LIGHT WAVE AS THE BASIC MEASURE OF LENGTH

M. F. Romanova

In 1791, during the French Revolution, the meter was adopted as the unit of length, defined as a “natural” measure of length equal to one forty-millionth part of the Paris meridian. Subsequently, the difficulties of geodetic measurements and their insufficient accuracy forced the abandonment of the “natural” unit of length and led to the decision that platinum-iridium meter standards not only reproduce but also define the meter. At present, the state standard of length of the USSR is the platinum-iridium meter standard bearing the mark “28,” whose length at \(0^\circ\) C is considered equal to \(1\ \mathrm{m} + 0.71\ \mu\).

The development in recent years of interferometric methods of length measurement has made it possible to return once again to the question of a “natural” unit of length, this time in the form of the length of a light wave.

Defining the meter by the number of wavelengths has great advantages over its original definition as a fraction of the meridian. In fact, interferometric methods make it possible not only to reproduce the length standard in light waves, but also to apply the light wave widely in practice as the basic measure in measurements of the length of end standards.

In proceeding to define the length of the meter with the aid of the length of a light wave and to express the length of the meter in wavelengths of light, the following three tasks must be solved:

1) the choice of the principal spectral line whose wavelength will define the length of the meter;

2) the development of convenient methods of interferometric measurements and their extension to measures up to one meter in length;

3) the establishment of the value of the wavelength of the principal light wave at which the new meter would come as close as possible to the length of the existing meter.

At present, the principal light wave is considered to be the wavelength of the red cadmium line in air under normal conditions. This spectral line has been comprehensively studied over the course of

more than fifty years; in particular, repeated comparisons of its wavelength with the length of the meter were made[^1].

The results of these measurements, reduced to the following normal conditions: dry air containing 0.03% CO₂, having a temperature of 15°C and a pressure of 760 mm Hg, are given in the table.

Table

Wavelength of the red cadmium line in angstroms

The corrections in passing to the values of the last column were made in connection with a refinement of the values of the temperature coefficients of expansion of the national meter standards and of the conditions defining normal air.

It should be noted that, beginning in 1933, the measurements were carried out not only in air but also in vacuum.

Assuming equal weight for all these measurements, we have the following arithmetic mean value of the wavelength of the red cadmium line under normal conditions:

\[ \lambda = 6438{,}4696\,\text{\AA} = 0{,}64384696 \cdot 10^{-6}\ \text{m}, \]

and the mean square error of the measurement result

\[ S = \pm 0{,}0004\,\text{\AA}. \]

The convergence of these measurements, made in different countries by different methods and at different times, shows that, on the basis of the wavelength of the red cadmium line, the length of meter line standards can be determined with a relative error of the order of \(1 \cdot 10^{-7}\).

As for plane-parallel end measures, the accuracy of their measurement had to be even higher. Indeed, direct measurements of distances of the order of 100 mm between two parallel plane surfaces showed that the red cadmium line makes it possible to measure length with a relative error of \(2 \div 3 \cdot 10^{-8}\).

Measurements of one and the same length with standard cadmium lamps showed that the wavelength could change, in passing from one lamp to another, by no more than \(0.0001 \div 0.0002\) Å.

Moreover, replacing the standard cadmium lamp by lamps of another type (with a heated cathode, a hollow cathode) gave the same reproducibility of the wavelength. Only transition to a mercury–cadmium arc, accompanied by a considerable increase in the line width, led to a change in the wavelength amounting, according to our measurements, to \(+0.006\) Å.

Among the shortcomings of the red cadmium line one must include its considerable width. As is known, the width of a spectral line is determined chiefly by thermal broadening, whose magnitude is directly proportional to the square root of the absolute temperature and inversely proportional to the square root of the atomic weight. The mean atomic weight of cadmium is 112.41, i.e., almost half the weight of such a heavy element as mercury. It is impossible to reduce the thermal broadening by lowering the temperature, cooling the lamp with liquid air or nitrogen, as is done with lamps filled with krypton, since a sufficient pressure of cadmium vapor is obtained only at a temperature of about \(300^\circ\mathrm{C}\).

Owing to the large line width, the limiting path difference at which it is still possible to observe interference in the light of the red cadmium line does not exceed 300–350 mm.

Another major shortcoming of the red cadmium line is the presence in it of hyperfine structure. Using a light source with a hollow cathode and interference standards of high resolving power, we were able at one time³ to establish the presence of the following four components of the hyperfine structure:

\[ -0.0035\ \text{Å};\quad 0;\quad +0.0035\ \text{Å};\quad +0.0095\ \text{Å}\ \text{(weak)}. \]

Under these conditions one cannot hope for any further increase in the accuracy of determining the wavelength of this line in comparison with that already achieved, corresponding to a relative measurement error of the order of \(1.5 \cdot 10^{-8}\).

It is known, however,³ that the most accurate measurements of the length of meter measures by comparison with the state standard of the meter on a comparator are accompanied by a relative mean square—

with a relative error of about \(1.2 \cdot 10^{-7}\). Thus, despite the shortcomings of the red cadmium line indicated above, interferometric length measurements that reduce to comparing the length of a measure with the wavelength of the red cadmium line not only make it possible to measure length by means of a natural invariable standard, but also provide the possibility of increasing the accuracy of length measurement.

On the basis of these investigations, we believe that the first and third of the problems posed above—the choice of a spectral line and the establishment of its value—may be considered solved in a first approximation.

Fig. 1. Path of the rays in a large horizontal interferometer.

It remained to solve the second problem—the creation of convenient and accurate methods for measuring plane-parallel end measures up to one meter long.

Interference methods for measuring end measures up to \(100\) mm long are at present widely used and are based on the observation, in monochromatic light, of interference for the path difference determined by the length of the measure. By establishing, with the aid of interference fringes, the number of wavelengths fitting into the path difference, we thereby determine the length of the measure in wavelengths of the radiation in which the interference is observed.

On the basis of preliminary comparisons with the red cadmium line, the wavelength of this radiation can be expressed in fractions of a meter, which makes it possible also to establish the value of the length of the measure in fractions of a meter. This method can be applied only for path differences at which interference is still visible. With cadmium and krypton lamps, by this method, corresponding

direct comparison of the length of the measure with the wavelength of light; in the best case this is possible for end measures no longer than 150–175 mm.

For measuring end measures up to one meter long, we proposed a method based on the combination of an interferometer with multiply divided beams and an interferometer with two interference beams.

On the basis of this method, as early as 1940 a large horizontal interferometer was designed and built at VNIIM,^4 the optical scheme of which is shown in Fig. 1.

The main parts of the interferometer are a tubular standard and a double prism.

The tubular standard 1 is a steel tube 58 mm in diameter and about 100 mm long, to the vertically polished ends of which are fitted two plane glass plates silvered by the cathode-sputtering method (reflection coefficient 90–92%).

The double prism 2 is a modification of the dividing plate; it divides the beam of light that has passed through the tubular standard into parts a and b; one of them then falls on the upper surface of the steel end measure 3 being measured and of the steel plate 4 wrung to it, while the other part of the beam falls on the steel plate 5.

Under these conditions it is possible to observe the interference of beams a and b at small path differences, using white light from an incandescent lamp 6, in the case when the surface of mirror 5 is distant from the free surface of the measure and from the surface of the plate wrung to the measure by distances equal to 0, \(l\), \(2l\), \(3l\), etc., where \(l\) is the distance between the mirrors of the tubular standard.

If the length of the measure \(L\) is a multiple of the length of the tubular standard \(l\), then mirror 5 can be set so that measure 3 will be divided into two parts equal to

\[ m_1 l \ \text{and}\ m_2 l, \]

where \(m_1\) and \(m_2\) are integers and \(m_1 + m_2 = m\).

With a slight inclination of the surfaces of the measure being measured relative to plate 5, under these conditions it is possible to observe in white light two systems of interference fringes of superposition, analogous to the interference fringes of equal thickness with a central black achromatic fringe (Fig. 2).

The displacement of the achromatic fringes of these two systems, one of which is represented as located on the free surface of measure 3, and the other on the surface of plate 4 wrung to the measure, corresponds to the difference between the multiple value of the length of the tubular standard \(l\) and the length of the end measure \(L\)

\[ ml - L. \]

By reducing the air pressure in the tubular standard by means of a small pump and thereby decreasing the optical length of the tubular standard, the two systems of interference fringes can be brought into coincidence, as is shown in Fig. 2,b. In this case

\[ m(l-\delta)-L=0 \]

and

\[ L=m(l-\delta). \]

Thus, the measurement of the length of the measure \(L\) on a large horizontal interferometer is reduced to the measurement of the length of the tubular standard \(l\) and of the small path difference \(\delta\). Both of these measurements are made by comparing these lengths with the length of the light wave.

a          b

Fig. 2. Interference fringes of superposition.

The length of the tubular standard \(l\), approximately equal to \(100\ \mathrm{mm}\), is determined by the method of coincidence of the fractional parts of the order of interference when observing interference rings of equal inclination, still distinctly visible both in the light of the red cadmium line and in the light of krypton lines in ordinary gas-discharge lamps.

The length of the tubular standard was measured systematically and, as experience showed, changed little with time. This length therefore did not have to be measured anew at each measurement of the length of measure 3.

The measurement of the small path difference \(\delta\), which changes in passing from one measured measure to another, was carried out by determining the reading of a micromanometer connected with the tubular standard at the moment of coincidence of the two systems of interference fringes (Fig. 2,b).

The micromanometer was preliminarily calibrated when observing the fringes of superposition with the measure \(L = 100\ \mathrm{mm}\) in monochromati-

LIGHT WAVE AS THE FUNDAMENTAL MEASURE OF LENGTH

... in monochromatic light. By gradually changing the pressure in the tubular standard, we established the relation between the change in pressure and the change in the path difference \(2(l - L_{100}) = 2\delta\) by one fringe.

In the first tests of this installation we succeeded in measuring the length of the tubular standard with a probable error of the result of measurement

\[ R_l = \pm 0.006\ \mu \]

and the length of the meter end measure with an error

\[ R_L = \pm 0.08\ \mu . \]

The installation that had been created, making it possible to determine the length of plane-parallel end measures that are multiples of \(100\) mm and do not exceed \(1000\) mm, satisfied the requirements of technology, since the sets of measures longer than \(100\) mm produced by industry consist mainly of measures that are multiples of \(100\) mm.

By measuring the length of plane-parallel end measures on the large horizontal interferometer, it was possible to establish observation of possible changes in the length of the state standard of the meter.

For measuring the length of both state and working standards of the meter, which are line measures, it was possible to apply the same method of auxiliary plates that had been successfully used in our comparisons of the wavelength of the red cadmium line with the length of the meter prototype\(^1\). The auxiliary plates consist of two plane-parallel measures about \(1\) cm long, on the side surfaces of which there are lines.

The auxiliary plates were first wrung to one another, and the distance between them was measured on a comparator.

After these auxiliary plates were wrung to the meter end measure, measured in wavelengths, the latter became a line measure, the length of which was slightly greater than a meter and could be compared on the comparator with the length of the line platinum-iridium standard of the meter.

Measurements of this kind were carried out by us in 1949\(^5\). By increasing the number of measurements we succeeded in raising the accuracy of the interference measurements on the large horizontal interferometer and in bringing the probable error of the result of measurement \(R_L\) to \(\pm 0.04\ \mu\).

Improvement of the auxiliary-plate method made it possible, in comparing the length of the meter end measure with the length of the line state standard of the meter, to obtain a probable error of the result of measurement of \(\pm 0.1\ \mu\). Interference measurements of the length of the plane-parallel meter end measure, based on the fact that the value of the wavelength of the red cadmium line in normal air is equal to \(0.64384696 \cdot 10^{-6}\) m, led to the value of the length of the measure

at \(20^\circ\)C, equal to \(1\ m — 1.73\ \mu\). Comparisons with the state standard of the metre on a comparator gave a value of \(1\ m — 1.81\ \mu\).

If, for brevity, we call the metre determined by the length of a light wave the “light metre,” then these measurements lead us to the conclusion that the state standard of the metre is longer than the “light metre” by \(0.08\ \mu\).

The comparison of the wavelength of the red cadmium line with the length of the metre, carried out by us in 1941[^1], was also performed with the aid of the state standard of the metre of the USSR. These measurements, which we made by another method and on another apparatus, led to a value of the red cadmium line in normal air equal to \(0.64384687 \cdot 10^{-6}\ m\), instead of \(0.64384696 \cdot 10^{-6}\ m\). It follows from this that the length of the state standard of the metre at that time was also greater than the length of the “light metre,” but by \(+0.14\ \mu\).

Comparing these results with the results of measurements in 1949 on the large horizontal interferometer, we see that the change in the length of the state standard of the metre over the 9 years that elapsed between these two measurements did not exceed \(0.06\ \mu\). Such a change lies within the limits of the accuracy of measurement.

Thus, at the present time it is possible, by a sufficiently simple method, to determine the length of the state standard of the metre in wavelengths of light and to monitor its possible changes. This situation corresponds to the actual transition in our country to a metre determined by the wavelength of the red cadmium line.

A characteristic feature of the method we have proposed for interference measurements of measures longer than \(100\ mm\) is the possibility of extending the limits of measurement with almost unchanged relative measurement error.

In the case described by us, the relative error in measuring a metre end measure reached \(4 \cdot 10^{-8}\) and only slightly exceeded the relative error in measuring the length of the tubular standard, equal to \(3 \cdot 10^{-8}\).

Our approach in this respect differs fundamentally from the approaches being outlined by metrologists in other countries. They are attempting to solve the two above-mentioned tasks—1) the choice of the principal spectral line and 2) the development of methods for interference measurements of measures longer than \(100\ mm\)—simultaneously. It is considered necessary, when measuring large end measures, to make direct comparisons of them with the length of a light wave, just as is done when measuring measures up to \(100\ mm\) long. Such measurements can be made only with spectral lines that make it possible to observe interference at path differences considerably greater than \(300—350\ mm\), corresponding to the red cadmium line.

If this path is followed, then simultaneously with extending the limits of measurement to \(1000\ mm\), an increase in measurement accuracy by approximately a factor of 10 must also be obtained.

Naturally, in this case the choice of a spectral line that makes it possible to observe interference at large path differences is of greatest importance. Such a line can only be a simple line, having no hyperfine structure. Such lines can be emitted by individual even isotopes. As a replacement for the red cadmium line, Kösters6 proposed the emission lines of the krypton isotopes Kr84 and Kr86; later Meggers drew the attention of investigators to a light source filled with mercury vapor Hg198, obtained as the result of a nuclear reaction7.

In recent years numerous comparisons have been made of the wavelengths of this source directly with the wavelength of the red cadmium line8.

The main attention was concentrated on the most convenient green line \(\lambda 5461\). These measurements confirmed that the width of the green mercury line is smaller than the width of the red cadmium line and that, with its aid, direct interferometric measurements of length measures up to \(400\) mm could be made. However, even now the investigations do not go beyond comparisons with the wavelength of the red cadmium line and are therefore carried out only at such path differences at which interference can be observed using the red cadmium line.

The wavelength of the green mercury line Hg198 in new light sources proved to depend strongly on the pressure of argon, inevitably introduced into the electrodeless lamps excited at high frequency in order to increase the intensity of the radiation. Changes in wavelengths were already observed for changes in argon pressure of \(2\div 3\) mm Hg8, and, on changing to discharge tubes filled with argon at a pressure of \(10\) mm Hg, the change in wavelength reached \(+0.001\) Å.

The same phenomenon of the dependence of wavelength on gas pressure was found to an even greater degree in lamps filled with krypton isotopes6.

It turned out that the reproducibility of the wavelengths of the spectral lines in these new light sources does not exceed the reproducibility of the wavelength of the red cadmium line.

Under these conditions the measurement of the length of measures at increased path differences would present great difficulties owing to the uncertainty in the value of the wavelengths of the light. To this it should be added that the path differences at which interference can be observed in the new light sources still do not solve the problem of direct measurement of length measures up to one meter.

In our opinion, what should be required first of all of the principal spectral line is high accuracy in the reproduction of its wavelength. An increase in the accuracy of reproduction of the wavelength as compared with the red cadmium line, as the investigations cited above have shown, is not achieved by merely changing over …

to spectral lines devoid of hyperfine structure. The line must be chosen with due regard for the features of the energy levels that determine it. In order to make a final transition to a new spectral line, it is necessary to test not one or two, but a large number of light sources with simple spectral lines.

In this respect, the method developed in our laboratory by N. R. Batarchukova^9 for isolating individual components of the hyperfine structure of complex spectral lines by means of an interference monochromator offers a great advantage. Applying this method, we need not each time carry out the complicated work of isolating individual isotopes in order to have radiation that is simple and has no hyperfine structure.

Fig. 3. Interference rings corresponding to the radiation of the green mercury line (path difference 40 mm): a) green mercury line emitted by a mercury arc with water cooling; b) individual component of this line isolated by an interference monochromator.

The principal part of the interference monochromator, its dispersive system, is a plane-parallel glass plate, half-silvered on both sides. Just as a prism decomposes the light emitted by a source into a spectrum, and the exit slit of a prism monochromator selects an individual spectral line, the plane-parallel plate separates the components of the hyperfine structure, while a specially calculated diaphragm with a circular aperture selects the central interference maximum corresponding to one of the components of the hyperfine structure.

This radiation can subsequently be investigated with the aid of any interference instrument.

By isolating in this way the individual components of the hyperfine structure of the mercury line, one can obtain radiation which, in its monochromaticity, does not differ from the radiation of the same line in a lamp with mercury Hg^198.

Figure 3 shows the interferogram corresponding to the green line emitted by a mercury arc with water cooling

(left) and an individual component of this line, corresponding to the isotope Hg \({}^{198}\), isolated with the aid of an interference monochromator (right).

Subsequently, for reasons of convenience, one of the intense components of the green mercury line was isolated, corresponding to the radiation of the odd isotope Hg \({}^{199}\) (component “A”).

Comparisons of the wavelength of this component\({}^{10}\) with the wavelength of the red cadmium line, using both a mercury arc and a lamp with heated electrodes, led to the following value of its wavelength:

\[ \lambda = 5460.8316\ \text{\AA} \]

with a probable error of the measurement result

\[ R = \pm 0.0001\ \text{\AA}. \]

From the known difference in wavelengths of the components of the hyperfine structure, it may be calculated that the wavelength of the radiation of the green line of Hg \({}^{198}\) is correspondingly equal to

\[ \lambda = 5460.7539\ \text{\AA}. \]

This value is greater by 8 units in the last decimal place than the value obtained at the National Physical Laboratory in England in measuring the wavelength of the radiation of an electrodeless lamp containing the mercury isotope Hg \({}^{198}\) and argon at a pressure of 3 mm Hg.\({}^{8}\)

The discrepancy obtained is explained, on the one hand, by a possible error in determining the position of the components of the hyperfine structure of the green mercury line, located close to the central maximum, and, on the other hand, by the established fact that the wavelength of mercury radiation increases with increasing pressure.

Despite a certain instability in the value of the wavelength of component “A” emitted by a mercury arc, recently in our laboratory it has been possible to use this radiation for direct measurements on a horizontal interferometer of plane-parallel end standards up to 400 mm long. Thus, the limits for measuring the length of plane-parallel end standards, carried out without the use of a tubular standard, have been extended almost threefold.

Work on finding a new, most advantageous spectral line cannot yet be considered completed, but further systematic investigations of new monochromatic radiations do not prevent us from proceeding now to the definition of the metre in terms of the wavelength of light.

On the basis of the experience of our measurements, we propose that a new definition of the metre be adopted immediately, taking the metre to be equal to an established number of wavelengths of the principal light wave. As the principal wavelength of light, the wavelength of the red cadmium line should for the time being be retained.

Such a transition provides a number of advantages in maintaining the constancy of the unit of length reproduced by measures, and makes it possible to carry out further work to increase the accuracy of measurement both of end standards and of line standards, since the red cadmium line already makes it possible to increase the accuracy of measurement of the latter by approximately a factor of 5.

In passing to a new, more monochromatic line, it will be necessary only to compare as accurately as possible the wavelength of the new line with the wavelength of the red cadmium line, in the same way as this is now being done with respect to the green mercury line Hg 198.

The value of the length of the meter determined by a light wave, or of the “light meter,” will not change in passing from the red cadmium line to a new line, but will be refined.

The situation achieved in our country, representing an actual transition to the “light meter,” enables us to maintain the constancy of the unit of length not only in our country but also on an international scale, without resorting to comparisons of our state meter standard with the meter standards of other countries.

References

1. M. F. Romanova, G. V. Varlykh, A. I. Kartashev, N. R. Batarchukova, Comparison of the wavelength of the red cadmium line with the prototype meter, DAN 37, No. 2, 54 (1942).
2. M. F. Romanova and A. A. Ferkhmin, Hyperfine structure of the red cadmium line ($\lambda 6438$), the green ($\lambda 5562$) and yellow-green ($\lambda 5649$) krypton lines, DAN, No. 2, 55 (1933).
3. V. A. Barinov, The present state of length standards, 1939.
4. M. F. Romanova and A. I. Kartashev, Investigation of an interference apparatus for reproducing the meter in wavelengths of light waves, Trudy VNIIM, issue 7 (67), 23 (1949).
5. M. F. Romanova, E. A. Volkova and L. K. Kayak, Comparison of the length of the state prototype meter with the wavelength of the red cadmium line, Trudy VNIIM, issue 16 (76), 4 (1951).
6. Kösters, On highly monochromatic radiation of krypton isotopes, Procès-verbaux C. J. d. Poids et Mesures, XXII, 137 (1950).
7. Meggers, Wavelength of radiation of artificial mercury as the primary standard of length, UFN, XXXIV, issue 1, 105 (1948).
8. H. Barrell, Comparison of the standard of wavelengths emitted by a lamp with mercury Hg 198, Proc. Roy. Soc., 209 A, No. 1096, 132 (1951).
9. N. R. Batarchukova, Interference monochromator, Trudy VNIIM, issue 7 (67), 47 (1949).
10. N. R. Batarchukova and A. I. Kartashev, Determination of the wavelength of one of the intense components of the hyperfine structure of the green mercury line, Izv. AN SSSR, ser. phys. XIV, No. 6, 753 (1951).