SOME REhIARKS ON THE CSE OF THERMOPILES FOR THE ABSOLUTE LIEASURENENT O F RADIANT ENERGY” BY PHILIP A . LEIGHTON AND WESLEY G. LE’IGHTON
Among the instruments which may conveniently be applied to the accurat’e measurement’ of radiant energy in absolute terms, * * the thermopile, used with a sensitive galvanometer,’ has come into almost universal use. In photochemist’ry, for example, almost every value of quantum yields which has yet’ been published depends, directly or indirectly, upon a calibrated thermopile as the instrument for the determination of the absolute amount of energy involved. The measurement of relative light intensities, it,self a matter demanding the most’ careful technique, is simple compared to the translation of these measurements into absolute units. During the past eight years, the authors have investigated thirteen thermopiles, involving seven distinct types of construction, with regard to their applicability to absolute energy measurements. Some of the results of these studies have been published in connection with the work for which the thermopiles were used, and descriptions of most of the errors involved, together with precautionary measures, have been published by others, but the statements are so widely scattered through the literature that the knowledge seems to be gained by each new worker largely through experience. It therefore seems worth while to publish in one account a description of the observations which have been made and the precautionswhich have been found necessary in order to obtain reliable results. 1. Remarks on Design and Construction Much of the work on the design and construction of line and surface thermopiles suitable for absolute energy measurements has been carried out by W. W. Coblentz,2 who gives detailed directions for their construction. The absolute thermopile of Coblentz and Em6rson merits more attention than it has received. The construction of line and surface thermopiles has also been described by J ~ h a n s e nV , ~~ e g e M011,~ ,~ and others.6 Single junction thermo* Contribution from the Chemistry Laboratories of Stanford University and of Pomona
College. ** The term “energy” as here used refers to energy per unit time. We believe this is preferable to the use of the term “intensity” since energy per unit area is usually not considered. 1 G. S. Forbes: J. Phys. Chem., 32, 489-90 (1928) Coblentz: Bur. Standards Bull., 4, 391 (1908); 12, 503 (1916); 9,,7 (1913); 11, 131 (1914); Bur. Standards Sei. Papers, 17, 187 (1921); J. Opt. SOC.Bmerlca, 5, Zjg (1921); 7, 439 (1923). Coblentz and Emerson: Bur. Standards Bull., 11, 157 (1914); 12, 505 (1916). 3 Johansen: Ann. Physik, ( 4 ) 33, 517 (1910). 4 Voege: Physik. Z., 21, 288 (1920); 22, 119 (1921). 6 hloll: Proc. Phys. SOC. London, 35, 257 (1923). 6 Weigert: “Optische hlethoden der Chemie,” 295 (1927).
ABSOLUTE MEASUREMENT O F RADIANT ENERGY
1883
couples of high sensitivity but with small sensitive surface are described by Moll and Burger,' Brackett and McAlister,* and Petit and Nicho1son.Q A single thermocouple adapted to absolute energy measurements has recently been employed by Beckmann and Dickinson.lo The majority of these instruments have been designed with cases which may be evacuated. Evacuation is found to increase the sensitivity from two to twelve times over that a t atmospheric pressure. In case a vacuum thermocouple or thermopile is used, care must be taken that the pressure is very low (less than IO-^ mm.) or that it is constant, since in the pressure range between I O mm. and 10-3 mm. the sensitivity changes rapidly with pressure.9 The sensitivity is also a function of the nature of the enclosed gas. Using a surface thermopile, we have found the sensitivity in an atmosphere of hydrogen is less than half of that in air, pressure being atmospheric in both cases, and even a t a pressure of 1 0 - ~ mm., the sensitivity in hydrogen is slightly less than that in air. The question of the position of the slit with respect to the radiation receivers must be considered in the design of vacuum thermopiles for absolute energy measurements, and is discussed in section 5. If the beam to be measured is of uniform energy distribution, and if it is of suitable dimensions, a surface thermopile offers the simplest means for absolute energy measurement. Variations in sensitivity over the surface make certain precautions necessary, which are discussed under section 6. If the beam of light may be focused to a spot not more than 5 mm. in diameter, a single thermocouple of the Beckmann and Dickinson type,6 with a single receiver large enough to include the entire beam, may be employed. For beams of varying size and intensity distribution, a line thermopile of the many-junction type, operated by the methods described in this paper, provides a satisfactory means of absolute energy measurement. I n the case of line thermopiles, an integration process, as described in section 7, must be carried out in order to obtain absolute energy values. To simplify this process, it is important that the length of the sensitive portion of the pile be equal to or slightly greater than that of one dimension of the beam-preferably the dimension showing the most uniform distribution of intensity. The integration process may be further simplified by using radiation receivers as wide as is compatible with uniform sensitivity over their surface. We have experimented with several types of construction with this end in view. The construction shown in Fig. I enables one to use receivers up to 3 or 4 mm. wide without loss in uniform sensitivity. The junctions are of silver and bismuth wire, 0.05 mm. and 0.1mm. diameter, respectively, the receivers of tin foil, about 0 . 0 2 mm. in thickness. The center receivers are each 3 to 4 mm. wide by 2 mm. high. the balancing receivers on the dark junctions are exactly half the area of the center receivers. Moll and Bur er 2 Physik 32, 575 (1925); Moll: Physica, 6, 233 (1926). Brackett and%McAlkter: Rdv. Sci. Instruments, 1, I81 (1930). 9 Petit and Nicholson: Astrophys. 56, 295 (1922);68, 279 (1928);Petit: Carnegie Inst. Wash., Year Book, 140 (1929). 10 Beckmann and Diokinson: J. Am. Chem. Soc., 52, 126 (1930). 7
8
I884
PHILIP A. LEIGHTON AND WESLEY 6. LEIGHTON
Welding and mounting are accomplished after the directions of Coblentz." A silver, then a bismuth wire of the proper lengths are welded in two places to each center receiver (Fig. I , b). Then two pieces of foil of half size are welded to the silver wire, about I cm. from each edge of the center receiver, Next these individual junctions are mounted, by means of the extending silver wires, on an ivory or bakelite block, as described by Coblentz. The final welding of adjacent junctions may be accomplished by carefully setting a glass plate mounted on a firm base, of just the size of the opening in the
FIG.I Construction of Thermopile with Wide Radiation Receivers.
block, directly behind and in contact with the junctions. The bismuth wires from one junction are then welded to the silver wires of the next junction, care being taken that the weld is in the center of each small piece of foil previously attached to the silver. DanielsL2has designed and constructed thermopiles with receivers of silver foil, sufficiently heavy so that their width may be extended to I O mni. while still retaining a uniform sensitivity over their surface. The heavier receiver extends the period of response of the thermopile, which allows time for a fairly uniform temperature to be attained throughout the receiver, no matter what part of i t is exposed. It is necessary to use these piles in a thermostat. In the case of line thermopiles, as will be shown in section 5 , it is absolutely essential to choose an instrument which is or may be fitted with a slit narrower than and very close to the radiation receivers. For this reason some types of commercial line thermopiles are not to be recommended for absolute energy measurements. 11 12
Coblents: Bur. Standards Bull., 9, I j F. Daniels: private communication.
(1913).
ABSOLUTE MEASUREMENT OF RADIANT ENERGY
1885
2. Avoidance of Errors due to Drift
A thermopile-galvanometer combination which is sufficiently sensitive to measure beams of monochromatic light of average intensity is naturally very responsive to small changes in temperature, air currents, and similar disturbances. On a bismuth silver thermopile with 2 0 junctions and a galvanometer of sensitivity 15 mm/pv, a difference of IO-^ degree between hot and cold junctions should produce a deflection of approximately I cm. on a scale 5 meters distant from the galvanometer. These disturbances result most commonly in a slow drift of the “zero point” of the galvanometer. The drift may be greatly reduced or avoided entirely by evacuating or thermostating the thermopile. There is, however, usually an additional drift produced on exposure to light, due to conduction along the wires to the cold junctions, Peltier effect, etc., so that even when a pile is completely protected, after exposure to light it requires some time to return to the original zero. The errors due to both types of drift may largely be avoided by what has been termed the “ballistic” or “swinging equilibrium” method of reading.’$ This differs from the method of reading with a ballistic galvanometer, in that a condition of swinging equilibrium is established by proper manipulation of a shutter between the light source and the thermopile. The shutter is first opened, then at the instant the mirror reaches a maximum deflection it is closed, the instant a minimum is reached it is again opened, and so on. With a thermopile of the Coblentz type these alternate maxima and minima will be reached within the period of the average d’Arsonval galvanometer-say three to five seconds. After allowing one or two complete swings in order to attain maximum amplitude, readings of maxima and minima are taken, then the average of two successive minima is subtracted from the intermediate maximum. As shown by the accompanying actually recorded example, a considerable drift during the course of a set of readings has little effect on the actual deflection as obtained by this method. Min.
Av.
Max.
Def.
54.3
19.3
35.5
54.6
19.1
36.0
55.2
19.2
36.35
55.5
19.15
36.6
55.8
35.8 36.2
36.7
19.2
Av. = 19.19
la
P.A. Leighton and G. S. Forbes: J. Am. Chem. Soo., 51, 3551 (1929).
1886
PHILIP A. LEIGHTON AND WESLEY G. LEIGHTON
Ordinarily, about one minute is required to obtain a set of readings of five maxima and six minima, giving five values of the deflection, which may be averaged to give a very reproducible figure. The foregoing method cannot be applied to thermopiles with periods longer than the period of the galvanometer. With such thermopiles it is necessary for the galvanometer to come to rest both for the maximum and minimum reading, and thermostating of the pile is essential to accuracy. With a low resistance d'Arsonval galvanometer (such as Leeds and Northrup Type HS zz85x, C. D. R. $2, I.R. 18Q, period 7 sec. and sensitivity 15.3 mm./pv.), easily readable swing maxima and minima are obtained when the thermopile resistance or external resistance is greater than the critical damping resistance, ratios of as high as six fold having been found satisfactory. The precautions required by the variation in sensitivity at different positions of the galvanometer mirror (section 8) could be avoided by using the galvanometer as a null instrument, but the effect of drift in the thermopile E.N.F., we believe, can be eliminated more simply by observing deflections a t swinging equilibrium. Moreover, if the light-flux being measured is itself subject to fluctuations during the course of a swing, the resulting deflection will tend t o represent the integrated intensity during the short exposure. 3. Calibration
If the thermopile is calibrated by means of standard carbon lamps, as furnished by the Bureau of Standards, two sources of error (assuming that the absolute intensity of the radiation reaching the thermopile window from the standard lamp is accurately known) are to be considered. These sources of error arise from the conditions that : I. The thermopile is usually calibrated in radiation of one wave length and used for another. 2. The thermopile may be calibrated for one range of galvanometer deflections and used for another. The calibration in one wave length and use in another involves the question of non-selectivity of the absorbing surface. A carefully prepared platinum-black, lamp black,14 or bismuth black'j surface may safely be assumed as non-selective in absorption throughout the ordinary range of ultra-violet, visible, and near infra-red radiations. Such a surface will reflect a small amount, about 0.5 to 1 . 5 7 ~of the incident radiation,14 and variation in the amount of this reflection with wave length will produce some error, but the error will in general be of the second order and may be neglected. On the other hand, we have found some commercial thermopiles to give values as much as 20% too high when calibrated in the visible and infra-red of the carbon lamp and used for X z 5 0 0 1 or shorter in the ultra-violet. If the radiation receivers are not apparently perfectly black to the eye, they should be re-blackened. I n most cases smoking with a sperm candle will suffice.14 l4
Coblente: Bur. Standards Bull., 9, 283 (1913); 11, 98 (1914);12, 510, 522 (1916). A. H. Pfund: Rev. Sci. Instruments, 1, 397 (1930).
ABSOLUTE MEASUREMENT O F RADIANT ENERGY
1887
Calibration in one wave length and use in another also involves a correction for changes in absorption and reflection of the thermopile window with wave length. On account of this change with wave length, the window will reflect and absorb different amounts of the standard lamp radiation for each current input. The transmission of the thermopile window should therefore be measured not only for every wave length for which it is to be used, but also for every current input of the standard lamp radiation. I n the case of the standard lamp radiation, these measurements of window transmission should not be made with a thermopile which is already protected with another window, but on an uncovered thermopile. Very careful shielding to avoid drift due to air currents will be necessary when the window is removed. We have calculated the reflection and absorption losses to be expected for a crystal quartz window I mm. thick, when placed in the radiation from a standard carbon lamp burning a t the four different current inputs a t which it was calibrated. These calculations were made as follows: I. The color temperature was estimated from measurements of the brightness temperature as made by an optical pyrometer. From this the spectral energy distribution of the radiation from the carbon filament was calculated from the radiation laws. 2. This spectral energy distribution was corrected for absorption by the glass bulb, using the data of Coblentz.I6 3. The reflection of quartz, using Fresnel's law, and the absorption of I mm. of quartz, using Coblentz' data, were calculated for a series of points in the wave length region covered by the standard lamp. 4. The net loss was calculated from the losses a t each wave length and the spectral energy distribution of the radiation. A set of these calculations, for a carbon lamp burning a t IOOOOK, and the final results for four temperatures in the range usually covered by these lamps, are given in Tables I and 11.
TABLE I Standard Carbon Lamp at Radiation region I*
4.0-3.5 3.5-3.0 3.0-2.5
Resulting Total radiation radiation by transmitted below glass wall through 4.0 p of lamp glass 21%
4.3%
23
27
.o
24 I7
85
.o-I . 5
I1
2.5-2 2
Transmitted
1.5-1.0 1.0-0.5
4 0.6 100%
71
89 90 90
1 12
7%
33 26 19
7
I
1000'
K
Amount Amount reflected absorbed by by quartz quartz window window
Amount of total radiation reflected
Amount of total radiation absorbed
0.08% .24
0.8
0.13% 0.93 2.69
0.5
2.18
. I3
0.2
1.63 0.61 0.09
.04
-
8.26%
0.76%
7.5%
5%
7.8 8.15 8.4 8.6 8.8 9.0
2.0
100%
Coblentz: Bur. Standards Bull., 9, 116 (1913).
-
.27
-
- -
1888
PHILIP A. LEIGHTON AND WESLEY 6. LEIGHTOS
TABLE I1 Reflection and Absorption Losses by I mm. Quartz Window in Radiation from Carbon Filament Lamp in Glass Carbon Filament Temperature 1000'
K
I200
I 400
1600
Quartz Window I mm. thick Absorbs Total Loss
Reflects
8 . 26y0
0.76% 0.69 o j6 0.36
8 34 8.44 8.61
8.97% 8 97 8 96 8 94
It is worthy of note that the changes in reflection and absorption with different current inputs are in opposite directions and almost exactly balance. iiccordingly, for a good quartz window of I mm. thickness the transmission factor may be taken as a constant for carbon lamp radiation, regardless of current input. Most quartz windows will closely approximate the results given in Table 11, but for the greatest accuracy the transmission should be directly determined for each window which is to be used. For example, as compared with our calculated value of 8.96%, CoblentP gives 8. 5%; we have found a range of values from 8.3% to 9.1%; while Beckman and Dickinson18 give 9.4% for a window of unspecified thickness. In the visible and ultra-violet region, down to ZOOOL, only the reflection correction need be considered for crystal quartz. If the same window be used in calibration and in measurement, the correction to be applied is the ratio of Fraction of standard lamp radiation transmitted Fraction of radiation to be measured transmitted The observed galvanometer deflection or energy calculated therefrom should be multiplied by this correction, the values of which for the principal lines of the mercury arc are given in Table 111. A series of observed values for an average window are also included.
TABLE I11 Quartz Window Reflection Losses and Corrections for Mercury Arc Lines Wave Length
A
Std. lamp radiation 5770
4350 3663 3130 2654 2 53 ..7 17 18
Quartz Window Reflects Calculated Observed
8.96% 9.2 9.5 9.7
Thermopile Correction Factor (calculated values)
-
10.2
9.0 9.2 9.4 9.5 10.3
.003 I ,006 1.008 I ,014
10.5
11.5
I ,017
10.9
I2
.o
1.022
Coblente: Bur. Standards Sci. Papers, 237 and 401. Beckman and Dickinson: loc. cit.
I
I889
ABSOLUTE MEASUREMENT O F RADIANT ENERGY
At shorter wave lengths, the observed values usually become higher than the calculated values. This illustrates again the importance of measuring the transmission directly for each window a t every wave length used. The second source of error to be considered in calibration arises from the fact that the thermopile may be calibrated over one range of galvanometer deflections and used over another. Our experience has shown that in very few cases is it safe to assume a linear relationship between incident energy and deflection produced, over any great range of deflections. Each thermopilegalvanometer combination shows a different set of characteristics and must be calibrated over the entire range in which it is to be used. As an illustration, Table IV shows the number of ergs per centimeter of deflection for a series of energies for two typical thermopiles.
TABLE IV Variations in Sensitivity with Size of Deflection Cms. Deflection Scale Dist. 5 meters 2
4 7 IO
I5 25
40 60 IO0 150 200
Total Energy on Pile, Ergs Pile No. I Pile No. 2 Surface Surface 24.15 mm* 314 mmz
30 69 101
144 216 3 63 585
888 1'498 2265 3045
Ergs per Cm. Deflection Pile No. I Pile No. 2
182 3 58 619 874 1290
14.7 14.4 14.4 14.4
$02090
14.5
3280 4900 8170
14.6 14.8
15.0
91.o 89.9 88.4 87.4 86 .o 83.6 82 .o
12300
15.1
81.7 81.7 82 . o
16450
15.2
82.2
1 5 .o
Pile No. I, a line thermopile of the Coblentz type, shows a fairly uniform sensitivity for the range 7 to 2 5 centimeters, with a decrease in sensitivity at very small deflections, and a fairly uniform decrease a t larger deflections. Pile No. 2 , a commercial surface thermopile, shows a very definite increase in sensitivity with deflection up to about 60 crns., followed by aslight decreasein sensitivity for deflections above IOO crns. I n each case the energies in the range covered by the standard lamps are in italics. We have employed three methods for extending the calibration over any desired range.19 All avoid any assumptions regarding distance. The first method is made possible by the fact that several energy outputs are known for a given standard lamp, and is based on the conclusion that regardless of distance these known energies should bear constant ratios to each other. The pile is first calibrated with the lamp a t the standard distance. If calibration for larger energies is desired, the pile is moved toward the lamp la
Forbes: loc. cit., p. 490.
1890
PHILIP A. LEIGHTOX AND WESLEY G. LEIGHTOS
until the deflection obtained with the lowest current input is approximately doubled. From the calibration in the first position and the observed deflection, the energy now falling on the pile with this lowest current input may be calculated. Each energy value of the lamp is now multiplied by the factor, Energy flux with lowest current a t new distance Energy flux with lowest current, a t standard distance This gives the energy flux from the standard lamp for the higher current inputs at the new distance, and by comparing with the deflections produced the calibration is extended. This process may be repeated as many times as necessary. If two points on the new setting overlap the old setting each time, the accuracy is much increased. The second method consists of setting up two lamps (not standards) alongside each other, with a shield in between and a shutter in front of each. The current in the lamps is so adjusted that either one alone gives a deflection in the range covered by the standard lamps. The energy flux from each lamp is thus calculated. Next the deflection produced when both shutters are opened simultaneously is measured, in which case the energy flux on the pile is the sum of the two single values. This process may be repeated with larger current inputs until any desired range is covered. A third method which we have tried for extrapolating the calibration curve beyond the range of the standard makes use of a monochromatic source of constant intensity, as follows: (I) Select a glass filter which transmits between 2 0 and Soy0 of light of the wave length available. With the source at such a distance that the incident and transmitted intensities, I, and I, fall within the range covered by the standard lamp, determine I/I, = K. ( 2 ) Move t,he source to a position at’which the new transmitted intensity, 1’,is approximately equal to I, of the first posit’ion. Observe deflections produced by I’ and I’,. As the absolute value of I’ may be read from the curve already established, 1’, follows as 1’, = I’.(I/K), where the only assumption is that I/Io = K is independent of intensit,y. The calibration curve, relat,ing deflection to absolute intensity, is thus extended t,o I’o. Further repetitions a t increasingly greater intensit’ies will obviously Eerve to extrapolat,e the curve as far as is required. At five times the maximum intensity available from a standard lamp this method agreed with the other methods to within 1%. Direct variation of the distance from the pile to the source, with assumption of the inverse square law, for extending the calibration to larger or smaller intensit,ies is limited by the fact that the carbon lamp is not a point source. TrumplerZ0has shown that for linear sources of half length X and pile distance d the inverse square law becomes modified t’o 12/11 = dl (arc tan X/dz)/dz (arc tan X/dl), 20
Trumpler: 2. physik. Chem., 90, 38j (1915).
ABSOLUTE MEASUREMENT O F RADIANT ENERGY
1891
but even this formula cannot be applied with accuracy to carbon lamps. As Table IV shows, an extension of the calibration to very small deflections is also necessary when these are to be used. The sensitivity of the galvanometer will in many cases vary with the position of the mid-point of the swing. We have found cases where the sensitivity changed by as much as 1% for a displacement of I O cms. of the mid-point or zero point on a scale 5 meters distant. It is, therefore, very important that some definite “zero point” or “low point of swing” be chosen on the galvanometer scale, and that all readings, both in calibration and use, be made with the galvanometer so set that the low point of the swing comes close to this predetermined value. Since, when
+ ! + FIG.2
Wiring Diagram for Shunt and Series Resistances.
using a constant “low point,” the mid-point of the swing will vary with the size of the deflection, the sensitivity will also change with the size of the deflection, and this is undoubtedly a contributory cause to those changes of sensitivity discussed in the preceding paragraphs. This and other questions relative to calibration will be discussed in section 8. 4. Auxiliary Resistance Patterns I n case the light intensities to be measured are so high that deflections in excess of the total scale length are produced, it becomes necessary to incorporate in the thermopile-galvanometer circuit a suitable combination of shunt and series.resistances. The conventional scheme of connections is indicated in Fig. 2 , where g is the galvanometer resistance, p the thermopile resistance, a the series, and s the shunt resistance. The same type of swing for all resistance patterns employed will be obtained by selecting such combinations of u and s that the resistance external to the galvanometer (Le., “damping,’), remains always the same as it was during the original calibrations. As the latter are usually carried out with the thermopile connected directly to the galvanometer, the desired condition requires an external resistance equal t o the thermopile resistance, p . From the law of combination of resistances in parallel, it is obvious that the external resistance must be I
a+ (I/S)
Rearranging,
+ (I/P) = external resistance = p. a = P”(P
+ s).
1892
PHILIP A . LEIGHTON AND WESLEY G. LEIGHTON
The question of extending the calibrations to include the auxiliary resistance patterns was first approached experimentally. As the result of numerous intercomparisons we have found that much labor can be saved by relating the sensitivity with an auxiliary pattern to the original calibration curve by means of the empirical equation (3 1
(E/E,)i = a constant,
where E, = the intensity required to produce a certain deflection (or galvanometer current, i), with a = o and s = m , while E = the intensity required t o produce the same deflection with some resistance pattern in which the relation in (2) is maintained. Our experimental results have proved equation ( 3 ) to hold independently of the magnitude of the deflection. This indicates that a linear proportionality exists between the thermopile E.M.F., T , and the incident light intensity, E. Thus, equation ( 3 ) may be expressed as (n/To)i = (E/E,)i = a constant.
(4)
We now proceed to an evaluation of the ratio ( n / r 0 )in terms of the resistances, Fig. 2 . Let i and il be the partial currents through the galvanometer and shunt, respectively. The thermopile current is then i il. When a = o and s = 0 0 , il disappears and, from Ohm’s law
+
r0 = i(p
+ g).
(5)
For any other resistance pattern with which the same galvanometer current, i, is produced by a thermopile E.M.F. = T , it follows from the laws of multiple circuits that T = i(a g) (i idp. (6) Similarly, n = ils (i i1)p (7)
+ + +
+ +
Equating (6) and ( 7 ) , and solving for il, il = i(a
+ g)/s.
(8)
+ g + P + (a + g)p/s).
(9)
Substituting for il in (61, T
=
i(a
Dividing by ( 5 ) ,
Substituting the restricting equation a = pz/(p (T/To)I
=
P/S
+
I.
+ s), (11)
Substituting for (r/n0)iin terms of (4), (E/Eo)i = P/S
+
1.
(12)
I n this final equation the galvanometer resistance has disappeared, and no function of the deflection appears, so that the constant (E/E,), may be cal-
ABSOLUTE MEASUREMENT O F RADIANT ENERQY
I893
culated for any proper combination of resistances. As Table V shows, this theoretical expression accurately predicts the experimentally observed energy ratios for a variety of combinations. It thus becomes a very convenient relation to employ when the energies are such that resistance patterns must be used.
TABLE V Energy Ratios for Various Resistance Patterns
WE" P
8
Obs.
Calc.
10.3 IO .3 36 36 31.6 31.6 31.6 28.8
7 4
2.4 3.7 2.76 6.3
3.6 2.72 6.2
21
7 7 I1 21
I1
2.5
5.5
5.5
3.8 2 .5 3.62
3.9 2.5 3.62
The fact that this relation (12) holds over a wide range of deflections justifies the assumption made in its derivation that the pile gives a linear ratio of incident energy to E.M.F. produced, and indicates that the decrease in sensitivity always observed a t high deflections (Table IV) is a function of the galvanometer and not of the thermopile. This is further indicated by the fact that even an intense beam of radiation falling constantly on the pile does not affect its response when simultaneously used to measure another, much weaker source of radiation, provided that the galvanometer suspension be so turned that the same zero point is obtained for all readings.
5. Effects of Diverging Light In many cases it is desired to measure the absolute energy of a beam of light all portions of which do not strike the surface of the thermopile a t perpendicular incidence. For example, in the laterally diverging beam of light behind a monochromator slit, the edges of the beam may deviate by several degrees from the direction of the central portion. It is absolutely essential that all of the light which passes through the thermopile slit should fall on the radiation receivers. Light which misses the receivers is a dead loss. To avoid this, it is essential that the slit of the thermopile be placed close to (within I mm. of) the sensitive junctions, and that it be slightly narrower than the radiation receivers. With thermopiles in which this is not possible, a laborious correction must be made, and even with this correction no large degree of confidence can be placed in the results. This requirement necessitates some reconstruction in most commercial thermopiles. The magnitude of the errors involved is showq by the three types of thermopiles indicated in Fig. 3. The upper figures show the relative positions of the radiation receivers, window, and slit in each case. The lower diagrams
1894
PHILIP A. LEIGHTOS AND WESLEY G. LEIGHTON
show the relation between the sensitivity of the pile and the deviation from perpendicular incidence of the incident radiation. No. I was a vacuum thermopile, in which the slit was placed outside the vacuum jacket a t a distance of 12 mm. from the junctions. This type of thermopile is useless for absolute energy measurements in diverging light. KO. z was a line thermopile, with a slit of the same width as the receivers placed about 2 mm. in front of them, with the window in between. In this case it is possible to make corrections. No. 3, also a line thermopile, had receivers 3.3 mm. wide, and a slit 3.0 mm. wide (Le., slightly narrower than the receivers) placed 0.8 mm. I.
2.
3.
I Degrees Divergence from Normal
FIG.3 Effects of Diverging Light on Three Types of Thermopiles
in front, with the window on top. With this arrangement no change in sensitivity is produced by divergence up to 5' in either direction from the normal. Although these illustrations all involve line thermopiles, the same considerations exactly apply to surface thermopiles. 6 . Surface Variations in Sensitivity If a spot of light of limited area be moved over the surface of a thermopile, the response produced will be found to vary with the position of the spot, and the smaller the area of this spot, the larger become the variations. Of the thirteen thermopiles which the authors have investigated, not one has proven an exception to this rule. In the case of line thermopiles of the construction described in section I , the chief variations to be considered are those along the long axis of the sensitive opening. These may be investigated by mounting an auxiliary slit of adjustable width in front of and at right angles to the thermopile slit, and, placing the thermopile in a uniform beam of light, taking readings at intervals
ABSOLUTE MEASUREMENT O F RADIANT ENERGY
I895
FIQ.4 Arrangement of Auxiliary Slit and Screw for Lateral Movement. SI,S2= Jaws of Auxiliary Slit. TV = Track for Vertical Movement of Auxiliary Slit. V = Screw for Vertical Movement of Auxiliary Slit. B = Base of Thermopile. Tw = Track for Lateral Movement of Thermopile. H = Screw for Lateral Movement of Thermopile. P = Thermopile Face.
as the auxiliary slit is moved along the thermopile slit. The details of such an apparatus are shown in Fig. 4, while in Fig. 5 , the observed variations for two typical line thermopiles, obtained when an auxiliary slit z mm. wide was moved along the surface, are shown as a function of the linear distance along the thermopile slit. The magnitude of the error produced by these variations is obviously a function of the uniformity of the beam of light to be measured. The radiation from the standard lamps may be considered as filling the entire sensitive opening of the thermopile, with a uniform distribution of intensity. If th6 measured radiation has the same characteristics, no error will be produced.
1896
PHILIP A. LEIGHTON AND WESLEY G. LEIGHTOS
If, however, it is of variable intensity distribution, or if it fills only a portion of the sensitive opening, a correction must be made. I n the case of monochromator beams, the intensity distribution is most uniform in the direction parallel to the monochromator slit. By placing the slit of the line thermopile parallel to the monochromator slit, and by adjusting relative lengths so that the light beam as it reaches the thermopile slit is exactly the length of the slit, it follows that the error due to surface variations will be reduced to a minimum. The authors have made and confirmed the interesting observation that, along the length of the although the pile sensitivity may vary by &IS%
Dzstance along
Pile Flit, n ~ m .
FIG.5 Variations in Sensitivity along Surface for Two Thermopiles
sensitive opening, in most cases even an irregular beam falling on the whole opening is fairly accurately integrated and its absolute energy given directly by the pile. A rather extreme case of this is illustrated in Table VI. Here E, represents the energy as calculated from the observed response as a z mm. wide auxiliary slit was moved at z mm. intervals along the thermopile opening while exposed to a uniform beam of light. E,, is the average value of E,, and r,, the relative sensitivity a t each setting, is the ratio of E, to Ea”. Similarly, E’, represents the observed response at different settings of the auxiliary slit when the pile was placed in a non-uniform beam. These values may be corrected for the surface variations in sensitivity by dividing by the corresponding value of r, in each case, as is done in the last column of Table VI. The close agreement between the sums of the uncorrected and the corrected values indicates that the thermopile in this case “smooths out” the irregularities in the beam and acts as its own integrator. We have found this to be generally true. If the slit be only partially illuminated, the error naturally becomes larger, but even if the beam be only half the length of the slit, in few cases does the error become greater than I to 2%. This encouraging result for line thermopiles cannot be said to hold for surface thermopiles. The three commercial surface thermopiles investigated by the authors showed such tremendous variations in surface sensitivity that
I897
ABSOLUTE MEASUREMENT O F RADIANT ENERGY
TABLE VI Energy Correction by Vertical Integration Setting
n
Ell
Uniform Beam
E*,
Relative Sensitivity
I
78.6 107.9 95.3 95.3 91. I 81.7 83.9 87 .o 82.8
89.2
0.88
2
3
4 5 6 7 8 9
1,
Non-uniform Beam
1.21
1,
I
1,
I
1,
.07 .07
I .02
11
0.91 0.94 0.97 0.93
11
17
11
E'n
E'n/rn
141.9 142.3 95.3 55.9 40.1 45.8 62.1 56.9
161 .o 118.0 89.3 52.5 39.3 50.5 66.1 58.4 52 . o 687. I
48.2
688.5 688. 5 Ratio,- E'ohs. = E torr. 687. I
Q
I .oo2
\o
C
FIG.6 Variations in Sensitivity over the Surface of a Surface Thermopile.
additional precautions become necessary. Fig. 6a is a typical example, and represents a surface thermopile with sensitive opening 2 2 mm in diameter, behind which 80 junctions were arranged in three rows. The pile was placed in a beam of uniform intensity, and a shield with an opening 4 mm. square moved across the face so that successive portions were exposed. The figures inserted in each portion represent the relative sensitivity, and were obtained by dividing the observed response by the area of that portion. Hence, the values given should be independent of the area exposed. I n Fig. 6b, a slit 2 mm. wide was moved at z mm. intervals across the face in a direction perpendicular to the rows of junctions, while in Fig. 60 the same slit was moved across the face in a direction parallel to the rows of junctions.* As is clearly shown, the region about the center of each row of junctions is one of maximum sensitivity, while the region between each row is one of very low sensitivity.
* We are indebted to Mr. R. A. Mortensen for these measurements.
1898
PHILIP A . LEIGHTON AND WESLEY G. LEIGHTON
Here, as with line thermopiles, if the thermopile be calibrated with standard lamp radiation which is of uniform intensity over the entire sensitive surface, and if it be used for measurement of a uniform beam which just covers the whole surface, no error will be introduced by the surface variations. But if the cross section of the beam is smaller than the sensitive opening of the pile, or if it is of non-uniform intensity, the error will become appreciable. For example, in one case the uncorrected use of the pile for an elliptical beam 20 mm x I O mm in cross section resulted in an error of 2 2 % in absolute energy values. Another example is given in Table VII, which shows the galvanometer deflection obtained when the thermopile was placed at’different distances from the point of focus in a diverging beam, so that the area of the cross-section of the beam as it reached the pile was varied, while the total energy remained the same.
TABLE1711 Effect of Varying Cross-Section Area, Total Energy Constant Diameter of Exposed Area 22
.o
mm.
20.7 19.4 18.1
16.8 15.6
Galvanometer Deflection
77.9 80.3
77.7 76.6 76.7 79.4
Diameter of Exposed Area
1 4 . 3 mm. 13 . o 11.7 10.4 9.7 7.8
Galvanometer Deflection
84.8 95.1 104.7
114.9 130.2 145.7
The error produced when the beam is 1/2 the diameter of the sensitive opening of the pile is about 45$’&. Three methods of overcoming this error suggest themselves, viz. : I . The radiation receivers may be covered with a disc of thin silver foil of the same size as the sensitive portion of the thermopile. The disc may be held in thermal contact with the junctions by means of a thin layer of shellac. The outer surface of the disc is blackened. Although this effectively reduces surface variations in sensitivity, it has the disadvantages of decreasing the total sensitivity of the pile and of prolonging the period, so that the swinging equilibrium method of-reading cannot be used and it is necessary to thermostat the pile. 2. The thermopile may be converted t o a line thermopile by shielding off all of the sensitive surface except a strip some z mm. wide along the center of the center row of junctions, and the energy of the beam integrated by the methods described in section 7. The thermopile so treated will not be as satisfactory as a simple line thermopile, because the unused junctions add unnecessarily to the resistance and materially increase the creep. 3. The cross section of a light beam from an ordinary prism monochromator usually shows a fairly uniform distribution of intensity in the direction parallel to the monochromator slit, and a shading off in intensity from center to edges in the lateral direction. Recalling that the thermopile is calibrated
ABSOLUTE MEASUREMENT O F RADIANT ENERGY
I899
in a beam of uniform intensity distribution which completely fills the sensitive opening, it is evident that errors due to surface variations will be minimized if: a. The monochromator beam be adjusted to give maximum uniformity of intensity over its cross-section. b. The thermopile be so turned that the direction of maximum variation in sensitivity of the pile shall coincide with the direction of maximum uniformity in intensity distribution of the light beam, in which case, of course, the direction of minimum variation in sensitivity will coincide with the direction of maximum variation in intensity distribution of the beam. c. The thermopile be covered with a shield, set close to the junctions, of exactly the size and shape of the monochromator beam as it falls on the pile, and this shield be used both in calibration and measurement. With bhese precautions, a surface thermopile will in many cases give reliable measurements of absolute energy. To illustrate, we have used a surface thermopile to measure the energy in a beam of X 313oA emerging from a prism monochromator by method (2) in which the pile was used as a line thermopile, and by method (3) in which the pile was turned on its side and the slit used in (2) replaced by a shield with opening of the exact size and shape of the beam. A. Results by method (2). (see section 7 for method of integration.) Micrometer Screw Galvanometer Reading (across beam) Deflection
o mm. 2
4
6 8
0.70
17.50 30.86 36.87 42.37
Micrometer Screw Galvanometer Reading (across beam) Deflection IO
mm.
I2
14 16 I8
45. I4 42.93 33.38 13.20 0.47
Sum = 263.4 Deflection with standard lamp = 16.77 cm. Radiation from standard lamp = 8.47 ergs/mm*sec. Dimensions of slit = 1.9 X 22.15 mm. Micrometer screw interval = 2 . 0 0 mm. 2 2. I 5 X 2 .oo X 8.47 X 2 63.4 = 5900 ergs/sec. Radiation from monochromator = 16.77 B. Results by method (3). Deflection, trial I . = 131.8 cm. trial 2. = 131.9 cm. Deflection, standard lamp = 71.7 cm. Radiation from standard lamp = 8.47 ergs/mm*sec. Area of thermopile opening = 380.7 mm2. Radiation from monochromator = 380'7x8*47x131*8 = 6930ergs/sec, 71.7
Summary: Result, used as line thermopile = 5900. Result, used as surface thermopile = 5930. Difference = 0.5%.
1900
PHILIP A. LEIGHTON A S D WESLEY G. LEIGHTOS
Even with the precautions observed in method (3) measurements with a surface thermopile must be checked with a line thermopile, as was done in the example just given, before any degree of reliance may be placed on the results. The surface variations in sensitivity of a surface thermopile are too complex to make a correction practicable, and in general, an ordinary line thermopile will be found more satisfactory for absolute energy measurements.
7. Methods of Integration For the measurement, with a line thermopile, of the total energy, in absolute terms, of a beam of cross section larger than the sensitive opening of the thermopile, it is necessary to take readings at intervals over the cross section of the beam and then to properly integrate these individual values to give the total energy. The process is much simplified if the length of the sensitive opening be equal to or slightly greater than the diameter of the beam in the direction of maximum uniformity of intensity distribution (section 6). The thermopile is mounted on a sliding base so that the long axis of the slit is parallel to this direction of maximum uniformity, and so that it may be moved across the beam in a lateral direction.21t22 If, now, the sliding base be equipped with a micrometer screw (Fig. 4) so that the readings may be taken at accurately known intervals, the procedure becomes still further simplified. If the intervals at which readings are taken are definitely known, it is only necessary to measure accurately the height or long dimension of the sensitive opening. Any desired width may be assumed for the sensitive opening, and the calculation is simplified by assuming the width is equal to the intervals through which the thermopile is moved. The following examples serve to illustrate this point. Example A . Let us assume that a thermopile, with sensitive opening or slit exactly 1.5 x 2 0 . 0 mm. in size, is to be used to measure the total energy in a square beam 2 0 X 2 0 mm. in cross section, of uniform energy distribution. When exposed to any part of this beam so that the opening is fully covered, a deflection of 85 cms. is obtained. When exposed to standard lamp radiation of intensity = 7.0 ergs/mm2sec., a deflection of 10.0 em. is produced. I . Take the thermopile slit width as 1.5 mm. The standard lamp radiation falling on the pile is 1.5 X 20 X 7 = z I O ergslsec. As this produces a deflection of I O ems., I em. A = 21 ergs/sec. falling on the pile (neglecting changes in sensitivity with size of deflection), which is equivalent to 2 1 X I / I . ~= 14 ergslsec. per mm. of beam wzdth.
Villars: loc. cit., p. 330. W. G. Leighton and G. S. Forbes: loc cit., p. 3141.
1901
ABSOLUTE MEASUREMENT O F RADIANT ENERGY
a. Moving the thermopile across the beam with the micrometer screw, take 20 readings I mm. apart. Each reading gives a deflection of 85 cm. Then, the total energy in the beam = 85 X 14 X 20 = 25800 ergs/sec. b. Take I O readings, 2 mm. apart. Total energy in beam = 85 X 14 X 2 X
IO
= 25800 ergs/sec.
2. Assume the thermopile slit width is 1.0 mm. The standard lamp radiation falling on the pile then becomes by this assumption 1.0 X 20 x 7 = 140ergs/sec., or I cm. A = 14 ergs/sec. falling on pile = 14 ergslsec. per mm. of beam width.
a. Take 20 readings, I mm. apart. Total energy in beam = 85 X 14 X 20 = 23800 ergs/sec. b. Take I O readings, 2 mm. apart. Total energy in beam = 85 X 14 X 2 X IO = 25800 ergs/sec. 3. Assume the thermopile slit width is 2.0 mm. The standard lamp radiation falling on the pile, by this assumption, becomes 2.0 X 2 0 X 7 = 280 ergs/sec., or I cm. A = 28 ergs/sec. falling on the pile, which is equivalent to 14 ergslsec. per mm. of beam width.
a. Take I O readings, 2 mm. apart. Total energy in beam = 85 X 14 X 2 X IO = 25800 ergs/sec. And so on. I n each case the same value is found for the No. of ergs/sec. per mm. of beam width required to produce I cm. deflection, regardless of what assumptions are made regarding the width of the thermopile slit, and the same value for the total energy is obtained, regardless of these assumptions. Example B. I n this example is presented the actual measurement of a beam of monochromatic radiation, of non-uniform intensity distribution laterally, as determined by two different thermopiles.
Pile No.
Slit 30.50 mm. long, assumed 3.0 mm. wide. Reading interval Readings taken at exactly I mm. intervals. Slit width I,
- -I
3'
Standard lamp calibration gave the following factors: Deflection, cms.
3 IO 25
50
Ergs/sec. falling on pile per cm. A
47.4 47.2 47.2 47.3
Ergs/sec. falling on pile Deflection, cms. per cm. A
75 IO0 125
150
47.3 47.4 47.4 47.5
1902
PHILIP A. LEIGHTOS AND WESLEY G. LEIGHTOh'
The readings across the monochromatic beam were : Setting I
Galvanometer Ergs/sec. Deflection on pile 3 . j cms. 166
Setting
Galvanometer Deflection
8 9
2
13.6
642
3
33.1
156.3
IO
4
60.6
2868
I1
99.5
8j.6 66.2 40.2
5
84.7
4006
I2
6
101.2
4795
I3
19.3 6.0
7
106.3
5010
I4
1.j
Sum =
34142
Total energy in beam = 31142 X 1/3 = 1138i ergs/sec. Pile No. 2 , Slit 24.38 mm. long. Assumed 1.0 mm. wide, and readings Reading interval = I. taken a t exactly I mm. intervals. Slit width Standard lamp calibration factors: Ergs/sec. falling on pile Deflection, Cms. per Cm. A
3
Ergs/sec. falling on pile Deflection, Cms. per Cm.
75 IO0
21.4
25
20.9 20.5 20.6
I 2j
21.j
50
20.9
I 50
21.6
IO
21.2
Readings across monochromatic beam: Setting
Galvanometer Deflection
cm.
Ergs/sec. on pile
I
I.j
2
13 . o
3 4
33.6 56.1
5 6
73.7 81.3
31 267 696 1174 1562 I 728
7
81.7
1737
Setting 8
Galvanometer Deflection 74.0
Ergs/sec. on pile I 568
9
57.2
I 198
IO
847 384
I2
40.7 18.7 3.3
I3
0.7
15
I1
Sum
69
= 11276
Total energy in beam = 11276 X I = 11276 ergs/sec. Ratio, Pile No. I 11381 -_ _ -- 1 .OOQ. Pile No. 2 11276 Thus the integrated values obtained by the two piles, for the total energy in the monochromatic beam, differ by only 0.9%.
ABSOLCTE MEASUREMENT O F RADIAKT ENERGY
I903
I n a beam of this sort, readings may be taken a t intervals greater than mm. without materially disturbing the accuracy. This may be demonstrated from the example just given. For either thermopile, if readings had been taken a t 2 mm. intervals, the alternative values of those given above would have been obtained, and if readings had been taken at 3 mm. intervals, every third value would have been obtained. Thus, for thermopile No. I , I
Readings at
2
mm. intervals (alternate Values from above set) Deviation from mean
Total Energy in beam
Odd settings 17008 X
'
11339
0.3%
Even settings 17134 X - = ll4M
0.3%
3
=
2
3
Readings a t 3 mm. intervals (every 3rd value from above set) Total Energy in beam
Settings I , 4, 7, Settings 2 , 5 , 8, Settings 3, 6, 9, For thermopile No.
2,
IO,
11, 12
Deviation from mean
13 11490 14 llSS4 11318
9% 0.4%
0
0.5%
readings at z mm. intervals,
Total Energy in beam
Odd settings 5623 X z = 11246 Even settings 5653 X z = 11506
Deviation from mean
0.3% 0.3%
The method just described may be termed the direct summation method of energy integration. For the greatest accuracy in the determination of total energy with a line thermopile, readings should be taken a t short intervals, a curve of energy vs. setting drawn, and the area under this curve determined by graphical integration. Fig. 7 represents a typical curve of this kind, for a beam of radiation issuing from a monochromator slit. The crosses represent thermopile readings. The direct summation method which we have illustrated in the preceding examples in effect takes the total energy of the beam as equal to the sum of the areas of the rectangles shown in Fig. 7, while the graphical method takes the energy as equal to the area under the curve. I n the case illustrated, the area under the curve, or energy by graphical integration, was 9133 erg/sec., while the area of the rectangles, or energy by direct summation was 9130 erg/sec., a difference of 0.03%. If alternate readings (2 mm. intervals) are taken, the direct summation method gives 9175 erg/sec. for the energy, a difference of 0.46% from the graphical integration value. The size of the interval between settings which may be used without material decrease in accuracy is a function of the width of the thermopile slit, the width of the beam, and the amount of variation in intensity across the beam. For narrow beams (less than 3 to 4 times the slit width) the interval should be equal to or less than the actual width of the thermopile
I904
PHILIP A. LEIGHTON A S D WESLEY G. LEIGHTON
slit. For relatively wide beams, of the order of ten times the slit width, if no sharp changes in intensity distribution occur, intervals of several times the slit width may be used. These methods assume that the thermopile is capable of acting as its own integrator in the long direction of the slit; that is, that a beam of radiation of variable intensity distribution along the slit, or covering only part of the slit, gives the same deflection as it would if the same amount of radiation were evenly distributed over the entire sensitive opening. The limitations
5 6 7 Settzng across Beam, m.m.
FIQ.7 Comparison of Graphical and Summation Methods of Energy Integration.
to this condition have been discussed in section 6. Precautions which must be observed in the direct integration of energy with a surface thermopile have also been discussed in section 6. 8. Variations in Sensitivity Variations in sensitivity of the thermopile-galvanometer system with size of deflection, and with the position of the zero point on the scale, were discussed in section 3 . The position of the zero point means, of course, the position of the mirror and moving coil with respect to the magnetic field. We have found the greatest sensitivity is produced when the mid-point of the swing finds the mirror parallel to the front face of the galvanometer, Le., the coil parallel to the magnetic field. Changes from this point may produce as much as a 1 % change in sensitivity for a I O cm. shift in the zero point or mid-point of the swing on a scale 5 meters distant. On the other hand, quite considerable movements of the suspension adjustment, which may be necessary to obtain the same zero point for all readings, seem to be without marked effect on the sensitivity. To demonstrate, two carbon lamps were set up in front of a thermopile. Lamp A, fitted with a shutter, gave a deflection of approximately 29 cm., while lamp B, which radiated
ABSOLUTE MEASUREMENT OF RADIANT ENERGY
I905
continually on the pile while burning, produced a deflection of ,120 cm. Deflections caused by “A” were observed with and without “B” burning, the mirror being always set to give the same low point of swing. Deflection, without B (before) = 29.35 om. Deflection, with B burning = 29.35 Deflection, without B (after) = 29.30 That is to say, with four times its own energy effect constantly flowing through the pile and galvanometer, the source A produced a swinging deflection identical with that produced when no energy came from B. Accordingly, it is not necessary to worry about outside radiation of constant intensity which falls on the pile during calibration or use. Thermopile-galvanometer systems in general show a slightly different response from day to day to the energy from a standard lamp. Temperature and humidity seem to be chief among the factors causing these variations. Why humidity should play a part is not known. It should not be due to the absorption of infra-red radiation by the water vapor. The variations are no doubt due, to some extent, to changes in the standard lamp radiation, and in part to changes in the sensitivity of the recording system. Thus it is not possible wholly to correct for them, and the magnitude of these changes marks the limit of accuracy which may be expected from this method of absolute energy measurement. A partial correction may be made by calibrating a well seasoned carbon lamp, burning a t definite amperage, by direct comparison with the standard lamps, and using this lamp as a secondary standard to check the thermopile sensitivity every day that measurements are made. Two secondary standards mounted side by side behind a shield, with another shield between and a shutter in front of each, gives a still more accurate check, as the danger of error due to individual variations in lamp intensity is lessened. Cob1entzs3 has suggested observation of the deflection produced by a known current generated by induction in the thermopile-galvanometer system as a means of checking the sensitivity. He also suggests the use of an induced current of known strength to attain the desired zero point and avoid drift. Usually the drift is too irregular t o be avoided by any method of control except thermostating, but this suggestion is worthy of consideration in obtaining the desired zero point, if trouble should be experienced in obtaining it by moving the suspension. In addition to day to day variations in sensitivity, slow changes extending over a considerable period are often experienced. Fig. 8 shows the variations in sensitivity of one thermopile-galvanometer system over a period of three years. Day to day variations were not included, the points given here representing average values. Experiments made over a period of several years also indicate that standard carbon lamps deteriorate somewhat both with use and age, and should be supplemented at intervals with new standards, at periods of not greater than three years. *3
Coblents: Bur. Standards Bull., 9, 33 (1913).
1906
PHILIP A. LEIGHTON AND WESLEY G. LEIGHTON
In the “Instruchons for using the Radiation Standards,” issued with each radiation standard, the precaution is stated that “these lamps should be used as reference standards, and other lamps used as working standards. . .” This precaution cannot be over emphasized. I t has been our experience, as illustrated in the following table, that a rate of deterioration of as much as I/Z% per hour of burning may be expected, at least during the first times the lamp is operated.
7YS
I
1
6
\-A
w
A+
a0
38
Time, Months
FIG.8 Change in Sensitivity with Time.
TABLE VI11 Rates of Deterioration of Radiation Standards Standard
c-39 C-40 C-69
Time of Burning
Deterioration
9 hours 5 ” 3/4 ”
Rate per hour
0.35% 0.35% 0.75%
3.1%
1.7% 0.56%
Av.
0 .j%
The above values were obtained as a result of a thorough inter-comparison of these three standard lamps, the calibration of C-69 being accepted as correct during the first few minutes of burning. The standards should best be used in pairs, so that any sudden deterioration of one lamp may be detected.
Summary The measurement of the absolute intensity of visible and ultra violet light by means of a thermopile-galvanometer system has been discussed with particular reference to the conditions existing at the exit slit of a monochromator. Various sources of error have been investigated, including those which are inherent in the galvanometer and in the thermopile, as well as certain sources of error created by employing a thermopile for the measurement of diverging light differing in wave length from that of the light from standard carbon filament lamps. Several important precautions have been emphasized, while, on the other hand, certain sources of error have been shown negligible. The advantages of linear thermopiles over certain surface piles of commercial make have been demonstrated.
ABSOLUTE MEASUREMENT OF RADIANT ENERGY
I907
The observation of galvanometer deflections under the conditions of ‘[swinging equilibrium,” successfully used by the authors and others at Harvard University and elsewhere, has been described. Details are included for integrating the total intensity of a light beam which presents a cross section greater than the active receiving area of the thermopile. Three methods of extrapolating the thermopile-galvanometer sensitivity curve are outlined, none of these requiring the assumption of the inverse square law. A simple equation has been derived and verified experimentally which extends the calibration curve to include various resistance patterns useful a t high intensities. In concluding the authors wish to express their appreciation to Professor George Shannon Forbes of Harvard University under the direction of whom certain of the investigations in this paper were begun. Thanks are also due Dr. Francis E. Blacet and Mr. Raymond A. Mortensen of Stanford University for some of the experimental data quoted, and to Dr. Curtis Haupt of Pomona College for his helpful criticism.
