FEBRUARY, 1933

Color Filters for Altering Color Temperature. Pyrometer Absorption and DayliteGlasses

H. P. GAGE, Optical Laboratory, Corning Glass Works, Corning, N. Y.

(Received July 30, 1932)

The analysis of the Wien equation shows that a colorfilter in which the density, 8(5=loglo transmission) followsthe equation 6= (6223/X)(1/03 -1/02) will reduce both thebrightness and the color temperature of a completeradiator at temperature 01 to that of a complete radiatorat a lower temperature 02. Such a color filter is useful as

an absorbing screen in an optical pyrometer. If a color

filter has a spectral transmission such that the logarithmof transmittance plotted against 1/X yields a straight linecutting the 1/X axis in a point corresponding to approxi-mately X1=0. 40,u, such a filter will serve to increase the

color temperature of a source although reducing itsbrightness. The spectral formula of such a filter isj't=0.4343 2(1/11 -1/X) (1/02-1/01), i being the colortemperature of the light source and 02 that of the trans-mitted light expressed in accordance with the Wienequation. With a given filter the reciprocal color tempera-

ture is raised by the same amount irrespective of the colortemperature of the source and the change in reciprocal

color temperature is proportional to the thickness of theglass color filter used. If two points 2 and 3 on the spectro-

photometric curve of such a Daylite glass are given, then1/01-1/02 =at =0.0001607(, 2 t-Tht)/(1 /X2-1 /X). With atto represent the change in reciprocal temperature for thegiven glass of thickness t, the change per unit thicknessis a. Artificial light sources may be described as havinga spectral energy distribution in accordance with Wien'sequation within the limits of the visible spectrum. Variousphases of daylight produce a visual sensation equivalentto the energy distribution as given by Planck's equationor by a suitable but different choice of 0 the same distribu-tion may also be represented by Wien's equation withinthe narrow limits of the visible spectrum, 0.4 0, to 0.70p.A table is included giving the color temperature of some

of the artificial light sources and their reciprocals, also theequivalent temperature with its reciprocal for variousphases of daylight expressed both according to the Planckand according to the Wien equation.

IN certain previous publications on the subjectof absorbing filters for producing artificial

daylight," 2, 4 the criterion by which the neces-

sary transmission characteristics of the glasswere judged was that starting with the spectralenergy distribution of a given light source and

the spectral energy distribution of the type ofdaylight which it was hoped to duplicate, theratio of the two energy values for each wave-

length was the desired transmission for the glass.As illustrated, the energy distribution of thetransmitted light was calculated from the energy

distribution of the source and the measuredtransmission curve for a given sample of glass.

If the resulting curve agreed fairly well with that

I Herbert E. Ives, Color Measurements of Illuminants.-

A Resum6, Trans. I. E. S., pp. 189-207, April (1910).

2 M. Luckiesh and F. E. Cady, Artificial Daylight-Its

Production and Use, Trans. I. E. S. 9, 839 (1914).3 H. P. Gage, Artificial Daylight-Discussion, Trans. I.

E. S. 9, 861 (914).4 Edward J. Brady, The Development of Daylight Glass,

Trans. I. E. S. 9, 937 (1914).

of some actual or assumed distribution curve forone of the phases of daylight it was concludedthat the light obtainable with the source andfilter combination would answer as a substitutefor natural daylight. In each case the source andresult were considered individually. A possible

shortening of the necessary calculations was indi-cated by Fabry in 19135 in which it was shownthat with light sources whose energy distributionis equal or closely similar to that of a completeradiator (black body) and therefore expressibleby Planck's or Wien's equation there is a general-ized relation between the color temperature ofthe source and that of the transmitted light pro-vided the transmission characteristics of the filtersatisfy certain conditions. Special blue glasseswere employed by Langmuir and Orange' toincrease the color temperature of the light froma standard tungsten vacuum lamp to that of a

5 C. Fabry, A Practical Solution of the Problem of Hetero-chromatic Photometry, Trans. I. E. S. 8, 302 (1913).

6 Langmuir and Orange, Tungsten Lamps, Tranis.

A. I. E. E. 32, 1946 (1913).

46

V OL UM E 2 3J. O. S. A.

COLOR FILTERS

gas-filled lamp at a higher temperature. Theyused the relation that the difference in reciprocaltemperature caused by a special blue glass is aconstant and if several such screens are used thethe resultant change in reciprocal color tempera-ture is the sum of the reciprocal color tempera-ture changes produced by each screen separately.

SYMBOLS

The symbols used in the following discussionof color filters are:

El. The radiant power for a given wave-lengthincident on the first surface of a color filter.

P,. The radiant power transmitted by the firstsurface of the filter is E, less the loss by reflectionat the first surface.

P2 . The radiant power incident upon the sec-ond surface which differs from Pi because of theabsorption of the substance of the filter.

E2. The radiant power transmitted by thesecond surface is equal to P 2 less the reflectionloss at the second surface.

T= E2/E1 is called the transmission of thefilter.

P2/P is called the transmittance of the filterand is its transmission corrected for reflectionlosses.

5=logio (E2/El), density, is the logarithm tothe base 10 of the transmission.

t. Thickness of the filter.fit= log1 (P2 /P 1 ). Logarithm to the base 10 of

the transmittance of a filter of thickness t.f. Transmissive index, logarithm to the base

10 of the transmittance of one millimeter of thefilter glass. As the transmission and transmit-tance of a filter are always less than unity thelogarithms 5, fit and fi are always negative. Allow-ing for a reflection factor of 4 percent at eachsurface, the transmission T is roughly 92 percentof the transmittance. The difference expressedlogarithmically is 6=fSt-0.0362.

X. The given wave-length expressed in microns.S. The absolute or Kelvin temperature of the

radiating body.e. The base of the Naperian logarithms.E(XO). In the Wien and Planck equations the

radiant power within equal wave-length intervalsAX of average wave-length X when dealing witha complete radiator at temperature 0.

Cl and C2 are constants whose values are sub-ject to experimental determination. For a com-plete radiator the value of C may be taken as3.703 X 10-5 ergs cm- 2 sec.-', i.e., 3.703 X 10-6

microwatts per square centimeters C2 has beenassigned different values from time to time. Ofthe more recent values, 14,320 micron degrees isthe value adopted in the International tempera-ture scale, 14,330 that adopted in the Inter-national Critical Tables and 14,350 that used inmany computations, such for example as thoseof Frehafer and Snow8 and the tables found inthe Davis-Gibson paper No. 1149 which weretaken from the Frehafer and Snow data.

logio e= 0.4343.

C2 C2XO.4343 1/(C2X0.4343)International tempera-

ture scale latest value' 14,320 6219 0.0001608Value generally used

I.C.T. 7 1 14,330 6223 0.0001607Used in Davis-Gibson

paper No. 1148 9 14,350 6232 0.0001604

ABSORPTION SCREENS USED IN OPTICAL

PYROMETER

In the optical pyrometer of the disappearingfilament type an image of the heated objectwhich is generally of the complete radiator typeis formed upon the filament of an electric lamp.This filament is heated electrically until it attainssuch a temperature that it disappears againstthe illuminated background produced by theobject. This occurs when there is an equality ofboth chromaticity and brightness. If the filamentwere a perfect black body (complete radiator)as well as the object, and no absorption or reflec-tion took place between it and the filament thiswould occur when both are at the same tempera-ture. If, however, this temperature is so highthat the life of the lamp filament is reduced or

7 F. E. Fowle, Int. Crit. Tab. V, 238.8 M. K. Frehafer and C. L. Snow, Tables and Graphs

for Facilitating the Computation of Spectral Energy byPlanck's Formula, Bur. Stand. Misc. Pub. No. 56 (1925).

9 R. Davis and K. S. Gibson, Filters for the Reproductionof Sunlight and Daylight and the Determination of ColorTemperature, Bur. Stand. Misc. Pub. No. 114.

10 Wm. F. Roeser, F. R. Caldwell and H. T. Wensel,The Freezing Point of Platinum, Bur. Stand. Res. Pap.326, vol. 6, p. 1119.

11 W. E. Forsythe, Intercomparison of High TemperatureScales, Phys. Rev. 38, 1247-1253 (1931).

47

H. P. GAGE

frequent recalibrations would be necessary itmay be desirable to insert an absorbing screenbetween the source and the filament. If theprevious assumption is maintained that both thesource and the filament are complete radiatorsand it is further desired not only to reduce thebrightness of the background but to cause thisbackground to have the same spectral energydistribution as that of the filament, certain rela-tions between the transmission and wave-lengthof the absorbing filter are required. Such relationswere pointed out by Foote, Mohler and Fair-child.2 "If the transmission of the absorptionglass has the form T'=eaC2x, we have 1/0-1/S= A = a= a constant independent of tempera-ture." With the usual type of optical pyrometersboth filament and background are observedthrough a red glass. The absorbing screen there-fore need follow this relation only between thelimits of the transmission of the glass and thesensitivity of the eye, or roughly between 0.61yuand 0.71A.

Another method of deriving this same relationfollows, by using as a basis the Wien equation

for the distribution of radiant power throughoutthe spectrum. While this is not so rigorous as themodified formula of Planck, within the visiblerange, i.e., from 0.4,u to 0.7,u, the difference be-tween the two is negligible as will be discussedlater.

The Wien equation in its usual form is

E(X0) = C,?cse-2/xO. (1)

Expressing this equation in the logarithmic formfor ease of calculation:

logio E(X0)

=logio C1+5 logio (1/X)-0.4343C 2 /XO. (2)

The relation between the radiant power forany given wave-length X and any two tempera-tures 0 and 02 is obtained by subtraction. Inas-much as it is required that the radiant powerdistribution of the source observed at tempera-ture 01, shall be converted to the distribution ofthe filament at temperature 02, the ratio of theradiant powers must express the transmission ofthe filter E 2 /E, whose logarithm is 8. We obtainEq. (3).

8=logio (E2/E)=logo E 2 -logo E,=-0.4343C 2/X02+0.4343C2/X0I (0.4343C2/X)(1/01-1/02). (3)

This equation may be expressed in the form of acurve plotted with 8 against 1/X and is a straightline passing through the origin, i.e., 8 and 1/Xboth equal zero. The meaning of this is that atwave-length infinity there would be perfecttransmission.

It is thus evident that the necessary trans-mission of the pyrometer absorption glass forany given wave-length X is

(4)

01 being the higher temperature.Substituting in Eq. (3) the numerical value

corresponding to C2 = 14,330, we get

8= (6223/X)(1/0 1 - 1/02). (5)

As 01 is greater than 02, (1/01- 1/02) is negativeas required.

12 Paul D. Foote, F. L. Mohler and C. 0. Fairchild,

Pyromiietry-The Proper Type of Absorption Glass for anOptical Pyrometer, J. Wash. Acad. Sci. VII, 545-549(1917).

Illustration of actual glasses. In 1918 a pair ofglasses, one of which (No. 1 in Fig. 1) was a bluegreen having decreasing transmission towardsthe longer wave-lengths, the other (No. 2 inFig. 1) had increasing transmission towards thelonger wave-lengths but to a greater extent thanwas desired, were combined in such proportionsthat the combination (1+2) had greater trans-mission towards the longer wave-lengths to ap-proximately the extent desired-between thelimits 0.60,u to the end of the sensitivity of theeye at about 0.71y. The use of two separateglasses being undesirable, an attempt was madeto combine two coloring agents in the sameglass in such proportions as to secure the desiredresult. The success of such a glass made in May,1932 is shown by curve 3, Fig. 1. The use of thisglass as an absorption glass in an optical pyrom-eter is reported 3 "very satisfactory. The difficulty

13 P. H. Dike, Leeds and Northrup Company letter,July 12, 1932, to H. P. Gage.

48

TX=E(X0,)1E(X01),

COLOR FILTERS

FIG. 1. Pyrometer absorption glasses. Curve 1, blue greenglass; curve 2, amethyst glass; curve 1+2, blue green andamethyst together-the ordinates flt or are additive whenexpressed logarithmically; curve 3, pyrometer brown.Beyond wave-length 0.60 to the limit of the visiblespectrum about 0.70, in the region transmitted by redglass these curves approximate straight lines passingthrough the origin. The curve 1+2 approximates the line

=1.03 X (1/X) corresponding to a temperature differenceof 166 micro-reciprocal degrees and curve 3 approximates3=0.728X(1/X), temperature difference 117 micro-recip-rocal degrees.

due to varying shades of red glass filter prac-tically disappears when this glass is used."

DAYLITE GLASS

Daylite glass may be defined as a blue glasswhich causes the transmitted light to have ahigher color temperature than the source withoutintroducing serious spectral irregularities. Whensuch a glass is used it is evident that the valueof C in the equation cannot be used because asthe color temperature goes up by the use of athicker glass the brightness must go down. Letus assume that the brightness of two surfacesare nonselectively varied, as, for example, bychanging on a photometer bench the respectivelamp distances. For any given wave-length it ispossible to adjust the brightness of the surfacesto equality but, in general, equality will not thenexist for any other wave-length. This may beexpressed in Eqs. (1) and (2) for each of thesources by using a value D instead of C to

indicate that the relative distribution of radiantpower throughout the spectrum is the same butthat its intensity is nonselectively reduced.These values of D can also be made to include theconstant nonselective reflection factor of theabsorbing glass so that instead of using thetransmission of the glass it is possible to use thelogarithm of the transmittance t. If the twovalues of D1 and D2 are so chosen that the pointof equality of the two curves is at some shortwave-length portion of the spectrum in theneighborhood of 0.4/u, this wave-length of equalityis designated as X1. Substituting D1 and D2 for C1in Eq. (2) to indicate the reduced values ofintensity, we get by subtraction

log1o E(X02 )-log1 E(X0) = logio D2-1og10 D1

-(0.4343C 2/X)(1/0 2 -1/0,). (6)

The values of D1 and D2 are so chosen that theintensities for wave-length X1 are the same, i.e.,E(XA)1 )=E(X1 02 ). The first member of Eq. (6)becomes zero when X= Xi and

logi 0 D 2 -logio D1

= (0.4343 C2/X 1) (1/02- /01). (7)

Substituting this value in Eq. (6) and factoringwe get

t=log 10 (E(X0 2)/E(XO1 ))

= log10 E(X02) -log 1 oE(X01 )

= 0.4343 C2(1/ 1 -1/X) (1/0 2 -1/0 1 ). (8)

If now it were possible to produce a coloredglass in which the spectral transmission wouldexactly satisfy this equation, then such a glasswould constitute a color filter which, if placedin front of a source whose distribution of radiantpower corresponds to Wien's equation for onevalue of 0 there is transmitted light whose spec-tral distribution also corresponds to Wien's equa-tion, with a different and in this case highervalue of 0.

It will be noted that Eq. (8) is of the firstdegree with respect to ,Bt and 1/X, and can beplotted as a straight line if these values areused as coordinates. Fig. 2 is such a plot inwhich the values of 1/X are plotted as abscissaeand t (with zero at the top) are plotted asordinates. No absorption occurs-that is, ,t= 0,at the Doint where /X= 1/Xi. The slope is

49

H. P. GAGE

WAVE - LENGTH,.40A. , I, Z,z4 , .50,,,.

-P'UQU

I-

I

M1 ICRONS;5 ,, .,60,,, _66 .74

- -= -sg/ _______-~- //

.6\%4 > . Q< L Iz;

,;6D____ =( ____'

1.d_ ^~~~~~~~~'. ?O ' , .' ^.n^ *.*. '

2.5' 'et XJ 2-1 2.1 E 0 I 1.8 1.7 1 GRECIPROCAL WAV- LENGTH

1.3 Wi

FIG. 2. Corning Daylite glass and other blue glassesshowing the closeness of approximation of the curve ofDaylite glass to a straight line when logarithm of trans-mittance (t) is plotted against reciprocal of wave-length.The other blue glasses show irregularities and do notcorrect at wave-lengths less than 0.45,u. The Daylite glassillustrated raises the color temperature by 195 micro-reciprocal degrees, e.g., it raises the color temperature of alight source at 28480K to the distribution correspondingto 6,400° if calculated by Wien's equation or 6,530'K ifcalculated according to Planck's equation.

0.4343C2(1/02 - 1/01). The position of Xi at whichthere is complete transmittance should be chosenso as to be just at the short wave-length end ofthe visible spectrum. If X1 is in the ultraviolet anexcessive amount of absorption will be requiredthroughout the rest of the spectrum, and if X1 istoo far in the visible spectrum insufficient correc-tion in the blue will result. It is thought that0.41,u is a suitable wave-length to choose for 1.If the spectrophotometric measurements of anactual color filter show that 13t plotted against1/N approximates a straight line, a color tem-perature altering filter is indicated and the close-ness of approximation of the observed points tothe straight line is a measure of the accuracywith which the filter gives the desired result.

From Eq. (8) it may be deduced that the sameglass will serve to increase the color temperatureof any source. The relation of the increased tem-perature of the source is such that14 the differencein reciprocal temperatures in accordance with theWien formula is a constant; i.e., (1/1-1102)= (1/03- 1/64).

A variation in thickness of the glass (from tto t3) will leave a unchanged and the relation is:

Otll/3ta= tl/t3= (1/01-l/02)/(/o- 1/03).

14 H. P. Gage, Comments on Hyde and Forsythe Paper,Trans. I. E. S. 16, 428 (1921).

That is, the differences in the reciprocal tempera-tures are in proportion to the glass thickness.

RELATION OF FORMULAE TO ACTUAL GLASSES

Having deduced the mathematical formula towhich a color filter must approximate with asgreat accuracy as possible, we will consider theapplication to an actual glass as measured on thespectrophotometer. Suppose the data for twocarefully chosen wave-lengths X2 and X3 have thecorresponding values of 2t and 0 3t as measured.Substituting these in turn in Eq. (8) and sub-tracting we get

12 t-i3t= 0.4343C 2 (-1/X 2 + 1/X3)(1/02-1/01). (9)

For the value 0.4343 C2 its numerical equivalent6223 may be substituted or it can be expressedin its reciprocal form 1/0.4343C 2 =0.0001607.

Also, (1/02-1/01) is negative and the signsmay be rearranged to give

12t-13t= 6223(1/X2- 1/X3)(1/01- 1/02),

1-8 = 0.0001607 121-13161 62 1/N2 - 1/N3 1

perhaps more conveniently expressed as

A(1/0) = 0.0001607At/A(1/?,).

Substituting at for A(1/0)

a = 0.000607A/A (1 /X) .

(10)

(11)

(12)

(13)

As an example of measurements on an actualglass, a 5 mm piece of Corning Daylite glassmade 7/13/29 gives

Point 1/X t at= 0.0001607- 1f',MI/X

0 845(2) 0.42tz 2.381 -0.108 =0.0001607 078

(3) 0. 6 2M 1.613 -0.953

Difference A(2) - (3)

=0.0001768,

+0.768 +0.845 =0.0000354.

WIEN EQUATION PASSING THROUGH Two GIVENPOINTS

To a close approximation any energy distribu-tion expressible according to Planck's formulawithin the narrow range of the visible spectrum

50

COLOR FILTERS

can also be expressed by Wien's formula by asuitable but different choice of . This followsfrom the fact that the curves for the two formulaeare much alike (see Fig. 3). While the differencebetween the curves becomes considerable when

FIG. 3. Wien and Planck equation curves plotted withE/Emax. against X/?max. When is 2890°, mX,, is 1g.8

The difference between the two curves is due to the Planckcorrection factor. The two curves have much the sameshape, the divergence between them being gradual. Thedifference is negligible on the short wave-length side of themaximum. The Planck curve was plotted with E/Ema.. 1when X/Xmax, is 1. The Wien curve calculated with thesame value of C and 0 is lower than the Planck curve atX/Xmax, = 1 by 0.7 percent.

working over the complete spectrum, the differ-ence is not great over a narrow range. If forexample the radiant power Ex at two wave-lengths X1 and X2 is known, then either a Planck'sequation curve can be drawn through these twopoints or a Wien's equation curve. The generalslope of the two curves will determine the valueof 0 to use; the curvature will depend on whichequation is chosen.

Two points, such as those for 0.45,t and 0.6 5 u,can be selected from a series of Planck equationcurves, such as those published by Frehafer andSnow,8 Davis and Gibson9 or by Fowle7 and aWien equation curve calculated which will passthrough these same points. The divergence of allother points is remarkably small and is much lessthan the divergence from either curve of meas-ured points on such high temperature sources asthe sun, blue sky, etc.

The calculation of a Wien equation curvepassing through two points (E1 , X1) and (E 2 , 2 )

follows by substituting these values in Eq. (2)and solving for 0. Thus

logio El-log 1 o E2 =5(log1 o (1/X1)-log 10 (1/X2 ))- (0.4343C 2 /0)(1/X 1 - 1/X2), (14)

1/0= [5(logio (1/X1) - 10g10 (1/X 2)) - (log10 E 1 - logio E 2 )]/[0.4343C 2 (1/X,- 1/X 2)]. (15)

By substituting the numerical value for 0.4343 C2 and inverting,

0= 6223(1/X 1- /X2)/[5(loglo (1/X1) -log 1 0 (1/X2))- (log109 E1 -log1 o E 2 )]. (16)

Example. The latest data for sunshine outsidethe earth's atmosphere as given by Abbot andFowlel' have a slightly wavy curve. By choosingthe crests of two such waves as indicative of theslope of the curve we get two points

Point i 0.4753Point 2 0.6858Diff.

(1)-(2)

1/X log (/X)2.104 0.323031.458 0.16380

E log E566 2.7528409 2.6117

+0.646 +0.15923 +0.1411

6223 X 0.646 40205X0.15923-0.1411 6550

6140. (17)

,6 C. G. Abbot, F. E. Fowle and L. B. Aldrich, TheDistribution of Energy in the Spectra of the Sun and Stars,Smithsonian Misc. Collections 74, No. 7, 1-30 (1923).

As shown later this corresponds to a value of 0of 62500 when used in the Planck formula. (SeeFig. 4.)

In a similar way calculations were made withthe points for 0.45,u and 0.65A from the Planckequation data given in the Davis-Gibson paper9

for each of the higher temperatures with theresults shown in Table I.

For the two wave-lengths 0.45,u and 0.65, theformula reduces to

0(wien) =4255/[0.7980- (log El-log E 2 )]. (18)

For such sources as the sun, sky, etc., thevalue 0 serves as a convenient method of express-ing a type of radiant power distribution. It maybe permitted in this discussion, therefore, to useWien's formula to express distributions repre-

51

H. P. GAGE

10 - t 6508 K

310 :q

too Cq0 go -.I1060 'A

40 -

30 'L

10-

-.3~," 40/u .50 Wve un-WL6

FIG. 4. Sun outside the earth's atmosphere, Abbot andFowle, 1923 data' 5 values multiplied by 1.94. Solid curveWien distribution for 6140°, circles Planck's equation for6250°, all curves adjusted to pass through common pointsat 0.454,A and 0.6 5 w. Within the visible region between0.4Ao and 0.7 m the difference between the two equations isnegligible compared to the difference between either andthe curve for the sun to which they are nearly equivalent.

senting stimuli approximating the various phasesof daylight as well as other light sources when-ever experiment justifies such use. Some otherterm than temperature might even be applied tothe value of 0 in these equations were it not forthe fact that some incandescent sources not onlyare similar to, but actually are complete radiatorswhose actual temperature may be measured. Itis to be pointed out, however, that with anyexperimentally obtainable incandescent sourcestemperatures exceeding 3780'K (crater of carbonarc) do not occur, and for such sources the correc-tion factor changing the Wien to Planck equationwithin the visible spectrum is negligible, beingbut 0.5 percent at 0.7, for 3780'K.

TABLE I. Equivalence of Wien and Planck temperatures byred-blue ratio.

Color temp. (0 K) Micro-reciprocal degreesPlanck Wien Difference 1/P 11W Difference

5,000 4,990 10 200 200.4 0.45,500 5,460 40 181.8 183.2 1.46,000 5,920 80 166.7 168.7 2.06,500 6,390 110 153.8 156.5 2.77,000 6,840 160 142.9 146.0 3.18,000 7,710 290 125.0 129.7 4.79,000 8,520 480 111.0 117.4 6.4

10,000 9,280 720 100.0 107.8 7.812,000 10,680 1,320 83.3 93.7 10.414,000 12,005 1,995 71.4 83.3 11.916,000 12,970 3,030 62.5 77.1 14.618,000 13,900 4,100 55.6 71.9 16.320,000 14,650 5,350 50.0 68.2 18.2

COLOR TEMPERATURE OF TYPICAL LIGHT

SOURCES

Ives' pointed out that the spectral energy dis-tribution of the noon sun approximated that ofa black body at 5,000° absolute.

The color temperature of various artificialilluminants was determined by Hyde, Forsytheand Cady and tables giving the resulting valueshave been published from time to time.", 17, 18

The color temperature of the carbon arc'9 20

and some phases of daylight 2 ' were measured byI. G. Priest using the method of rotatory dis-persion22 and a preliminary standard of artificialsunlight, the "Abbot-Priest Sunlight"23 was pro-posed. Another standard is average noon sun-light as shown in charts Nos. 1 to 20 of the Davis-Gibson filters.9 According to Davis2 4 the corre-lated color temperature of this distribution comesout 53940K (Planck) as compared to the spectralcentroid method of Priest2 2 which gives 5578°.In addition to the above sources of information,summaries of these determinations are publishedin the Report of the Colorimetry Committee, L. T.Troland, Chairman,25 by Norman Macbeth,26 and

1 Hyde, Forsythe and Cady, Color Temperature Scalesfor Tungsten and Carbon, Phys. Rev. 10, 401 (1917),Table I.

17 E. P. Hyde and W. E. Forsythe, Color Temperatureof Various Illuminants, (Abs.) J. 0. S. A. 1, 99 (1917);J. Frank. Inst. 183, 353-354 (1917).

18 E. P. Hyde and W. E. Forsythe, Color Temperatureand Brightness of Various Illuminants, Trans. I. E. S. 16,419 (1921).

19 I. G. Priest, Measurement of the Color Temperature ofthe more Efficient Artificial Light Sources by the Method ofRotatory Dispersion, J. 0. S. A. 6, 27-41 (1922).

20 I. G. Priest, Measurements of the Color Temperature ofthe more Efficient Artificial Light Sources by the Method ofRotatory Dispersion, Bur. Stand. Sci. Pap. No. 443 (1922).

21 I. G. Priest, Color Temperature of Various Phases ofDaylight, J. 0. S. A. 7, 78 (1923).

22 I. G. Priest, The Colorimetry and Photometry of Day-light and Incandescent Illuminants by the Method of RotatoryDispersion, J. 0. S. A. and R. S. I. 7, 1175-1209 (1923).

23 I. G. Priest, Standard Artificial Sunlightfor ColorimetricPurposes, J. 0. S. A. and R. S. I. 12, 480 (1926).

24 Raymond Davis, A Correlated Color Temperature forIlluminants, Bur. Standards J. Research 7, 659-681 (1931),Research Paper 365.

25 L. T. Troland, Chairman, Report of Committee onColorimetry, J. 0. S. A. and R. S. I. 6, 527-596 (1922).

26 Norman Macbeth, Color Temperature Classification of

Natural and Artificial Illuminants, rrans. . E. S. 23,302-324 (1928), Figs. I and 2

52

COLOR FILTERS 53

TABLE I Ia. Color temperature of selected light sources.I.C.T., V. 247.

Color temp. Micro-reciprocal(0K) degrees

Source 0 1/0

Signal lamp, kerosene 1900 526.3Hefner lamp 1880 531.9Paraffin candle 1925 519.6Kerosene-flat 2055 486.6Acetylene, whole flame 2380 420.2

"1 Mees burner 2360 423.7Vacuum lamps, carbon

4Wpc carbon 2080 480.83.1 treated 2165 4622.5 Gem 2195 455.5

Osmium -2 Wpc 2185 457.7Tantalum-2 ' 2260 442.5Tungsten, 10 watt 2390 418.4

Standard value 2360 423.7Straight filament, 25 watt 2493 401

40 " 2504 39960 " 2509 398

Gas-filled tungsten, 75 watt 2705 369.6100 " 2740 365200 " 2810 355.9

Standard 2848 351.1Movie, 900 " 3220 310.6

30,000 " 3300 303.0Electric arc, +crater

Solid carbon 3780 264.5Cored carbon 3420 292.4

Temp. Color temp. ReciprocalSource (0C) (0 K) temp.

Complete radiator at the freezing point ofGold2 8 1063 1336 748.5Palladium 2 8 1555 1828 547Platinum' 0 1773.5 2046.5 488.6Rhodium 2 8 1955 2228 449Iridium 2 8 2350 2623 381.3

in the International Critical Tables.27 It was fromthe latter source that most of the data for TableII were taken except where indicated.

The sun, outside the earth's atmosphere, ac-cording to the data of Abbot given to the Bureauof Standards in 1917 (see Davis and Gibson,9

Table I, p. 16), gives a correlated color tempera-ture of 6565 0K or a spectral centroid corre-sponding to 6724 0K. If, however, it is plotted ona curve for 65000 Planck or 6390° Wien there isa close agreement of all points for wave-lengthsgreater than 0.45/u. The 1923 data of Abbot'5

come to a close agreement to the curve for 6250°Planck or 6140° Wien as has been previouslydescribed and as illustrated in Fig. 4. Thismethod is, however, not considered rigorous fordetermining color temperature.

27 Temperature, Brightness and Efficiency of SelectedSources of Illumination, Int. Crit. Tab. 5, 247, Table VII.

TABLE I lb. Color temperature of various phases of daylight."

Planck 1/P Wien 11W

Extremely blue sky 24,150 41.4 15,800 63.3

Blue sky range 19,000 52.6 14,000 70Blue sky range {14,000 71.4 11,850 84.4

Whole sky 9,800 102 9,340 1076,000 166.7 5,900 169.5

Sun 5,300 188.7 5,260 190'n 4,510 221.7 4,510 221.7

Sun outside earth's atmos-phere,

1923 value of Abbot5 andas illustrated in Fig. 4 6,250 160 6,140 162.9

Ditto, 1917 value, corre-lated color temperature,Davis2 4 6,565 152.3 6,445 155.2

Mean noon sun, correlatedcolor temperature 4 5,394 185.5 5,360 186.6

Abbot-Priest sun, corre-lated color temperatures 5,229 191.6 5,200 192.3

Complete radiators at the temperature of thefreezing point of gold, palladium, platinum, havebeen used as standards for radiant energy. Thefreezing point of gold and palladium as given inthe International Critical Tables28 agree with thoseused by Forsythe", 18 and Roeser, Caldwell andWensel10 in their work on the freezing point ofplatinum but a new value for the freezing pointof platinum, 1773.50 C, or 2046.50 K, has beendetermined and it is this temperature which isused in the discussion of the Waidner-Burgessstandard of light.2 9 The freezing points of rho-dium and irridium might similarly be used ifsatisfactory refractories can be found. Theselatter temperatures are as given in the criticaltables.

COLOR OF TRANSMITTED LIGHT FOR THICK

PIECES OF DAYLITE GLASS

It has been noted that a thickness of Dayliteglass may be found such as to reduce the recip-rocal color temperature of a source to zero, andincreased thicknesses will reduce it to less thanzero. In this way chromaticities may be produced

28 Int. Crit. Tab. 1, 103-104.29 H. T. Wensel, Wm. F. Roeser, L. E. Barbrow and

F. R. Caldwell, The Waidner-Burgess Standard of Light,Bur. Stand. Res. Pap. 325, 6, 1103-1117 (1931).

53

H. P. GAGE

corresponding to the energy distributions definedby Wien's equation for infinite and also fornegative temperature. Although no physicalmeaning is to be attached either to infinite or tonegative temperature, the Wien equation doesgive the actual distribution of the transmittedlight. For example, 10 mm of the melt of Dayliteglass of 7-13-29 changes the color temperatureby an amount corresponding to 353 micro-reciprocal degrees, and 353 micro-reciprocal de-grees corresponds closely to the standard gas-filled tungsten lamp. The spectral distribu-tion resulting in such a case may be determinedby substituting, 1/0=0, in Wien's equation:E6= Cl/X5, that is, the radiant power is inverselyproportional to the fifth power of the wave-length.

One might readily suppose the interpretationaldifficulties to be a consequence of the inapplica-bility of the Wien equation to very high tem-peratures. Similar difficulties, however, appearwith the Planck equation which is perfectlyapplicable by reason of its-agreement with experi-mental data. For example, the Planck equationindicates that a radiator at infinite temperaturewould yield an energy distribution inversely pro-portional to the fourth power of the wave-length.This corresponds to a chromaticity even lessblue than that indicated by the Wien equationfor infinite temperature; and this chromaticitycan, of course, also easily be obtained by meansof Daylite glass.

ACKNOWLEDGMENT

The author wishes to acknowledge the helpfulsuggestions made by Dr. W. E. Forsythe on anearly draft of the present paper.

Special acknowledgment is due the late IrwinG. Priest for stimulating the revision of a 1921laboratory report into suitable form for publica-tion. During the early part of this year Mr.Priest's letters to the author revealing his clear-cut conception of clorimetric problems ex-pressed in his concise and exact diction were

largely directed towards the simplification of themethods of using color temperature as a tool inexpressing the characteristics of heterogeneousradiation caused by temperature. At least one ofthese letters dealing with an allied use of hisrotatory dispersion method is worthy of ampli-fication into a special article.

During my visit to Washington in May 1932Mr. Priest discussed rather extensively and inconsiderable detail the advantages of using thereciprocal of color temperature as representinga more evenly graduated scale than do the tem-peratures themselves. Moreover, in the deriva-tion of the radiation equations, temperatureenters in as the reciprocal and, except for thefortuitous way in which the first thermometerswere graduated, has as much reason to be con-sidered fundamental. Mr. Priest therefore desiredto express color temperature in the reciprocalform, using as a unit the microreciprocal degree,resulting in a scale in which 50 to 500 micro-reciprocal degrees covers the useful range fromblue sky to candle light.30 He was not ready toaccept without further consideration the use ofthis scale based on the Wien equation ratherthan the Planck equation although the advan-tages to be gained in calculations involvingthickness of color filters had been brought to hisattention by Mr. Guild of the National PhysicalLaboratory in England. The purpose of the sug-gestion could he said, be equally well served bya table showing the differences between the twoscales. A letter written by him on the last day ofhis life was a request for a filter to raise the colortemperature of a light source by approximately75 microreciprocal degrees and a hope expressedto discuss the matter further.

Acknowledgment is also given to Dr. Gibsonand Dr. Judd of the Bureau of Standards fortheir careful study and suggestions regardingthis paper, and to help received from severalothers as well.

30 1. G. Priest, A Proposed Scale for Use in Specifyingthe Chromaticity of Incandescent Illuminants and VariousPhases of Daylight, J. 0. S. A. 23, 41 (1933).

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