New Instruments and Methods of Measurement

Current State of the Question of Defining the Meter by the Length of a Light Wave

M. F. Romanova

During the last two years the question of adopting a new definition of the meter has twice been considered at international metrological meetings.

It is known that at the present time the unit of length—the meter—is defined by the distance (under specified conditions) between two marks engraved on the surface of a platinum-iridium bar kept at the International Bureau of Weights and Measures and serving as the prototype of the meter. As early as 1927 the General Conference on Weights and Measures was faced with the question of the advisability of defining the meter by the length of a light wave. Such a transition would make the meter invariable in time and would ensure an increase in the accuracy of length measurement.

In 1953 the question of the transition was discussed in the newly established Advisory Committee on the Definition of the Meter. The Advisory Committee drew up a number of proposals for the International Committee of Weights and Measures.

The first of these proposals stated that “the time has come to consider favorably the question of passing to a definition of the meter based on the wavelength of light radiation, in order to give the fundamental unit of length at the same time a higher accuracy and the unquestionable character of universality and invariability”[^1].

The subsequent proposals defined the procedure for the transition to the new definition of the meter and gave general provisions concerning the conditions for reproducing the wavelength that defines the meter. It was stated that it is not yet possible to make a final choice of a new standard of the lengths of light waves, and that the continuation of scientific investigations in this direction is necessary. Finally, in the last

proposals, it is recommended that the International Committee ask the 10th General Conference on Weights and Measures, after a decision in principle on the matter, to grant the International Committee the right finally to establish the procedure and date for the transition to the new definition of the metre, without waiting for the next General Conference.

Thus, the question of transition to a new definition of the metre, when considered at the meeting of specialists, was in principle decided positively.

The 10th General Conference on Weights and Measures met in the autumn of 1954. At its sessions the proposals of the Consultative Committee were heard, but on the question of the metre a different decision was adopted.

In this decision it is proposed that the major metrological laboratories continue their work on the study of monochromatic radiations, with the aim of enabling the 11th General Conference to adopt a final decision, and at the same time it is emphasized that it has been decided for the present not to change the definition of the metre.

Thus, the 10th General Conference, at which specialists were represented not only in length measurement but also in other fields of metrology, did not agree with the latest proposal of the Consultative Committee.

There were no broad debates on this question at the conference, nor at the Consultative Committee. The scientifically grounded objections to the transition to a new definition of the metre may be found in articles written on this subject by the French metrologists: Pérard²˒³, Volle⁴, and Terrien⁵.

A sufficiently complete exposition of the question touched upon is given in Lenny’s article: “Standards of Length. Will Light Radiation Soon Replace the Metre Prototype”⁶, cited in the present journal under an abridged title⁷.

The principal objections to the transition to a metre defined by the length of a light wave reduce to the following two:

1. In order that the length of a light wave could be reproduced with high accuracy, a number of requirements must be observed regarding the conditions of emission of the light.

The necessity of fulfilling these conditions, as it were, deprives the length of a light wave of its “natural” character.

1. The transition to defining the metre by the length of a light wave will not entail an increase in the accuracy of length measurement.

Let us dwell on the first, most essential objection. Indeed, the profile of a spectral line depends on a number of causes: the natural width of the line, thermal broadening, broadening under the action of external electric and magnetic fields, broadening depending on the pressure of the gas or vapor inside the light source, the phenomenon of self-reversal, and the presence of hyperfine structure⁸.

These causes may give the line contour a complex asymmetric character. When the line contour changes depending on the conditions of emission, the position of the maximum that determines the effective wavelength of the spectral line may change. Moreover, the effective wavelength of a spectral line having incompletely resolved hyperfine structure, even with a stable contour, changes when the path difference in the interferometer changes[^9].

There is no doubt that the conditions of emission must be standardized in one form or another. The need for a specification for reproducing the principal wavelength (the wavelength standard) becomes entirely clear if one recalls that this wavelength must be reproduced with an accuracy of up to 0.0001 or even 0.00005 Å, i.e. the error of its reproduction must be approximately 10,000 times smaller than the dimensions of the emitting atom. It is impossible that achieving such high accuracy should not require observance of a number of precautions; this, in our opinion, does not deprive the light wave of its “natural” character and does not prevent it from being regarded as invariable with time.

Since the causes that can broaden the line contour or make it asymmetric are numerous and varied, it is expedient to abandon the standardization of the radiation source—its dimensions, current density, voltage, and the pressure of vapors and gases inside the light source—as is now done in reproducing the red cadmium line in Michelson’s standard lamp[^10].

It is much more correct to impose requirements on the emitted spectral line itself, requirements that would make it possible to conclude that the asymmetry of the contour and the associated displacement of the maximum are small and cannot have a noticeable influence on the value of the wavelength of this line[^11],[^12].

Without forgetting the necessity of establishing a number of conditions in reproducing the spectral line, one should not exaggerate the difficulties of observing them. Numerous investigations of the reproducibility of the wavelength of the red cadmium line, both in Michelson’s standard lamp and in other light sources, have shown that this wavelength can be reproduced with an error not exceeding 0.0001–0.0002 Å.

On the basis of what has been set forth, the problem of rationally choosing the principal wavelength is reduced to choosing such a spectral line as would allow the established specification to be met with the least difficulty. This means that the energy levels determining the given line must be least subject to the influence of emission conditions. In brief, the requirements for the principal spectral line may be reduced to one: the wavelength of the principal spectral line must possess the highest reproducibility.

Let us dwell on the second objection to the transition to a new definition of the meter. It is pointed out that such a transition will not lead to an increase in the accuracy of length measurement in comparison with the existing situation, when the length of the meter is defined by the platinum-iridium prototype of the meter.

The accuracy of length measurement, for both line measures and end measures, is determined not only by the measuring instruments and methods, but also by the perfection with which the measures themselves are made: by the macro- and microgeometry and the mutual parallelism of the surfaces bounding the end measure, and by the width and quality of the lines engraved on the line measure. At the present time the lines on the prototype meter and on the meter standards are wide (about \(8\ \mu\)) and insufficiently perfect. With such lines, when comparing the lengths of two meter standards, only as a result of 8–10 measurements can the mean square error of the measurement result be brought down to \(\pm 0.1\ \mu\). The same error will accompany the determination of the length of a working decimeter standard.

Our experience shows that, in 10-fold measurements of the length of a 100-millimeter end measure by comparing it with the wavelength of light by the interference method, the error can without difficulty be brought down to \(0.005\ \mu\), i.e., the end measure can be measured 200 times more accurately than the line measure. In passing to a greater length, in particular to a meter end measure, the multiplication method is applied\(^{13}\). In this case the relative error remains constant and is equal to the relative error of determining the initial length. Taking the red line of natural cadmium as the basis, it is expedient to take the initial length equal to \(100\ mm\), which gives an error of the order of \(0.05\ \mu\) in measuring the length of a meter end measure.

In passing to the new definition of the meter it will be necessary to measure line standards of the meter in wavelengths of light. At present, for this purpose the method of end contacts is used, which reduces to converting an end measure, previously measured in wavelengths of light, into a line measure.

The error accompanying this transition is often exaggerated, i.e., the error in determining the distance between the lines on two end contacts rubbed onto the surfaces of the end measure. Our experience shows that the error in determining the length of a meter standard by this method reaches a value of \(\pm 0.1\ \mu\), i.e., it is of the same order as the error obtained when comparing this standard with the state standard of the meter\(^{14}\).

In the future it will be possible to use other, more perfect methods for comparing the length of a line measure with the wavelength of light\(^{15}\). To implement one of these methods, M. B. Brzhezinsky has at present created at VNIIM a universal interference comparator, allowing more direct

method compare the length of a line measure with the length of a light wave.

Thus, in the transition to a new definition of the meter, the accuracy now obtained when measuring meter line measures, when the unit of length is defined by the length of the prototype meter, may without difficulty be achieved.

As for a further increase in accuracy, for this what is needed first of all are measures with more perfect lines than the lines on the prototype and on the national standards of the meter.

If the transition to a new definition of the meter does not in all cases increase the accuracy of length measurement, it will increase the reliability of these measurements, since the length of any measure can, if necessary, be compared “with the light meter,” something that is completely excluded at present, when the unit of length is defined by the length of the prototype meter.

In putting forward the rather substantial objections cited above, none of the authors believes that the transition to defining the meter by the light wave, i.e. the transition to the “light meter,” is in principle inexpedient.

Some metrologists, both in the USSR and abroad, believe that the present prototype meter (meter-standard) fully meets the requirements of contemporary practice and that, consequently, it is possible to “wait” before moving to a new definition of the meter for a considerable period of time. Thus, for example, P. M. Tikhodeev writes: “in concluding the survey of the state of affairs with the unit of length, it is useful to emphasize that in general it is capable of satisfying the high requirements of practice in the sense of accuracy and invariability for many years yet” ^15.

This point of view is not shared by specialists in the field of length measurement; in particular, it is not shared by the metrologists of the International Bureau of Weights and Measures, where the prototype meter is kept. A. Pérard, objecting to a hasty transition to a new definition of the meter, nevertheless believes that the measurement of the length of end measures cannot be fully provided by the line prototype of the meter. Therefore measurements of length must be based on two standards—the line standard and the light standard. The task of the unity of measurements is reduced to establishing the exact relation between these two standards.

The director of the International Bureau, Ch. Volet, believes that in its present form the meter-prototype does not provide the necessary accuracy even with respect to line measures. A situation in which two standards of the meter, after new, more perfect lines have been engraved on them, will be compared with one another with greater accuracy than each of them with the meter-prototype cannot be considered normal. Volet therefore considers it necessary in the near future to engrave new, considerably more perfect lines on the national standards and copy standards, and to compare these meter standards with

with one another and once, as accurately as possible, with the prototype of the metre, and to assign to each of these standards its value. This set of metres will subsequently form a group standard defining the unit of length.

In the future, the metre-prototype will no longer be used in international comparisons[^3].

Thus, in Vole’s opinion, the transition to a new definition of the metre is inevitable, but it is possible not to connect the new definition of the metre with the length of a light wave.

It seems to us that objections to the transition to a “light metre” arise mainly because, after this transition, the methods of maintaining the unity of measurements will have to change substantially. Instead of preserving the prototype of the metre and periodically comparing national metre standards with it, the International Bureau will have to undertake the organization of comparisons of the results of measurements in various countries of end standards, and then of line standards, in light waves. The International Bureau of Weights and Measures began such comparisons only in 1952–1953. At present the processing of the comparison results has not yet been completed.

These new methods are more familiar to the metrologists of our country. In the USSR a system has been established of mandatory state verifications of the length of steel plane-parallel end measures. In these measurements the standard of length is the length of a light wave[^17]. Direct measurements of the length of end measures in light waves, or “verification of plane-parallel end measures of the 1st grade by the absolute interferometric method,” are carried out in the laboratories of the All-Union Scientific Research Institute of Metrology (Leningrad), its Sverdlovsk branch, three State Institutes of Measures and Measuring Instruments (Moscow, Kharkov, Novosibirsk), and in the Leningrad Administration of Measures and Measuring Instruments.

For the purpose of maintaining the unity of measurements with respect to end measures (up to 100 mm), the listed laboratories annually measure four measures (5, 20, 50, and 100 mm) and send them to VNIIM. Here the measures are verified a second time. The magnitude of the discrepancy between the measurements in one of the listed laboratories and at VNIIM gives an estimate of the suitability of the interferometric installation and of all measurement conditions for ensuring the required measurement accuracy. Such annual comparisons were begun as early as 1939 and resumed in 1945.

Analyzing the results of these comparisons, one can see how gradually the laboratories improve their installations and increase the accuracy of measurement. Whereas earlier the permissible discrepancy in these measurements for a measure of 100 mm was set equal to 0.1 μ, in recent years the permissible discrepancy has been reduced to 0.07 μ. The greatest accuracy was achieved in comparisons

results of measurements between the KhGIMIP and VNIIM laboratories in 1954; the discrepancy between the results of measurement of all four measures did not exceed 0.01 μ.

The data presented refute the statement made by Lennuier^6 in the previously cited article, which says that reproduction of the standard in the form of a light wave is a difficult task, inaccessible to an ordinary laboratory.

Preserving the definition of the meter by the length of the meter prototype inevitably leads to a duality in the definition of the unit of length, which became especially noticeable after interferometric measurements had been mastered and the red cadmium line began to be used as a standard not only in spectroscopy for measuring wavelengths, but also in practice for various precise measurements of length.

In our country, interferometric methods were developed and interferometers were created for measuring end standards up to 1 meter and up to 1.2 meters. The state standard of the meter, by means of a one-meter end standard, is periodically compared with the wavelength of the red line of natural cadmium. The state standard of the meter of the USSR may therefore be considered a reproducible standard. Such a situation corresponds to the actual transition to the light meter^13.

A dual definition of the meter does not cause great difficulties in practice so long as the prototype meter preserves its length. As soon as a discrepancy appears between the length of the “light meter,” determined by the established value of the red cadmium line, and the length of the prototype meter, the transition to the light meter will become inevitable. Otherwise it would be necessary to assume, without sufficient grounds, that the wavelengths of all spectral lines had changed their value.

CITED LITERATURE

1. Proc. Verb. C. I., Pds. et Mes. (tirage à part), XXIV, M—22 (1954)
2. A. Pérard, Comptes rendus 237, 284—287 (1953).
3. A. Pérard, Comptes rendus 237, 364—367 (1953).
4. Ch. Volet, Proc. Verb. C. I. Pds et Mes., XXIV, M—12 (1954).
5. J. Terrien, La Revue Française de l’Élite Europ., 41, 21—24 (1952).
6. Robert Lennuier, Astronomie 67, 357 (1953).
7. N. Malov, UFN 53, 3, 433 (1954).
8. A. Pérard, La créature du Bureau international des Poids et Mesures et son oeuvre, Gautier-Villard, 259—292 (1927).
9. A. Pérard, Rev. d’Optique 7, 1 (1928).
10. Comptes rendus des séances de la septième conférence générale Pds. et Mes. en 1927, 40, 53 (1927).
11. Same, in 1948, 85 (1949).
12. See 1, M—87 (1954).

1. M. F. Romanova, UFN, XLVII, 2, 161 (1952).
2. M. F. Romanova, E. A. Volkova, L. K. Kayak, Trudy VNIIM, issue 16 (76), 4 (1951).
3. J. Terrien, Comptes rendus 238, 1001 (1954).
4. P. M. Tikhodeev, Essays on Fundamental Measurements, Mashgiz, 51, 1954.
5. OST 85000—39—Flat-parallel end measures of length.