LINEAR M E A S U R E M E N T S

NEW D E F I N I T I O N

OF T H E

METER*

E. A. V o l k o v a Translated from I z m e r i t e l ' n a y a Tekhnika, No. 8, pp. 5-.8, August, 1962 GOST (All-Union State Standard) 9867-61 which was approved by the C o m m i t t e e of Standards, Measures and Measuring Instruments on September 18, 1961, and comes into force on January 1, 1963, provides in accordance with the Tenth and Eleventh General Conferences on Weights and Measures ['L] the following definition of the meter: " T h e meter is a length equal to 1650763.'/3 wavelengths of radiations in vacuum, corresponding to the transition between levels 2pt 0 and 5d 5 of a krypton 86 atom." In the XIX CenturyBabinet pointed out, in connection with the successes of the wave theory of light propagation, the possibility of using the light wavelength as a natural standard of length. It is known that incandescent solid bodies radiate white light which, after passing through a prism, provides a continuous spectrum with wavelengths ranging from 0.4 to 0.7 ~. Hot vapors and gases radiate light whose spectrum has a number of lines, it is a l i n e s p e c trum. Each ling in the spectrum corresponds to radiations at a definite wavelength and provides a monochromatic light. The position of the lines in the spectrum and their wavelengths have a strict relationship to the a t o m i c structure of the radiating substance. The atoms radiate light owing to changes in the inner atomic energy which depends on the relative position of the atom nucleus and the external layers of its surrounding electrons. Moreover, the atoms can assume only definite energy states. The energy of these states is at different levels. The differences between the energy levels and the levels themselves differ for atoms of different elements. In their normal condition the atoms do not radiate and possess then a m i n i m u m energy E0. After excitation an atom passes to one of the possible states with a higher energy level E1, E2, etc. The atom then returns spontaneously to one of the possible lower states of energy. This process is a c c o m p a n i e d by radiation of light. According to the quantum theory of the atom t h e r a diated frequency u is represented by equation

EnmEra ~-----

h

'

(1)

where En is the energy level in the atom from which the transition is made; E m is the energy l e v e l to which the transition is made; h is Planck's constant. The wavelength corresponding to frequency v for a light propagated in vacuum with a velocity C is equal to

L=

C .g

"

(2)

Each transition of an atom from one energy state to another corresponds to the radiation of one line. There is a large number of atoms in various energy states when light is excited. Hence, a large number of lines is observed in the spectrum simultaneously. The wavelengths of the radiated lines are the most suitable for measurements in studying spectra. The reciprocal 1 / h of a wavelength is known as the wave number and is expressed in reciprocals of centimeters (cm-l). Having substituted for u in (1) its value from (2) we obtain the following expression in terms of wave numbers

1 L

m

En--Ern Ch

(3)

* In connection with the new definition of the meter the Editorial Board publishes the article by E. A. Volkova, who describes in a popular manner the essence of the new definition of the meter, its significance, and the possibility it provides for a further raising of the accuracy of linear measurements.

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Quantities En/Ch are c a l l e d spectroscopic terms. Thus, the wave numbers of the lines are proportional to the differences in the energy conditions of the radiating atoms. In studying radiation spectra of elements, term diagrams are produced on the basis of c a l c u l a t e d wave numbers. This provides the possibility of evaluating the peculiarities in the radiation of the e l e m e n t under investigation, of obtaining an idea coucerning the structure of its atoms, and providing a precise energy allocation to each s p e c t r a l l i n e . Monochromatic light is obtained by passing an e l e c t r i c current through a gas or a vapor. Separate spectral radiation liues of such a source are separated by means of a light filter or a monochromator. Lamps filled with inert gases, such as krypton, h e l i u m , neon, and lamps with mercury and c a d m i u m are used for measuring distances by means of wavelengths. The mercury and c a d m i u m lamps are filled for producing light with an inert gas, most frequently with argo n. The wave nature of monochromatic radiations and its periodic characteristic provide a s i m i l a r i t y between the series of wavelengths and a line measure with calibration spaced at a distance of a wavelength ~. The accuracy of measurements by means of line measures depends on the regularity of calibrations, the thickness of the calibrating lines and file method of counting them. Intercepts of a straight line can be measured in terms of wavelengths by means of interferomerers. Monochromatic sources of light radiate wavelengths which can be compared to graduations with a line thickness of 0.01 /J. The regularity of such *graduations" exceeds by a factor larger than 10,000 the best line scale. The accuracy of measurements by means of interferometers is 1-2 orders higher than that of comparators used for c o m paring line scales. In order to produce an interference pattern the light oscillations must be coherent, i.e., they must have a constant phase difference between them. For the purpose of obtaining coherent light waves, the light beam coming from a single source is divided in the interferometer into several parts, each of which traverses different paths. On c o m ing together again these wavelengths produce interference. Various interferometers are used at present for measuring lengths. Tile source of light Used for measuring lengths by means of interferometers must m e e t certain requirements which are determined by the adding characteristics of the wavelengths. Each spectral line occupies a definite segment of the spectrum, i.e., it has a certain width. The intensity of radiation of various lines in the spectrum is represented by a curve along whose v e r t i c a l axis is plotted the intensity of radiation, and along the horizontal axis the wavelength. The distance between the points on the curve which correspond to half the m a x i m u m intensity of r a d i a tion is c a l l e d the h a l f - w i d t h of the spectral line. The width of the s p e c t r a / l i n e determines the m a x i m u m difference in paths for which interference can be observed. This difference in paths is known as the length of coherence, The m a x i m u m length that can be measured in terms of wavelengths by means of a certain spectral line or a section of the spectrum depends on the length of coherence. Thus, for instance, an interference pattern can be seen in white light for a difference in paths not e x c e e d i n g 5 p , i.e., it is possible by means of Michelson's interferometer to m e a s ure a distance not e x c e e d i n g 2.5 g. When c o m p l e x light filters are used which can isolate spectral lines with a h a l f width of 50-100 A, the length of coherence will amount to 10-20 p. The red line of c a d m i u m has a half-width of the order of 0.01 k and its length of coherence varies betweeen 300 and 350 mm depending on the construction of the lamp. Distances which e x c e e d considerably the length of coherence are measured in terms of wavelengths by first measuring by the interference method small segments correspondingto the coherence length of m o n o c h r o m a t i c sources. Next the s m a l l sections are c o m p a r e d by means of the interference method with larger distances, and for this purpose sometimes several comparison stages are used. A brief e x a m i n a t i o n of the m o n o c h r o m a t i c light radiation sources is necessary for their evaluation. Since the radiating atom does not r e m a i n in an e x c i t e d state for an infinitely long t i m e , the m o n o c h r o m a t i c source of light does not radiate a strictly determined frequency, but according to (1) it covers a certain interval of the spectrum with frequencies in the range of u + ~ u and v - k u . This segment is known as the natural width of the line and it amounts to 0.000119 A. Moreover, the atom during radiation is subjected to certain external effects which produce certain changes in the frequency and a m p l i t u d e of oscillations of electrons in the atoms. This increases the width of the spectral line. The width of the line depends on the nature of the radiating substance, the position of the line in the spectrum, the

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construction and temperature of the source of light, and the method of generating the glow. The greatest widening of spectral lines is produced by the Doppler effect due to the thermal agitation of atoms. The width of the lines due to this effect becomes 40-100~ greater thanits natural width. The width of the lines is also affected by the gas pressure at the source of light and by electric and magnetic fields (Stark and Zeeman effects). A careful study of the distribution of spectral line intensities by means of instruments with a high resolution has shown that natural elements radiate complex lines. These lines possess a so-called hyperfine structure. Each line with a hyperfine structure consists of several closely placed components whose spacing is extremely small, of the order of one-hundredth of an angstrom. Different intensities of the hyperfine structure components of a complex line may produce an asymmetrical contour of the line. The hyperfine structure, according to the quantum theory of light, is due to the nucleus and electrons of an atom possessing both mechanical and magnetic moments, Depending on the nature of the radiating substance and the wavelength of the spectral line, the number of hyperfine structure components and the spacing between them may differ. The outline of a spectral line can be measured by means of the self-reversal effect. The light source layers with a low luminence located near the walls of the bulb absorb part of the radiated spectral line. The greater the number of absorbing atoms of the substance placed in the path of the light, the greater becomes the self-reversal effect. A narrow strip in the center of a spectral line is most frequently absorbed. The self-reversal effect in lines depends on the design of the source of light and on the radiation process peculiarities due to the atomic structure of the radiating substance. The width of the spectral line, its hyperfine structure and the shape of the outline are of great importance for metrological work. An unsymmetrical outline and complex structure of the line may produce in the interference pattern a redistribution of intensities, according to the length of the path differences, thus producing a displacement of the maximum points. For a large number of hyperfine structure components the variation in the path differences may even produce a periodic fading-out of the interference pattern. A variation in the path difference with an asymmetrical contour of lines produces an apparent variation in the wavelength. Hence, the concept of an effective wavelength which corresponds to the center of gravity of a complex line has been introduced.

Type of lamp and element used Cd n4, with incandescent electrodes HEtgs, without e l e c trodes Kr ~6, with incandescent electrodes

Length Temperof coherence, ture of of spectral source,*C line wave, A em +300

6438

33

+ 20

5461

55

-210

6057

91

Drawing another parallel between graduations of a scale and wavelengths, it should be noted that the latter, like the former, have a systematic error which can distort the results. Thus, it is necessary for accurate measurements in terms of light wavelengths to select a monochromatic spectral line which should possess with a sufficiently symmetrical outline a small width, adequate brightness and reproducibility of its wavelength. A large number of experiments with spectral lines radiated by natural elements has shown that a hyperfine structure of lines limits the accuracy of distance measurements. In 1940 scientific advances in the sphere of atomic physics made it possible to obtain separate isotopes of various elements. Spectral lines of even-even isotomes, i.e., isotopes with even ordinal numbers in the periodic system and atomic weights expressed by even numbers do not possess a hyperfine structure. Thus the possibility of obtaining isotope substances has opened up new prospects for raising the accuracy of interference measurements of distances. In 1948 the Ninth General Conference of Weights and Measures adopted a resolution which noted the necessity for a scientific study of spectral lines radiated by isotopes with a view to applying them in the future for a new definition of the meter. In the Soviet Union [2] as well as in other countries a large number of radiation sources was

628

tested, which consisted of even isotopes of krypton (Kr 84, Kr86), mercury (Hg t98) and c a d m i u m (Cd tt~, Cd I14, CdU6). These tests have shown that, from the m e t r o l o g i c a l point of view, the best are the lines radiated by lamps with incandescent electrodes and consisting of the red line of Cd n4, the y e l l o w - g r e e n and orange lines of Kr s6, and the green line of Hg 198. The attached table shows the characteristics of radiations provided by lamps with even isotopes. A study of the Hgrt~ green line has shown that it is subject to the self-reversal effect even at a source t e m p e r a ture below 20~ The width of the line is also affected by the pressure of argon in the lamp. The width of the red line of Cd 114 is affected by the temperature of the source and the pressure of argon. The orange line of Kr 86 with a wavelength of 6057 A was studied with a temperature of the source lowered to the triple point of nitrogen (-210"C). The pattern of variations of this l i n e - w i d t h with respect to the pressure of krypton and the strength of the e l e c t r i c field in the lamp was studied. This made it possible to select for a lamp with incandescent electrodes a Kr 86 e x c i t a t i o n condition which provided a radiation process of the orange line due to an electron transition in the atom between levels which were least subjected to external effects. Such radiation can be reproduced with great precision. The Kr s6 radiation used for specifying the meter is c h a r a c t e r i z e d in the international resolution by spectral terms denoted according to Pasehen. The inert gas krypton was discovered as a component part of air in 1894. Its amount by volume in a i r i s e q u a l a p p r o x i m a t e l y to 0.0001%. Krypton belongs to the zero group of the periodic system, its ordinal number is 36 and its a t o m i c weight 83.7. Krypton is obtained by ratification of liquid air. Natural krypton is a mixture of six isotopes with a t o m i c weights of 78, 80, 82, 83, 84 and 86. It is known that the o p t i c a l properties of atoms are d e t e r m i n e d by the number of electrons in the external shell. The krypton atom, like other atoms of inert gases, has 8 peripheral electrons which form a closed and very stable shell. The krypton spectrum is very rich in lines which amount to some 200 in the visible portion. For the first t i m e the spectrum of an inert gas, neon, was deciphered byPaschen in 1919. He then introduced his own notations for terms. Investigators found it advisable in subsequent and modern work for studying the spectra of inert gases to use notations originated by Paschen [3]. The attached figure shows a diagram of a krypton atom in ~.M"q terms denoted according to Paschen [3]. Each term is I K'~on: represented b y a horizontal line. Wave numbers in re'~S ,.r162162 I " g3" 1/29fs 21 ~ _ ciprocals of centimeters are plotted from the bottom ~lgO00 7 os =-- " upwards along the v e r t i c a l axis. The normal condition ,]$---of a krypton atom corresponds to l e v e l P0 (line P0 is fO000O 2s shown conventionally since the distance 0-800000 cm -t is out of scale with respect to the graph). Where an ~000o electron is detached from an atom the latter becomes ,0 ionized and can occupy one of the levels denoted by gOOO# f$ -p,i 2p0~189or 2P~89 A neutral e x c i t e d atom can be in a n y o f s the terms classified on the graph into four groups s_ p, 0~////////////////////////////////////////////////2//////////i d and f_ In e a c h group the condition of the atom is c h a r a c t e r i z e d by the value of the internal quantum n u m ber which determines the full angular m o m e n t u m of the atom [8]. In all the groups the value of the terms rises according to the m a i n quantum numbers. -

-

Each term is denoted by a large figure proportional to the main quantum number, a l e t t e r indicating in what group the t e r m is located, and a small figure in the form of a subscript which indicates the number of the sub-group. For instance term s has notations lss, 3s4, etc. For g r o u p s the term numbers begin with 1, for group p with 2, and for group d with 3. In order to f a c i l i t a t e the p r a c t i c a l d e t e r m i n a t i o n of the newly defined m e t e r an instruction* has b e e n issued for obtaining the radiation of Kr s6 at levels of 2pt0-5d ~. * See a r t i c l e by N. R. Batarchukov, Yu. P. Efremov, and G. S. Popov which appears in this issue.

629

The orange line of Kr s6 radiated by a l a m p which was recommended by the International Bureau was carefully tested [4]. These tests revealed that the wavelength of the orange line can be reproduced with an error of the order ~ 3 . 1 0 "9, i . e . , the new standard provides measurements of a considerably higher precision than that obtained with the old definition of the meter. Measurements by means of the newly-defined meter are carried out with the standard Kr 86 l a m p placed in front of the interferometer which is used for measuring block gauges or line measures. The accuracy of measuring distances in terms of wavelengths depends to a great extent on the construction of the interferometer and the conditions of measurement. The D. I. Mendeleev A l l - U n i o n Scientific Research Institute of Metrology (VNIIM) had developed in our country a method [5] and produced interferometers for measuring block gauges up to 1.2 m long by means of light wavelengths [6]. Block gauges up to I m long have been certified by means of a VNIIM horizontal interferometer for the past five years. The relative value of the quadratic mean measurement error of a block gauge amounts to 5- 10 "s. Another interferometer [7] has also been produced by the VNIIM for measuring line measures up to 1 m long. This provides facilities for measuring line measures in terms of wavelengths, for comparing line measures and block gauges, or comparing with each other the lengths of two line measures or two block gauges. For measurements in terms of wavelengths this interferometer operates on the same principle as the VNIIM horizontal interferometer. Other measurements are carried out by means of various original devices which provide high precision of m e a s u r e ment. The interferometers* produced by the VNIIM provide measurements in terms of the Kr sa orange line w a v e length. Thus, the new definition of the meter brings further considerable progress to our national economy.

1. 2. 3. 4. 5. 6.

LITERATURE CITED I z m e r i t e l ' n a y a tekhnika, 1960, No. 11. N.R. Batarchukova, UFN, 1955, VI, No. 2. J. Terrien, Mesures, 1961, No. 294. E. Engelhard and J. Terrien, Rev. d'Opt, 1960, 39, 1. M . F . Romanova and A. I. Kartashev, Transactions of the VNIIM, 1949, No. 67 (7). E . A . Volkova, A. I. Kartashev, M.F. Romanov, and V. S. Stepanov, Transactions of the VNIIM, 1955, No. 26

(86). 7. 8.

M . L . Brzhezinskii, Transactions of the VNIIM, 1955, No. 26 (86). A. Z o m m e r f e l ' d , Structure of an Atom and Spectra [in Russian] v. 1, GITTL (1956).

MEASUREMENT

OF L A R G E P A T H

OF AN I N T E R F E R E N C E A. I . K a r t a s h e v

DIFFERENCES

BY M E A N S

MONOCHROMATOR and

A . P. K i r i c h e n k o

Translated from I z m e r i t e l ' n a y a Tekhnika, No. 8, pp. 9-11, August, 1962 Papers have recently appeared ['1, 2] on the possibility of observing interference for large path difference by means of an interference monochromator equipped with a spherical Fabry-Perot standard (FPS). However, the fact that interference can be observed for large path differences does not m e a n that lengths can be measured a c c u r a t e l y over such distances. The problem of the stability of wavelengths obtained by filtering the radiation is e x t r e m e l y important, e s p e c i a l l y if it is required to measure distances with an error of 1 - 2 . 1 0 -8 . It can be stated c a t e g o r i c a l l y that despite a n y a r t i f i c i a l narrowing of spectral lines it is impossible to determine a wavelength more a c c u rately than the precision with which the original wavelength has been determined. To provide a reproducibility of the isolated segment with the required accuracy is not an easy task. Hence, the o b j e c t of the present work is to find * See articles by N. R. Batarcbukova and A. P. Kirichenko and b y A. I. Kartashev and A. P. Kirichenko, which a p pear in this issue.

630