problem of realizing the primary standard of light

Journal of the

OPTICALof

SOCIETYAMERICA

VOLUME 52, NUMBER 7 JULY 1962

Problem of Realizing the Primary Standard of LightC. L. SANDERS AND 0. C. JONES*

Division of Applied Physics, National Research Council, Ottawa, Canada(Received September 21, 1961)

Although the accuracy required of a primary standard of light is of the order of 0.1%, there is a spreadof 1% in the size of the candelas derived from the primary standards constructed at several national labo-ratories. In this paper, the standard has been critically appraised: Some of the suspected weaknesses havebeen studied experimentally, others are discussed at length.

A tantalum susceptor, used around the crucible containing the platinum to absorb the induced currentsand heat the platinum indirectly, increased the photometric precision by an order of magnitude. Thetechnique unfortunately introduced excessive contamination of the platinum.

Since none of the modifications has created the desired improvement in accuracy, other types of lightstandard may need to be reconsidered.

INTRODUCTION

THE history of the development from the oil lampswhich were used as national standards to the

present internationally adopted standard was treatedin detail by M. Debure in 1959.1 The primary standardof light, which was internationally adopted in January1948,2 is a blackbody at the freezing point of platinumwith a luminance by definition of 60 candelas per cm2 .This form of standard was first suggested by Waidnerand Burgess in 19083 and was first realized in 1930 byWensel et al.4 at the National Bureau of Standards inWashington. Several subsequent realizations have beendescribed in the literature.5-8

Figure 1 illustrates the experimental arrangementused in comparing the primary standard with a sub-standard lamp. Until 1952 a visual photometer wasused in place of the photocell. The equation in theinsert in Fig. 1 equates the illuminance per unit reading

* Now with the Light Division, National Physical Laboratory,Teddington, Middlesex, England.

' M. Debure, Lux 83 (September 1959).2 Proc. Verb. des Seances du C.I.P.M., 2nd series 20, 119 (1946).3 C. W. Waidner and G. K. Burgess, Elec. World 52, 625 (1908).4 H. T. Wensel, W. F. Roeser, L. E. Barbrow, and F. R. Cald-

well, J. Research Natl. Bur. Standards 6, 1103 (1931).6 H. Buckley and W. Barnett, Proc. Verb. des Sances du

C.I.P.M., 2nd Series 18, 247 (1937).6 Z. Yamauti and T. Iizuka, Proc. Verb. des Sances du

C.I.P.M., 2nd Series 19, Annex P41 (1939).7 M. H. Willenberg, Physik. Z. 40, 391 (1939).8 M. Debure and N. Leroy, Rev. opt. 31, 529 (1952).

of the photometer, obtained with the standard, to theilluminance per unit photometer reading, obtainedwith the substandard lamp. The various symbols in theequation given in Fig. 1 represent the following quanti-ties: A, area of lens diaphragm in cm2; T, transmit-tance of the lens and prism; 60, number of candelasper cm2 emitted from the primary standard (thisnumber is given by definition); R 2 , photometer readingwhile platinum is freezing; D2, distance from photocellaperture to lens diaphragm; R,, photometer readingat distance D from lamp; I, intensity of lamp incandelas.

After the NBS experiment had been repeated atNational Physical Laboratory, Teddington, England(NPL), and at Laboratoire Central d'Electricite, Paris,France (L.C.E.), with very nearly identical apparatus,the Consultative Committee on Photometry in 1937asked that participating laboratories should comparelamps with this form of standard and that the lampsshould be intercompared.9 This request was fulfilledand the agreement within 1% was considered to beadequate.'0 It was proposed to make the new standardeffective in January 1941, but international eventscaused the postponement of the effective date untilJanuary 1948.

9 Proc. Verb. des Sances du C.I.P.M., 2nd Series 18, AnnexP239 (1937).

10 Proc. Verb. des. Sances du C.I.P.M., 2nd Series 19, AnnexP58 (1939).

731

732 C. L. SANDERS AND 0. C. JONES Vol.52

CARBON

PROTOCELLIS SD, SUB- STANDARD LAMP

LENS

PHOTOCELL-PR S----

IGHT TUBE

LENS - DIAPHRAUM I AP RTURE

0 ~~0PORCELAIN 0RCL \

THURIA POWE 0THORIA CRUCILE 0

(4.5CM LONG2. CMS : 0SIGHT TUBE 0zo

O~~~ ~0= I ~~POWDER mo 7 /

60.A. ID 0 o0 o

INDUCTION HEATER COIL

FIG. 1. Illustration (not to scale) of the use of theprimary standard of light to calibrate a lamp.

The adoption of the blackbody at the freezing pointof platinum as the international standard in 1948 meantthat for the first time all the national laboratories wereusing the same standard. This was an important ad-vance which was expected to result in essential agree-ment in future international comparisons of lampstandards embodying the new unit, the candela. How-ever, the agreement in the 1952 or 1956-1957 inter-national comparisons"" 2 did not meet expectations.The results obtained in 1956-1957 are given in Table I.The total spread for the seven laboratories was 1.33%.Although part of this lack of agreement is attributableto the uncertainty involved in the exchange of smallgroups of lamp standards, it is probable that the majorcause is lack of reproducibility of results obtained withthe blackbody standard as it is set up and used at the

TABLE I. Values of the national candelas relative to the meanof seven laboratories in 1956-1957. The present NRC results aregiven for comparison purposes.

Country National candela

Germany (P.T.B.) 1.0065U.S.A. NBS) 1.0031Canada (N.R.C.) 0.9929France (CNAM) 1.0032Japan (E.T.L.) 0.9982Great Britain (N.P.L.) 0.9951U.S.S.R. (I.M.) 1.0009Canada (N.R.C.) 1960

(Corrected only for absorption) 0.9942Canada (N.R.C.) 1960

(Corrected for all errors listed above) 1.0019

l Proc. Verb. des Seances du C.I.P.M., 2nd Series 23, AnnexP99 (1953).

12 Proc. Verb. des S6ances du C.I.P.M., 2nd Series 26-8, AnnexP97 and P105 (1958).

participating laboratories. The number of freezes whichwere made to obtain the value for each nationallaboratory varied from about 10 to over 80 and bothPreston'3 and Tikhodeev'4 stated that a variation ofthe luminance of as much as i2% was found from onefreeze to the next. The experience was similar at theNational Research Council of Canada.

The photoelectric measurements made at N.R.C. in1953 showed more precisely the undesirable changes ofluminance during a freeze which were evident fromearlier visual observations. The changes in mean lumi-nance from one freeze to the next were also confirmed.The four curves in Fig. 2 were obtained photoelectricallyin 1953 and show the variation of luminance during afreeze and from one freeze to the next. The curves arearbitrarily displaced for a better comparison. On eachcurve the portion between the two asterisks was used todetermine the mean luminance of the blackbody at thefreezing point. The mean value of this portion is givenfor each freeze relative to the average value for 84freezes,1 6 set equal to 60 cd/cm2 . (The Canadian unitwas found by the 1956-1957 international comparisonsto be 0.7% smaller than the world mean as indicatedin Table I.) The selected portion of the curve wasquite arbitrary since the freeze was still in progressfor some time after the final asterisk and in some casesthe luminance had decreased by more than 10% beforeall the platinum was frozen. Therefore a large part ofthe error in the primary standard was thought to becaused by the poorly shaped cooling curves and the con-sequent arbitrary method of selecting the usableportion.

The ideal freezing curve would show the luminancedecreasing with a constant slope until the freezingluminance was reached, then a constant luminancewould persist until all of the metal was frozen. Theconstant luminance would be followed by a luminancedecreasing with the same constant slope which wasdisplayed before the onset of the freezing process? Beforethe initiation of the freezing process, a slight super-cooling of the ingot below the freezing temperature ispermissible, but the excessive supercools exhibited inthe curves in Fig. 2 are likely to originate inconsistentfreezing curves. The reason may be that the freezingprocess is likely to start in a different part of the ingoteach time. This inconsistent freezing pattern mayresult in a different luminance level during the freeze.

An ideal arrangement would be one in which theplatinum ingot lost heat slowly from only the outsidesurface. No heat should be radiated from the blackbodycavity. In that case, the ingot would freeze from theoutside in toward the cavity, and once the surface wasfrozen, the cavity, being surrounded by the interface

13 J. Preston, Proc. Verb. des. S6ances du C.I.P.M. 2nd Series26-B, Annex P42 (1958).

14 P. M. Tikhodeev, Proc. Verb. des. Seances du C.I.P.M., 2ndSeries 26-B, Annex P46 (1958).

" C. L. Sanders, B. A. Stevens, and W. E. K. Middleton, J. Opt.Soc. Am. 44, 88 (1954).

July 1962 REALIZING THE PRIMA

between the liquid and solid platinum, would be at thefreezing point of platinum. The cavity would remain atthe freezing point until the interface crossed the wallof the sight tube which bounds the cavity. At thatinstant, the temperature of the cavity would startfalling below the freezing point of platinum.

For the ideal arrangement one may assume that theflat portion on the freezing curve is at the luminance ofa blackbody at the freezing point of platinum. Thefreezing point of a pure metal is invariable. Therefore,in an experimental case where the luminance at zeroslope changes between one freeze and the next, onemust conclude that the zero slope indicates a tempera-ture maximum after a supercool and not a true freezingtemperature. It is likely that this conclusion could besupported by a proper extension of the theoreticalwork of Berger 6 or that of de G. Allen and Severn. 7

Consideration of these papers strongly suggests thata satisfactory realization of the primary standard oflight can only be achieved if the complete cavity is at auniform temperature. If the temperature is nonuniformthen the resulting luminance curve will be impossibleto interpret unambiguously. It is also essential that thetemperature remain constant at the freezing point for asufficient period that it will be unmistakably recognizedas the freezing point. Any curve displaying a slopewhich lasts over an appreciable luminance range is in-admissible because of our limited knowledge of thedetailed thermal behavior of the system.

The alternative to a system which provides an in-variable luminance during the complete freeze, is oneproviding a luminance plateau for part of the freezeonly, but under reproducible conditions. Such a standardwould be defined by a set of conditions and not by ageneral definition such as "the luminance of a completecavity radiator at the freezing point of platinum." Alist of the conditions would probably have to include thefollowing: size and shape of ingot; ceramic material,its porosity, smoothness, and thickness; position, por-osity and thickness of all insulation and radiationshields; frequency of induction current; shape andposition of induction coil; rate of cooling and heatingfor a sufficient preceding time that the temperature dis-tribution would be definitely determined; the opticalproperties of the lens, its shape, size, position; thesection of the image effective in the photometric deter-mination; and probably many other things.

When this approach was followed in the system wherethe platinum was heated directly by the inducedcurrents, the luminance of the flat portion of the curvevaried by up to -t2%."3 '4 The possibility that the condi-tions were not adequately controlled is suggested bythe work of Teele'8 at the NBS who found that dis-

18 F. Berger, Z. angew. Math. Mech. 11, 45 (1931).17 D. N. de G. Allen and R. T. Severn, Quart, J. Mech. Appl.

Math. 5, part 4 (1952).18 R. P. Teele, J. Opt. Soc. Am. 50, 1135 (1960); 52, 826

(1962).

RY STANDARD

`:00

0I-Z

.E

OF LIGHT 733

o 2 4 6 8 10 12 14 16 18Time (min)

FIG. 2. Portions of representative freezing curves obtained atNRC in 1953 on a conventional type of blackbody, with curvesdisplaced arbitrarily for better comparison.

torting the induction heating coil made the freezingplateau much more reproducible. However, this pro-cedure would be expected to cause a nonuniform heatingof the ingot which might force the freezing process tostart always at the same point and to allow the samecourse each time. Whether or not the fulfillment of thisadditional condition is sufficient to provide a satis-factory standard can only be ascertained by furtherexperiments.

It has been shown'9 that the change of luminance of ablackbody near 20420K amounts to 0.6% per deg K.This means that the freezing point of platinum wouldhave to be reproducible to 0.1 deg K in order to obtaina luminance reproducible to 0.06%, which would besatisfactory.

ZINC AND GOLD BLACKBODIES VSPLATINUM BLACKBODY

In view of the considerable difficulties in realizingthe primary standard of light by a platinum blackbody,it might be enlightening to compare the arrangementsand techniques which have been developed to producesatisfactory freezing point determinations for othermetals.

Tingwaldt and Kunz, using an improved gold pointapparatus,2 0 have shown that the freezing temperature

19 H. T. Wensel, W. F. Roeser, L. E. Barbrow, and F. R. Cald-well, J. Research Nati. Bur. Standards 13, 161 (1934).

20 C. Tingwaldt and H. Kunz, Optik 15, 333 (1958).

I I I I I I I I I

:ii

I I I I I I I

C. L. SANDERS AND 0. C. JONES

is reproducible to at least 0.05 deg K, which meansthat the luminance is constant to 0.06%. Since thetemperature was obtained with a visual pyrometer, thepyrometric error would make it impossible to determinethe constancy of the freezing point. In fact, Selin-court, 21 using a silver bath surrounding the gold ingot,found that the reproducibility of the gold point was0.01 deg C. Selincourt used a platinum thermocoupleto measure the temperature changes at the center ofan ingot 7.5 cm long and 2.5 cm in diameter. Wagen-breth22 has calculated the error in the gold point whichis caused by radiation out of the cavity. The calcula-tions were confirmed experimentally and the correctionis several degrees Kelvin for the gold-point determina-tions of Tingwaldt and Kunz.23

Although the freezing point of zinc, 693°K, is at toolow a temperature to be considered as a standard oflight, it is instructive to consider the elaborate precau-tions taken by McLaren24 in order to obtain a long-term reproducibility of 0.001 deg K in the freezing pointof zinc. The precautions which were incorporated indetermining the zinc point included the use of a copperblock surrounding the crucible containing the zinc.The copper block was heated with an electrical resist-ance-heating coil. Both coil and copper block werethree times as long as the zinc ingot. About 15 cm ofthermal insulation was provided on all sides. Thetemperature distribution was monitored with thermo-couples to make certain of its uniformity. The molteningot was seeded with a crystal of zinc to initiate freez-ing at a temperature very slightly below the freezingpoint, thus preventing deep supercools which wouldreduce the reproducibility of the freezing curves. Theproper freezing process was confirmed by dumping themolten zinc from a partly frozen ingot, and it wasfound that the zinc froze first in a thin layer all over thesurface of the cylinder. The ingot was 16 cm long andweighed 1 kg.

In comparison, the arrangement customarily used inthe primary standard of light determination consistsof an ingot of platinum about 5 cm long and 2 cm indiameter weighing about 300 g. The ingot is heateddirectly by induced current from a water-cooled rf in-duction coil. The insulation on the sides is 8 cm ofthoria or zirconia powder. There is about the same in-sulation under the ingot but on top there is a space topermit radiation to the photometric system. There is agreat deal of radiant energy emitted through the cavityaperture which has no counterpart in McLaren's appa-ratus, where the temperature is determined using ther-mocouples. Since the heating current flows directly inthe platinum, there can be no equalization of heat suchas is provided by the copper block in McLaren's

21 M. De Selincourt, Proc. Phys. Soc. (London) 51, 695 (1939).22H . Wagenbreth, Proc. Verb. des Seances du C.I.P.M., 2nd

Series 26A, T123 (1959).23 C. Tingwaldt and H. Kunz, Wiss. Abh. P.T.B. 9, 32 (1957).24 E. H. McLaren, Can. J. Phys. 35, 1086-1106 (1957).

apparatus. Thus a temperature difference can only bereduced by thermal conduction in the platinum or bythe stirring of the molten platinum, the latter beingcaused by the induced current in the platinum reactingwith the inducing current. Once the surface of theplatinum freezes this stirring action ceases since thecurrent penetration is limited to a fraction of a mm bythe rf skin effect. The initial part of the freezing curvecannot be used because of the supercool, and since thetime constant of the ingot in establishing a thermalequilibrium is about 1 sec, it follows that the stirringaction can be discounted as an effective means of re-ducing the thermal gradients in a freezing ingot.

It can be demonstrated that the efficiency of heatingby rf induction is greater for molten platinum than itis for solid platinum. Thus if, at any time, part of thesurface is frozen and part is molten, then the tempera-ture gradient will be accentuated by induction heating.The change in efficiency is caused by the change inelectrical resistance of platinum.

Considering the vastly superior arrangement at thezinc point, it is surprising that the reproducibility ofthe platinum point is as good as it is.

INDIRECT HEATING METHODS

The first step in approaching more reasonable thermo-dynamic conditions is to eliminate the direct heating ofthe platinum by induction. The platinum may be heatedindirectly or by a wire-wound resistance or by inducingrf currents in a metal container surrounding the ingot.

The wire-wound resistance heating method has theadvantage that the spacing between turns may beadjusted to give a fairly uniform temperature inside thecoil.25 This provides an invariable set of conditions.However, if the coil is wound in three parts, thecurrent in the various sections may be adjusted toreduce the thermal gradient.2 6 2 7 When heated, theresistance wire expands more than the ceramic whichrequires locating the turns in grooves in the ceramicto keep them in position. The grooving process mayweaken or contaminate the ceramic and, in turn, con-taminate the platinum. The turns of wire are some-times held in place by alumina cement. Unfortunately,the cement usually contain additives which may beexpected to contaminate the platinum or to lower themaximum operating temperature of the alumina. Mostrefractory metals such as molybdenum, tungsten, andtantalum become very brittle after heating and unlessprecautions are taken, this can be a very seriousproblem.

Platinum is readily contaminated by most elements,which makes it essential to guard against excessive im-purities in the ceramics. Thoria, Zirconia, beryllia,magnesia, and alumina are the ceramics which will

25 M. J. Laubitz, Can. J. Phys. 37, 1114 (1959).2 6 A. W. Gray, Bull. Bur. Standards 10, 451 (1914).2 7 J. B. Ferguson, Phys. Rev. 12, 81 (1918) .

734 Vol. 52

REALIZING THE PRIMARY STANDARD OF LIGHT

withstand the temperatures required to melt platinum.Thoria may be obtained in a very pure form, but it isvery difficult to fabricate and therefore does not lenditself to the experimental approach. In actual experi-ments it was found very susceptible to thermal shock,which meant that the thoria parts did not last long.Zirconia is available in various shapes and sizes butcontains impurities introduced to stabilize it. Berylliais reported to be very resistant to thermal shock. Never-theless, it is highly toxic to most people and should beused cautiously. Magnesia in the commercially availableform contains impurities introduced to facilitate firing.Tricrystallized alumina, which is easily available, isprobably the most suitable ceramic and it was used to alarge extent in this work. Unfortunately the best com-mercially available alumina has the disadvantage thatit contains about 0.2% Na2O and a trace of silica. Itseffect on the contamination of platinum thus introducedwill be discussed later.

In spite of the ultimate advantages of the wire-wound resistance heating technique, it was felt thatthe technically simpler induction heating techniqueshould first be tried since a power supply for inductionheating was available and its use was more familiar tothe authors. The ceramics could then be commerciallyavailable cylinders and disks, except for the relativelyshort cylindrical end-heaters which were grooved bymeans of a circular saw studded with diamond dust. The

-Cu ELECTRODE

.Pt WIRE CONNECTOR

-TUNGSTEN HEATER

-COPPER INDUCTIONCOIL

- ALL ALUMINA PARTSUNLESS OTHERWISE STATED

-PLATINUM INGOT

-THORIA CRUCIBLE

-THORIA POWDER

-Ta SUSCEPTOR

-BRASS

-BRASS LEVELINGTRIPOD

PUMP

refractory metal for absorbing the induced currents wasformed into a closed cylinder completely surroundingthe crucible containing the ingot. The arrangement isdescribed in the next section.

To be complete, one should mention the possible useof ceramics which at high temperatures become elec-trically conducting for rf. The important advantages ofusing oxide resistors instead of refractory metal resis-tors are that the furnace may be operated in air, and thechance of contamination is largely reduced. Eitherthoria, or zirconia stabilized with yttrium oxide2829

may be used. The resistance of these materials changeswith temperature in such a way as to make the furnaceheat exponentially. This makes it difficult to stabilizethe heating.

DESCRIPTION OF MODIFIED FURNACE

The furnace, shown in Fig. 3, incorporates a numberof features designed to improve the performance of theplatinum blackbody and to make it more acceptable asa primary standard of light. Since platinum vaporizesrapidly in vacuum at its melting point, a neutralatmosphere of argon was used in the furnace. Tantalum,

28 W. H. Davenport, S. S. Kistler, W. M. Wheildon, and O. J.Whittemore, Jr., J. Am. Ceram. Soc. 33, 333 (1950).

29 M. H. Leipold and J. L. Taylor, Fourth Symposium onTemperature, Columbus, Ohio, 1961, paper C. 5.2.

FIG. 3. Modified furnace formelting platinum.

735July 1962

736 C. L. SANDERS

which has a low vapor pressure at 18000C, was used toform the susceptor which is shown surrounding thecrucible containing the platinum. The tantalum wasobtained in sheet form 0.005 in. thick and the cylinderwas readily formed by bending the tantalum around abrass cylinder and then folding the tantalum severaltimes to form a joint. This thickness was chosen becauseit is thin enough to provide a high resistance to theinduced current while at the same time it is thick enoughto support the necessary weight.

The top and bottom plates of the cylinder were madeof tantalum 0.010 in. thick, since the additional strengthwas needed to support the weight of the ceramicmaterial. A tungsten cylinder with a -in. wall placedinside the tantalum susceptor, to act as a thermalconductor, improved the uniformity of the temperature.Wire-wound tungsten end-heaters were placed aboveand below the susceptor to permit fine adjustmentsof the temperature gradient while the furnace wasoperating.

The argon was introduced just under the prism andits downward flow prevented convection currents fromcarrying any deposit up to the prism. A vacuum systemconsisting of a backing pump with a rated speed of0.8 liter/sec and a diffusion pump rated at 50 liters/secpermitted the furnace to be first heated slowly invacuum to remove oxygen and water vapor from theceramics. The backing pump had an adjustable airballast to facilitate the removal of water vapor. Thepressure was kept below 0.1 Hg while the temperaturewas raised slowly to 1100C. After about 1 h at 11000Cthe furnace was cooled, before introducing the argonwith the furnace power switched off. The temperaturewas then raised to the melting point in about 3 h. Thedifficulties caused by the low arcing potential of argonat the operating pressure of 20 lb/in.2 were minimizedby taking several precautions.

The clear fused quartz tubes surrounding the inletsof the induction coil were essential. The coil, 3 in. indiameter and 6 in. long, consisted of seven or lessevenly spaced turns of ,' flexible copper tubing. Thepeak voltage on the ends of the coil had to be less than10 000 V to prevent arcing to the earthed brass cylinderor between turns of the coil. Because of these precau-tions, the power available was limited and was onlysufficient to melt platinum through use of a susceptorof not more than 3 in. in length. Although the 3-in.susceptor definitely improves the temperature uni-formity in the ingot, a much longer cylinder would havebeen desirable.

After repeated use of the furnace, the alumina cyl-inders which acted as radiation shields became blackdue to a deposit of tantalum oxide. This decreased theefficiency of these radiation shields to a point where in-sufficient power was available to melt the platinum.The alumina cylinders had then to be replaced. Thecylinders were also replaced whenever serious cracksappeared, since the heat lost through the cracks was

0. C. JONES

O 2 4 6 8 10 12 14 16 IN 20 22 24 26 28 30 32 34 36 38 40

TIME-MINUTES

FIG. 4. Five representative freezing curves and one melting curveobtained in argon on ingot No. 1 using modified furnace. Thecurves have been displaced arbitrarily.

sufficient to introduce temperature gradients at thecenter of the furnace.

Thermocouples of tungsten vs tungsten-26% rhenium30

were used up to 18000C to measure the temperaturegradient in the thoria powder surrounding the platinum.With four couples connected differentially, the gradientin the powder from top to bottom of the ingot wasfound to be as high at 25C, but this could be reducedto about 2C by adjusting the number of radiationshields in the top and bottom end-heaters and thenusing the heating coils for a fine control.

One could observe how the gradient in the thoriapowder decreased while the platinum was freezing andincreased again after the freeze. The end which washotter could be determined and appropriate actiontaken. However, the uniform temperature was notpermanent, since blackening of the alumina tubing orcracks in the tubing changed the radiation losses anddisturbed the uniformity of temperature.

Also, since the thermocouples were at slightly differentdistances away from the surface of the ingot, the tem-perature difference indicated by the thermocouples maynot be truly indicative of the temperature difference inthe ingot itself. When the thermal emf was actuallybeing measured, the light flux reaching the photocellwas temporarily reduced. The photometric readingwas reduced approximately 0.5% within a second afterthe potentiometer was touched by the operator. Themechanism of this effect is not certain, but it is believedto be caused by a discharge between the thermocouplewires and the lid of the susceptor. This increased currentcauses sodium vapor to be introduced into the light pathbetween the blackbody aperture and the prism. For-tunately, the measurement of the sodium absorption,

30 C. T. Sims, G. B. Gaines, and R. I. Jaffee, Rev. Sci. Instr.30, 112 (1959).

---- ------- - - - - - -

\ S~ * 4J O \O1JA1990.0 As'

/ NO CORRECTIONS FOR No ABSORPTION

Vol. 52IAND

I-.

IIIIIIE

II


as described later, enables a correction to be madewhich eliminates the resultant error.

With the modified furnace good freezing curves wereobtained, some of which are shown in Fig. 4. The uppercurve is one of the longest recorded. After 1 hr, thepower was reduced to hasten the freezing process butuntil that time, the slope was constant and in 1 hr theluminance decreased by only 0.6%. This constant slopeis characteristic of all very slow freezes. It appears thatany temperature gradient in the ingot shows up to itsfull extent during a very slow freeze, whereas for afaster freeze, a fiat portion is obtained for the earlypart of the freeze and a sloping section follows asshown in the other four freezing curves. The fractionwhich is flat is a function of the thermal gradient in theingot just before the freeze. If the gradient is large,there is only a short fiat section.

It should be noted that the average luminance variedfrom one freeze to the next. This variation is believedto be due to changes in the absorption of light by sodiumvapor which was not measured on the day in question.

It has not been possible to obtain freezing and meltingcurves both with flat plateaus for the same furnacearrangement. When the furnace was adjusted to giveflat freezing curves, the melting curves usually slopedas shown in the lower curve of Fig. 4.

The primary standard determination made in 1960is based on 18 freezes obtained with ingot No. 2 of whichfour typical freezing curves are shown in Fig. 5. Thesecurves were obtained at a faster rate of cooling than

>1'0

.'

0

C

0

0

o 2 4 .6 8 10Time (min)

12 14 16 18.

FIG. 5. Typical freezing curves obtained with modified furnaceand used in 1960,NRC standard determinations. The curves havebeen displaced arbitrarily.

0

z6 t

*6L

.4 .6 .8 59.0 2 .4 .6 .8 60.0 .2 .4 8 61.0 2 .4 6 .8 62.0 .2

LUMINANCE IN CANDELAS PER S CM

FIG. 6. Diagram showing the frequency of occurrence of freezingluminances. Luminance unit is the 1953 NRC unit. (a) Diagramfor 59 visual observations in 1953. Standard deviation of mean,cTM=0.

2 3 %. (b) Diagram for 25 photoelectric observationsin 1953. M=0.12 %. (c) Diagram for 18 photoelectric observa-tions using tantalum susceptor and argon atmosphere in 1960.aM=0.13%. If three low values are rejected ,f,=0.01 7 %.

those shown in Fig. 4. No prolonged attempts were madeto obtain a good thermal balance which would require anumber of preliminary freezes. From the experiencewith ingot No. 1, which was found to be contaminatedafter several months use, it was felt that the repeateduse of the platinum for this purpose would unnecessarilyincrease the contamination and reduce the accuracy ofthe results. Because of this it was also decided to as-semble the furnace in the way which had alreadyproven to give satisfactory thermal conditions withingot No. 1. The thermal gradients were not ideal andthe shapes of the typical freezing curves obtained usingingot No. 2 and shown in Fig. 5 are not as satisfyingas those obtained with ingot No. 1 and shown inFig.4.Nevertheless the standard deviation of the meanluminance for any day was generally less than 0.1% andsometimes even less than 0.05%.

The three diagrams in Fig. 6 show the frequency ofoccurrence of the luminances obtained by: (a) visualobservation in 1953; (b) by photoelectric observationsin 1953; and (c) by photoelectric observations in 1960.The 1960 results which were obtained by using the in-direct heating system described above exhibit much lessvariation. The reason for the improvement evident inthe 1960 results is almost certainly due to the improveduniformity of temperature achieved by the indirectheating method. The three low luminances recorded in1960 were obtained all on one day and are suspected ofbeing affected by an unidentified bias.

After the exclusion of the three low values, the 1960mean becomes 60.083 cd/cm2 and the standard devia-tion of this mean of 15 freezes is M= 0.02%. This figurecompares very favorably with 0.12% for 25 freezesobserved photoelectrically in 1953 and with 0.23% for59 freezes observed visually in 1953.

I I I I I I

FREEZES IN ARGONINGOT* 2

3 MAR 17, 1960 INGOT*2

5 MAR 11,1960 INGOT S-

60.08 cd/cm\ 1%

\ *2 APRIL 8,1960 INGOT#2

\ 60.08 c/ >

3 MAR 29,1960 INGOT#259.65 cd/cm2

737July 1962


FIG. 7. Method 1 for measure-ment of the transmittance of lensand prism.

SPHERE POSITION I

SPHERE POSITION 2

SOURCES OF ERROR

Errors will be considered under two main headings:photometric errors, caused by difficulties encounteredin comparing the luminance of the blackbody sourceswith the mean intensity of a group of standard lamps,and blackbody errors, which arise from the fact thatthe practical cavity does not conform to the theoreticalspecification of the primary standard.

The basic comparison between the primary standardand a lamp is illustrated in Fig. 1. The relative im-portance of the various factors may be readily deter-mined from the following equation, the symbols ofwhich were defined previously:

I 60AT

Rld 12 R2 d2

2

Photometric Errors

1. Transmittance of the Lens and Prism

The transmittance of the lens and prism was deter-mined as illustrated in Fig. 7. This method is essentiallythe same as one used by Collier3 ' at the NPL in 1954-1955, except that a spherical collector with a vacuumphotocell is used instead of the barrier-layer cell whichCollier used. In our tests, it was established that thesensitivity of the barrier-layer cells available to us wasextremely variable over the surface and therefore thetransmittance measurement depended too critically onthe alignment of the cell in the two positions. Byusing a sphere to collect the light, this difficulty waseliminated.

For the measurement of the transmittance of thelens and prism, the optical arrangement should approxi-mate as closely as possible the condition prevailingwhen the lens and prism are used to form an image ofthe blackbody on the photoelectric receiver. The imageof the blackbody is formed at about 2.8 m from the lensand therefore the blackbody cavity is near the focalpoint of the lens. In the transmittance measurement bymethod No. 1, the rays travel in the reverse direction.The lens L, forms an image of the strip filament lamp

31 L. J. Collier (private communication).

on a 1-mm aperture. The aperture is in the focal planeof lens L2. Thus collimated light leaves L2 and entersthe sphere in position 1 and causes a response Rloo onthe attached photocell. If the sphere is in position 2, thelight passes from lens L2 into lens L3 through the prismand forms an image of the 1-mm aperture which is ofapproximately the same size and in the same positionrelative to the lens and prism as the blackbody aperture.The light then diverges, enters the sphere and causes aresponse on the photocell RT. The ratio RT/R1 oo is equalto the transmittance of the lens and prism system. Thecolor temperature of the strip filament lamp is adjustedto be approximately 2042°K and the receiver has a two-component filter to correct it approximately to thespectral sensitivity of the CIE standard observer.

The main source of tramittance error arises fromhaving the beam of light, which enters the lens, in adifferent position or of a different size from the beamwhich leaves the lens and passes through the lensdiaphragm in the arrangement shown in Fig. 1. Theerror due to this cause may be 40.3% for quite smallchanges in the beam. Therefore, in order to be sure thatthe lens and prism assembly was always insertedcorrectly into the transmittance-measuring apparatus,the lens and prism assembly was adjusted to be in thecorrect position on a kinematic mount. Thereafter,the assembly could be easily inserted and removed.The two assemblies which were used were interchange-able on the mount and therefore only the initial adjust-ment of the optical arrangement needed to be pains-taking. The alignment was checked periodically to becertain that no change had occurred. The lens dia-phragm was removed before the transmittance wasmeasured.

Although the optical arrangement is such that themain bundle of rays describes the correct path there issome possibility that more of the inter-reflectionsbetween the glass surfaces may reach the photocell inthe measuring arrangement than reach the photocellin practice. The reason is that during the transmittancemeasurement, the receiver is closer to the lens andprisms. Similarly, if there is scattered light leaving theglass components, then a larger portion of this will bemeasured than the photocell receives when viewing

APERTURE UNIT IMAGEOF IRIS

PHOTOCELL-

Vol. 52738


the blackbody. On the other hand, when the blackbodyis being viewed, the blackbody aperture is surroundedby an area which is nearly as bright as the apertureitself. The light from this surrounding area will bescattered into the image area and will raise the levelabove that which is in effect in the transmittancemeasurement. The effect of all these errors was assumedto be negligible but should receive more detailed atten-tion before the transmittance error is unequivocallyreduced below the requisite 0.05%. In order to check thetransmittance measurements, the method shown in Fig.8 was used. This was devised after discussions withR. P. Teele at the NBS. In this arrangement, the lightenters the prism first just as it does when leaving theblackbody aperture. Therefore, the conditions are morenearly as they are in practice. There was no significantdifference in the results obtained by the two methods,provided that the beam of light was correctly aligned.

By means of a Gillod-Boutry photocell in a circuitdescribed by Jones and Sanders32 it is possible to meas-ure the transmittance with a precision of better than0.1%. However, the accuracy would only be estimatedas being 0.15%.

A special furnace lid was designed to enable the lensand prism to be removed without admitting air; thus theprisms could be interchanged whether the furnace washot or not. Usually the transmittance did not changeby more than 0.1% during the course of four or fivefreezes. However, if the argon flow was interrupted, acoating rapidly formed on the prism face, therebyshowing the necessity for the flow of argon.

2. Errors Arising from Lamp Variations, Distance Meas-urements and Aperture-Area Measurements

The standard deviation of the measurement of theintensity of a standard lamp is about 0.2%. This in-cludes variations in positioning the lamp, in receiversensitivity, and in lamp intensity. The distances fromthe lens aperture and from the lamp to the photocellaperture were measured with a stick micrometer. Thetotal systematic error due to distance measurementsshould be less than 0.05%. The diameter of the lensaperture was 1.3251±t0.0003 cm.

3. Loss of Light by Scattering

Since the flow of argon into the furnace was directlyin the light path from the blackbody to the prism, itseemed possible that there could be turbulence wherethe cold stream of argon met the hot convectioncurrents. In this case some loss of light might occurby scattering from the refractive index inhomogeneities.Since the refractive index of a gas changes linearly withpressure, changing the pressure in the furnace shouldalter the effect of turbulence on the light beam. There-fore, the pressure was varied over a range of 2 to 1 and

3 0. C. Jones and C. L. Sanders, J. Opt. Soc. Am. 51,105 (1961).

POSITION. I

1.5mm /APERTURE

POSITION 2

FIG. 8. Method 2 for measurement of the trans-mittance of the lens and prism.

the luminance of the blackbody was measured for eachpressure. No change in luminance was detected,although a change of 0.05% would have been noticed.

The scattering of light by the atmosphere in thelaboratory was measured by the method used byBeuttel and Brewer.33 The loss by scattering wasestimated from the results to be only 0.05% in 2.8 m.The method was not sufficiently accurate to place muchreliance on this figure, but it is fairly certain that theloss by scattering in our laboratory will be less than0.1%, although Terrien34 reported that in measure-ments at the Bureau International des Poids et Mesures(BIPM) a loss of 0.2% per meter was measured.

4. Variation in Angular Sensitivity of the Receiver

The lamp filament with a maximum dimension of4.5 cm is at a distance of 150 cm from the receiver andthus subtends an angle of 1.7 deg at the photometeraperture, whereas the lens aperture subtends only 0.22deg, since it is 1.25 cm in diameter and is at a distanceof 330 cm from the photometer aperture. Consequently,it is necessary to determine whether the sensitivity ofthe photometer varies with the angle of incidence.

The angular sensitivity was determined with a pieceof flashed opal glass before the photocell in the alter-native positions A and B shown in Fig. 9. The receiverwas placed on a lens test bench and rotated with adiameter of the 4-mm aperture as the axis of rotation.An image of a pinhole was formed on the 4-mm apertureby a lens which subtended 0.43 deg at the center of theaperture.

As shown in Fig. 9, the relative angular sensitivity ismuch more constant with the opal in position B, i.e.,

33 R. G. Beuttel and A. W. Brewer, J. Sci. Instr. 26, 357 (1949).4 J. Terrien, Recent Developments and Techniques in the Main-

tenance'of Standards (Her Majesty's Stationary Office, London,1952), p. 68.

July 1962 739


4 6 8 10RIGHT

FIG. 9. Curves showing angular dependence ofsensitivity of photometer.

close to the aperture. It was therefore used in that posi-tion for the standard determinations. With the opal inposition A and both the blackbody and the test lamplocated in the direction of the peak sensitivity, the sensi-tivity of the photometer to light from the blackbodywould be greater by perhaps 0.2%. If the two were indirections separated by 1, an error of -i0.5% couldoccur. Therefore, it is necessary to ensure that thephotometer used in the calibration of standard lampsby comparison with the primary standard possesses anegligible angular variation of sensitivity.

5. Spectral Sensitivity and Linearity of the Receiver

The spectral sensitivity of the receiver is relativelyunimportant because the color temperatures of thelamp and the blackbody are adjusted to be virtuallythe same. Nevertheless, the sensitivity of the Gillod-Boutry photocell with a Cs-Bi cathode, preceded by aflashed opal diffuser, was corrected by means of threeglass filters in subtractive combination. The filterswere: Corning 3307, 4.0 mm thick; Corning 9788, 3.0mm thick; and Corning 3389, 1.5 mm thick.

The departure from linearity of the receiver was foundto be less than +0.4% for a 30: 1 variation in illumina-tion level. During the comparison of lamps with theblackbody the ratio of readings R/R 2 was close tounity (1.00-0.15) so that errors from this source arenegligible.

6. Errors Due to Diffraction

During the course of the investigations, the dis-tribution of illuminance on a diameter across the imageof the blackbody aperture was measured. The illumi-nance was greatest at the center and decreased towardthe edge of the image. The measurements were made

by means of a photomultiplier with the output fed intoa recording potentiometer. The distribution of illumi-nance across the image is not known exactly becauseof the limitation in reading the recorder trace, but isabout 0.3 to 0.5% greater at the center of the imagethan at the edge. Since the fraction of the image whichis used in the primary standard measurements variesfrom one laboratory to another, this effect will un-doubtedly influence the size of the candela derived fromany particular experiment.

Various experiments to determine whether the lumi-nance varied over the blackbody aperture gave negativeresults and therefore diffraction was considered as apossible cause.

In general when an extended object is used, oneassumes that the illuminance of the image is notappreciably affected by diffraction and in fact, this as-sumption is usually justified. However, in this particularcase we are interested in having a rather more accurateestimate of the diffraction losses than is usually con-sidered significant in optical imaging, and in addition,the f value (aperture ratio) of the system is 220 whichis much larger than those generally used.

Since the radius of a particular ring in the well-knownAiry pattern depends directly on the aperture ratio, thevalue of 220 suggests that a significant portion of thelight from the image may be removed by diffraction.Although the ultimate solution to this problem must beleft to the experts35 in the field of diffraction, it seemsdesirable at this time to determine a tentative valuewhich could be used in assessing the relative importanceof the diffraction error.

According to geometrical optics the illuminance in-side the geometrical image of an extended object of uni-form luminance B is given by E= T7rr2B/D2

2 , where D2is the distance from the lens to the image, r is theradius of the lens aperture, and T is the transmittanceof the lens as reduced by reflections at the surface andabsorption in the glass. In the presence of diffraction,the illuminance in the image plane at a distance p fromthe center of the image is E(V) =F( V)Twrr2 B/D2

2 , whereV =27rrp/D2 and F(V) is in general a complicated func-tion which is difficult to evaluate rigorously. However,for the center of a circular image, the value of F(V)has been determined.

It has been shown by Airy36 that when a point sourceproduces unit illuminance on a lens aperture, theilluminance in the image plane is given by

7r2r4 4 1

2 (V)E(V)=-

X2D22 V2

where J1 (V) is the Bessel function of order 1. Therefore

35 It i a plcasurc to acknowlcdge the helpful discussions on thisproblem with Dr. M. De of the University of Calcutta (formerlyan NRC Postdoctorate Fellow).

36 G. B. Airy, Cambridge Phil. Trans. 283 (1834) or T. Prestonand A. W. Porter, Te Thieory of Lighit (Macmillan and CompanyLtd., London, 1928), p. 324.

92

,.-

!a

I

o LIGHT URCER

3 COMP MPONENT-

P RIAR STA LARDLENS APERTURE ATEST APERTURE ~ A

EXPERIMENTAL ARRANGEMENT SITInON

OF RECEIVER\

PHOTOCELL FILTER SOURCE

ANDE- UA B PERUR 4 \ IM

ALTERNATIVE POSITIONSOF FLASHED OPAL

I I 1 . I I I I I

90

88

86

10 8 6 4 2 0 2LEFT ANGLE DEGREES

740 Vol. 52

100

98

96

94


the flux through an area da in the image plane is givenby E(V)da. Rayleigh3 7 has shown that the total fluxwithin the area of a circle which is centered on the imageof the point source is given by

ro PO 2 r4 4J1 2 (V)JE(V)da=f E(V)27rpdp= 22 2wpdp

JoX2D 22 V 2

= 7rr2[1 -J 2(Vo) -J 2(Vo)],

where Vo=27rrpo/XD2 and Jo(V) is the Bessel functionor order zero, and po is the radius of the circle.

If, instead of considering a point source of unit in-tensity one uses a self-luminous object of luminance Band infinitesimal area ds, then the flux through thearea da in the image plane is given by (Bdsda/Do2 )E(V),where Do is the distance from the source to the lens.Making the reasonable assumption that E(V) is stillvalid for points off the optical axis of the lens by smallamounts, one can extend the results to an extendedcircular source and calculate the flux passing throughthe area da centered on the image of the source. Supposethat ds is a portion of the annulus between the twocircles of radius x+2dx and x-2dx. Then, for a sectionof the annulus of length dl the flux through da will be

(Bdxdlda/Do2)E(V),where

V= 2rrp/XD2= 27rrx/XDosince

p/D2 = x/Do.

Since the flux passing through da is independent of theposition of dl on the annulus, it follows that the fluxthrough da, due to the complete annulus, is given by

Bdx2rxdaE(V)/Do 2 .

Therefore, the flux due to the circular source of radiusxo is expressed by

Bda xo Bda r r 7 2r4 4J (V)N=- E(V)27rxdx= | 27rxdx.

Do2 Jo D 02 Jo X2 D2

2 V2

By using the following well-known relationships be-tween Jo(x) and Ji(x), that is,

Jl(x) =-dJo(x)/dx, J(x) = xJo(x)-xdJ1(x)/dx,one obtains

N= (Bdarr2/D22)E1-Jo 2(Vo) -J 1

2(Vo)],

whereVo= 2-rrpo/XD2.

If N is multiplied by T, the transmittance of the system,and then divided by the area da, the result is the illumi-nance N' at the center of the circular image, that is,

7rr2

N'= -TB[1 -Jo2 (Vo) - J12 (Vo)].

D2r37 Lord Rayleigh, Sci. Papers 1, 513; Phil. Mag. 11, 214 (1881).

This is the maximum illuminance for any position onthe image, and therefore the minimum fractionalerror 'caused by diffraction is Jo2(Vo)+J2(Vo), whereVo= 2rrpo/D2. For a large value of V, it follows,according to Stratton,3 8 that

JP ( V);z (2/7rVo)i cos[Vo-4 (2 p+ 1)],

and consequently,

Jo2(Vo)= (2/7rVo) cos2 [Vo-mir],and

J 2 (Vo)>(2/irVo)cos 2 (Vo-3r)=(2rVo)sin(Vo-i7r).

The minimum error at the center of a circular image isthus given (approximately) by

J0 2(Vo)+J 12(Vo) = 2/7rVo.

It can be shown that the error at the edge of the imagemust be larger than the error at the center despite thefact that the value of Vo is now doubled.

Typical values of the constants involved in the calcu-lations are given by: r=0.65 cm, X=55X 10- 6 cm,D2 = 280 cm, po=0. 9 cm. These values lead to V 0= 240,which may be used in computing the error at the centerof the image. It follows that

J 02(Vo)+J1 2(Vo) = 2/7rVo= 0.0026,

which is equivalent to an error of 0.26%. Since it hasbeen ascertained from tables of Bessel functions thatthe error from using the approximate formulas for Joand J is only 33X10- at V0=99, the approximateformulas are certainly adequate at V0= 240.

From these results, it appears that the neglect ofdiffraction causes a significant error which depends onthe optical components and their arrangement. Sincenone of the results obtained at any of the standardizinglaboratories has been corrected for diffraction and theirarrangements have all been different, the effects ofdiffraction would cause appreciable systematic discrep-ancies. The correction to our present result should beabout +0.26% with an estimated error of 40.10%.

It should be noted that these calculations neglect thepossibility of coherent light from the blackbody aper-ture which may occur due to the inter-reflections in thesight tube. It is also assumed in the above calculationsthat there are no lens aberrations and that the photocellaperture is at the image of the blackbody aperture. Ifthese additional phenomena were considered3 9 it mightbe found that the errors become significantly largerthan in the presence of diffraction alone despite the factthat r<<D2 tends to minimize lens aberrations and de-focusing errors.

38 J. A. Stratton, Electromagnetic Theory (McGraw-Hill BookCompany, Inc., New York, 1941), p. 359.

39 M. Born and E. Wolf, Principles of Optics (Pergamon Press,London, 1959), Chaps. 8, 9, and 10.

July 1962 741

AND 0. C. JONES

FIG. 10. Graph to explain the method of correcting for absorption.

The measurement of the transmittance of the lensand prism is also subject to diffraction errors but nocalculations have been attempted since the situation iscomplicated by the fact that the aperture of the sphereis not at the image of the 1-mm aperture. This meansthat the diffraction is of the Fresnel type. However,since the distances from. the lenses are relatively shortin the transmittance-measuring apparatus and theopening in the sphere is considerably larger than thelight beam, it is likely that the error due to diffractionin the transmittance measurement is negligible.

7. Absorption of Light by Sodium Vapor

Since the argon is changed relatively slowly, a con-centration may occur of any gas given off by theceramics in the furnace. As mentioned above, theparticular gas which was troublesome in this experimentwas sodium. Either sodium absorption or emission linesor both were visible in the spectrum of light. By meansof a Zeiss spectrograph, with an RCA 1P21 photomulti-plier tube mounted behind a slit in the position usuallyoccupied by the photographic plate, it was possible toscan the spectrum for 10 A on each side of the absorp-tion lines. The scanning operation was performed byturning the wavelength drum very slowly by a motorand a worm gear. The output of the photomultiplierwas recorded on a Brown recorder with a 25-mv range.From the recorded data, it is possible to calculate theeffect of the absorption and/or emission on the lumi-nance of the blackbody. Since the sodium absorption oremission is almost entirely concentrated in the twoyellow lines at 5890 and 5896 A, only this region of thespectrum needs to be considered.

In Fig. 10, the curve kA* shows the type of tracewhich would be recorded in the presence of absorption.kHx is the response which would be obtained withoutabsorption on the assumption that over this small range,both the blackbody energy distribution and the spectralsensitivity of the photomultiplier change linearly withwavelength. The absorption is negligible where thestraight line kHx meets the recorded response kHn* atwavelength X1 and X2 .

The average response of the photomultiplier in thewavelength interval from XI to X2 is given by

)2

F? kHxd/()Xl-X2)

and the bandwidth of 100% absorption which would beequivalent to the absorption shown in Fig. 10 is given by

1 X2

N=- (kHx-kHx*)dx.R ,~

This band is illustrated in Fig. 10. Since He is the energydistribution of a Planckian radiator at 20420 K, theenergy distribution is known; and using the followingequation, one can calculate F, the fraction of the totalluminance which is due to the energy in a band 1 Awide centered at 5893 A. This is given by

M700A

/h7d~ 1 800A

where x is the relative spectral luminous efficiencyfunction of the CIE standard observer (1931). If H isthe spectral energy distribution of a Planckian radiatorat 20420 K, then F=0.094% per A. The product NF isthe fraction of the total light which is absorbed by thesodium vapor. If emission is present, as well as orinstead of absorption, the same procedure may be used.The result is independent of the bandwidth of the spec-trograph as long as the resolution is sufficient to showthe absorption on the record. The correction to the lumi-nance which was necessary due to the sodium vaporwas from +0.6% to -0.3%, and the error in the correc-tion is estimated to be about 0.06%.

Blackbody Errors

1. Impurities in Platinum

When the ingots were analyzed, the discouragingresults given in Table II were obtained. The spectro-scopic analysis shows silicon and aluminum as being theimpurities which are most likely to depress the freezingpoint. The absence of tantalum, tungsten and thoriumfrom the list of impurities in ingot No. 2 is no doubtdue to the fact that the minimum detectable amountsin a spectroscopic analysis are 100, 100, and 300 ppm,respectively. Thorium was detected in ingot No. 1 tothe extent of 1000 ppm and was probably introducedinto the ingot when it was used to cement the sight tubeto the lid. Alumina was used for this purpose in ingotNo. 2. The freezing point depression, estimated veryapproximately from data in references 40 and 41,accounts for only a fraction of the decrease in luminance

40 M. Hansen and K. Anderko, Constitution of Binary Alloys(McGraw-Hill, Book Company, Inc., New York, 1958).

41 R. F. Vines, The Platinum Metals and Their Alloys (Inter-national Nickel Company Inc., New York, 1941).

742 C. L. SANDERS Vol. 52

II

.1

Io

.1I

Io

I

5893.5A

F=92.6A


of ingot No. 1 which was observed before the analysis.Furthermore, since ingot No. 2 was heated three timesin vacuum and twice in argon after the usable value of60.08 was obtained,42 it is impossible to decide whetherthe platinum was then contaminated or not. For thisreason, the correction for the freezing point depressionof 0.5C caused by the contamination is very approxi-mate and is estimated at +0.15dt0.15% in luminance.9

The values of Riooc/Rooc, given below, are perhapsa better indication of contamination due to Ta, W, andTh, but no relationship between these ratios and thefreezing point depression is available. In fact, the workof Bradley and Entwistle43 indicates that the ratioRioo/Ro is reduced by heating platinum in argon ornitrogen at 1365TC. The changes which they found arecomparable with those indicated in Table III, and it istherefore quite possible that the low coefficient ofresistance is mainly due to the fact that oxygen isremoved from the platinum by using an argon atmos-phere. Bradley and Entwistle found that the effect wasreversible and that subsequent heating of the platinumin air brought the resistance ratio back to the valueusually expected for pure platinum. The emf of the testplatinum vs Pt 27 at 1200TC is also used to indicateimpurities, but once again, no correction can be madefrom these figures.

The question which remains is whether the contami-nation is inherent in this method or whether it may beeliminated by the use of purer ceramics. The contami-nation may be retarded by purchasing a solid ingot of

TABLE II. Analysis of platinum ingots after use.'

Pt beforeIngot No. 1 Ingot No. 2 use

Approx Maxi- Maxi- Maxi-AT per mum mum mumppm of impurity impurity impurity

Element impurity ppm AT C ppm AT C ppm

°CAg 0.001 <1 0.001 <1 0.001 <1Al 0.002 200 0.4 200 0.40 ?Au 0.002 3 0.006 1 0.002 ?Ca ? 2 ? 2 ? <1Cu 0.001 10 0.010 5 0.005 <1Fe 0.0015 30 0.045 20 0.030 1Mg ? 5 ? 5 ? ?Ni 0.001 20 0.020 2 0.002 ?Na ? 1 ? ? ? 1Pd 0.0002 5 0.001 5 0.001 <1Pb ? ? ? ? ? <1Si 0.017 40 0.68 2 0.034 1Th ? 1000 ? ? ? ?Zn ? N.d. ? 3 ? ?

Total 1.163°C 0.475°C

aThe question marks (?) indicate that no estimate of the value canbe made.

41 Ingot No. 2 was heated in vacuum to about 1100°C on 11 daysand in argon to above 1700°C on 10 days before it was analyzed.Ingot No. 1 was used about twice as many times before it wasanalyzed.

43 D. Bradley and E. G. Entwistle, Fourth Symposium onTemperature, Columbus, Ohio, 1961, paper B.7.3.

TABLE III.

Coefficient ofemf vs Pt 27 resistance

Sample at 1200'C Rioo'c/Rooc

Thermopure Pt Approx 0 ttV 1.390Pt before use Approx 0 uV 1.39255Pt ingot No. 1 Not measured 1.3399Pt ingot No. 2 292 uV 1.366594 ingots 1953 Max -5 AV Not measured

platinum, since this would avoid any contaminationresulting from the cutting of the wire and from thepreliminary freezes required to fill the crucible.

It should be noted that when a thoria crucible wasused to contain the ingot, a large amount of thoriumwas detected in the spectroscopic analysis of theplatinum. Such contamination may alter the freezingpoint of the ingot. The use of calcium oxide as theceramic might be desirable to investigate, since thisceramic tends to remove base metals from the plati-num.4 4 However, the water vapor usually present incalcium oxide would have to be eliminated since watervapor would quickly oxidize the tantalum. Berylliacrucibles are now available and this material is morerobust than thoria or calcium oxide. It does, however,have the disadvantage of being highly toxic.

There is a possibility that the use of an inert atmos-phere increases the likelihood of contamination, sincethe ceramics in the inert gas are subject to the samereduction reactions which occur in vacuum. Bunshah45states that "the performance of a given ceramic isusually poorer in vacuum melting than air melting andthere can be greater contamination of the melt withproducts of reduction from these ceramics." For thisreason, it would seem to be desirable to make somepreliminary experiments in which samples of platinumwould be melted in the various possible ceramics beforemaking further photometric determinations in an argonatmosphere.

2. Temperature Drop in the Wall of the Sight Tube

As suggested by Teele,18 a correction should be madefor the temperature drop in the wall of the sight tubeThe temperature difference AT between the outer walland the inner wall of a cylinder is given by the followingequation 4 6 :

Ql loge(r 2 /r1 )AT=

27rK

where Q is the number of calories conducted throughthe wall per second per unit length, r2 is the radius of

4 4 J. W. Whiteley and C. Dietz, Tech. Publ. No. 84, AIME.4 5 Rointan F. Bunshah, Vacuum Metallurgy (Rheinhold Pub-

lishing Corporation, New York, 1958), p. 202.4G M. Fishenden and 0. A. Saunders, An Introduction to Heat

Transfer (Clarendon Press, Oxford, 1950).

July 1962 743


the outside of the tube, r is the radius of the inside ofthe tube, and K is the thermal conductivity of thematerial from which the tube is made. If the openingat the end of the tube has an area a, and radiates to aneffective surround temperature of TS0 K, then the tubeat TK and an emissivity of practically unity willradiate energy Q2 given by

Q2= 1.37X 10-'2 (T4 - T84) (a) cal/sec.

T, depends on the temperature and the emissivity ofthe surrounds. In the usual case where the platinum isheated directly by induction, the temperature T willbe quite low, perhaps 1100'K. For an opening 1.5-mmdiameter, the value of Q2 will be 0.40 cal/sec. The energyradiated by the aperture must equal the energy con-ducted through the wall. If it is assumed that AT isconstant along the length of the cylinder, then Qi willbe constant and QjL=Q2 . Therefore from Eq. (1),

0.40 log(1.3/1.0) 0.40(0.262)AT= - _ _-= 0.96 0K

L(27r)0.005 3.5 (0.0314)

when r2= 1.3 mm, r1 = 1.0 mm, K= 0.005 cal/sec-1 cm72

cm 0 C-1 for thoria,47 L= length of cylinder= 3.5 cm.According to Wensel et al.5 the luminance of a

Planckian radiator changes 0.6% for every degreeKelvin change in temperature at the freezing point ofplatinum. Therefore, the luminance decrease AB, dueto the temperature drop in the sight tube wall, will be0.96X0.6 which approximately is equal to 0.6%.4 Ifalumina is used, the thermal conductivity is tripledand AB=0.2%.

In the case of the present experiment, the effect isnot as serious, since the ingot is heated indirectly bymeans of the surrounding tantalum susceptor whichmeans that the net radiation loss from the sight tube isreduced. In some cases, the luminance of the aluminalid surrounding the aperture could not be distinguishedfrom the aperture. Therefore the correction for tem-perature drop in the sight tube wall is estimated to beonly +0.054-0.05% when the platinum is heatedindirectly.

3. Emergence of Sight Tube from Ingot

Another correction which Teele'8 applied to theluminance of the blackbody was to correct for thedecrease in luminance which occurs when the sight tubeis not completely immersed in the molten platinum.

47 I. E. Campbell, Highz Temperature Tecknology (John Wiley &Sons, Inc., New York, 1956), p. 52.

48 Teele'8 has shown that the temperature drop in the sighttube is not constant along its length. Most of the energy is ap-parently conducted through the wall at the top of the sight tubenear the opening and the temperature drop in the wall near thebottom is much less. Therefore if the lens views only the bottomof the sight tube there will be a luminance decrease from the idealof less than 0.1% instead of 0.6%.

Once again the use of the tantalum susceptor shouldreduce the size of the possible error since both the topof the sight tube and crucible lid are in a very nearlyisothermal enclosure. Consequently, although there isundoubtedly some error due to the top of the sighttube being at a lower temperature than the ingot, thesize of the error cannot be estimated from Teele'sempirical data. A separate experiment would be re-quired also because the sight tube and lid are made ofalumina with a different thermal conductivity from thethoria used in Teele's work. An error of 0.05%=t0.05%is, however, tentatively estimated.

4. Variation and Error in the Luminance Due tothe Formation of Cavities in the Ingot

Teele 8 has also found that cavities sometimes formnext to the sight tube when the ingot freezes. Thecavities are probably formed by the evolution of dis-solved gases as the ingot freezes. His work has shownthat the formation of the cavities can be avoided if theinduction heating coil is distorted to provide nonuniformheating of the ingot. The cavity is then induced to formalong one side of the cylinder. His experiments weremade in air by using the direct heating system wherethe induced currents cause a stirring of the platinum.Since in our experiments no void formation has beennoticed even though every attempt has been made toproduce a uniform temperature in the ingot, it ispossible that two things have reduced the absorption ofgas by the platinum. First, since argon is inert, it isprobably not as soluble in platinum as the atmosphericgases and second, the stirring action is not present in thecase where the tantalum susceptor is used.

Since the intentional production of a temperaturegradient in the ingot is an undesirable procedure becauseit may produce a systematic error in the result, it wouldappear to be advisable to try using a nitrogen atmos-phere instead of air in the direct heating system (argonis not favored because of its low arcing potential). Thenit might be possible to avoid the cavities and still retaina uniform temperature.

Burton4 9 gives some of the other precautions whichmay be taken to reduce the solution of gases in moltenmetal. These include heating the metal above themelting point for as short a time as possible and to assmall an extent as possible. On p. 141 of his book, hesuggests that slow cooling reduces the possibility of theformation of cavities. Since in the presence of tempera-ture gradients it is necessary to cool the metal quicklyin order to produce a flat plateau on the cooling curve,the very slow cooling procedure is not usually feasible.

5. Emissivity of the Cavity Radiator

The emissivity of the cavity radiator has beentheoretically considered several times in the litera-

l' M. S. Burton, Applied Metallurgy for Engineers (McGraw-Hill Book Company, Inc., New York, 1956).

744 Vol. 52


ture.5 052 The theory usually considers the emissivityof a small part of the bottom of the cylinder whereasin practice part of the wall is also used.

Using the data in Table 1 of De Vos' paper5 2 andassuming that the distribution of reflected light ispartly diffuse and partly specular reflection as shownin Fig. 3 of his paper, and using the ratio of the depthof the cylinder/radius of cylinder=30, and that theemissivity of alumina at 20420 K is 0.45, one arrives ata figure of about 0.999 for the emissivity of the cavity.According to Fig. 4, where the specular reflectance isincreased, it would be 0.995. Tests would need to bemade of the angular reflectance properties of aluminaat 20420 K before the figure could be relied bn sufficientlyto make a correction accurate to better than 0.1%.Tentatively, it is assumed that the emissivity is 0.998-10.001 in the present case.

During the process of the present work, an experi-mental attempt was made to find the effect on theluminance of the cavity which would result from havingthe optical axis of the system not aligned with the axisof the cylindrical cavity radiator. By keeping the photo-cell aperture fixed in the arrangement shown in Fig. 1and moving an aperture of 3-mm diameter over thelens, the light from different parts of the wall of thecavity are permitted to reach the photocell, althoughthe same part of the opening in the cavity is still imagedon the photocell. By this technique, it was expectedthat any change in emissivity or temperature ofdifferent parts of the cavity wall would be detected.However, any changes which may have been presentwere so small that they were masked by the change intransmittance of the lens which varied over the surfacedue to tiny flaws or to changes in the Fresnel reflection.A record was kept of the orientation of the axis of thesight tube relative to the optical axis of the system, incase future theoretical calculations should indicate asignificant change of luminance with orientation. Theluminance of the blackbody is significantly less if thesight tube is badly tilted, but for tilt angles between 0°and 2.50, the variation in luminance is not detectablein our results.

Summary of Errors

The values given in Table IV are summarized fromthe above discussion.

When these errors are considered and the resultsapplied to the value of 60.083 obtained in 1960, thecorrected value is 60.544:0.18 cd/cm2 . The relationbetween the final corrected value and the 1956-1957world mean unit is given in Table I. Although theN.R.C. unit is now larger than the world mean of1956-1957, it should be realized that when the pertinentcorrections are applied to the units of the other labora-

50 M. Z. Yamauti, Proc. Verb. des Seances du C.I.P.M., 2ndSeries 16, 243 (1933).

51 A. Gouffe, Rev. opt. 24, 1 (1945).52 J. C. De Vos, Physica 20, 669 (1954).

TABLE IV. Summary of errors.

Estimated un-corrected error Estimatedin the N.R.C. std. deviation

1960 value, of errorpercent = percent

Photometric errors(i) Transmittance of lens and

prism 0.00 -+0.15(ii) Errors in standard lamp

comparison 0.00 140.05(iii) Light scattering +0.05 i0.05(iv) Variation in angular

sensitivity 0.00 :4:0.05(v) Receiver spectral sensitivity 0.00 d0.05

(vi) Diffraction +0.26 40.10(vii) Sodium absorption 0.00 1:0.06

Blackbody errors(i) Impurities in platinum +0.15 140.15(ii) Temperature drop in wall of

sight tube +0.05 -4-0.05(iii) Emergence of sight tube +0.05 40.05(iv) Cavities in ingot 0.00 0.00(v) Emissivity +0.20 -40.10

tories, the NRC candela will probablythe mean candela again.

be smaller than

POSSIBLE ALTERNATIVES TO THEPRESENT STANDARD

In order to compare favorably with the precisionreadily obtainable in photoelectric measurements onstandard lamps, both the precision and accuracy of theprimary standard should be better than 0.1%. Thedirectly heated version of the standard as used atpresent does not fulfill these conditions. The indirectlyheated version described here is not at present suffi-ciently accurate. If further work proves that it is im-practicable to avoid contamination with the indirectheating method, it might be justifiable to consider theadoption of another type of primary standard of light.

One approach would be to abandon the materialstandard and to adopt the procedures of absoluteradiometry combined with agreed values for the spectralluminous efficiency function of radiant energy. Thisapproach is already under investigation by Preston atthe National Physical Laboratory in England. Theresults so far are not conclusive because of the possi-bility of systematic errors in the absolute radiometer,the difficulty of determining the absolute transmittanceof visibility correcting filters to the necessary accuracyand the uncertainties involved in the intermediatesteps in the comparison of low-intensity standard lampswith the relatively insensitive radiometer. The useof higher-color-temperature secondary-standard lampswould be expected to reduce the importance of thesecond of these factors.,

An alternative would be to adopt the blackbody atthe gold point or another low-temperature freezing

745July 1962


point as a primary standard of light. This could bephysically realized more easily and would relieve thehpotometrist from working in the unrelated field of hightemperature physics and chemistry. Such a sourcecould also be of interest to the radiometrist as a stand-ard of spectral energy distribution. However, the com-parison between a blackbody at the gold point andmodern, high-color-temperature lamps would place asevere strain on photometric procedures, since theluminance of a blackbody at the gold point is only0.11 cd/cm2. Nevertheless, the problem would then bein the correct field for a photometric standard andperhaps the skills acquired in correcting the nonlinearityof receivers and in measuring their spectral sensitivitywould produce dividends in routine photometry.

CONCLUSION

By the use of the techniques described here, one of themajor causes of uncertainty in the primary standard,the temperature gradient in the ingot during the freeze,has been greatly reduced. Consequently the precision ofthe experiment is improved and a smaller number of

freezes may be used in establishing the standard. Anysystematic errors due to temperature gradients in thedirectly heated ingot would also have been muchreduced.

The great disadvantage of the method as describedis the serious contamination of the platinum by the im-purities in the commercially available alumina. It issuggested that the use of purer ceramics would avoidthis difficulty. If further work with this apparatus showsthat it is not practicable to reduce the rate of contami-nation it is suggested that some alternative to theblackbody at the freezing point of platinum may bepreferable as the primary standard of light.

ACKNOWLEDGMENTS

It is a pleasure to acknowledge with thanks theadvice and assistance which has been received fromDr. G. R. Hanes and from Dr. M. J. Laubitz duringthe course of this work. The assistance of Dr. G.Wyszecki in the preparation of the manuscript is grate-fully acknowledged. The technical assistance of W. Gawis greatly appreciated.

Vol. 52746

problem of realizing the primary standard of light

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