The Continuity of the Meter: The Redefinition of the Meter and the Speed Of Visible Light

The product of the frequency and wavelength of the ith hyperfine component of the 11-5, R(127) transition of 127I2 yields a value for the speed of visible red light. This value of c, the most accurate ever measured for visible light, agrees with the value defined in the redefinition of the meter within the 3σ error limits of the krypton length standard.

The speed of light has intrigued scientists for several centuries and during the short quarter century of the laser it has not been different.  [2] This definition for the meter fixes the speed of light to be exactly 299 792 458 m/s. With this definition the meter could be realized from the wavelength of any coherent optical source whose frequency is known, for example, a laser which is stabilized to a narrow atomic or molecular absorption for which the frequency is known. The wavelength A would be determined from the relation A=clv, where c is the fixed value of the speed of light, and v is the measured frequency of the transition. Since the measurement in 1972 there have been four speed of light measurements [3][4][5][6]; two at a wavelength of 3.39 p.m and two at a wavelength of9.31 p.m.These measurements have been summarized [7], and the average value for the speed of light is 299 792 458.1 mls with a fractional uncertainty of ±4 X 10-9 (30-), which is the recognized uncertainty in the realization of the meter from the krypton definition.
Weare reporting a value of c using visible rather than infrared radiation. This has been made possible by the absolute frequency measurement of the visible He-Ne laser stabilized on the r h hyperfine component of the 11-5, R(127) transition of the molecule 12712 [8]. The reported value for the frequency of this transition is 473 612 214.830 MHz with a fractional uncertainty of 1.6x 10- 10 . The wavelength for this transition is obtained from four published values which are 632 991 399.0±0.8 fm [9], 632991 399.8±0.9 fm [10], 632991 400.0± 1.2 fm [11], and 632 993 398.0±3 fm [12]. These four wavelengths are from direct wavelength measurements referred to the wavelength of krypton. The weighted average of these measurements is 632 991 399.4±0.6 fm. The value for the speed of light is, of course, the product of the frequency and wavelength and is c =299792 458.6±0.3 mis, with a one sigma uncertainty.
This value of c, the most accurate ever measured for visible light, is in good agreement with the defined value of c proposed by the CCDM within the recognized uncertainties in the use of the krypton length standard (± 1.2 mis, 30-) [11], and was the final confirmation in the choice of the new definition for the standard of length.
The fractional uncertainty of the meter realized through the new definition and use of a laser stabilized on either this frequency measured iodine transition [8], or another in the yellow region [13] is 10 times smaller than the uncertainty as realized through the krypton definition and would represent a tenfold improvement in accuracy for length metrology. Future frequency measurements in the visible will undoubtedly be even more accurate, ultimately being limited by the time standard itself. In fact, length metrology need not be limited by the frequency measurement of the laser used to realize the meter. Thus, with the new definition, a new era of length metrology is at hand, one in which the uncertainty will not be due to the length standard but with the measurement techniques. by means of one of the radiations from the list below, whose stated wavelength in vacuum or whose stated frequency can be used with the uncertainty shown, provided that the given specifications and accepted good practice are followed; and that in all cases any necessary corrections be applied to take account of actual conditions such as diffraction, gravitation, or imperfection in the vacuum.

LIST OF RECOMMENDED RADIATIONS, 1983
In this list, the values of the frequency I and of the wavelength A should be related exactly by the relation AI =c, with e =299792458 mls but the values of A are rounded. "Each of these radiations can be replaced, without degrading the accuracy, by a radiation corresponding to another component of the same transition or by another radiation, when the frequency difference is known with sufficient accuracy. Details of methods of stabilization are described in numerous scientific and technical publications. References to appropriate articles, illustrating accepted good practice for a particular radiation, may be obtained by application to a member laboratory of the CCDM, or the BIPM.

Radiations 01 Lasers Stabilized by Saturated Absorption
"The one-way· intracavity beam power is obtained by dividing the output power by the transmittance of the output mirror. with an estimated C overall relative uncertainty of ±6X 10-10 [which results from an estimated relative standard deviation of 2 X 1O-1~ apply to the radiation of a dye laser (or frequency-doubled He-Ne laser) stabilized with a cell of iodine, within or external to the laser, having a cold-finger temperature of 6 °C±2 0c. The unit of length is the meter, defined by the distance, at 0°, between the axes of the two central lines marked on the bar of platinum-iridium kept at the BIPM, and declared Prototype of the meter by the 1st CGPM, this bar being subject to standard atmospheric pressure and supported on two cylinders of at least one centimeter diameter, symmetrically placed in the same horizontal plane at a distance of 571 mm from each other." "Considering: that the present definition does not allow a sufficiently precise realization of the meter for all requirements, that progress made in the stabilization of lasers allows radiations to be obtained that are more reproducible and easier to use than the standard radiation emitted by a krypton 86 lamp, that progress made in the measurement of the frequency and wavelength of these radiations has resulted in concordant determinations of the speed of light whose accuracy is limited principally by the realization of the present definition of the meter, that wavelengths determined from frequency measurements and a given value for the speed of light have a reproducibility superior to that which can be obtained by comparison with the wavelength of the standard radiation of krypton 86, that there is an advantage, notably for astronomy and geodesy, in maintaining unchanged the value of the speed of light recommended in 1975 by the 15th CGPM in its Resolution 2 (c =299 792 458 m/s), that a new definition of the meter has been envisaged in various forms all of which have the effect of giving the speed of light an exact value, equal to the recommended value, and that this introduces no appreciable discontinuity into the unit of length, taking into account the uncertainty of ±4 X 10-9 of the best realizations of the present definition of the meter, that these various forms, making reference either to the path travelled by light in a specified time interval or to the wavelength of a radiation of measured or specified frequency, have been the object of consultations and deep discussions, have been recognized as being equivalent and that a consensus has emerged in favor of the first form, that the CCDM is now in a position to give instructions for the practical realization of such a definition, instructions which could include the use of the orange radiation of krypton 86 used as standard up to now, and which may in due course be extended or revised, "The 17th CGPM invites the CIPM to draw up instructions for the practical realization of the new definition of the meter to choose radiations which can be recommended as standards of wavelength for the interferometric measurement of length and to draw up instructions for their use."