrology as an independent science enjoying full rights and 
having its own large domain of specially arranged knowledge, 
theorems, methods of investigation, is complicated. 

The practical requirements and continuous growth of the 
role of measurements urgently demand that the progress of 
metrology must be accelerated. The aim of the present paper is 
to show the directions and ways of the further development of 
metrology. As examples you will become acquainted with some 
actual problems of modern metrology and measurement theory. 

2. COMMON TRENDS IN THE DEVELOPMENT OF RESEARCH 
AND APPLICATION IN THE FIELD OF METROLOGY AND 
MEASUREMENT TECHNOLOGY 

In the 20th century natural, technical and social sciences 
have become a decisive productive force. As a result of such 

This is a reissue of a paper which appeared in ACTA IMEKO 1979, Proceedings of the 8th IMEKO Congress of the International 
Measurement Confederation, “Measurement for progress in science and technology”, 21-27.5.1979, Moskow, vol. 3, pp. 607–626. 
Common interest of both metrologists and representatives of science and technology in constant improvement of measurements as 
well as general trends in the development of research in the field of metrology, measurement technology and instrumentation at the 
present-day stage are shown. Problems of general metrology, of improving systems of units and standards (“natural” standards in 
particular) are considered in detail.



 

ACTA IMEKO | www.imeko.org May 2014 | Volume 3 | Number 1 | 24 

sharp increase in the practical role of sciences, more and more 
technical subjects go over from empirically descriptive 
representation of the observed facts to generalizing theoretical 
considerations and concepts. In doing so, the peculiar features 
of the modern progress in scientific research are: 
– a sharp increase in the use of systems approach to all 
problems 
– an increase in the scope and intensity of fundamental research 
in the total volume of research work. 

The above-mentioned statements are not only valid for 
metrology, but are also especially characteristic of the present 
stage in its development. It is determined by substantial 
qualitative and quantitative changes. 

The most prominent quantitative changes are: 
1. An increase in the number of measurements and in the 

number of fields in which measurements are employed. 
Practically, there are no technical fields where 
measurements are not made; the measurement expenses 
reach 50 to 60% of the total production expenses in the 
most advanced industries (Figure 1) [2]. 

2. Measurements provide indispensable technical key information 
for evaluating and controlling specialized cooperative 
production. They are carried out on a large scale and 
provide the decision criteria for acceptance or refusal of  
labor having been realized in masses. 

3. Natural, technical and social sciences operate an instrument 
technique possessing industrial dimensions and demanding 
universal knowledge as well as a concerning behaviour of  
the scientists (in the fields of  nucleonics, microelectronics, 
space research, radiology, electron-scan microscopy, 
psychological behavior research). Planned experiments are 
intended to prove the correctness of  theoretical 
considerations. 

4. Measurements have two main functions: 
 an increased observability of  preferred technical-physical-

chemical states or procedures, widely exceeding the 
natural limit being set to the sensing organs of  the 
measuring persons. 

 the objectivation of  observations made by measuring 
persons. It is achieved by comparing measured 
quantities with known and settled standards. 

Qualitatively new requirements concerning measurement theory 
are additionally caused by the following facts: 
5. The accuracy of  measurements required both in scientific 

experiments and in industry is more and more approaching 
the level of  standard measurements. 

6. Due to the high sensitivity of  measuring instruments the 
environmental conditions and external influencing factors are 
producing ever-increasing effects on the measurement 
results. 

7. Sophisticated measuring systems whose calibration by 
traditional methods presents big problems are becoming 
widespread. 

8. Greater sophistication of  measuring instrumentation in 
respect of  both the operating principle and the design 
features makes still higher demands of  its operators. 
Thus, today in measurements, measurement technology and 

instrumentation take place those qualitative and quantitative 
changes which not only require the proper investigation of 
individual metrological problems but also inevitably result in an 
urgent need for the development of a general theory of 
metrology and, first of all, a general (unified) theory of 
measurements. 

The development of a general measurement theory is 
complicated by the following state of affairs: 
1. Measurement science has a long history and therefore a 

mighty tradition. In our days this tradition is still aimed at a 
further differentiation. 

2. Measuring has two different definitions: 
 measuring in a narrow sense, that is experimental comparing 

of  a measured quantity to a known comparison quantity 
of  the same kind (quality) which had been determined 
to be the unit of  measurement. The measurement of  
physical quantities and the use of  ratio scales are typical 
procedures. (Figure 2) [3]. 

 
Figure 1. Acquisition of measurement information in production. 



 

ACTA IMEKO | www.imeko.org May 2014 | Volume 3 | Number 1 | 25 

 measuring in a wide sense is the coordination of  numbers 
with states or procedures, following some rule. Scaling 
technical and no technical matters without special 
knowledge and using low value scales are typical 
procedures (Figure 2) [3]. 

At measuring in a narrow sense the subjective influence of  the 
measuring person can little by little be diminished. This 
does not apply to measuring in a wide sense. At measuring 
you will observe disadvantages and inaccuracies if  it is not 
considered 
 that each quantity is always a quantity of  a certain 

quality 
 that the coordination of  numbers with objects is also 

possible without knowing their quality 
 that formal operating with numbers for any data you like 

(measured values or non—measured values) is possible 
and 

 that mathematical models cannot express themselves if  
they represent correct facts or arbitrary phenomena [3, 
p. 37]. 

3. Historically we are just beginning to provide generalized 
knowledge in the fields of  measurement engineering and 
measurement theory. The example of  mass measurement is 
to prove that. 
Already 2500 B.C. the equal-armed balance had been 
graphically represented in a pyramid in Gizeh in ancient 
Egypt. About 300 B.C. Aristotle, Euclid and Archimedes 
provided the theory for this balance. Electromechanical 
balances, with strain gages and radiometric balances are 
developments of  the 20th century [4, 5]. 

4. The special language of  measurement engineering 
comprises a great number of  terms. Numerous terms have 
not yet been well defined. Synonyms and polysems are 
frequently used [5]. Classifications and teaching conceptions 
in measurement engineering have the following points of  
view: 
 measured quantities (length, force, temperature 

measurement engineering) 
 measuring devices (strain-gage, oscillograph and digital 

measurement engineering) 
 measurement principles (isotope, ultrasonic, infrared 

measurement engineering) 
 field of  measurement (production, process, laboratory 

measurement engineering). 

3. PROBLEMS OF THE GENERALIZED MEASUREMENT 
THEORY 

Topical tasks of  measurement theory are 
1. To increase the uniformity of  measurements 
2. To assure correct measurements 
3. To get valid models of  measurements and its aims. 
Working with models has methodical advantages. In contrast to 

the originals (measured signals, measuring systems and 
measurement processes) models are simpler, cheaper, more 
easily described, can be transformed in time and space, varied, 
limited and optimized. 

As a rule, modelling is associated with a certain 
simplification of  the original. For example, a certain body is 
characterized by the following properties: length, surface 
roughness, volume, mass, density, temperature, colour, etc. 
Usually, only selected parameters of  the object are considered 
exactly. Physical (homolog) models transform the scale of  the 
original only or just simplify the original; the measured 
quantities of  the original and model coincide. Mathematical 
(analog) models describe similar (analog) processes in different 
fields of  knowledge; the measured quantities of  the original and 
model do not coincide. 

Models consist of  a certain number of  elements and 
relations (links) between them. A great advantage is that in 
gaining knowledge and building up a theory the originals of  
different nature can produce similar images that allow a 
uniform treatment and interpretation. 

In any case the knowledge that was gained using a model in 
the image field should be confirmed in practice for the actual 
object. Otherwise the value of  this knowledge is subject to 
argument. 

The measurement theory deals mainly with well-defined or 
poorly-defined models of  behaviour [6] expressed as algorithms. 
These models describe: 

 measured signals and measuring systems in terms of  
mathematical algorithms, 

 measurement processes in terms of  heuristic algorithms. 

 
Figure 2. Classification of scales and their properties after [3]. 



 

ACTA IMEKO | www.imeko.org May 2014 | Volume 3 | Number 1 | 26 

Specific features of  mathematical algorithms are determinism, 
finiteness, universality and guarantee of  solution [7]. 

Heuristic algorithms are not associated with such strict 
requirements and still they guarantee only a solution probability 
0<p(L)<1 which tends to 1 [8]. 

Both mathematical and heuristic algorithms take the shape 
of  measurement rules or definitions. One should bear in mind 
that mathematical relationships obtained by a deductive 
reasoning cannot be used for scientific substantiation of  
metrological characteristics if  they do not agree with the 
empirical knowledge (Figure 3) [9-11]. 

There are no good or bad models. A model can be 
considered a good one if  it meets the practical requirements 
and is in good agreement with empirical data. 

There is always the danger of: 
 using too simple or too complicated models; 
 solving partial problems only for which certain models 

are known; 
 ascribing greater significance to those stages of  

processes that are described by mathematical algorithms 
than to those that can for the time being be described in 
terms of  heuristic algorithms only. 

Here are some typical examples of  this sort: 
 in the preference of  random errors rather than 

systematic ones in the measurement error analysis; 
 in the description of  a measurement process the 

preference of  an estimate to the detriment of  the 
measurement process itself, with the measurement 
preparation being almost totally ignored; 

 the preference of  the normal distribution even when 
considering events whose distribution differs from the 
normal one; 

 the preference of  incompletely formulated measurement 
problems (research problems) rather than completely 

formulated measurement problems (repetition 
problems); 

 the neglecting of  ergonomic aspects when developing 
new measuring instruments or processes; 

 the neglecting of  economic consequences as a result of  
incorrect measurements or the absence of  
measurements. 

Operations (actions, decisions) aimed at an optimum 
solution of  measurement problems are called the measurement 
strategy. 

As a rule, the measurement strategy consists of  numerous 
mathematical and heuristic algorithms. An algorithm 
transforms the input quantities into output quantities in 
accordance with a system of  rules. The use of  algorithms is 
inevitable for automation of  measurement processes. The 
measurement strategy should cover the preparation, realization 
and evaluation of  measurements (Figure 4) [2]. 

When one looks up in metrological literature for possible 
ways of  solving measurement problems, one discovers a totally 
unsatisfactory situation. First of  all, there is no clarity as to the 
necessary contents of  measurement problems with guaranteed 
solution. The same applies to the choice of  measuring 
instrumentation and the construction of  measuring systems 
[12]. 

Mathematization of  the measurement theory is, first of  all, 
of  great importance for microprocessor application. 
Neugebauer is of  the opinion [13, p.44] that mathematics 
originated from metrological problems. In any case, afterwards 
it developed by a deductive method independently of  
metrological and other technical problems and at present it has 
in part surpassed the limits of  practical problems. 

A sharply increasing interest in mathematization of  
measurement processes results in a greater interest for 
publications on the axiomatic foundation of  measurements. We 
are speaking here about literature devoted to the algorithmic 

 
Figure 3. Characteristic functions of dynamics properties of measurement systems. 



 

ACTA IMEKO | www.imeko.org May 2014 | Volume 3 | Number 1 | 27 

theory of  measures and measurement theory [14-17]. 
The algorithmic theory of  measures deals with the determination 

of  the contents of  geometrical structures or point sets. It is 
especially important for integral or probability calculations. In 
integral calculations the use of  a measure instead of  the 
contents results in the Lebesgue integral (expansion of  the 
Riemann integral). 

When estimating the probability, one random event is 
interpreted as a particular quantity xai of  the set of  all 
elementary events and the measure p(xai) is considered to be the 
probability of  the event xai. 

In mathematics the point sets having the contents are called 
measurable. The prerequisite is the possibility of  generating a 
set M of  natural numbers and their resolution. This is true, for 
example, for the set of  all even numbers, Fibonacci numbers 
and prime numbers which can be produced recursively. 

The algorithmic theory of  measurements proceeds from the fact 
that non-numerical algorithms also can be reduced to recursive 
functions and recursive sets of  natural numbers if  the class K 
of  non-numerical input and output quantities can be coded 
using natural numbers. 

For this purpose it is necessary to have: 
 an algorithm that controls the coding; 
 an algorithm that checks whether a certain natural 

number is the image of  a non-numerical object from K; 
 an algorithm that reconstructs the object from its image; 
 an algorithm that encodes the non-numerical class K as 

a whole. 
Numerous publications on algorithmic theory of  

measurements are devoted to these problems. Mainly, they deal 
with consistent classifications and establishment of  scales. 
There is a certain process which is determined by specific laws 
of  the development of  deductive theories and which is still to 
be investigated by metrologists. On the other hand, it was 

found that any sufficiently powerful theory cannot be resolved. 
Here are the natural limits of  the axiomatic method. 

4. MEASUREMENT THEORY AS AN EDUCATIONAL FACTOR 
The measurement theory concentrates the knowledge about 

the status of measurement technology and instrumentation, 
reduces the immense quantity of metrological phenomena to a 
limited number of fundamental methods, principles and means 
and makes for the understanding of measurements. Solving 
measurement problems in a systematic and planned manner 
with the help of the measurement theory one can optimize their 
solutions, limit possible incorrect actions and spending and 
predict future requirements (Figure 5) [18]. 

Until now the educational programs and those of refresher 
courses were hardware-oriented. However, automation of 
measurements and modern technology can be introduced only 
if specialists will also be software-oriented. One must 
understand not only instruments but processes as well. 

The software-oriented thinking is not restricted by the 
writing of computational programs and includes the following 
problems: 

 choice of  appropriate concepts and definitions; 
 target-oriented exact formulation of  measurement 

problems; 
 discrimination between hardware-oriented and software-

oriented functions; 
 discrimination between central and decentral functions; 
 clearing-up of  the relationships between the system 

operator and the measurement system, between 
measurement systems as well as between operators; 

 automation of  measurement processes after 
consideration of  economic criteria, of  the costs 
associated with measurements that were or were not 
carried out, with the measuring instrumentation that is 

 
Figure 4. Components and functions of automatic measuring devices. 



 

ACTA IMEKO | www.imeko.org May 2014 | Volume 3 | Number 1 | 28 

already available or is to be purchased and with the 
training of  the personnel. 

The more productive is the measurement theory, the easier 
are solutions and the smaller is the educational expenditure. 
However, the ever-increasing training costs should not be 
underestimated. It is through education and training that the 
results of scientific research add to the efficiency of production 
(Figure 6). 

5. PROBLEM OF IMPROVING SYSTEMS OF UNITS 
The theory of building up a system of units, which could 

adequately meet complicated requirements of science and 
practice has become one of those few branches of general 
metrology, that was successfully developed and logically 
completed in 1954–1960 by accepting the unquestionably 
progressive International system of units (SI). However, some 
old unresolved problems have still remained in this field and 
new ones that require immediate solution have appeared since. 

It can be explained by the fact, that the number of 
independent and derived measurands is constantly increasing. 
Now the international system of units already consists of 135 
units of physical quantities and the number of parameters, 
measured in science and technology, can reach 700 in 1980 and 
increase up to 2000 in the nearest future, according to the 
existing forecast. Such a quantitative growth causes difficulties 
from the point of view of SI, whose aim is to establish simple 
relations between existing units, and suggests the necessity of 
introducing some alterations. 

Thus, at present we are faced with the problem of reviewing 
the definition of the metre as the old definition doesn’t allow to 
improve the accuracy of realization of the unit. 

Till nowadays the definition of the unit of temperature 
(using the thermodynamic scale) is in a certain contradiction 
with its realization (using IPTS). 

The problem of reviewing the definitions of most important 
units in the field of electricity and magnetism is an urgent one. 

A number of fundamental questions of the theory of 
systems of units remains unsolved as well. So during several 
years a discussion about the status of angular units is underway. 
Some metrologists consider it necessary to speak out in favour 
of introducing the unit of plane angle into the number of basic 
units and placing the solid angle unit among derived units. 

All these questions demand additional theoretical study and 
broad discussion by the scientific community. 

6. PROBLEM OF IMPROVING BASIC STANDARDS AND 
ESTABLISHING A SYSTEM OF INTERRELATED 
STANDARDS 

The problem of improving standards is closely related to 
the problem of improving the systems of units, though this 
relation is not a straightforward one. At present the change 
from standards, forming a certain set to a system of interrelated 
standards, based on stable physical phenomena and 
fundamental physical constants should be considered the main 
trend in this field. Undoubtedly first of all we must think about 
improving the standards of basic units. But it is not obligatory 
that a system of basic standards should coincide with the set of 
basic units. The system of standards of electrical units, where 
the main standards are the standard of the e.m.f. unit – the volt 
(and not the ampere) – and the standard of the farad can serve 
as an example of such a non-antagonistic difference. We are 
going to show below that such a structure of the system of 
standards is not in contradiction with the definition of the 
ampere as a basic unit of SI. 

From the point of view of accuracy the best system would 
be such a system of standards, in which all the basic standards 
were “countable”. At present the standard of the second (based 
on the counting of the number of periods of 137Cs radiation) 
and the metre (based on the counting of the number of 
wavelengths corresponding to the orange line in 86Kr radiation) 
are designed in such a way. The prospect of a changeover to the 
definition of the mass unit, according to which the kilogram 

 
Figure 5. Working steps for computer-supported coordinate measurement, after [18]. 



 

ACTA IMEKO | www.imeko.org May 2014 | Volume 3 | Number 1 | 29 

will represent the mass of countable number of atoms of a 
certain  element, most  probably the 28Si  isotope. The  fact that  
there will be no less of accuracy in transferring the value of the 
unit into the field of molecular and atomic masses (though the 

accuracy of realization will be comparable with the accuracy of 
the existing standard or even lower) can be considered one of 
the main advantages of such a definition of kilogram. 

 
Figure 6. Development of measurement devices, working fields and educational requirements. 



 

ACTA IMEKO | www.imeko.org May 2014 | Volume 3 | Number 1 | 30 

In principle it’s also possible to design the standard of one 
of the electrical units on the basis of counting the number of 
elementary charges. However in spite of the fact, that modern 
technology allows to realize such counting the realization of a 
standard on such a basis is a matter of the future. 

After the establishment of basic standards of a system on 
the basis of counting the set of values of fundamental physical 
constants (both dimensional and dimensionless) can be 
measured. The obtained values of constants should be 
mathematically processed in order to determine most reliable 
adjusted values and then the standards of derived units should 
be established on their basis. The system of such standards will 
be self-consistent and will not contradict the system of units. 

The principle of building up such a system of standards as 
illustrated by the realization of the e.m.f. unit – the volt using 
the Josephson effect and the fundamental physical constants is 
given in [19] and besides will be considered in detail in a special 
report to the section “Metrological assurance”. The aim of the 
creation of such a system is not only to establish a more 
objective internal interrelation and self-consistency of the 
standards of units of physical quantities, but also to improve 
the accuracy of all standards of the system. 

The necessity of radical rearrangement of the system of 
standards (primary and secondary ones) for another basic unit – 
the kelvin – through the transfer to the thermodynamic 
temperature scale from the International practical temperature 
scale is quite evident. It is due to the fact, the absolute 
temperature values are needed for fundamental physical 
research, as absolute thermodynamic temperatures come into 
physical equations. The problems associated with this go 
beyond the bounds of metrology per se. Thus, a further 
improvement of the gas thermometer aimed at practical 
realization of the thermodynamic temperature scale demands 
the development of the theory and methods of molecular 
dynamics, the theory of the virial equation of the state of real 
gases and more accurate determination of appropriate virial 
coefficients for pure gases and of the universal gas constant. 

The improvement of the accuracy of the determination of 
the gas constant and the Avogadro number in its turn allows to 
have a more precise value for the Boltzmann constant and the 
second constant in the Planck radiation law, which is essential 
for building a high temperature thermodynamic scale and for 
many thermodynamic calculations. 

On the other hand, the improvement of these constants 
allows to go over to a new method of realization of another 
basic unit – the candela – and to improve the whole system of 
standards in the field of photometry in a wide spectral range 
using the “black body” radiation and to effect the change-over 
to the energy photometry. 

7. PROBLEM OF DEVELOPING “NATURAL” STANDARDS AND 
USING FUNDAMENTAL PHYSICAL PHENOMENA 

This problem, that arose at the moment when it was felt 
that the international uniformity of measurements, should be 
ensured, reflects the natural and therefore constant tendency 
among metrologists to use the most stable natural phenomena 
for the realization of units of physical quantities, that is to 
establish reproducible standards. 

100 years of intensive investigations of metrologists in this 
direction have resulted in the establishment of natural standards 
of the above mentioned length unit and time unit. In recent 
years the standards of magnetic induction (for high fields), 
angular velocity, etc. whose operating principles are based on 

relatively easily reproducible natural phenomena. At present 
“natural” standards are being developed in the following fields: 
of thermometry (the use of the phenomenon of the nuclear 
quadrupole resonance), of voltage measurements (the effects of 
Josephson, Stark and Pockels), of radiation energy (the 
monochromaticity of atomic and nuclear transitions), etc. 

The following two common trends can be rather clearly 
seen in all these studies: 

 a wide use of  quantum effects which even resulted in 
the coining of  the term “quantum metrology”; 

 the use of  fundamental physical constants that are most 
stable realizations of  natural laws as references in 
standards. 

In this connection, the problem of a more accurate 
determination and adjustment of fundamental physical 
constants is in itself becoming very important. It was shown 
above what is the role of this problem in the establishment of 
an interrelated system of standards. If one also takes into 
account the fact that the accuracy of physical constants 
characterizes the depth of our notions of physical phenomena 
and laws interrelating them, then it can be said with confidence 
that everybody – from physicists and metrologists to practical 
engineers – is interested in the improvement of accuracy of 
fundamental physical constants. In this respect, the work done 
at VNIIM has shown that, from the point of view of the 
progress of metrology, in the first place it is necessary to 
improve the accuracy of the constants involved in the 
realization of the volt using the Josephson effect. 

As to the other trend in the improvement of standards, i.e. 
the trend of a wide use of quantum effects and phenomena that 
are not substantially influenced by environmental factors, the 
use of the superconductivity phenomenon is the most 
characteristic feature of the present stage. 

This phenomenon has attracted a special attention of 
metrologists after it was shown that superconductivity presents 
a unique manifestation of the existence on a macroscopic scale 
of such quantum mechanical phenomena as the Meissner effect 
(of ideal diamagnetism), the phenomenon of quantizing the 
magnetic flux in superconductors with multiple links, a whole 
class of contact phenomena united by the common name 
“Josephson effects” as well as the phenomenon of quantum 
interference of currents in superconductors which is related to 
the latter effects. 

The ideal diamagnetism of superconductors provides a 
unique opportunity for the development of magnetic 
suspensions and bearings that will undoubtedly enhance the 
improvement of high-precision measuring instrumentation in 
the field of mechanical measurements where the total absence 
of friction is of exclusive importance. 

The main (classical) property of superconductors (the 
absence of dissipative losses, i.e. the ideal conductivity) together 
with the Meissner effect (ideal diamagnetism) have long ago led 
to the idea of constructing superconducting magnets with high 
values of induction and highly uniform magnetic fields that 
practically do not consume any energy. At present 7.5 T 
magnets have been produced with a field inhomogeneity of less 
than 2×10–7 in a 0.5 cm3 volume (England). Such a magnet 
made a resolution of approximately 5×10–9 possible. The work 
on the development of new materials having high 
superconducting transition temperatures and stable structures 
that is underway in the whole world allows to expect the 
emergence of magnets with field inductions up to 20 to 30 T. 

Various quantum-mechanical properties of  superconductors 



 

ACTA IMEKO | www.imeko.org May 2014 | Volume 3 | Number 1 | 31 

(from ideal diamagnetism to the Josephson effects) open the 
prospects (and are already used) for the development of  
superconducting gravimeters for relative measurements of  
gravity that have an extremely high sensitivity. The theoretical 
limit of  one of  the designs of  such gravimeters proposed by 
NBS [20] is ~10–14 g. 

A dilatometer based on the principle of  superconducting 
cavity resonator and having a sensitivity of  ~10–14 m was built 
at the Institute of  Physical Problems of  the USSR Academy of  
Sciences. The gravimeter which is an embodiment of  this 
principle makes it possible to obtain a sensitivity of  ~10–10 g for 
averaging time of  ~1 minute. 

Apparently, widest prospects for the use of  unique 
properties of  superconductors are open in the fields of  
electrical and magnetic measurements. Already at present 
Josephson volt standards are used in the majority of  
metrological laboratories of  the world for the maintenance of  
the volt value with an accuracy ~ (3-5)×10—8. This brings 
about, in particular, an important task of  developing a 
transportable transfer standard for the e.m.f. unit in which all 
achievements of  physics and low-temperature technology 
should be used. 

Numerous applications will be found for superconducting 
quantum magnetometers using the phenomenon of  quantum 
interference of  currents and Josephson effects. The sensitivity 
of  the transducers of  these magnetometers (SQUIDs) may be 
close to the fundamental limit whose value can be estimated as 

  2/1
08

2/1
x

Hz
10

minF
Φ

Δ
δΦ    (1) 

where 

xδΦ  is the minimum detected change in the magnetic flux; 
FΔ  is the frequency bandwidth of  the signal; 
0Φ  is the magnetic flux quantum equal to 2×10–15 Wb. 

These magnetometers are beyond competition in respect of  
their sensitivity and accuracy as compared with all other types 
of  magnetometers in the field of  measurement and stabilization 
of  low and medium magnetic fields. Of  no less importance is 
the fact that together with other superconducting devices, such 
as current comparators, magnetic flux transformers, super 
conducting screens, these magnetometers provide great 
opportunities for increasing the sensitivity and accuracy of  a 
wide class of  electrical measuring devices. In particular, they 
make feasible measurements of  voltages of  the order of  10–12 
to l0–15 V comparisons of  d.c. currents with a relative 
uncertainty of  10–8 to 10–10, inductance comparisons with a 
sensitivity of  the order of  10–14 H, attenuation measurements at 
radio frequencies with a relative uncertainty of  10–3 and in a 
number of  other measurement fields requiring high accuracy. 
We should also note that among the promising fields are 
applications of  superconducting cavities for frequency 
stabilization of  microwave oscillators (at present relative 
frequency instabilities of  1.2×10–12 for one hour and 1.2×10–13 
for 10 seconds have been achieved) and the use of  non-linear 
properties of  Josephson junctions for multiplication of  
frequencies in the 3-cm band up to the far infrared part of  the 
spectrum which is of  great importance for bridging a gap 
between the frequencies of  cesium clocks and lasers. 

8. CONCLUSIONS 
Even this brief  review of  individual problems, that are most 

important for the development of  metrology and measurement 

technology and instrumentation, shows that metrology 
(including the general theory of  measurements) is a rapidly 
developing field of  scientific knowledge, i.e. a science whose 
progress will undoubtedly enhance further progress in various 
branches of  industry and scientific research and whose actual 
formation can be promoted by concerted efforts of  
metrologists in collaboration with scientists and practical 
workers in various fields. 

REFERENCES 

[1] V.D. Komarov, Nauchno-tehnicheskaja revoljuzia I nekotorye, 
metodologicheskye problemy tehnicheskih nauk (scientific-
technical revolution and some methodological problems of 
technical sciences). Leningrad 1970. 

[2] D. Hofmann, Handbuch Messtechnik und Qualitätssicherung 
(Handbook Measurement Engineering and Quality Assurance) 
Berlin: VEB Verlag Technik 1979. 

[3] W. Gutjahr, Die Messung psychischer Eigenschaften 
(Measurement of psychological properties). Berlin: VEB 
Deutscher Verlag der Wissenschaften 1971. 

[4] P.S. Sawelski, Die Masse und ihre Messung (Mass and its 
measurement). Moscow: MIR, Leipzig: VEB Fachbuchverlag 
1977. 

[5] G. Hofmann, Effektivitätssteigerung durch Monosemierung der 
Fachsprache der Messtechnik (Improving Efficiency by using 
monosemantic term in the terminology of measurement 
engineering). Feingertetechnik 28(1979) H. 5, S. 216–218. 

[6] M. Peschel, Modellbildung für Signale und Systeme (Models for 
signals and systems). Berlin: VEB Verlag Technik 1978. 

[7] N.A. Krinickij, Algoritmy vokrug nas (Algorithms around us). 
Moscow: Nauka 1977. 

[8] D. Hofmann, Heuristische Algorithmen zur Rationalisierung 
von Messprozessen (Heuristic algorithms for the rationalization 
of measurement processes). messen – steuern – regeln 14(1971) 
H.5, S. 172–174. 

[9] F.H. Lange, Methoden der Messstochastik (Methods of 
stochastical measurements). Berlin: Akademie Verlag 1978. 

[10] G.I. Kavalerov, Mandelstam, S.M.: Vvedenie v informacionnuyu 
teoriyu izmerenii (Introduction in measurement-information 
theory). Moscow: Energija 1974. 

[11] L. Finkelstein, Instrument science. Introductory article. Journal 
of Physics E: Scientific Instruments 10 (1977) S. 566–572. 

[12] D. Bosman, Instrument science. Systematic design of 
instrumentation systems. Journal of Physics E: Scientific 
Instruments 11(1978) S. 97–105. 

[13] A.P. Stachov, Vvedenie v algoritmicheskuyu teoryu izmerenija 
(Introduction in algorithmic measurement theory). Moscow: 
Sovetskoye radio 1977. 

[14] P.R. Halmos, Measure Theory. New York, Heidelberg, Berlin: 
Springer Verlag 1974. 

[15] J. Pfanzagl, V. Baumann, H. Huber, Theory of Measurement, 
2nd. ed. Würzburg, Wien: Physica Verlag 1971. 

[16] L. Finkeistein, The relation between the formal theory of 
measurement and pattern recognition, in: Practical Measurement 
for Improving Efficiency. ACTA IMEKO 1976. Budapest: 
Akademiai Kiado 1977. 

[17] Y. Morita, A. Kobayashi, H. Iida, M. Ishigami, Of classification 
and industrial measurement, in: Practical Measurement for 
Improving Efficiency. IMEKO VII. Preprint Vol. 3, 1976. 

[18] W. Lotze, M.W. Hartmann, Maus (2D) Programmsystem zur 
Berechnung von Mass, Form und Lage punktweise gemessener 
ebener Werkstücke. Nutzerbeschreibung (Maus (2 D) 
Programmsystem for the calculation of measure, shape and 
position pointlike measured plane objects). Dresden: Technical 
University 1977. 

[19] Y.V. Tarbeev, Izvestija AN SSSR. Ser. Energetika i transport, 
1978, N. 3. 

[20] R.P. Giffard, J.C. Gallop, B.W. Petley, Progress in quantum 
electronics, 1978, vol. 4, p.4.