Contains reports on five research projects.Lincoln Laboratory (Purchase Order DDL B-00306)United States Air Force (Contract AF19(604)-7400)United States NavyUnited States Arm

Funkhouser, A. T.

King, J. G.

Papa, D. Cosmo

Stroke, G. W.

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VII. MOLECULAR BEAMS*Prof. J. R. Zacharias R. S. Badessa F. J. O'BrienProf. J. G. King V. J. Bates J. E. SteelmanProf. C. L. Searle H. H. Brown, Jr. C. O. ThornburgDr. G. W. Stroke D. Buhl R. WeissE. L. KamenA. MEASUREMENT OF THE VELOCITY OF LIGHT1. RESUMPTION OF MEASUREMENT AND OBJECTIVESAfter a three-year interval, during which G. W. Stroke was engaged in theoreticaland experimental work involved in the improvement of high-resolution diffractiongratings, we have resumed this measurement which should result in the first measure-ment of the velocity of light carried out in terms of primary constants. We are firstaiming for an accuracy of 10 - 6 , which we estimate to be at least one order of magnitudebetter than the accuracy of measurements that have been described thus far.A study of past experiments shows a spread in the centers of gravity of the valuesof c of almost 10 - 4 , even though the greatest precision given is of the order of 3 X 10 - 7The most recent value for c is now given as c = 299, 792.5 ± 0. 1 km/sec. It thusbecomes clear that the accuracy of c in past measurements was not nearly as great asthe precision of the experiments, and one can easily attribute the lack of accuracy touncertainties in the values of the length standards which have been used heretofore. Infact, any attempt to read more into past discrepancies in various measurements, ofdifferent types, carried out at various periods of time (even within the past 50 years)are found to fail because of the inability of checking the length standard used in a partic-ular experiment (or of estimating the absolute error made in its use). (The situation is,of course, somewhat better for the frequency or time standards; here, astronomicalrecords and references to the period of rotation of the earth are of help). It is clear,of course, that we shall make our measurement directly in terms of primary constants(Hgl 9 8 light source for the length, and Cs 1 3 3 atomic clock for the frequency). Thus wehope to get an accurate value in terms of these standards, provided that any systematicerrors are avoided or properly accounted for, as is usually the case in such measure-ments.We shall first use our microwave cavity resonance apparatus, which has been1 . -6described previously, in an attempt to measure c accurately to 10 . We have alsopreviously reported2 that variations in the diameter of our cavity are suppressed by a* This research was supported in part by Purchase Order DDL B-00306 with LincolnLaboratory, a center for research operated by Massachusetts Institute of Technologywith the joint support of the U. S. Army, Navy, and Air Force under Air Force ContractAF 19(604)-7400.105(VII. MOLECULAR BEAMS)factor of 10 in the TE 0 1 n mode, as a result of a judicious choice of the diameter andlengths for our precision optically ground and polished quartz cavity (which will besilver-plated on the inside). Therefore, if there were only a simple geometrical effect(which is in accord with an estimate of the effect of a small perturbation of a perfectcavity, and in terms of a solution of Maxwell's equations), it would appear that a varia-tion in diameter of 10 - 5 (or approximately 6 optical fringes, or 3 optical wavelengthsin the visible domain) in the 6-inch diameter would be tolerable. In reality, the pertur-bations enter asV (H 2 -E 2 ) dv (1)in a particular perturbed volume region within the cavity; they can thus be estimatedsomewhat more exactly than they could from geometrical considerations, but the orderof magnitude given above is a good one to guide the progress of the experiment. In fact,it immediately appears that the first investigation necessary for the advancement of theexperiment is one that is designed to verify the uniformity of the precision cavity thatwe obtained in 1957 (and which was mechanically measured by the manufacturer to beuniform within approximately 1 optical wavelength).3 Should the cavity be found to begood within a few optical wavelengths (in accord with the information given by the opticianwho made it), then a measurement of c that is accurate to 10 - 6 might be obtainedrapidly, and undoubtedly with much greater reliability than would usually be associatedwith correction calculations (even though these may be carried out satisfactorily). Theuse of a scheme of pneumatic distance-variation detection and the availability of themoving piston (the straightness of motion of which has now been ascertained) are newelements that will permit a considerably more accurate, and much simpler, measure-ment of the uniformity of the cavity (in diameter and straightness) than the interfero-metric means that was available at the time of the manufacture of the cylinder. Wenote also that this new cylinder-measuring scheme might permit a local opticalretouching of cylinders, which would not be unusual, neither costly nor long, and wouldbe similar to that used in finishing astronomical mirrors of comparable quality.Preliminary measurements indicate that the cavity may be sufficiently uniform topermit a measurement of c without the necessity of perturbation calculations, at leastfor measurements that are accurate to 10 - 6We can report on a number of significant points of progress in this direction. Theseare discussed in the following sections. All of this work should be referred to previousreports published from 1956 to 1958.G. W. Stroke(References on following page)106(VII. MOLECULAR BEAMS)References1. G. W. Stroke and J. R. Zacharias, Measurement of the velocity of light,Quarterly Progress Report No. 61, Research Laboratory of Electronics, M.I.T.,October 15, 1958, pp. 69-73.2. G. W. Stroke and C. L. Searle, Measurement of the velocity of light, QuarterlyProgress Report, Research Laboratory of Electronics, M.I.T., July 15, 1956,pp. 27-30.3. J. R. Zacharias and G. W. Stroke, Measurement of the velocity of light,Quarterly Progress Report, Research Laboratory of Electronics, M.I.T., January 15,1958, pp. 57-59.2. STRAIGHTNESS OF TRAVEL OF A MOVING PISTON IN THE 10-7RADIAN DOMAINThe new alignment interferometer which has been developed by one of us1 for therapid measurement of the straightness of travel of a moving carriage with a sensitivityof the order of 10 - 7 radian (1/50 second of arc) has been applied to the measurementof the straightness of travel of the moving piston that serves to obtain the resonance inthe cavity. The piston is moved by a Pyrex cylinder, 2 inches in diameter and 20 incheslong. It is guided by two sets of three brass cylinders (1/4 inch in diameter), tangentialto the Pyrex cylinder and set 6 inches apart. We have found that this arrangement movesthe piston parallel to itself (in the direction of the Pyrex cylinder axis) within ±1 fringe(10 - 5 inch) measured across a 6-inch lever arm (equal to the cavity diameter), or approx-imately ±0. 3 second of arc. Recall that the 2-inch Pyrex cylinder was optically polishedto be straight, after having been ground on the cylindrical grinder in the machine shopof the Research Laboratory of Electronics. This work had been carried out, however,at a time when no straightness measuring tool (such as the new alignment interferometer)was available. This cylinder straightness is good enough to permit measurement of theuniformity of the quartz cavity with the help of pneumatic detection, which will be dis-cussed in the next section. However, we may have to further improve the straightnessof the piston motion for the actual resonance measurement, with the help of servo controlof the brass-cylinder position, or alternatively use two alignment interferometers to helpin calculating the effects of small tilts in the measurement.A schematic diagram of the interferometer is shown in Fig. VII-1. The interfero-meter consists of a folded Michelson-Twyman-Green arrangement in which the two mir-rors, (5) and (6) in Fig. VII-1, may form part of the same "moving mirror," which, whenit advances in the y-direction without any rotation about the z-axis, results in an increaseof the same amount in the path lengths SAD and SBCD', and therefore in no additionalpath difference of fringe shift in the observing region R. In fact, it can easily beseen that a fringe shift will be detected at R only if there is any rotation of the107(VII. MOLECULAR BEAMS)- -MOVING MIRRORMIRROR(2)(5)A DFILTER MIRROR(3) zBEAMEXTENDED SPLITTER Z-AXIS UPLIGHT SOURCE )C OUT OF PAPERMIRROR(4) I D (6)IN LINTERFEROMETER SUPPORT(FIXED)OUTPHOTOELECTRICR FRINGE LOCATIONOR RETICULEFig. VII-1. Alignment interferometer."moving mirror" about the z-axis, which gives the desired sensitivity. It is also clearthat the interferometric sensitivity is obtained without any of the usual interference fringe"counting" involved in interferometric control interferometers; this feature permitsmeasurement at very high piston speeds if they are necessary. A full description of theinterferometer has been given in a paperl that will appear in the Journal of the OpticalSociety of America.G. W. Stroke, A. FunkhouserReferences1. G. W. Stroke, An alignement interferometer for precision straightness measure-ments (to be published in J. Opt. Soc. Am.).3. CAVITY DIAMETER MEASUREMENTWe have previously come to the conclusion that a measurement of the absolute diam-eter (in optical wavelengths) of the silver-coated cavity could best be obtained by settinga Fabry-Pdrot interferometer with its plates tangential to the cavity, with the help ofa pneumatic null-reading method such as that described in the next section. The separa-tion of the FP plates can be measured by mere inspection of the coincidence of fringesof different wavelengths originating from different light sources. In future reports weshall give more details about a program prepared for this purpose, during the pastquarterly period, on the IBM 709 computer. This program is designed to permit108(VII. MOLECULAR BEAMS)carrying out such an "absolute" measurement after only a comparatively crude mechan-ical length measurement to 1/1000 inch. In the past, it was necessary to carry outrather precise mechanical length measurements to better than 1/10, 000 inch when usingvisible wavelengths of 2 X 10- 5 inch. The new element here is that we have looked forcoincidences of several wavelengths at a particular FP plate separation. This permitsus to "slice up" space, as it were, into regions that are rather well separated (by dis-tances of approximately 1/1000 inch).G. W. Stroke, A. Funkhouser4. PNEUMATIC DETECTION OF SMALL MOTIONS IN THE MICROINCHDOMAINPneumatic measurements of the variation of the distance of a plate from a nozzlewith sensitivities of displacement of a liquid column in a manometer up to 1 inch per10- 5 inch of plate displacement have been used for more than 20 years, but remarkablylittle theory has been published. In fact, we have now been able to show that the physicaldescription of the situation can be rather simple and, as a result of the simple descrip-tion, significant improvements in the present remarkable sensitivity and accuracy havebecome possible. While past arrangements used only a single nozzle, we are using twonozzles set at approximately the same gap, as shown in Fig. VII-2. Also, by using analmost horizontal, only slightly inclined (10 per cent slope) manometer tube (draft gauge),we have been able to obtain sensitivities of up to 10 inches per 10- 5 -inch gap variation(Ah), as shown in Fig. VII-3.With the help of a series of experiments, we have been able to satisfy ourselves thatwith the nozzle dimensions shown in Fig. VII-4 and pressures at the nozzle of from 5 cmto 20 cm of mercury above atmospheric, the flow through the gap was indeed laminar,as is desirable. This is the case with the gaps from 2/1000 inch to 4/1000 inch usedin this series. Bernoulli's equation in the form2 p+ - = constant (2)2g pgappears to apply to this situation (v is the velocity of flow through a cylindrical crosssection of length h and diameter O.D. as in Fig. VII-3a, p is the pressure at the nozzleas in Fig. VII-3b, p is the density of the gas, and g is the acceleration of gravity). Weobtaindv dp2 dv (3)v pand, since dv/v = -dh/h, we also have109BEING MEASUREDFLEXIBLETUBEBP NOZZLE- REFERENCEB 7777 GAPFig. VII-2. Differential arrangement forsmall surface displacementspneumatic measurement ofAh P hr--- O.D. SURFACE OFI I Ah IS BEINGNOZZLEGAP-F-" WHICHMEASUREDh-T--Fig. VII-3. (a) Nozzle geometry.(b) Flow geometry.110FLEXIBLETUBEA(VII. MOLECULAR BEAMS)dp dh- 2 (4)p hwhere dp/p is the variation that is being measured by the manometer (draft gauge). Witha 4 X 10-3-inch gap and p = 10 cm of mercury (approximately 1/8 atmosphere) gauge,a Ah = 10- 5 inch results in a dp/p = 1/200 and Ap = 1/1600 atmosphere, with a gaugeinclined at 10 per cent (giving a water-level rise of 4070 inches per atmosphere) weshould expect column displacement of approximately 2 1/2 inches, which is in almostperfect agreement with the experimental value illustrated in Fig. VII-4. Furthermore,as can be seen for Eqs. 3 and 4, the sensitivity Ap/p = 2Ah/h is independent of thedensity of the gas, provided, of course, that the flow velocity (Reynolds number) issmall enough to have laminar flow. This density independence is also very well borne10-IO92/1000 INCH GAP 2/1000 INCH GAP(HELIUM) (NITROGEN)S 8-zZ 7/W 54 o 4/1000 INCH GAP0 U (HELIUM)a -  Oii / 4/1000 INCH GAP3 70 2 4 6 8 10 20 30po (CM Hg) PRESSURE AT DRAFT GAUGEOVER ATMOSPHERIC0()0 0 0 5 '//////////// ////////0 2 4 6 8 00920 GP(b)Fig. VII-4. Experimental values of liquid displacement per 10- 5 inch ofdisplacement of surface A in Fig. VII-2.111(VII. MOLECULAR BEAMS)out by the comparison of the measurements of helium and nitrogen (for which the approx-imate specific gravities are 18 X 10-5 and 13 X 10-4, respectively). All calibrationswere carried out by observing the interference fringe displacement when the gap wasvaried (1 fringe = 10-5 inch in the visible domain). We are now applying the scheme ofpneumatic detection to the measurement of the straightness of the cylinder, as well asto the measurement of its diameter, as we have mentioned. We shall report in moredetail on the corrections that need to be observed when comparing the gap either betweenthe nozzle and a cylinder or between the nozzle and a flat surface. It is clear from thephysical description given above that the same pressure reading will be obtained witha flat plate in a position where it cuts a segment out of the cylinder, rather than in a-5tangential position. Errors up to 15 X 10-5 inch could arise if this correction wereneglected in our experiment. This correction can be made negligibly small with a rec-tangular rather than a circular nozzle cross section. We plan to use such a nozzle forthe absolute diameter measurement that has been described. We recall I that an absolutediameter measurement is not essential in our velocity of light experiment (except pos-sibly for skin-depth corrections). We can indeed eliminate a diameter measurementby simply measuring the guide wavelength at two frequencies both of which are lockedto the atomic clock and can therefore be made to have an exactly known ratio.G. W. Stroke, J. G. King, D. C. Papa, A. FunkhouserReferences1. J. R. Zacharias, G. R. Harrison, G. W. Stroke, S. J. Mason, and C. W. Searle,Proposed measurement of the velocity of light in terms of two primary standards,cesium (Cs133 ) and mercury (Hgl98), Quarterly Progress Report, Research Laboratoryof Electronics, M.I.T., January 15, 1956, pp. 59-68.112

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