Source: Procedures in Experimental Physics
by John Strong

A RADIOMETRIC instrument consists of a blackened receiver, which is heated by the radiant energy to be measured. The instrument is provided with some physical means for measuring the rise in temperature of the receiver produced by the radiant energy. For the most delicate measurements the means employed must be responsive to a rise of temperature of the order of a few millionths of a degree.

In comparison with other methods of measuring light intensity, a radiometric instrument is characterized by the direct and simple way in which the response depends on the intensity of the light; the relation between these two quantities is linear. Also, the instrument is generally characterized by equal sensitivity for all wave lengths.

For measuring the intensity of radiant energy at wave lengths less than 1, radiometric instruments are more reliable but less sensitive than other instruments such as photoelectric or photographic photometers. Accordingly, a radiometric instrument is frequently used as a reference instrument for the calibration of photoelectric and photographic photometers. In infrared spectroscopy, however, the radiometric instrument is the most sensitive instrument now available.

When a radiometric instrument is giving its full response to a beam of light incident on the receiver, the rate at which the heat is lost by the receiver is in equilibrium with the rate at which heat is absorbed from the light beam, . Inasmuch as the heat lost by the receiver is proportional to the produced rise in temperature, , we can write

where the L's represent the heat losses in unit time per unit temperature change. Thus, L₄represents the loss of heat by radiation from the receiver, L₂ the loss by air conduction, L₃ the loss by conduction through members touching the receiver, and L₄ any other means of losing heat, such as, in the case of a thermopile, Peltier heat loss. Obviously, it is desirable to have the L's small, and for this reason the energy is to be concentrated onto a small receiver to reduce L₁. Furthermore, the receiver is usually mounted in a high vacuum in order to make L₂ vanish.

The response of the instrument is determined by the magnitude of , and different radiometric instruments are characterized by the manner in which is measured.

A thermopile measures by means of one or more thermoelectric junctions attached to the receiver.¹

A microradiometer measures in the same manner as a thermopile.² In this instrument, however, the thermojunctions and receiver are attached to the moving system of a galvanometer coil, which is suspended on a fine quartz fiber. The superiority of the microradiometer over a thermopile lies in the fact that, because no outside lead wires are required, energy losses in electrical resistance are diminished. However, the combination of the thermopile and galvanometer makes an instrument which is awkward to use in a spectrometer, because it must be protected from vibration in its operating position.

A bolometer consists of a blackened thin metal strip with electrical connections.³ This strip forms the receiver for the radiations. It is connected as one arm of a balanced Wheatstone bridge. The change in the electrical resistance of the strip, as measured by a sensitive bridge galvanometer, is a measure of .

A radiometer consists of a system composed of a receiver and a mirror which is mounted in a partially evacuated case. The system is suspended by a fine quartz fiber. The back of the receiver is thermally insulated from the front, so that when a beam of light falls on the receiver, the front is heated more than the back.⁴

The radiometer is most sensitive at a gas pressure of about 0.06 mm of mercury. The gas molecules which strike the side of the receiver which is warmed by the radiations leave it with a greater velocity than those which strike the opposite and cooler side, and therefore a net backward recoil is exerted. This results in a deflection of the system until the recoil torque is balanced by the torque arising from torsion of the quartz fiber. The deflection of the system, as indicated by the mirror, is a measure of the temperature difference, , between the front and back surfaces of the receiver.

Anyone interested in radiometers will find some of the important papers on this subject listed in the footnotes. One of the features of the radiometer is its constant sensitivity. This reproducibility of the deflection is due partly to the use of a quartz suspension but mostly to the fact that the required pressure (0.06 mm of mercury) is one that is easily maintained permanently in a closed-off system. The radiometer has been used successfully in the microphotometer. The application of the radiometer to the microphotometer places but little demand on flexibility.

When maximum sensitivity is desired for very delicate measurements, the problem arises of choosing which type of radiometric instrument will be most sensitive, and further, which design of a given type will be most sensitive.

There are conflicting reports on the ultimate sensitivities obtainable with the different types of radiometric instruments. The thermopile is certainly almost as sensitive as any other radiometric instrument, and although other instruments might be made slightly more sensitive than vacuum thermopiles, they are usually more difficult to construct and use.⁵ Accordingly, in our treatment here, the construction details of radiometric instruments other than the thermopile will be omitted. Vacuum thermopiles are widely used by experimenters in infrared spectroscopy, possibly more often than all other types of radiometric instruments taken together.

Construction and evacuation of a sensitive thermopile. The construction of a vacuum thermopile of the type shown in Fig. 1 will be described here.⁶ This thermopile has two independent junctions and receivers. Four external leads are provided, so that these junctions either can be used separately or can be connected together in series or in opposition. The thermopile is, made compensating by connecting the junctions in opposition. The receivers are rectangular and are placed end to end–an arrangement especially suited to spectroscopic investigations. For special problems the shape of the receivers as well as other features of the design can, of course, be altered.

A crystalline quartz window is attached with Apiezon wax "W." This wax is also used to seal the other joints Apiezon wax "W" is easy to apply and has an extremely low vapor pressure–a valuable feature for maintaining a permanent high vacuum.

A porcelain rod of inch in diameter containing four holes holds the relatively heavy copper wires on which the thermojunctions are mounted. The projecting copper wires are fastened together by mica as shown in Fig. 1 or by Alundum cement as shown in Fig. 2 so that they will not vibrate. Four flexible and insulated copper leads are soldered to these heavier copper wires, as shown in Fig. 1, and these are brought outside the housing through one of the wax seals.

Fig. 3 shows one method for maintaining a high vacuum of better than 10^-4 mm of mercury in a thermopile. The Pyrex tube shown here is filled with activated charcoal. The charcoal tube is evacuated and baked for several hours to outgas it before the stopcock is closed to isolate the system from the pumps. At first the vacuum will be maintained at better than 10^-4 mm of mercury for only a few hours. However, each time the thermopile is re-evacuated the vacuum lasts longer, so that after about five evacuations, if the system is tight, the vacuum will remain good for a month or so. The vacuum is tested by measuring the sensitivity of the thermopile under some convenient standard condition, such as that of exposing the thermopile to a 60-watt lamp placed 10 inches away and measuring the response of the junction with a relatively insensitive galvanometer. The degree of vacuum obtaining in a thermopile should not be tested with a spark, since electrostatic forces may destroy the junctions.

Wires for the thermojunctions. One thermoelectric wire is made of pure bismuth, and the other is an alloy of bismuth and 5 per cent tin. The selection of this combination of wires to form thermojunctions has been made after a consideration of the Wiedemann-Franz coefficients, as well as of the thermoelectric powers of various possible combinations, including such metals as tellurium and the other bismuth alloys.⁷

The resistance of each thermoelectric wire should be at least 10 ohms, and the wire should not be longer than 3 mm. A bismuth wire 3 mm long with a resistance of 10 ohms has a diameter of about 24. The bismuth-tin alloy wire should have about 20 per cent more electrical resistance than the pure bismuth wire, because of the influence of the Wiedemann-Franz coefficient. However, owing to the greater specific electrical resistance of the bismuth alloy wire, its diameter will be about 7 greater than the diameter of the pure bismuth wire.

Preparation of the alloy wires. Thermoelectric wires can be purchased from the Baker Company, Newark, New Jersey, or they may be prepared by the Taylor process. To make the wires by the Taylor process, the thermoelectric metal is melted and sucked up into a thin-wall capillary tube of soft glass. (See Fig. 4.) This tube, containing the metal as a core, is heated in a small electric furnace and drawn out in the manner shown in Fig. 5. The diameter of the wires produced in the composite drawn fibers is controlled by the temperature of the furnace and the speed of drawing. When the temperature of the furnace is properly regulated, the wires obtained are single crystals which can be bent and straightened repeatedly without breaking. Wires which are brittle should be discarded.

The glass is removed from the composite fibers with hydrofluoric acid, which dissolves the soft glass readily but scarcely corrodes or etches the metal. The hydrofluoric acid, usually diluted with a little water to suppress fuming, is conveniently held either in a shallow dish which has been coated with paraffin or simply in a groove melted in a block of paraffin. The wires are withdrawn from the acid with metal forceps and washed in a weak solution of Aerosol.⁸ (Avoid letting the acid come in contact with the fingers.) The wires must be freed from all glass or difficulty in cutting and soldering will be encountered. About 5 minutes in the acid is required.

The good wires are mounted in flat cigar boxes, one for each of the metals. The electrical resistance of each wire should be measured and its resistance per unit length noted on a small label attached opposite the wire. After an assortment of wire sizes has been collected and measured, one is prepared to proceed with the construction of junctions of prescribed characteristics.

Construction of the junctions. A microscope of about 10power magnification facilitates the manipulation and soldering of the thermoelectric wires. An erecting binocular type giving stereoscopic vision is ideal.

Fig. 6 illustrates the manner of soldering the thermoelectric wires to the copper supporting wires with a hot tinned sewing needle. The hot-wire device used for heating the needle is electrically heated, the heat being regulated by a resistance. The temperature of the tip of the sewing needle can be further controlled by varying the point of contact between the hot wire and the tip of the needle.

Wood's metal is used for soldering. A solution of pure zinc chloride in distilled water is used as flux. After the soldering is completed, the excess zinc chloride should be carefully removed with a small brush wet with distilled water.

When the thermoelectric wires, which are selected for size so that each will be about 3 mm long, are soldered to the tinned copper supports, they are then "cut" to the proper length by touching them with the hot tinned needle as shown in Fig. 7. This not only "cuts" the wires but tins their ends at the same time. Difficulty with this operation will be encountered unless all of the glass has been These thermoelectric wires are now manipulated with a cold needle so that their ends are in contact. A little flux is added to their junction, and the soldering is effected by heat radiated from the hotwire device. (See Fig. 8.) The junction is to be carefully watched. The instant to withdraw the heat is indicated by a slight jerk of the tips of the wires due to surface tension of the fused metal. If the resistance is too great, each wire is shortened by heating the Wood's metal at the base of the wire. Molten Wood's metal pulls in the thermocouple wire by surface tension. The needle is used to heat the Wood's metal. In this way, it is easy to construct two junctions with only a fraction of an ohm difference in their electrical resistances; and, if the wires used have been taken from the same stock piece of bismuth or alloy wire, the sensitivities of the junction will match closely.

Ruggedness in the final thermopile is obtained by the use of fine quartz fibers to support the thermoelectric wires and attached receivers. The quartz fibers are fastened to the copper supporting wires by thin lacquer as illustrated in Fig. 9.

The receivers are made of thin gold foil of about 0.5 thickness. This is considerably thicker than sign painters' gold leaf.⁹ The receivers are cut to size (3 mm by 0.3 mm is a convenient size for spectroscopy) on the stage of the l0X microscope by means of a razor blade as shown in Fig. 10. The receivers are strengthened mechanically by giving them a cylindrical curvature in the following manner: The receiver is placed on a sheet of thin fine-grade paper mounted on blotting paper, and a rod of about 0.5 mm in diameter is pressed against it. (See Fig. 10.) Gold is particularly suitable for receivers because it is easily soldered.

A tiny bit of Wood's metal fused to the junction by radiation and wetted with flux facilitates attaching the receiver. The gold receiver is laid in contact with the thermojunction and soldered by heating it with radiation from the hot-wire device. (See Fig. 11.) A slight jerk of the receiver indicates when the heater should be withdrawn.

After the receivers are soldered in place, they are blackened with lampblack or other blackening material with the aid of a very small amount of glue as a binder. This mixture is applied to the receiver with a small camel's-hair brush as shown in Fig. 12.

Finally, two quartz fibers are fastened over each receiver for added ruggedness. The fibers are so fine and at the same time such poor heat conductors that the ruggedness gained by their use more than compensates for the negligible heat leakage which they introduce. Fig. 13 illustrates the method of securing the receivers and shows the completed thermopile.

Alternative methods of constructing thermopiles. Some experimenters prefer to make the housing for a thermopile from blown glass. Fig. 14 shows a popular type of glass housing. Fig. 15 shows how the junctions are manipulated in the field of the binocular microscope.

The selection of the proper window material for the thermopile is governed by the spectral region in which it is to be used. The appropriate choice can be made from the data given in Table I.

High-melting-point paraffin for use in the far infrared, listed in Table I, should not be confused with ordinary low-melting-point paraffin. High-melting-point paraffin is a crystalline material that does not deform when it is subjected to small stresses. In order to obtain strength and at the; same time have the paraffin window very thin, it is advisable to make the window cylindrical. Fig. 16 illustrates a method of using a tube of paraffin turned out in the lathe. It is sufficient to have the cylindrical paraffin window only 1 mm thick. Inasmuch as the thermopile cannot be seen through the paraffin window, it is necessary to adjust the receivers to the focal point of the radiations with the help of the galvanometer.

An alternate method of joining the thermocouple wires and attaching the receivers involves welding the thermoelectric wires together by means of a condenser discharge. The details of this procedure are given in the paper cited below.¹⁰

The receiver may be waxed to the welded thermojunction with Apiezon wax "W." This method of attaching the receiver yields almost the same sensitivity as soldering.

It is easier to construct a multiple-junction thermopile if one large receiver is waxed to the junctions than to undertake the delicate task of soldering separate small receivers to each junction. The electrical insulation between the junctions of a multiple-junction thermopile can be effected by coating each junction with lacquer before applying the wax used for holding the receivers.

Some experimenters eonstruct thermocouples in an order almost opposite to that described. The junction is formed, the receiver is fastened to the junction, and, finally, the thermocouple is soldered to the supporting wires.^ll This procedure is especially suited to the construction of a thermocouple with a small circular receiver, such as may be required for stellar radiometry. For a stellar thermocouple the junction may be soldered with a larger bit of Wood's metal so that there is formed at the junction a small sphere of metal, which is then compressed to form a flat receiver of circular shape and of the desired diameter.

Fig. 3 illustrates the use of active charcoal for maintaining a high vacuum in the thermopile. An alternate method involves the use of calcium as a getter. This method has been used by Dr. Pettit of the Mount Wilson Observatory and is quite satisfactory. Its use amounts to replacing the active charcoal in the thermopile in Fig. 3 with fresh calcium filings. These calcium filings are baked out while the tube is connected to the pump. Later, from time to time when the sensitivity of the thermopile falls off, owing to a decay of the vacuum, maximum sensitivity can be re-established simply by reheating the calcium.

The use of sensitive thermopiles. As ordinarily used, the radiant energy focused on the active receiving surface of the thermopile is interrupted periodically to isolate the effect of this radiation from the effect of other radiations falling on the receiver. The excursion of the galvanometer resulting from interrupting the measured beam is ascribed to changes in the temperature of the junctions produced by the radiant energy. Considering that delicate measurements may produce a change in temperature of only 10^{-6 ░} C., it is necessary to interrupt the light rather accurately to compensate for the first-order drifts which arise owing to a constant warming or cooling of the surroundings of the entire thermopile. As a result, just as much time is required for controlling the zero position of the galvanometer as for determining the deflection produced by the energy being measured.

It is evident that care is required in selecting the best position for the shutter in an optical system. For example, it is required that the change in the radiant energy falling on the thermopile due to closing the shutter should be the same as the change produced by removing the source of the radiations without changing the position of any object "seen" by the thermopile. Otherwise, the variation of radiation from closing the shutter may falsify the measurement. The shutter is to be put before the entrance slit of the spectrometer rather than after the exit slit in order to minimize this possibility.

Compensated thermopiles. While first-order drifts in the galvanometer can be eliminated even for an uncompensated thermopile by properly timing the exposures of the thermopile to the radiant energy, second-order drifts (due to a change in rate of the drift) can be eliminated only by the use of a compensated thermopile. In practice, it is difficult to construct a compensating receiver that will effect the elimination of more than 90 per cent of the galvanometer drift, but further compensation can be achieved by shunting an electrical resistance across the most sensitive of the junctions, either the active or the compensating ones. The junctions to be shunted and the value of the shunt resistance are determined experimentally. When the shunt resistance has the proper value, severe temperature changes of the surroundings of the thermopile housing produce a minimum deflection of the galvanometer. If care has been taken in constructing a compensated thermopile, the shunting resistance will be great enough so that the sensitivity of the thermopile is not appreciably impaired. One method of testing the compensation is to hold a hot soldering iron a few centimeters in front of the thermopile. When, for example, a particular thermopile of the type shown in Fig. 1 was compensated, the galvanometer drift was diminished to a twentieth part of the original drift, and it was reduced further a hundredfold by the shunting resistance.

Ordinarily, the energy to be measured is concentrated on one receiver; the compensating receiver then acts as an external resistance in the galvanometer circuit, and therefore the deflections are somewhat diminished. In most cases the reduction of first- and second-order drifts justifies compensation and the attendant smaller deflections.

By another procedure the image of the exit slit of the spectrometer covers both receivers, while a shutter in front of the entrance slit of the spectrometer obscures first the aperture of the half of the slit focused on one receiver and then the half focused on the other receiver.^l4 Thus the area of each of the two receivers is half the area of the slit

Theoretically, this scheme is expected to yield about 40 per cent more sensitivity than the ordinary compensated thermopile which has the area of the active receiver, as well as that of the compensating one, each equal to the area of the slit. In order to realize this 40 per cent gain in another but less desirable way, the mirror used for concentrating the radiant energy may be tilted periodically, so that the image of the exit slit of the spectrometer covers first one receiver and then the other.

Auxiliary apparatus. Ordinarily a galvanometer having a period of about 7 seconds and a low resistance of about 10 to 15 ohms is used with a thermopile. For making delicate measurements, the wires leading from the thermopile to the galvanometer should be shielded, so that alternating currents will not be induced in them by stray electromagnetic fields. When the wires are not properly shielded, induced alternating currents are, in a sense, rectified by the thermopile, especially by an uncompensated thermopile, and give a spurious galvanometer deflection.

A simple method of measuring the galvanometer response is to observe a well-illuminated scale with a telescope. The galvanometer should be arranged so that the scale is at a distance of about 5m. A telescope of about 32-power magnification, placed as close as possible to the galvanometer, should be used. With a galvanometer mirror 10 mm in diameter, it should be possible to see the millimeter divisions so clearly on a scale at a distance of 5 m that deflections on the scale can be estimated to a small fraction of a millimeter.

A lack of definition is often erroneously attributed to the galvanometer mirror, but it is usually due to the use of optically imperfect glass for the galvanometer window. However, there is a limit to the definition attainable, because of the finite size of the galvanometer mirror and the effect of diffraction. A simple rule is that the scale distance as measured in meters must not be greater than the diameter of the galvanometer mirror as measured in millimeters. Thus, for a scale distance of 5 m, the galvanometer should be at least 5 mm in diameter. About mm deflection at a distance of 5 m corresponds to the unavoidable natural fluctuations in the position of the galvanometer due to Brownian motion.

The accuracy with which the position of a cross hair on a millimeter scale can be estimated is much greater than might at first be supposed. A standard laboratory experiment for students at the University of Berlin is to estimate the positions of extra marks made on a millimeter scale. All of the extra marks are made on a ruling engine, so that their positions are accurately known. Although the lines are all about mm wide, the student is asked to estimate the position of each extra line to mm. In estimating these positions, a student seldom makes an error of mm, and an experienced observer will have a probable error for a single reading of about 0.03 mm. Accordingly, it is significant to estimate galvanometer readings to mm.

Fig. 18 shows an ingenious and accurate arrangement used by Professor Czerny for determining the magnitude of small galvanometer deflections.¹⁵

Relays. A convenient method of reading galvanometer deflections is to use an optical amplifier. Also, when it is desirable to record radiometric measurements photographically, the primary deflections should be amplified by means of some type of relay, and the deflections of a secondary galvanometer recorded on moving photographic paper.

The Moll and Burger thermo-relay may be used for amplifying galvanometer deflections until Brownian motion becomes conspicuous.^l6 Other amplifiers include the barrier-layer photocell amplifier described by Barnes and Matossi¹⁷ and the thermopile with two triangular-shaped receivers described by Cartwright.¹⁸

The Barnes and Matossi type of relay is made by dividing the active surface of a barrier-layer photocell by scratching along a diameter so as to make two contiguous semicircular areas of active surface. The arrangement of this amplifier is illustrated in Fig. 17, Chapter X. Leeds and Northrup produce an amplifying galvanometer and photocell combination of this type.¹⁹

The above methods of amplifying galvanometer deflections also magnify the drift of the primary galvanometer. This is undesirable. Pfund and Hardy have devised a resonance radiometer, which tends to "ignore" drift and separate it from the response to the measured radiation.²⁰

Their scheme is somewhat elaborate and requires the use of a tuned pendulum shutter, in addition to two identical galvanometers. However, the instrument has advantages, especially when the thermopile is not adequately protected from extraneous thermal effects. Pfund describes the resonance radiometer briefly as follows:

If primary and secondary galvanometers are underdamped and adjusted to the same period, then, by interrupting the radiation falling on the thermopile with a periodicity corresponding to that of the galvanometers, a condition of resonance is set up. As a class, resonating systems are characterized by high sensitivity for "tuned" periodic disturbances and by indifference to random disturbances.

This indifference to random disturbances unfortunately does not include Brownian motions of the primary galvanometer. Hardy has measured the effect of the Brownian motion on the resonance radiometer and has found that the fluctuations in the deflection of the secondary galvanometer are magnified in accord with theoretical predictions for fluctuations due to Brownian motion.²¹ Nevertheless, Hardy feels that delicate measurement to the limit set by these effects is definitely facilitated by the use of the resonance radiometer. The slowness of the resonance radiometer (it takes about 90 seconds to make a measurement) is one of its disadvantages.

Firestone²² has made an ingenious variation from the Pfund scheme. It depends on charging and discharging a condenser through the secondary galvanometer with a circuit controlled by the amplified thermocouple current. A photocell amplifier is used. Naturally, as the output galvanometer circuit has infinite ohmic resistance, owing to the condenser in the circuit, no net current can flow, and consequently all deflections are excursions about an unchanging zero position.

We have emphasized the importance of using a compensated thermopile to diminish galvanometer drifts as well as to make the circuit electrically insensitive to high-frequency electromagnetic radiations. For the most delicate measurements, it is also necessary to have the galvanometer free from mechanical vibrations. This can be accomplished by the use of a vibrationless support such as the type shown in Fig. 19. The description of this vibrationless support is given in Chapter XIV.

Construction of thermojunctions by evaporation and sputtering. There are other applications of thermopiles and thermocouples, such as their use for vacuum manometers, for measuring alternating currents, for measuring sound intensities, for magnifying deflections of a spot of light in thermo-relays, and for total-radiation pyrometers. We cannot go into all these applications in detail, but the present chapter and the references cited should serve to guide an experimenter in these fields. The construction of thermopiles by evaporation and sputtering, however, warrants a description.

Thermopiles made from films of the thermoelectrically active metals, produced by evaporation or sputtering, can be constructed having a very low heat capacity, so low, in fact, that they will respond to the adiabatic heating produced by separate sound waves of 5000 cycles frequency.²³

One of the metal films used is bismuth and the other is antimony. The foundation on which the metal films are deposited must be extremely thin and strong. For this purpose, glass, mica, or 1acquer films are used.

When a soft-glass tube is fused at one end and strongly blown out with air pressure so as to expand and explode a thin bulb, the shattered bulb wall yields fine ribbons of glass about 1 or 2 mm wide and 1 or 2 cm long. These ribbons are of such a thickness as to give interference colors and make a suitable foundation for evaporated thermocouples.

When the thermoelectric metal is deposited on the foundation film by evaporation, the heat of condensation of the metal vapor, as well as the heat radiated by the filament and absorbed by the film, tends to elevate the temperature of the foundation. It is necessary to prevent the temperature of the film from rising to a point at which it might be destructive: The films are mounted in the evaporation chamber in contact with mercury or, better yet, in contact with a copper cooling block.

To form an area to which electrical contact may be established, gold is sputtered or evaporated at appropriate points on the metal films. The connector wires may then be soldered to the gold.

Evaporated thermojunctions are especially useful for making the Moll and Burger type thermo-relay. Burger and van Cittert were able to obtain a sensitivity about two and one-half times as great as that obtained with the ordinary rolled Moll and Burger element.

Considerations in thermopile design. The thermopile shown in Fig. 1 and described above can be adapted to meet most of the needs of an experimenter interested in making radiometric measurements. Some experimenters, especially those intending to make extremely delicate measurements, will be interested in the theory for the design of thermopiles. For example, the experimenter designing a vacuum thermopile of a given area has several decisions to make. He must decide which metals to select for the thermocouple wires and determine whether to make few or many junctions. Also, he must decide on the material to be used for coating the receivers. Or, he may wish to design a thermopile to operate at atmospheric pressure.

The equations expressing the theoretical dependence of the galvanometer response on the number of junctions, area of receiver, characteristics of thermoelectric wires, and so forth, have been completely developed.²⁷ Calculations based on this theory require a knowledge of the characteristics of the thermoelectric wires, namely, their thermoelectric power, electrical conductivity, and heat conductivity. The calculations also require a knowledge of the optical properties of receiving surfaces, such as their emissivity and reflectivity for various wave lengths. With this information, it is possible to design the thermopile which will give optimum response under the obtaining conditions.

The characteristic sensitivity of a thermopile determines its response and, in the theory, this quantity Q is defined as follows:

The expression for Q for an uncompensated vacuum thermopile of n junctions in terms of the quantities on which it depends is

The quantity in the brackets represents the total heat losses of the receiver. The middle term in the brackets represents heat loss by conduction through the wires, and the third term represents heat loss due to the Peltier effect. Ordinarily the influence of Peltier heat on the design may be neglected.

It is desirable, from a practical point of view, to have a minimum number of junctions to build. The information given in Fig. 21 facilitates making the compromise between this practical consideration, on the one hand, and the desire to have a maximum sensitivity on the other. From curves in this figure, it is apparent that the energy should be concentrated onto a receiver which is as small as possible.

By reference to Eq. 3 we see that when the third term in w= the brackets is small in comparison with the first and second terms, the sensitivity, Q, appears to be proportional to the thermoelectric power, P. This is not always the case in practice, and a thermoelectric metal should not be chosen on the basis of the thermoelectric power alone. As a matter of fact, most metals with a high thermoelectric power have an unfavorable Wiedemann-Franz coefficient, which may, in the end, make them even less desirable than metals such as the bismuth alloys, which are convenient to manage.²⁸

It has been customary to compare the sensitivities, S, of the various radiometric instruments. This has led to some confusion in the literature. Actually, in making the most delicate radiometric measurements, we are not interested primarily in the value of S (which can be made as large as desired by the use of an amplifier) but rather in the accuracy with which the radiant energy can be measured in a given time, or, what amounts to the same thing, in the smallest intensity of radiant energy that can be measured in a given time with a given accuracy. The magnitude of this smallest deflection is influenced by disturbances acting on the instruments.

The average deflection due to the potential energy is involved in the expression

Potential energy = (6)

It can be shown that this expression is a general one applicable to any radiometric instrument. Combining Eq. 7 3 with Eq. 4, we get an expression for the least energy that can be measured:

The of a thermopile and galvanometer can be expressed in terms of the factor g, the Q of the thermopile, and the period of the galvanometer, as follows:

watt. (9)

With the values of Q given by the curves in Fig. 12 it is therefore possible to estimate the minimum energy falling on the receiver in unit time that can be measured with a proposed apparatus. It is to be observed that the sensitivity of the galvanometer does not enter Eq. 9. Eq. 9, however, does imply that the deflections are measured either directly or with the help of an amplifying device to the limit set by Brownian motion.

General summary of the work on thermopile design. The remainder of this chapter will be devoted to a summary of the results of experimental and theoretical investigations made by one of the authors, C. Hawley Cartwright, on the relative merits of the different radiometric instruments, and in addition will present some general (although not necessarily final) conclusions resulting from these studies.

Vacuum microradiometers can be made which will measure less energy, , than the best vacuum thermopiles used with a separate galvanometer. This advantage is not sufficient to offset the practical advantage of greater flexibility of the thermopile with separate galvanometer.

Vacuum bolometers and vacuum thermopiles have at present practically the same limit, . If a material with better characteristics than nickel were available for the construction of the bolometer strip, this situation would be altered.

Radiometers will not respond to as small energies, , as thermopiles. The direct comparisons made by the author, especially in Berlin and Brussels, between vacuum thermopiles and radiometers yield results in favor of vacuum thermopiles. Radiometers are usually much more sensitive ~ than thermopile and galvanometer combinations, owing to the use of a much lighter moving system than is possible with a galvanometer. Brownian motions are, however, increased, so that they more than offset the advantage of the larger primary deflections.

A question of considerable importance and one which bears on the above conclusions is the following: Why is there often considerable variation in the sensitivity of vacuum thermopiles, in fact, sufficiently large variations to be responsible for many of the publications that have appeared on improving thermopiles? The answer is that many vacuum thermopiles are not constructed with the maximum possible sensitivity, for the following reasons:

1. The sensitivity of a thermopile depends on the skill exercised in its construction.

2. For the most part, thermopiles have been constructed without first calculating the proper design or, if this is done, without dependable information on the physical properties of the materials used.

3. A sufficiently high vacuum is not always used. A properly designed and constructed thermopile should be about twenty times more sensitive in high vacuum than in air, and, on increasing the vacuum from 10^-3 to 10^-6 mm of mercury, the sensitivity should be doubled.

5. The influence of deviations of the properties of bismuth, and especially bismuth alloys, from the predictions of the Wiedemann-Franz law is generally neglected, with the result that thermoelectric wires with a resistance which is too small are used so that the sensitivity falls on the left-hand steep part of the curves corresponding to those shown in Fig. 21.

It is well to keep in mind that although tin has ten times less specific electrical resistance than bismuth, an alloy of bismuth and 5 per cent tin has twice the specific electrical resistance of pure bismuth. This should be considered when better thermoelectric metals are being sought. Bismuth itself is an unusually favorable metal for thermopiles, not only because it has a relatively high thermoelectric power, but also because it is a pure metal element having a small specific electrical resistance and does not depart greatly from the Wiedemann-Franz law.

In order to improve the sensitivity of thermopiles, there !Y' is the possibility of using them at low temperatures, where Q can be increased, owing to a greater thermoelectric power, a more favorable Wiedemann-Franz ratio, and less radiation loss from the receivers. However, liquid-air thermopiles have several practical disadvantages.³²

¹ Brackett, F. S., and McAlister, E. D., Rev. Sci. Instruments, 1, 191 (1930). Burger, H. C., and van Cittert, P. H., Zeits. f. Physik, 66, 210 (1930).Coblentz, W. W., Bureau of Standards, Bull., 11, 131 (1914). Firestone, F. A., Rev. Sci. Instruments, 1, 630 (1930). Johansen, E. S., Ann. d. Physik, 33, 517 (1910); Phys. Zeits., 14, 998 (1913). Lebedew, P., Ann. d. Physik, 9, 209 (1902). Moll, W. J. H., Inaug. Dissertation Utrecht (1907); Arch. Neerland, 13, 100 (1908). Moll, W. J. H., and Burger, H. C., Zeits. f. Physik, 32, 575 (1925); Phil. Mag., 50, 618 to 631 (1925). Paschen, F., Ann. d. Physik, 33, 736 (1910). Pettit, Edison, and Nicholson, Seth B., Astrophys. J., 56, 327 (1922). Pfund, A. H., Phys. Zeits., 13, 870 (1912). Rubens, H., Zeits. f. Instrumentenk., 18, 65 (1898).

² Boys, C. V., Roy. Soc., Proc., 42, 189 (1887), 44, 96 (1888), 47, 480 (1890); Roy. Soc., Phil. Trans., 180A, 169 (1889). Coblentz, W. W., Bureau of Standards, Bull., 2, 479 (1906). Paschen, F., Ann. d; Physik, 48, 272 (1893).

³Langley, S. P., Am. Acad., Proc., 16, 342 (1881); Annals of the Astrophysical Obs., 4, 45 (1904), 5, 75 (1905). Leimbach, G., Ann. d. Physik, 33, 308 (1910).

⁴Abbott, C. G., Aitrophys. J., 69, 293 (1929). Coblentz, W. W., Bureau of Standards, Bull., 4, 391 (1908), 9, 15 (1913). Crookes, Sir William, Roy. Soc., Phil. Trans., 11, 166, 325 (1876). Sandvik, O., J.O.S.A., 12, 355 (1926). Hettner, G., Zeits. f. Physik, 27, 12 (1924). Nichols, E. F., Phys. Rev., 4, 297 (1897). Smith, S., Nat. Acad. Sci., Proc., 16, 373 (1930). Tear, J. D., Phys. Rev., 23, 641 (1924).

⁵ Cartwright, C. H., Physics, 1, 211 (1931). Klumb, Hans, Zeits. f. techn. Physik, 17, 279 (1936).

⁶ We wish to acknowledge the contributions to this design of Professor Firestone and Mr. Paul Weyrich, of the University of Michigan.

⁷ Cartwright, C. H., Zeits. f. Physik, 92, 153 (1934); Ann. d. Physik, 18, 656 (1933).

⁸ Aerosol or the detergent Dreft, the latter of which is sold in grocery stores, has many uses around the laboratory. Besides its usefulness in washing glass, aluminum mirrors, and so forth, it ean be added to water to decrease its surface tension and increase wetting power. This is advisable for washing thermocouple wires, as the solution wets the wires and dissolves the hydrofluoric acid. Also, for coating the receivers, the solution with added Dreft has less "attraction" due to surface tension, and accordingly there is less danger of destroying she work when the brush with its blackening material is applied.

⁹ Gold leaf of the required thickness is prepared by evaporating a proper amount of gold in vacuum (see "Coating of Surfaces: Evaporation and Sputtering") from a tungsten eoil onto a glass plate. The film is then washed off the glass with a stream of water.

¹⁰ Cartwright, C. H., Rev. Sci. Instruments, 3, 73 (1932).

¹¹ Firestone, F. A., Rev. Sci. Instruments, 1, 630 (1930).

¹² Pfund, A. H., "Radiation Thermopiles," Rev. Sci. Instruments, 8, 417 (1937).

¹³ Woltersdorf, W., Zeits. f. Physik, 91, 230 (1934). Forsythe, W. E., Measurement of Radiant Energy, page 210. New York: McGraw-Hill Book Company, 1937. Pfund, A. H., J.O.S.A., 23, 375 (1933), 2S, 270 (1933). Strong, J., Rev. Sci. Intruments, 3, 65 (1932)

¹⁴ Badger, R. M., J.O.S.A., 15, 370 (1927).

¹⁵ Czerny, M., Zeits. f. Physik, 90, 468 (1934). Czerny, M., Heins, H., and Woltersdorf, W., Zeits. f. Physik, 95, 262 (1935).

¹⁶ Moll, W. J. H., Phil. Mag., 60, 624 (1925). The Moll and Burger thermo-relay is sold by Kipp and Sonen, Delft, Holland.

¹⁷ Barnes, R. B., and Matossi, R., Zeits. f. Physik, 76, 24 (1932).

¹⁸ Cartwright, C. H., Rev. Sci. Instruments, 5, 221 (1932).

¹⁹ Leeds and Northrup Company, Philadelphia, Pennsylvania.

²⁰ Hardy, J. D., Rev. Sci. Instruments, 1, 429 (1929), 5, 120 (1934). Pfund, A. H., Science, 2, 69 (1929).

²¹ See also Van Lear. G. A., Jr., Rev. Sc. Instruments, 1, 21 (1938).

²² Firestone, F. A, Rev. Sci. Instruments, 3, 163 (1932).

²³ Harris, L., and Johnson, E. A., Rev. Sci. Instruments, 5, 153 (1934).

²⁴ This is the technique described in Burger, H. C., and van Cittert, P. H., Zeits. f. Physik, 66, 210 (1930).

²⁶ Burger, H. C., and van Cittert, P. H., Zeits. f. Physik, 66, 210 (1930).

²⁷ Cartwright, C. H., Zeits. f. Physik, 92, 153 (1934).

²⁹ Ising, G., Phil. Mag., 1, 827 (1926)

³⁰ Cartwright, C. H., Physics, 1, 211 (1931). Czerny, M., Ann. d. Physik, 12, 993 (1932).

³¹ Bridgman, P. W., Am. Acad., Proc., 63, 347 (1927-1928).

³² Cartwright, C. H., Rev. Sci. Instruments, 4, 382 (1933).