1

NBS TECHNICAL NOTE 594-1

Optical Radiation Measurements:

Fundamental Principles of

Absolute Radiometry and the

Philosophy of This NBS Program

(1968 to 1971)
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Optical Radiation Measurements:

Fundamental Principles of

Absolute Radiometry and the Philosophy

of This NBS Program (1968 to 1971]

Jon Geist

Heat Division

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

Work supported in part by the National Aeronautics

and Space Administration under Contract C-41584-B.

J.

\

'-,': \«o^

U.S. DEPARTMENT OF COMMERCE, Peter G. Peterson, Secretary

NATIONAL BUREAU OF STANDARDS, Lawrence M. Kushner, Acting Director,

Issued June 1972
National Bureau of Standards Technical Note 594-1

Nat. Bur. Stand. (U.S.), Tech. Note 594-1, 59 pages (June 1972) CODEN: NBTNAE

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (Order by SD Catalog No. 03.46:594-1). Price 60 cents.
Preface

This is the first issue of a series of Technical Notes entitled OPTICAL RADIATION MEASUREMENTS.

The series will consist primarily of reports of progress in or details of research conducted in

radiometry and photometry in the Optical Radiation Section of the Heat Division and will appear about

every six weeks.

The level of presentation in OPTICAL RADIATION MEASUREMENTS will he directed at a general technical audience. The equivalent of an undergraduate degree in engineering or physics plus familiarity

with the basic concepts of radiometry and photometry [e.g., G. Bauer, Measurement of Optical Radiations (Focal Press, London, New York, 1965)] should be sufficient for understanding the vast majority

of material in this series. Occasionally a more specialized background will be required such as a

few of the mathematical techniques required in this issue. Even in such instances, a careful reading

of the assumptions, approximations and final conclusions should permit the non-specialist to understand the gist of the argument if not the details.

At times, certain commercial materials and equipment will be identified in this series in order

to adequately specify the experimental procedure. In no case does such identification imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the material or

equipment identified is necessarily the best available for the purpose.

Any suggestions readers may have to improve the utility of this series are welcome.

Henry J. Kostkowski , Chief,

Optical Radiation Section

National Bureau of Standards

iii
Contents

Page

1. Introduction 1

2. Definition and Historical Review of Absolute Radiometry 1

3. Fundamental Considerations in the Present Program 2

3.1 Error in the Measurement Process 2

3.2 The Principle of Operation of an Absolute Radiometer 3

3.3 Sources of Error in Absolute Radiometers k

h. Techniques for Measuring Corrections for the Various Errors Affecting

Absolute Radiometers 6

k.l The Theory of the Responsivity of the Receiver to Power Inputs

from Various Locations 7

k.2 Techniques for Measuring the Variation in Responsivity Over the

Surface of the Receiver Disk 20

U.3 Techniques for Measuring the Non-Equivalent Heat Losses from the

Receiver due to the Emission and Reflection of Electromagnetic Radiation 22

U - i+ Techniques for Measuring the Non-Equivalent Heat Loss from the

Receiver due to Air Conduction and Convection 2k

U.5 Techniques for Measuring Corrections for the Remaining Sources of

Error 26

5. Electrically Calibrated Radiometer #10 and the Third International

Pyrheliometric Comparisons 27

5.1 Construction of the Radiometer 27

5.2 Measurements of Corrections for the Various Errors Affecting ECR #10 3^

5.3 The Participation of ECR #10 in the Third International

Pyrheliometric Comparisons U1+

6. Conclusion 52

7. References 53
Fundamental Principles of Absolute Radiometry and The Philosophy of this NBS Program

(1968 to 1971)

Jon Geist

The philosophy of the present NBS program in realizing a scale of

total irradiance with electrically calibrated (absolute) detectors, a theoretical analysis of the sources of error in such a scale realization, a description of the electrically calibrated detector developed

from 1968 to 1971, and participation in the Third International

Pyrheliometer Comparison are presented.

Key words: Absolute detector radiometry; electrically calibrated

detectors; International Pyrheliometric Scale; irradiance; radiometry.

1. Introduction

This report describes work performed on a program to develop an electrically calibrated

detector (also called absolute radiometer, absolute detector, and electrically calibrated

radiometer) that could be used to realize, maintain, and transfer a scale of total irradiance. The program included a comprehensive investigation of the theoretical basis of

absolute detector radiometry, as well as the design and construction of a number of detectors.

This part of the final report covers the period from the inception of the program through the

end of 1970, and concentrates on two areas. Sections 2, 3, and k of this report describe all

of the theoretical work carried out under the program with the exception of work reported in

a paper, "A New Type of Boundary Value Coupling for Second Order Sturm-Liouville Systems",

J. Res. Nat. Bur. Stand. (U.S.), B, 75B (Math. Sci . )

, Nos. 3 and U, 121-132 (July-Dec. 1971).

Section 5 describes one of the detectors designed and constructed under this program and its

participation in the Third International Pyrheliometer Comparisons in Davos, Switzerland in

September of 1970.

2. Definition and Historical Review of Absolute Radiometry

The measurement of certain radiometric quantities such as reflectance and emittance does

not require a knowledge of the power levels of the fluxes which are used in the measurement.

Only the ratios of the fluxes are important. Thus we could classify such measurements as relative radiometry. The rest of radiometry is concerned with power levels through the quantities, radiance, irradiance, and intensity.

How are scales of these radiometric quantities to be realized? One way is to compare

the flux to be measured with the flux emitted by a blackbody, either directly, or using a standard which in turn has been calibrated by comparison with a blackbody. Here the ultimate accuracy with which the radiometric scales can be realized will depend upon the accuracy

with which the thermodynamic temperature scale can be realized, and the validity of the

Stefan-Boltzmann and Planck laws of blackbody radiation. Any other method of realizing

radiometric scales can be classified as absolute radiometry. Of course this is not a particularly good name, since it is not at all descriptive of the activity to which it is

applied. However, this name does have historical precedent. I think it arose in reference

to absolute electrical measurements. At any rate, it is important to understand that it is no more absolute to realize a radiometric scale through absolute radiometry, than to realize

it by reference to blackbody radiation.

By far the most common absolute radiometric measurements are made with thermal detectors

(power meters) which have an electric heater built into their receivers. Here the power

carried by the radiant flux which is to be measured is compared with the power carried by an electrical current. This, in turn, can be determined by relatively straightforward voltage

and current measurements. In this case the ultimate accuracy with which the radiometric

scales can be realized will depend upon the accuracy with which the (absolute) voltage and current scales can be realized.

If all is well with the laws of physics, and the realizations of the thermodynamic

temperature scale and the absolute voltage and current scales, then a blackbody radiometric

scale should be consistent with an absolute radiometric scale of the same quantity, to within
the combined estimated uncertainties of the scales, provided these estimates are realistic.

The actual situation as to the consistency of radiometric scales derived from blackbody

and absolute radiometric measurements is uncertain. A large amount of work has been done,

most of it quite early, which has shown a discrepancy of at least 1/2% between the measured

value of the Stefan-Boltzmann constant, a, and its theoretical value as calculated from

atomic constants. It is interesting that in 1929 the errors in the measured values of

Planck's constant, h, and the Boltzmann constant, k, were of just the right magnitude and

direction (about 1% each) to make the value of a calculated by Birge [lP using these values

agree to better than .1% with the value that had been measured over ten years earlier by

Coblentz [2]. Later measurements of o were consistently higher than Coblentz's value [l,3] so that by the time the errors in h and k were discovered, no redeterminations of a were

attempted. After a 2U-year period between 1933 and 1957 when no measurements of a were

reported, Eppley and Karoli [k] reported a value higher than that of Coblentz, but they chose

not to discuss the discrepancy between their value and the theoretical value. In 1962

Gillham attempted to measure a but discovered evidence of systematic errors in his results

and did not publish them. However, his result, which was a little higher than that of

Coblentz, was reported in the literature by Stair [5] with a reference to a personal communication from Gillham. To complete the picture, it must be noted that most scientists who were

aware of the lingering discrepancy between the measured and theoretical values of a , had

concluded that some source of error must have been overlooked by all of the investigators [6],

3. Fundamental Considerations in the Present Program

As mentioned in the last section, the consensus of opinion is that the discrepancy

between the theoretical and experimental values of a is due to experimental errors in the

absolute radiometric measurements. Consequently any attempt to resolve this issue must be

carried out in an extremely careful manner, so that whatever the outcome, no doubts will

persist as to the experimental technique. Furthermore, any results from absolute radiometric

techniques must be viewed with suspicion until this issue is resolved. In view of this fact we approach this problem from as fundamental a viewpoint as possible. First, we analyze the

fundamental concepts of error in the measurement process.

3.1 Error in the Measurement Process

Some people would reserve the word error for the difference between the result of a measurement and the "true" values of the measured quantity. However, in order to describe

the measurement process in detail, the word error is sometimes used in a different sense. This sense is best described in terms of the measurement process itself. Here one starts

with a physical principle, a law of physics, which describes a particular phenomena. An instrument whose behavior is governed primarily by this physical law, is designed and used

to measure the physical quantity described by the physical law. Any deviations of the

instrument's behavior from the ideal behavior predicted by the law are due to the fact

that the instrument must obey all of the other laws of physics s and can be called an error.

In this view, every other law of physics is a possible source of error in the instrument.

If no corrections are made for any of the instrument's departures from the ideal behavior

predicted by the physical law, the difference between the two possible meanings of the word

error is not important. However, if a correction is applied to compensate for a particular

error, the different uses of the word error become quite significant. For want of a better

word, we will use the word error in the second sense .

There are at least two different philosophies with respect to errors which can govern

the design of scientific instruments. Under the first of these philosophies, we would strive

to minimize each of the errors which affect the instrument. The actual magnitudes of the errors may be subject to considerable uncertainty, but at least they are as small as possible

within the design constraints imposed by other factors. Under the second philosophy, we no longer strive to minimize each error. Instead we try to minimize the uncertainty with which

1 Figures in brackets indicate the literature references at the end of this paper.

2 The semantic problem is further complicated in that as long as we do not make corrections

for these errors, we call them errors, but as soon as we make a correction for them, we call

them corrections, or else we don't refer to them.
each error is known. This can be accomplished by designing the instrument in such a way that

the actual value of each error can be precisely and accurately determined in a definitive

measurement. Of course, it is possible that an instrument design which permits some particular error to be measured, will be such that this error is much larger than its minimum

achievable value. However, this is not an unsatisfactory situation. While the error itself

is not a minimum, the uncertainty with which it is known is a minimum. This is certainly the more desirable situation. So much so, in fact, that at this point, one might wonder why any

instrument would be designed under the first philosophy. However, the whole picture has not been presented yet.

It is obviously more difficult to use an instrument which has been designed under the

second philosophy, than one which has been designed for the same purpose under the first

philosophy because the measurements of the errors have to be conducted in addition to the

measurements which are associated with the normal use of the instrument. Furthermore, if

the measurement process is examined in detail, it usually turns out that the measurements of

the errors are more difficult and time consuming than the measurements for which the instrument was designed. As a result, most instruments are designed (consciously or not) according

to the first philosophy for some sources of error and the second philosophy for other sources

of error. Those errors which are easy to measure are measured, and those errors which are difficult to measure are minimized.

A popular compromise of the two philosophies must also be considered. One might design

an instrument in such a way as to minimize the errors, and then attempt to calculate their

actual magnitude from property data for the materials from which the instrument was con- structed. The second philosophy is still represented, since measurements have been performed

to determine the magnitude of each error. However, they were not performed on the instrument

itself, but on materials which are similar to those incorporated into the instrument. The

advantages of this approach are usually illusory. It often happens that no reliable uncer- tainties can be associated with the property data that is available in the literature and

hence no reliable uncertainty can be associated with an estimate of error which is based on this data. Secondly, it is often the case that the samples of the material upon which the

property measurements were made are not representative of the samples of the material which

were incorporated into the instrument. Again no reliable uncertainties can be obtained.

We turn our attention now to a practical example of the two philosophies. In sophisticated measurement systems, it is possible to distinguish two different types of instruments

which roughly correspond to the two philosophies with respect to error. Here we differentiate between instruments which are used to realize a scale of a physical quantity and those

to which this scale is transferred and which are used to maintain and transfer the scale but

which are not used to realize it. The more the second philosophy governs the design of

instruments which are used to realize a scale, the less uncertain the scale will be. However, instruments which are not used to realize scales, but only to transfer scales, are often best designed under the first philosophy. In effect, the transfer of the scale from

the instrument which has realized it to the secondary instrument is a measurement of the sum

of all of the errors associated with the secondary instrument. The uncertainty in the

knowledge of the sum of all the errors in the secondary instrument is just the combined

uncertainty in the sum of all of the errors in the instrument which was used to realize the

scale, and the uncertainty in the transfer of the scale. The advantage of minimizing the

;rrors in this type of instrument is that under these conditions the minimum number of variations in experimental conditions need be performed in the scale transfer. The reason for

this is that interpolation between various experimental conditions will be more accurate when

the errors are small.

3.2 The Principle of Operation of an Absolute Radiometer

The purpose of the absolute radiometer developed on this project is to accurately

realize a scale of irradiance which can be made available to the scientific and technical

community. Consequently the second philosophy with respect to error was chosen as the

primary design philosophy for this instrument. The past difficulties associated with the

experimental determinations of the Stefan-Boltzmann constant imposed a total commitment to

this design philosophy.

In this section we first state the Principle of Operation of an Absolute Radiometer.

3
By examining this principle we then determine the various sources of error in all absolute

radiometers. Then we can attempt to design the instrument so that all of the errors arising

from all of these sources can be measured in definitive experiments. The actual instrument

design which was finally adopted will be described in section 5.

The Principle of Operation of an Absolute Radiometer can be simply stated in the following manner:

If a) irradiation of the receiver with radiant power and dissipation in the receiver

of electrical power result in the same temperature distribution throughout the entire

radiometer, then b) the amount of radiant power absorbed by the receiver must equal the

amount of electrical power absorbed by the receiver.

This principle follows from conservation of energy and a few laws of heat transfer. As might be expected, other physical laws prevent any absolute radiometer from behaving in such

a way that the principle can be realized. It is impossible to design a radiometer in which

the temperature distributions under radiant and electrical heating are identical. Also, it

is impossible to measure the exact temperature distribution within the radiometer. What is

usually measured is a voltage which is proportional to some weighted average temperature

difference between the receiver of the radiometer and its thermal environment, (plus a ran- dom noise voltage). We will restrict the following discussion to such radiometers. If we

assume this much, it is possible to isolate the sources of error which affect this type of

radiometer. Then we can determine the type of measurements which must be conducted in order

to obtain corrections for the sources of error which have been isolated.

3.3 Sources of Error in Absolute Radiometers

In this section we examine in a detailed but qualitative manner the sources of error associated with absolute radiometers. Figure 1 is a schematic diagram of a "general"

absolute radiometer from which the various sources of error can be obtained by applying the

Principle of Operation. First of all, in order to employ the principle we must measure the

voltage across the thermopile and the voltage across and the current in the heater during

the periods of electrical and radiant heating of the receiver. And if we wish to realize a scale of irradiance, we must also measure the area of the aperture. Thus any sources of error in these measurements are sources of error which must be accounted for in the absolute

radiometer. However, there are more subtle sources of error affecting absolute radiometers

than these.

Referring to figure 1, first consider the heat transfer taking place within the radiometer during a period of electrical heating. The electrical current generates heat in the

heater leads as well as in the heater itself. The resulting temperature distribution within

the radiometer is such that some of the heat generated in the heater is conducted to the

receiver and some is carried to the thermal environment of the receiver by radiation and

convection. The heat conducted to the receiver is distributed throughout the receiver and

the high absorptance coating of the receiver (its distribution being governed by the equations of heat transfer) and is ultimately carried to the thermal environment of the receiver

by conduction down the thermopile legs and the heater leads, and by convection and radiation

from all of the surfaces of the receiver, including the high absorptance coating, the thermopile legs, and the heater leads. Likewise, some of the heat which is generated in the

heater leads is carried to the thermal environment of the receiver by conduction down the

leads and by convection and radiation from the surfaces of the leads. While none of the

heat generated in the leads is conducted to the receiver, the heat generation in the leads causes the temperature distribution within the radiometer to be different from that which

would be obtained with no lead heating. Thus two of the sources of error which prevent an absolute radiometer from rigorously fulfilling the Principle of Operation are (l) not all of

the power generated in the heater is absorbed by the receiver, and (2) the heat generated in

the heater leads modifies the temperature distribution within the radiometer.

Now let us consider the heat transfer taking place within the radiometer during a period

of radiant heating. Electromagnetic radiation (indicated by the arrows in figure l) is

incident on the aperture and on the thermal environment of the receiver. The portion of the

incident flux which passes through the aperture is incident on the high absorptance coating

of the receiver. Some of this flux is reflected off of the coating, the rest is absorbed in
Figure 1. A "general" absolute radiometer. 1 - receiver disk,

2 - high absorptance coating of receiver disk,

3 - heater, h - thermocouple, 5 - thermal environment

of receiver, 6 - aperture. The word receiver usually

applies to 1, 2, and 3.

the coating causing it to have a different temperature distribution than during a period of

electrical heating. Some of the flux absorbed by the high absorptance coating is carried to

the thermal environment by convection and radiation, and the rest is conducted to the

receiver. From this point on it suffers a fate similar to that suffered by the heat generated electrically, but the temperature distribution in the receiver will be somewhat different since the power enters the receiver from a different location. In a similar manner, a portion of the flux incident on the thermal environment of the receiver is absorbed by the

thermal environment causing it to have a different temperature distribution than that which

it has during a period of electrical heating. Thus, three more sources of error are

(l) not all of the flux incident on the high absorptance coating is absorbed, (2) the flux

incident on the thermal environment modifies the temperature distribution within the

radiometer, and (3) the temperature distributions within the high absorptance coating and

the receiver are different during periods of electrical and radiant heating.

The above described sources of error can be divided into two categories:

I. Errors associated with the measurement of physical quantities

- voltage across thermopile

- voltage across heater

- current in heater

- area of aperture

II. Errors associated with getting the power into the receiver

- not all of the electrical power ge:erated in the heater is absorbed

by the receiver.
- not all of the radiant power incident on the high absorptance coating

is absorbed by it

- power generated in the heater leads modifies the temperature distribution within the radiometer

- flux incident on the thermal environment of the receiver modifies the

temperature distribution within the radiometer

- the temperature distribution in the receiver and high absorptance

coating during radiant heating is different from that during electrical

heating.

Having isolated the sources of error, we must next design definitive experiments in

which corrections for the various errors can be measured and which will provide reliable

uncertainties associated with each correction. This problem will be discussed in the following sections. However, before doing so it is useful to consider the distinction between

the two different categories into which we have divided the sources of error. Presumably,

the instruments which we use to measure the physical quantities listed under the first

category were designed according to the first design philosophy described in section 3.1,

that is, to minimize the various errors affecting the instrument. Furthermore, it is

reasonable to assume that each of them has been calibrated against some other instrument

which was designed according to the second philosophy and which was used to realize a scale

of the physical quantity in question. In this case the cumulative correction and associated

uncertainty describing the ability of each of these instruments to transfer the scale it is

maintaining is well known and well documented, for instance, in a calibration report. Consequently, we will assume that the sources of error in the first category are known and we will restrict our efforts in the following sections to studying the problems associated with

measuring the correction factors which apply to the sources of error in the second category.

We conclude this section by pointing out that while it is possible to calculate these

corrections using published values for material properties, the problems which were mentioned

in section 3.1 in regard to this approach are especially severe here. The estimates of

uncertainty which accompany thermal data, particularly thermal-radiative data are usually

unreliable, and it is questionable whether the samples on which the published measurements were made are representative of the same material incorporated into the absolute radiometer.

Thus the uncertainties associated with corrections obtained in this manner cannot be con- sidered reliable. For emphasis the general conclusion reached earlier in this paper will be

restated. Any detector that is going to be used to realize a scale of total irradiance must

be constructed in such a way that all of the measurements which are necessary to obtain the

corrections for the errors in the second category can be made on that detector. This must

be the primary design consideration.

k. Techniques for Measuring Corrections for the

Various Errors Affecting Absolute Radiometers

In the following sections we will describe experiments by which corrections for the

various errors identified in the last section can be measured. In order to understand these

experiments, and in fact, in order to convincingly demonstrate that these experiments do

indeed measure the quantities of interest, we will need to look more deeply and in a quantitative manner into these various errors. First we note that all of the experiments which we will describe are based on the following principle which depends upon the Principle of

Operation of an Absolute Radiometer. Each of the sources of error causes a different temperature distribution within the radiometer and this different temperature distribution produces

a different thermopile voltage than that which would be produced in the absence of that

particular source of error. In other words, the different thermopile voltage is how the error manifests itself.

Now suppose that we can devise an experiment in which one of the sources of error can be turned on and off while all other conditions within the radiometer are maintained identical to those existing during some particular irradiance measurement. Then the difference

between the thermopile voltages existing when the source of error is turned on and off will

be the error produced when the conditions of the particular irradiance measurement exist

within the radiometer. The negative of this difference is, therefore, the exact voltage
correction to be applied to the radiometer output in order to correct for that particular

source of error during the actual irradiance measurement.

We will attempt to devise such an experiment for each of the sources of error described

earlier. However, it is clear that we will not be able to make the conditions existing within the radiometer during each of these experiments identical to those existing during some specified irradiance measurement. But we will be able to make them similar in each case, and we will be able to establish limits on the systematic error introduced by our failure to

keep them identical.

In the following section, we will investigate from a theoretical point of view, the

responsivity as a function of position over the surface of a simplified model of a receiver.

This model most closely resembles the radiometers which have evolved at the National Bureau

of Standards during the period covered by this report. However, significant conclusions

about the radiometers of Guild [7], Gillham [8], Blevin and Brown [9], Bischoff [10] and

Kendall and Berdahl [ll] will be inferred from the results of this analysis. Sections k .2 and U.3 will describe correction factor experiments whose design is based on the results of

this analysis. Finally, section k.h will describe the experiments needed to determine the

rest of the correction factors for the sources of error identified in section 3.3.

k.l The Theory of the Responsivity of the Receiver

to Power Inputs from Various Locations

In this section we derive an equation which is simple enough to be solved analytically,

but which is at the same time general enough to accurately describe the important characteristics of the steady state operation of the receiver. The analytic techniques that we will

use include delta functions, the solution of inhomogeneous partial differential equations

with Greens functions, and special functions. These techniques will not be developed in

detail since they can be found in numerous mathematical texts.

An exploded view of the specific receiver configuration to be analyzed is shown in

figure 2. The radiant power is incident on the top of surface 1, the high absorptance

coating. It must be conducted through this coating and the insulating substrate before

reaching the receiver disk which acts as a thermal averaging device.

We will start with the equation [12] which describes the temperature distribution,

T (p, <)>, z), in the receiver disk. It is

k, V

2 T

d

1 9_

P 3p

9T_ 3pJ

1 9 2 T 9 2 T

+ — — + —

p 9t)> 9z

, :u

where k

d

is the thermal conductivity of the material in the disk. The coordinate system is shown in figure 3. Next we obtain a simpler equation for the average temperature distribution along the height of the disk, by integrating eq. (l) with respect to z. The average

temperature, U (p, <|>), is given by

U = — f

d T (p, $, z) dz. (2)

The result of this procedure is the equation,

Z d

k d

1 9_

p 9p

3U

9p

1_ 9jU

2 2

P 9<J>

+ k

9T

9z !3)
-f^Sc^c^y^

s _.-1

Figure 2. A specific receiver configuration for

theoretical analysis. 1 - high absorptance

coating, 2 - heater, 3 - electrically insulating heater substrate, h - high thermal

conductivity receiver disk, 5 - radial

thermopile to measure average temperature

difference between edge of receiver disk

and thermal environment.
Figure 3. Coordinate system used to analyze

the temperature distribution in

the receiver disk.

Now we assume that heat flows only in the z direction through the substrate and high

absorptance coating, or at least that any other heat flow is negligible. This is a good

assumption as long as the substrate and high absorptance coating are thin compared to their

own radii and the dimensions of the receiver disk, and as long as their thermal conductivity

is much less than that of the receiver disk. We further assume that the variation in

temperature in the z direction in the receiver disk is negligible in comparison with the

difference in temperature between the disk and its environment. In other words, T

(p , (J>, z) is approximated by U (p, <f>). This is a very good approximation because any

variation in temperature in the z direction which does exist is small. Moreover, it is

virtually independent of the mode of heating and therefore will cancel out when electrical

and radiant heating are compared. Applying the law of conservation of energy and these

two assumptions to the upper and lower surfaces of the receiver disk yields the following

boundary conditions:

kK -^

d 3z o-Vu - T

o

J ' :k)

and

9T

c d 3z

= -h (U - AT - Tj + E , z , c d

(5)

where

AT = U - T (6)

Here, h

Q is the heat transfer coefficient of the bottom surface of the receiver and h is

the heat transfer coefficient of the top surface of the high absorptance coating (surface 1 in figure 2). They are measures of the rate at which power is lost by these surfaces per

unit area and temperature difference between the surfaces and their environment [13]. The

product of a heat transfer coefficient and an area is a thermal conductance which is the

reciprocal of the thermal resistance. T„ is the temperature of the environment, and T

is the temperature of the top surface of the high absorptance coating, at the point, (p, <)>). Finally, E = E(p, <J>) is the power density input to the detector, an arbitrary function of

position. Now we must examine the cases of radiant and electrical heating separately.
The case of radiant heating: let AT and AT denote the temperature differences across the high ahsorptance coating (T - T ) and the substrate (U - T ), respectively. Thus

AT = AT + AT , c s (7)

Referring to figure k and making the same approximations which were made in order to derive

eqs. {k) and (5) , one obtains

(k /z )AT = h (U - AT - T.) - E , c c c c (8)

T.

T.

yz,

U receiver

Figure k. Network for analyzing one dimensional heat transfer

through the substrate and high absorptance coating

during radiant or electrical heating. T and T are the temperatures at the top of the high absorptance

coating and electrically insulating substrate,

respectively. U is the average temperature of the

receiver at the point (p, <)>). The arrow labled P

r represents the radiant power incident on the high

absorptance coating and the arrow labled P represents

the electrical power generated in the heater located

between the coating and the substrate. In the analysis,

E is used to represent the power density from either

P or P .

10
and

(k /z )AT = h (U - AT - T ) - E , (9)

where z /k and z /k are the thermal resistances per unit reciprocal area of the substrate

s s c c and the high ahsorptance coating, respectively. Now let

z/k = z /k + z /k

s s c c (10)

be the thermal resistance per unit reciprocal area of the substrate-coating combination.

Equations (8) and (9) can be combined to yield

AT(1 + zh

c /k) = z/k [h

c (U - T ) - e"| .

Substituting the expression for AT from eq. (ll) into eq. (5), and letting

k -l

Y = (l + zh /k)*

yields

3T

: d 3z -Y h (U - T ) + Y E.

(11)

(12)

(13)

Finally, substituting eqs. (h) and (13) into eq. (3) and letting

g

2 = ( Yh

c + h ) / z d

k

d

one obtains the approximate differential equation for the case of radiant heating,

UK

1 3_

P 3p

3U

3p + hH= g2 (u - T ° } - Y E/z

d

k

d

P 3<l>

(15)

The case of electrical heating: referring to figure h and making the same assumptions

mentioned in the discussion of the case of radiant heating, one obtains

(k /z \AT = h (U - AT - T

V C C I c c

u

an d

/k /z <iAT = h (U - AT - T ) - E . V S' S I s c

u

These can be combined to yield

AT = Y [(z/k)h

c (U - T ) - (Vk

s) F

]

•

Substituting this result into eq. (5) yields

3T

d 3z

= -y h (U - T ) + y (1 + h z /k ) E

C C C' c

(8a)

(9a)

Ilia)

(13a)

Repeating the remaining steps as in the discussion of the case of radiant heating, one obtains

1 3 3U 1 3 ZU

2 2 = g2 (U ~ To) "

Y ( 1 + h

c

Z c/k

c

) E/Z

d

k

d ' P 3<t> P 3p \ 3p,

as the approximate differential equation for the case of electrical heating.

(15a)

11
Next make the substitution,

V = U - T

in "both eqs. (15) and (15a) , to obtain equations of the form,

1 3_ 9V"

P 9p '3P + ~^|-g2 V = -Q(p, *)

P 3<f> for <_ p <_ p and <_ <j) <_ 2tt, where

Q(p, if.) = y«-E(p, <f>) / z d

k

d

where i = 1 in the case of radiant heating, and

(16)

(IT)

(18)

(19)

1 = i 1 + h

c VkJ (20)

in the case of electrical heating. It can be verified that the Green's function [ik] for

eq. (IT) is

CO CO G (P. t; P . * ) " E E A

mn

Im

(gp) I (gp ) e i(m

* + n

*o)

CO

(21)

m = _ 00 n

- k Ko{g[p2 + P

° 2 " 2PP

° C °S ^"Op

where the A are determined by the boundary conditions and where I and K are the modified

Bessel functions of order n. Physically, the Green's function describes the response at the

point (p, <(>) due to a unit point source at (p , <f> ). A useful property of the Green's

function is that

V(p, <j>)

P, 2tt -/ /« , = <J>„ =

Q(p n

, O G(p, <j>; p a) p. dp '0' "0 0' *0' M "^0 (22)

P =

For a receiver with a radial thermopile, the boundary condition for the Green's

function is

k

d 9^

g (p^;p '*o ) = -h

a

(<j>) G(p 19 <();p g) <J) ) , (23)

where hj (<j>) is the heat transfer coefficient of the edge of the disk as a function of

location. It is the sum of contributions from conduction down the thermopile legs, convection, and radiation. For simplicity and because of the high thermal conductivity of the

receiver disk assume that h, (<j>) is independent of 4>. Under this assumption it is convenient to define an averaged Green's function as

G ( p l> p o' *o) = / G(P 15 <t>; P , <L) d<j> /<j) =

(2k)

Substituting eq. (21) into eq. (2k) and carrying out the indicated integrations [15] yields

CO G(P 15 P , * ) = E 2 ^ A

o n

T ( gp

l

} Xn

(gp } ein<f>

° "K isP l

] T igp ] ' (25)

12
where the A are still to he determined hy the boundary condition [eq. (23)] which reduces

to ° n

k . 8 5( Pl> p ' *o ) d

3p

x = -hj G( Pl , p

Q

, *

Q

) . (26)

This requires that A =0 for n 4 0, and

[e k ( gPl ) - Kj (gpj)]

2 " A

°o =

[? i (gPl ) ? Ij (gPl )-] ' (2T)

where

% = hj/gkj . (28)

Combining the above results and making use of the Wronskian relations among Bessell

functions Il6], results in

- T

o

( sp ) G(p

i> p o> *o } = —

;—;—

100 (29)

gPl [? I ( gPl ) + Ij ( gPl )) The voltage across the radial thermopile is given by

2tt v = / WU) V( Pl , $) d* , (30)

<f> =

where W(<J>) is the sensitivity (per unit angle) of the thermopile as a function of position

around the edge of the receiver. Now, assuming that W(<)>) is independent of <|>, and combining

eqs. (22), (2k), (29), and (30) yields

v = —

gP jHo Zo]) + h ( gPl )j y

X

o <«>o> Q<Po> Po^o > (3D

P = where

2ir

Q(Pn) '.>-fc = ^T // Q(Pn» O dPn (32) 0' Y

o K

o *0

=

°

Now we will use this result to calculate the ratio of the thermopile voltages obtained

when a quantity of radiant power is absorbed by the receiver and when the same quantity of

electric power is absorbed. Let the radiant power density and electrical power density

distributions be given by

E

r

(P 0> o) = P f

r

(p 0> *0 }

'

( 33)

and

E

e

(p 0' *„> " P

o f

e

( P » V ' C3U)

respectively, where f and f have the dimensions of reciprocal area and P is a quantity

of power. Both f ana f are defined to satisfy the relation,

13
2w p

x / /

'0 = °

P = °

f(p

Q

, +0 ) p d p

Q d t = 1 . (35!

Combining eqs. (33) and ( 3M with eqs. (l8) , (31)

(32) , and letting v and v denote the

thermopile voltages for the cases of radiant and electrical heating respectively, results

in the expression,

Pi 2tt J

I„ (8P ) J

fr

(P « V d*0 PO dP

p = * =

P

1 2tt (36)

(l+h

c

Z c/

k

c

) /

I (gP ) / f

e

(p 0' V d

*0 P <*(

p = d, =

First notice that the error arising from the fact that the radiant power and electrical

power are each absorbed in different parts of the receiver depends only upon two parameters

of the radiometer, g and h z /k . Furthermore, eq. (36) can be interpreted to mean that

this source of error can be factored into two separate effects. The first of these will be

called the relative responsivity effect , since it is described by I (gp ). The second effect

is the increase in the emission of radiation during radiant heating°over that during electrical heating due to the different temperature distributions that exist in the high absorptance coating during these two modes of heating. This will be called the excess emittance

effect. It is described by (l + z h /k ) _1. c c c The above results suggest that it may be worth-while to measure the excess emittance

and relative responsivity errors in separate experiments. Indeed this is the case. Moreover, it turns out to be highly desirable to measure the excess emittance error and the error caused by the non-zero reflectance of the high absorptance coating in the same experiment , since it is very difficult to distinguish between the powers reflected from and

emitted by the coating. Both of these power loss mechanisms affect the error in the same

way. These points will be discussed in more detail when the experiment to measure the

absorptance of the receiver is described.

Now we turn our attention to the theory of the measurement of the relative responsivity

of the receiver. Ideally this will be measured by observing the variations in thermopile

output as a point power source is applied at different locations on the receiver surface.

Thus to describe a point source power input let

P 6(p - p

Q

) 6(t|> - <|> ) E(p

Q

, <j, ) = P S(p - p ) = H (3T)

M o

where Pq is a quantity of power, and 6 is the Dirac delta distribution function. Combining

eq. (37) with eqs. (l8), (3l), and (32) results in an expression for the responsivity as a function of position on the receiver,

v

W y* Io (gP)

P^

=

gp

1 z d

k

d

[i I

Q (gPl ) + i

:

( gPl )j (38)

According to this equation, the variation in responsivity of the receiver is governed by

the variations of the modified Bessel function, I (gp). The variations of this function are small only when gp«l: a condition satisfied by a good (useful) radiometer. We can, therefore, substitute the series expansions of Iq and Ij into eq. (38) and drop terms of order

(gp) 3 and higher. The responsivity is then given by

F(p)=

W

li (1 + g2 p2A)

(39)

P

a z d

hj (1 + g

2 Pl

2 /U ) +V2

P

x

2 (y h

c + h

Q

)

Ik
In order to discuss the physical interpretation of this equation we will rewrite it in

the form,

F(p) = 2w WR (p) / (H

1 + H

c + H

Q

) (1*0) where

r (p) = l + g

2

P

2 A , (Ui)

H

1 = 2tt Pi z d

hj R (p

x

) / ySL (1+2)

H

c = tt Pl

2 h

c /£ , (1+3)

H =

^Pi

2 h / ^ Jl

• ( ^)

Recall that W is the thermopile sensitivity at the edge of the disk and notice that R(p)

describes the relative responsivity of different locations on the surface of the receiver

if the entire receiver is geometrically perfect and if its thermal parameters are independent of location. H, , H , and H. can he interpreted as the thermal conductances from

the edge, top and bottom surfaces of the receiver disk to its thermal environment, respectively. For instance, consider H . Here 2-irp^z is the area of the edge of the disk, h. is

the heat transfer coefficient from the edge of the disk, to the thermal environment of the

disk, and R(p

1 )/y)l is a correction factor.

It was assumed in the derivation of eq. (38) that the receiver is geometrically perfect

and that its thermal parameters are independent of position, hut in actual fact these

parameters will vary with location in some unknown manner due to imperfections in materials

and fabrication techniques. It is to be expected that z , z , and the thermal resistances

of the joints where the thermopile junctions are attached to the receiver and its thermal

environment will be subject to the largest variations. The differential change in y,H,

and g due to differential changes in z and z are given by

dY

= -h y

2 (dz /k + dz /k ) (1+5) c s s c c

d(g2

) = h

Q dY /z d

k

d

(1+6)

&l = (1+7)

in the case of radiant heating, and

ai = h dz /k (1+8) c c c

in the case of electrical heating.

Notice that each of these is proportional to h c

. This fact will be significant later when

we discuss cavity type receivers. Right now, however, we will pursue the analysis assuming that all of the geometric and thermal parameters of the receiver are independent of

location on the receiver. Results obtained from this analysis will provide significant

physical insight, and the amount by which the predictions of the analysis differ from

experimental results is a measure of the variation of these parameters.

Equation (1+0) could have been written down without solving the differential equation

of heat conduction; however, the exact form of eqs. ( Ul ) , (1+2), (1+3), and (UU) can only be

obtained from the solution to the differential equation for a specific receiver geometry.

Now it is of interest to examine the order of magnitude of the various parameters in

eq. (1+0). This will be done for the receiver configuration used to test the responsivity

15
to electrical heating. This receiver, shown in figure 5» is very similar to a receiver

configuration described by Gillham 18] and later by Blevin and Brown 19]. Here z =0.1 cm,

Figure 5- The receiver configuration used to examine the

magnitude of the various parameters in eq. (Uo).

1 - receiver disk, 2 - radial thermopile, 3 - thermal

environment of receiver.

p = 0.5 cm, and the top and bottom surfaces of the receiver are 0.3 cm and 0.5 cm from the

thermal environment of the receiver, respectively. H, , Hq , and H each have contributions

from thermal radiation, air conduction and air convection. Hj also has a contribution from

conduction across thermopile legs, and heater leads. If the top and bottom surfaces of the

receiver, as well as the thermal environment of the receiver are nearly black to infrared

radiation,

h - k a T

3

, >9)

where T is the absolute temperature of some point on the receiver, and a is the Stefan - Boltzmann constant. Thus (assuming that y and I are not much different from one) the

thermal radiation contribution to h and ho is on the order of 0.6 mw/cm°C, so that the

thermal radiation contribution to H and Hq is on the order of 0.5 mw/°C. Empirical

formulae which describe the contribution of air conduction and convection to H and Hq do

exist, but to apply them to this small geometry would be equivalent to extrapolating various

experimental data parameters over many orders of magnitude. It is better instead to measure

the responsivity of this receiver in air and in vacuum to determine the magnitude of the

contribution of air conduction and convection to Hj, H , and Hq.

In order to analyze this experiment, we will rewrite eq. (kO) to distinguish not between

the thermal conductances of the top, bottom and edge of the receiver but between the modes

of heat transfer which exist in vacuum and those which require air to exist. Let H denote

the thermal conductance between the receiver and its environment in vacuum, and let H. denote the thermal conductance between the receiver and its environment due to air conduction and convection. Thus

Fy

= 2^ V R/H

y

(50)

and

FA

= 2* W R/d^ + HA

) (51)

where F and F are the responsivities to power applied at some point on the receiver in vacuum and air respectively, and where R is the relative responsivity at that point. Eliminating H between these equations yields,

HA

= 2* W R A

(52)

The receiver on which the measurements were made had a 20 junction copper-constantan

(~l+0uv/°C) electroplated, radial thermopile, so 2^ W 800 yv/°C.

0.0195 v/w and F was measured to be 0.0214 7 v/w, so H vection contributes approximately 10 mw/cm 2 °C to y h^ + ho

16

F„ was measured to

- 8 mw/°C and air conduction and con-
Adding the contributions from radiation to that of air conduction and convection we

obtain a value of approximately 11 raw/cm2 °C for y h + hp. From this result and the fact

that the receiver disk was aluminum (k = 2 w/cm °C) we calculate that g = 0.056/cm2 for

this configuration. Thus if all of the geometric and thermal parameters of the receiver

are independent of location on the receiver, the percentage difference between the responsivities at the edge and center of the receiver should be g

2

p 2 A - 0.35$-

Now we will discuss some experimental data on the uniformity of responsivity of absolute

radiometer receivers in light of the above analysis. Gillham [8] and Blevin and Brown [9J

have described absolute radiometers with a receiver configuration similar to that which we

have analyzed in detail. There are, however, three important differences in design. The

first is that their aluminum receiver disks are only one half as thick as the receiver disk

which we analyzed. Reference to eq. (ik) shows that this difference would be expected to

double g and hence to double the maximum percentage difference in responsivity. The

second difference is that the distance between the thermal environment and the top and

bottom surfaces of their receivers are more than double those in the receiver which we investigated. Since air conduction makes by far the largest contribution to h and ho , this

difference should reduce g by a factor of two. Thus the first two differences approximately cancel. The third difference is that Gillham and Blevin and Brown employed a thermopile whose 28 junctions were distributed approximately uniformly over the bottom surface of

the receiver instead of a 20 junction radial thermopile. This difference should cause a significant decrease in the maximum difference in responsivity of 0.35% which we calculated,

yet Gillham and Blevin and Brown report measuring a maximum variation in responsivity of 1%.

The above mentioned discrepancy between the predicted and measured maximum difference in

uniformity in the radiometers of Gillham and Blevin and Brown, is probably due to the fact

that some of the assumptions we made in deriving eq. (38) do not apply for their radiometers.

As mentioned earlier, it is likely that the thermal resistances of the high absorptance

coating, the substrate, and the joints where the thermocouple junctions are attached to the

receiver and its thermal environment all vary with position over the receiver, due to variations in the thickness of the adhesive joints and coatings. The relative importance of

these various components in increasing the non-uniformity of responsivity of the receiver

cannot be estimated from the limited data which has been disclosed by the various authors.

In order to perform better than ± 0.5$ accuracy irradiance measurements with a radiometer whose receiver is non-uniform in responsivity to 1% , it is necessary that the electrical and radiant power distributions be almost identical over the surface of the receiver.

This requirement severely limits the types of radiant source and viewing geometries which

the radiometer can accommodate. This in turn makes intercomparisons of different irradiance

scales and radiant power scales difficult, if not impossible, since most of these scales

are realized with considerably different source and viewing geometries. For instance, the

laser power scales require that the receiver aperture not be irradiated at all.

As an example of the importance of having a highly uniform responsivity over the

receiver, consider the measurement of the Stefan - Boltzmann constant reported by Blevin

and Brown [7]- Of the twelve sources of error which they considered, the four largest

uncertainties arose from the uncertainty in the thermodynamic temperature scale, the uncertainty in the calibration of the thermocouple, the uncertainty in the effect of diffraction,

and the uncertainty in the effect of the non-uniformity of responsivity of the receiver,

contributing uncertainties to the final result of 0.06$, 0.06$, 0.06$, and 0.05$, respectively. The first three of these corrections are source related, that is, they are uncertainties associated with the irradiance produced by the source at some point in space, and

not with the way that the radiometer measures irradiance. Thus the largest radiometer

related uncertainty in the measurement of the Stefan-Bo It zmann constant was caused by the

non-uniformity of responsivity of the receiver, even though the radiant and electrical

power distributions were made as similar as possible under the constraints imposed by the

radiometer design. This is seen to be even more significant when one realizes that the source related uncertainties do not contribute at all to other irradiance measurements,

such as comparing two lamps or calibrating other detectors.

Finally, let us consider the uniformity of responsivity of a cavity type receiver. The

receiver we have been discussing can be made into a cavity type receiver by affixing a top

IT
to it as shown in figure 6. A top whose thermal properties are similar to those of the disk

will be approximately isothermal, so as a first approximation h will he reduced by the con- figuration factor from the disk to the cavity opening which is typically on the order of

0.1. This means that g

2

, and hence the contribution to the non-uniformity in responsivity

described by fi (p), can be reduced by almost a factor of two by incorporating the receiver

s

TS

Figure 6. Cavity receiver made from the type of receiver

that was analyzed theoretically in section k.l.

The upper cavity, 1, can be formed by drawing

silver sheet, and it can be affixed to the

receiver disk, 2, with a high thermal conductivity

adhesive.

into a cavity configuration. However, we have shown that all of the contributions to the

non-uniformity of responsivity of the receiver which arise from variations in z and z are proportional to h . Thus these contributions to the non-uniformity of responsivity of the

receiver can be reduced by a factor equal to the configuration factor (O.l). It is harder

to determine the effect of decreasing h on the contribution to the non-uniformity of the

receiver due to variations in the thermal resistances of the joints where the thermopile

junctions are attached to the receiver and its thermal environment. However as a first

approximation, for a radial thermopile the decrease in non-uniformity would be proportional

to the decrease in yh + ho , while for a thermopile whose junctions were distributed

approximately uniformly over the bottom surface of the receiver, the decrease in non- uniformity would be proportional to the decrease in yh + h^.

From the discussion presented here, it should be clear that one of the more important

design criteria for an absolute radiometer is a highly uniform receiver. A considerable

amount of effort in the current program has been directed toward solving this problem.

Now let us turn our attention to the theory of the measurement of the corrections for

the various sources of error affecting the detector. Let v be the thermopile voltage that

is measured during radiant heating, then from conservation of energy the equation describing

v can be written as

r

= S (P - Z P

r r r

- 6 P ) r r S'P'

r r

(53)

Here S is the average responsivity of the receiver to the quantity of radiant power, P , that enters the detector aperture and is incident on the receiver, and S' is the average

responsivity of the receiver to the radiant power, P' , that does not enter the aperture but

is incident on the detector case. The fraction of P that leaves the front surface of the

receiver as radiant power is Z and the fraction of P lost through all other mechanisms

except conduction down the thermopile or radiation from the front surface of the receiver

18
A similar equation can be written for the thermopile voltage, v , measured during a period of electrical heating:

v = S (P - £ P -6P) + S'P' . (5I+) e ee ee ee ee w '

All of the terms in this equation are the electrical heating and loss equivalents of the

radiant heating and loss terms in eq. (53) except for S', which is the average responsivity

of the receiver to the electrical power, P' , that is generated in the heater leads during

electrical heating.

If vreand v are made equal during the measurement, then

P = PS (1 - 5 - 6 )/S (1 - ? - 6 ) + (S'P' - S'P')/S (1-5 - <5 ) ,„x r e e e e r r r e e r r r r r (55)

which can he expanded in a binomial series to yield

P =P + P (? - ? ) + P (6 - 6 ) r e e r e e r e (56)

+ Pee(s - s )/s + s'p'/s - s'p'/s

r r eer rrr +

The second term on the right-hand side of eq. (56) is the correction for the non-zero

reflectance and non-zero thermal resistance of the coating of the receiver. The third

term on the right-hand side of eq. (56) is the correction for other non-equivalent heat

transfer mechanisms from the top surface of the receiver to its thermal environment, i.e.,

air conduction and convection. The fourth term is the correction for the variations in

responsivity over the surface of the receiver that was discussed previously. The fifth

term is the correction for lead heating during periods of electrical heating of the

receiver, and the sixth term is the correction for the heating of the detector case by the

radiation that does not enter the aperture during radiant heating. The higher order terms

which have been omitted are interaction terms which in the case of well designed cavity

receivers are smaller than 10 , and the modifications of the theory necessary to take them

into account are trivial.

By dividing eq. (53) by eq. (5^)> setting P = P and assuming that S'P' and S'P 1 are negligible, we obtain an expression for v /v which by comparison with eq. \36) (and under

the same simplifying assumptions that were made in deriving eq. (36*) yields

(1 - 5e- 0/(l - Cr

- 6r

) = (1 + Vc /k

c

) • (5T)

where h , z and k have been defined previously. Recall that h includes contributions

c c c c both from air conduction and from radiation.

Equation (57) provides an estimate of the magnitude of the excess emittance error due

to the different temperature distributions existing in the high absorptance coating during

the periods of radiant and electrical heating. Such an estimate is useful when evaluating

proposed detector designs. Experimental techniques for determining corrections with reliable uncertainties for both the radiation and the air conduction contributions to the excess emittance error are described in sections U.3 and UJi.

•This includes an implicit assumption that the high absorptance coating has zero reflectance.

19
k.2 Techniques for Measuring the Variation in Responsivity

Over the Surface of the Receiver Disk.

In this section we will discuss two measurements which can be performed to determine

the responsivity as a function of position over the surface of the receiver disk. Ideally,

this measurement would he performed by introducing a fixed quantity of power into different

portions of the receiver, and recording the thermopile output voltage for each of the positions. An approximation to this idealization which is readily realized is to irradiate the

high absorptance coating of the receiver with the image of an aperture which itself is

irradiated by the image of the filament of a lamp, as shown in figure 7- However, there are some problems with this technique. The first problem is that we are not measuring just the

variations in responsivity of the receiver disk, but instead we are measuring some combination of the desired quantity and the variations in reflectance and thermal resistance of

the high absorptance coating. The second problem is that it is very difficult to irradiate

much of the interior of the cavity, and even more difficult to know exactly what location on

the interior surface is actually being irradiated. The third problem concerns the quality

of the image with which the receiver is irradiated. It is possible that the area around the

image will not be of negligible irradiance compared to the image itself, due to scattering

and/or aberrations in the imaging optics. Thus in order to obtain reliable results by this

technique it is necessary to map out the irradiance as a function of position in the image

plane, and if the irradiance in the area around the image is not negligible, to apply correc- tions for it.

The consequences of measuring the responsivity as a function of position by this technique

without knowing the irradiance distribution in the image plane can be more serious in the

case of the detector we have developed, than in the case of the detectors of Gillham [8],

Blevin and Brown [9, 17] » and Bischoff [lO].t Since the detector developed on this project

has a radial thermopile, it has a higher responsivity at the edge than at the center of the

receiver disk. Thus if the irradiance around the image decreases with increasing distance

from the image at just the right rate, the decreased power incident on the receiver when

the image falls near the edge of the receiver would just compensate for the increased

responsivity of the edge of the receiver and the output voltage of the detector would be

independent of the location on the receiver upon which the image falls. This would result

in an underestimate of the maximum variation in responsivity over the receiver, and more seriously, an underestimate of the uncertainty in irradiance measurements due to this source

of error. However, the detectors of Gillham, Blevin and Brown, and Bischoff have receivers

whose responsivities decrease near the edge of the receiver. Consequently, the two effects

described above would add in this case, and the maximum variation in responsivity over the

receiver would be overestimated. Since all of these authors use this measured maximum

variation in responsivity to calculate an uncertainty due to this source of error, they

obtain, at worst, an overly conservative limit of error. However, if they were to apply

corrections based upon the receiver responsivity distribution measurements in the absence

of image plane irradiance distribution measurements, it is clear that they would underestimate

the limit of error associated with this source of error.

There is a second technique, which while not ideal, does have some advantages. It is

to put two heaters at different locations on the receiver disk (under the high absorptance

coating) , and to compare the thermopile outputs with the same quantity of power being dissipated in one heater or in the other. Modern materials advances make this technique more practical than in the past. Wow the heater and leads need not be wire coils and/or evaporated

metal films. Instead, silver or graphite filled enamels can be used. These have the

advantage that they can be quickly applied like paints, and that they can be quickly removed

with solvents. The silver filled materials yield resistances on the order of 10 -2 ohms per

square, which are handy for heater leads. The graphite filled materials can yield resistances

greater than lO 4 ohms per square which are ideal for small area heaters. This technique

shows promise in reducing the first and third problem mentioned above.

tStrictly speaking these comments apply only to non-cavity receivers,

20
Figure , xz2 - ptaTe

^^^^^-^^

mirror, 3 - lenses, k - aperture in opaque

screen, 5 - radiometer, 6 - indexing table.

21
k.3 Techniques for Measuring the Non-Equivalent Heat Losses from the

Receiver due to the Emission and Reflection of Electromagnetic

Radiation

In this section we will describe a very versatile technique which is a combination and

extension of two previously described techniques {l8, 19], and which can be used to determine a single correction for the cumulative effect of two different sources of error. The

first source of error is the imperfect absorption of radiant flux by the receiver due to the non-zero reflectance of the high absorptance material with which it is coated. The second

source of error is the emission of more flux when the receiver is heated radiantly than

when it is heated electrically due to the non-zero thermal resistance of the high absorptance

material with which it is coated. The theory of these sources of error has been investigated

in section k.l.

The second term on the right hand side of eq. (56), P (

t, - ? ),is the correction for

the cumulative effect of these two sources of error. Figure 8 is a diagram of the type of

apparatus which can be used to determine £ and t, . The flux from a tungsten strip lamp is

focused on an aperture. The flux passing through the aperture is in turn focused through

the hole in the hemispherical mirror onto the receiver of an electrically calibrated detector.

The hemispherical mirror can be rotated to reflect the flux which leaves the front surface

of the receiver either back onto the receiver or onto a portion of the thermal environment

of the receiver which has been coated with a high absorptance material. A shutter located

in the plane of the aperture is synchronized with a switch in the electrical heater circuit

so that the receiver is heated radiantly when the shutter is open and electrically when it

is closed.

The spherical aberation of the hemispherical mirror place some restrictions on the type

of receivers that can be accomodated by this type of apparatus. The receiver must be large

enough to intercept all of the flux that has passed through the hole in the hemispherical

mirror, and been reflected back toward the receiver. Blevin has mentioned this point. In the case of a cavity type receiver, reflected flux can leave the receiver from any point in

the plane of the cavity opening. Thus the image of the aperture must be smaller than the

cavity opening, and the cavity opening must be surrounded by a flat annular region that is

coated with a high absorptance material.

The apparatus has four distinct states. If the shutter is open and the hemispherical

mirror is so oriented that the flux leaving the front surface of the receiver is reflected

onto the thermal environment of the receiver, the thermopile output is given by

A =SP (1-5 - 6

)'.'+ e' (58) r r r r r r

where e' is an offset voltage (note that the case heating effect is not present). Now if

the mirror is rotated so that the flux leaving the front surface of the receiver is reflected

back onto the receiver, the thermopile output is

Brrr =SP (1-5rr-6)+S?Prrr (1 - c rr- 6 ) + e' . (59)

r

assuming spherical mirror reflectance is unity. When the shutter is closed (electric

heater on) and the hemispherical mirror is so oriented that the flux leaving the front

surface of the receiver is reflected onto the thermal environment of the receiver, the

thermopile output is given by

A =SP (1 - 5 - 6 ) + e , (60)

e e e e e e

'

where the offset voltage e includes the voltage generated by the power dissipated in the

heater leads (S'P' in section U.l).

e e When the mirror is rotated so that the flux leaving the front surface of the receiver

is reflected back onto the receiver, the thermopile output is

Beee =S P (l - 5 ee- 6 ) + S eeet, P (1 - ? rr- 6 ) + e . (6l)

e

22
2^ Lnses, 3 - aperture in opaque screen, U - hemispherical

mirror 5 - thermal environment of receiver, 6 -cavity

feceiver! Notice that to avoid chromatic aberations the lens

between the screen and the hemispherical mirror should be

replaced by a reflectance focusing element.

23
Thus

C = (B - A )/(A - e

1 ) (62) r r r r r

'

and

E /(l - E - 6 ) = (B - A )/( A - e Hi - E - 6 ) . (63)

e e e e e' ' e e rr

Once 6 and 6 e are known, E e can be obtained. We discuss techniques for measuring 6 and

6 e in the next section.

k.k Techniques for Measuring the Non-Equivalent Heat

Loss from the Receiver due to Air Conduction and

Convection

In this section we will describe a technique which can be used to determine a correction

for the non-equivalent heat loss from the receiver due to air conduction and convection.

The third term on the right-hand side of eq. (56), P (6 r

- <5 ) , is the correction for this source of error. Figure 9 is a diagram of the type of apparatus which can be used to

determine 6 r and 6 . The flux from a tungsten strip lamp is focused on an aperture. The

flux passing through the aperture is in turn focused through the window in an evacuable

chamber onto the receiver of an electrically calibrated radiometer. It is essential for

this measurement that the lamp be stable in radiance over fairly extended periods of time,

whereas, this was not a requirement for the measurement described in the preceding section.

Furthermore, it is necessary that the receiver have the same thermal environment during

this measurement as it had during the measurement described in the preceding section. If

this is the case, then when the chamber is at ambient pressure, the thermopile output

voltage during radiant heating will be given by

C=SP(l-£-6)+e, (6k)

r r r r r r

where the offset voltage e includes the case heating effect. The thermopile output voltage during electrical heating will be given by

C =S P (l - E - 6 ) + e . (65)

e e e e e e

However, when the chamber is evacuated, the thermopile output voltage during radiant

heating will be given by

D=SP(l-?)+e, (66)

r r r r r and the thermopile output voltage during electrical heating will be given by

D =S P (l - E ) + e . (67)

e e e e e

Thus

6 = (i _ c )( D - C )/(D - e ) , (68) r r r r r r and

6/(1-5 - 6 ) = (D - C )/(C - e ) . (69)

e e e e e e e

Notice that E r was already expressed in terms of measurable quantities in eq. (62) so 6 r can be calculated. However, in order to express 6 e in terms of measurable quantities, it

is necessary to solve eqs. (63) and (69) simultaneously. The result is

C e = E/(l + E + F) , (TO)

2k
Figure 9. Apparatus for measuring the non-equivalent

heat loss from the receiver due to air

conduction and convection. 1 - detector

2 - evacuable bell jar, 3 - lenses,

k - aperture in opaque screen, 5 - tungsten

strip filament lamp.

25
and

6 e = F/(l + E + F) ,

( T1 )

where

F = (D - C )/(C - e ) , ( T2 )

and

E = (B

e - Ae )/(A

e - e e )(l - ?r

- S^ . ( T3 )

h.3 Techniques for Measuring Corrections for the

Remaining Sources of Error

The two remaining sources of error that will be considered in this section are the

power dissipated in the heater leads, and the radiant flux incident on the thermal environment of the receiver. Both of these sources of error are basically different from the

sources of error discussed in sections k.2, k.3, and k.k. Those sources of error can be

characterized as imperfect absorption and sensing by the receiver of the power that it is

supposed to sense; whereas, the two sources of error discussed here can be characterized as a sensing by the receiver of power that it is not supposed to sense.

Gillham [20] has devised the lead configuration shown in figure 10, in order to measure

the lead heating correction. During a period of electrical heating the circuitry external

to the heater leads is arranged so that equal currents, of magnitude 1/2, flow into the

heater through leads 1 and 3, and out of the heater through leads k and 6, while the voltage across the heater is measured between leads 2 and 5. Letting S' be the responsivity of

the receiver to the power, P* , generated in the heater leads, the voltage across the thermopile during this period is given by

G = S p (1 - e - 6 ) + S' P

1 . e e e e e

( 7 M e e (TtJ

To measure the lead heating correction, the external circuitry is rearranged so that a current of magnitude 1/2 flows from lead 1 to lead 3, and from lead h to lead 6, while

maintaining zero voltage between leads 2 and 5- Then the detector is irradiated so that

the voltage across the thermopile,

G' = S P (1 -

r

? - 6 ) + S' P' (75) r ^r r e e ^ t:"

is just equal to G . Then the external circuit is open so that the current ceases to flow

in leads 1, 3, h, and 6. Now the thermopile output voltage is given by

G

r

= S r P

r

(l " ? r " V C?6)

Thus the voltage error during the period of electrical heating is G' - G . The reason for

irradiating the detector during this measurement is to eliminate any error arising from nonlinearity in S '

In order to measure the error caused by the radiant flux incident on the thermal environment of the receiver, Gillham [2l] built a heater onto the front of his radiometer. A problem with this technique is that it is difficult to get the power distributions under radiant

and electrical heating to be the same in the vicinity of the aperture. An alternate approach

is to build a "dummy" aperture holder identical to the aperture holder in every way except

that it has no aperture. Then the receiver can be alternately shuttered from and exposed

to the radiation from the lamp. However since there is no aperture, none of the radiation

from the lamp can be incident on the receiver. Thus any change in thermopile voltage is

26
Figure 10. Heater lead configuration for measuring the effect of

lead heating. 1, 3, h, and 6 - current leads, 2 and

5 - voltage leads, 7 - heater.

due to heating of the thermal environment of the receiver including the aperture holder.

This experiment is the exact compliment of the technique described for measuring the lead

heating error. If H is used to represent the thermopile voltage output during these

measurements, and if P

1 and S' represent the power supplied to the thermal environment of

the receiver, and the responsivity of the receiver to that power respectively, then all of

the equations describing this measurement can be obtained from eqs . (7*0 5 (75), and (76)

by substituting H for G, r for e, and e for r at every occurrence.

5. Electrically Calibrated Radiometer #10 and the Third Inter- national Pyrheliometer Comparisons

In this section we will describe Electrically Calibrated Radiometer (ECR) #10. The

design of this radiometer differs in some important respects from the final design which

evolved during this project, and the radiometer is no longer functioning. However, since

it did participate in the Third International Pyrheliometer Comparisons at Davos, Switzerland

in September of 1970 (IPC 1970) [22], its construction, design, and testing, as well as the results obtained during IPC 1970 are of more than passing interest.

For the most part ECR #10 was built and tested in accordance with the principles described in the preceding sections of this report. Construction of the radiometer is described

in section 5-1, measurements of correctors for the various systematic errors affecting the

radiometer are described in section 5-2, and the measurements performed during IPC 1970 are described in section 5-3.

5.1 Construction of the Radiometer

Figure 11 is a cross sectional view of ECR #10. The water cooled heat shield was con- structed from two pieces of copper plate and soldered together. A cross section through

the solder joint is shown in figure 12. A top view of the main chassis is shown in figure

13. The aperture insert shown in figure 1**, was eloxed from hardened steel, and the edge

of the aperture itself was ground. The resulting hole was traced on a Talyrond [23] and

found to be circular to within ±20 u inches. The average diameter of the hole was measured

to be 0.10296" with a ±0.00003" limit of error. Referring back to figure 11, the aperture

27
Figure 11. Cross section of ECR #10 (Full Scale). 1 - watercooled heat shield, 2 - heat shield support, 3 - aperture insert holder, h - main chassis, 5 - back

plate, 6 - receiver assembly, 7 - thermopile leads,

8 - heater leads, 9 - aperture insert.

Figure 12. Cross section through solder joint of water- cooled heat shield (Full Scale).

28
f

1

...

4 f O J ) A^

3

Figure 13. Top view of main chassis. 1 - recess for heat shield

support, 2 - recess for receiver assembly, 3 - access for thermopile leads , h - access for heater leads

(Full Scale).

L_ ; \\

\\

X \\

Figure lU. Magnified view of the aperture insert. 1 - aperture,

x - 0.006 inches. The dotted line shows the relation

of the aperture to the water-cooled heat shield.

29
2 essss^

n

3 CZZZZZZ3 E Z Z Z Z ^

Figure 15. Exploded view of the receiver assembly. 1 - upper

cavity, 2 - receiver disk, 3 - thermopile cold

junction support, h - thermopile (rotated through $ for better view).

Figure l6. Isometric view of edge of thermopile jig

- 1, showing wire - 2 being sewn through

holes in jig.

30
insert holder (3) and the receiver assembly (6) are attached to the main chassis (h) with

silver filled silicon rubber adhesive in order to assure good thermal contact, while still

permitting the parts to be disassembled if necessary.

Figure 15 is an exploded view of the receiver assembly, which consists of the receiver

disk, the cold junction support, the radial thermopile, and the upper cavity. The radial

thermopile was made by electrodepositing copper on constantan wire. The theory of such

thermopiles is well known [2k] , but considerable difficulty was encountered in attaching

these thermopiles to the receiver disk and the cold junction support, both of which were

made of anodized aluminum. The general plan of construction was as follows.

A 5 mil diameter constantan wire was sewn through holes drilled in a 1 mm thick jig as shown in figure l6 (materials from which jig was made will be discussed below). One side

of the jig was then coated with a suitable lacquer to prevent any copper from being plated

on the wire which was on that side of the jig. The jig was then placed in a solution of

copper sulfate and sulfuric acid in water, and the wire on the uncoated side of the jig was

electroplated. After plating was complete, an adhesive was applied to the thermopile in

the region where it would contact the receiver disk, and the thermopile-jig combination was clamped to the disk until the adhesive had hardened. Then the jig was removed by melting

or dissolving it in a suitable solvent.

One of the problems encountered was that the bond between the adhesive and the disk was attacked by many of the solvents which were tried. Part of this problem was that the disk

was made of anodized aluminum in order to allow good thermal contact between it and the pile

without it shorting electrically. Many adhesives do not bond well to anodized aluminum.

Another contributing factor was that the adhesive layer was quite thin and its edges were unprotected from the solvent.

A number of different adhesives were tried including epoxy , cellulose acetate dissolved

in acetone, shellac dissolved in ethyl alcohol, and sodium silicate cement. Among the

different jig material-solvent combinations that were tried were polystyrene-benzene,

cellulose acetate-acetone and ethyl cellulose-ethyl alcohol. Attempts were made to construct

the Jig of materials which melt at low temperatures without swelling. Rosin and a number

of waxes were tried alone and in combinations. The problem here was that the Jig would

either be too brittle for drilling or too soft to keep the wires from cutting through it.

Only two techniques which were considered suitable resulted from this work. In the

first of these techniques calcium carbonate was suspended in a sodium silicate solution and

used as an adhesive. The jig was made of polystyrene, and was dissolved away in benzene with

no noticeable effect on the silicate adhesive. It is difficult to get this adhesive to wet

the thermocouple leads, but it can be done. In the other technique, dental molding compound

was cast in an aluminum ring. By itself the molding compound was too brittle to be useful,

but held in compression by the ring it could be drilled with no fear of breakage. Epoxy was used as an adhesive. The molding compound was removed by immersion in molten beeswax. The

temperature of the beeswax is important. Higher temperatures favor the disintegration and

complete removal of the molding compound, but if the temperature is too high, the epoxy is

softened sufficiently for the thermopile to loosen. The optimum temperature of the molten

beeswax has not yet been determined.

In the end, neither of these techniques was considered ideal, and the general plan of

construction was modified as follows. The constantan wire was sewn through a polystyrene Jig

to which was glued an outer ring and an inner disk of 5 mil cellulose acetate as shown in

figure 17A. The polystyrene jig was then dissolved in benzene leaving the thermopile held

loosely in shape by the cellulose acetate ring and disk. To these a small quantity of epoxy

adhesive was applied and the pile was clamped to the receiver disk as shown in figure 17B.

This method of clamping resulted in the desired intimate contact between the receiver disk

and the thermopile. The disadvantage of this technique is that the cellulose acetate disk

increases the thermal mass of the sensitive area of the detector. However, the ease of

construction and the increased strength of the bond Justifies its use.

The configuration of the heater and heater leads on the receiver is shown in figure 18. The leads between the thermopile cold Junction support, and receiver disk were 3 mil diameter

platinum wire arranged in the Gillham configuration. They are brought over the surface of

the receiver to the heater by a commercially available si l led lacquer of high elec31
Figure IT- A - Thermopile supported by cellulose acetate

ring - 1, and disk -2. B - Method of clamping

the thermopile to the receiver disk while the

epoxy hardens. 3 - teflon rod, h - cellulose

acetate disk, 5 - receiver disk, 6 - cellulose

acetate ring, 7 - thermopile.

32
Figure 18. The configuration of the heater and the heater leads on the

receiver disk and the thermopile cold junction support. The

thermopile is not shown. 1 - heater, 2 - silver filled

lacquer heater lead, 3 - three mil diameter platinum wire.

trical conductivity which was applied by spraying though a mask. The heater itself was made

by suspending graphite in a lacquer vehicle and was also applied by spraying through a mask.

The upper cavity was drawn from 10 mil thick silver and finished by eloxing. It and the

receiver disk were coated with Eppley-Parsons Optical Black Lacquer [23] and were joined by

a silver filled epoxy adhesive chosen to yield the lowest thermal resistance between the

receiver disk and the upper cavity.

In order to use ECR #10 as a pyrheliometer , it was necessary to construct the special

view limiting aperture shown in figure 19- Also constructed was a special support plate

hf / /<x/^~7

^ ^ ^ ^ ^ M

\ \ \ \ ^ / / / / ~

Figure 19. Pyrheliometer view limiting aperture and mount for ECR #10.

1 - water-cooled heat shield, 2 - polyurethane foam insulation,

3 - ECR #10.

33
that allowed both ECR #10 and one of the PACRAD I 11 J detectors of J. M. Kendall, Sr. to he

attached to it at the same time, and the whole assembly mounted on an equatorial mount which

Kendall provided. A hole in the tube supporting the view limiting aperture was provided so that visual observation of the alignment of the detector relative to the solar axis could

be made with a dentist's mirror. Since ECR #10 could be aligned independently of the

equatorial mount, it was possible for both radiometers to be aligned with the solar axis.

5.2 Measurements of Corrections for the Various

Errors Affecting ECR #10

In this section we will describe the measurements which were performed on ECR #10 to

determine corrections for the various errors affecting it. Unfortunately, an unstableresistance-short circuit developed across the heater in ECR #10 before the apparatus to measure the non-equivalent effect of air conduction and convection was completed, so this

measurement could not be performed. The consequences of this circumstance will be discussed.

All of the other types of measurements described earlier in this report were performed.

First we describe the measurement of the responsivity of the receiver disk as a function

of position. This measurement was performed at the point in the construction of the radiometer just before the heater and the upper cavity were to be affixed to the receiver disk. To prepare the receiver disk for this measurement, it was spray coated with Eppley-Parsons

Optical Black Lacquer following the instructions supplied by the manufacturer. This coat- ing was removed after the measurement, so that the heater could be applied. After the

heater was applied the receiver disk was recoated in the same manner.

The apparatus used in this measurement was of the type described in section h.2. The

image of the aperture on the receiver was nominally one mm in diameter. However, measurements of the irradiance as a function of position in the image plane showed a significant

amount of scattered flux outside the area of the image, and a correction (to be described

later) for this effect was necessary. The indexing table on which the detector was mounted

was driven by a stepping motor. The detector-thermopile voltage was amplified with a linear dc nanovoltmeter , read with a digital voltmeter (DVM) , and recorded on punched paper

tape with a teletype.

The points on the receiver disk of ECR #10 at which measurements were made are shown in

figure 20. (All distances in the figure are measured in thousandths of an inch.) First the

detector was aligned on the indexing table so that the image of the aperture was centered

at the point (0,y) on the receiver disk (relative to the coordinate system which has its

origin at the center of the disk, see figure 20), and so that the indexing table motion was along the x axis, where y was set at either 0, ±0.050", or ±0.100". The data acquisition

sequence was as follows

1) move table x inches to right, wait 90 seconds, read DVM, punch paper tape,

2) move table x inches to left, wait 90 seconds, read DVM, punch paper tape,

3) move table x inches to left, wait 90 seconds, read DVM, punch paper tape,

h) move table x inches to right, wait 90 seconds, read DVM, punch paper tape,

5) repeat sequence starting at step 1.

Thus the data format on the paper tape was w

V

1

, (0,y)

V

1

, 3 (x,y)

V^o.y)

3U
V

i

, 3 U,y)

V^CCy]

V

n ^C0,y)

where V. , . (f ( j )x,y) is the j — measurement in the i— series of measurement of the thermopile voltage for irradiation incident at the point (f(j)x,y) on the surface of the receiver

disk, and where n is one-fourth of the total number of measurements. The function f(j) has

three values, 0, ±1, and is defined in the data sequence above. The values of x were

chosen from 0.050", 0.080", 0.100" depending upon the value of y as can be seen from figure

20.

Figure 20. The points on the surface of the receiver of ECR ^10

at which the relative responsivity of the receiver was measured - 3, the area that was heated by solar radiation

at Davos - 2, and the area of the electric heater - The scale is in thousandths of an inch and the origin

is in the center of the receiver.

35
Next the detector was rotated 90° so that the table motion was along the y axis and so that the image of the aperture was centered on the point (0,0) of the receiver disk (relative

to the coordinate system of figure 20). The data acquisition sequence described earlier was again employed resulting in the paper tape format

'n+1' ^0,-y)

V

i

, 1 (0,-y)

v.,

2 (o,o)

V.,

3(0,y)

V., ^(0,0)

Vu(0 ' 0)

The values of y were either 0.050", or 0.100", and m-n is one-fourth of the total number of

measurements performed with the table motion along the y axis.

From the data on the paper tape we calculated,

n _

R(f(,

Y>T 2 V. (f(j)x,y) I )x,y;0,y)=2^

V. (o,y)' + V. .(0,y)

i=l L !j2 is 4 J and

R(0,f(j)y;0,0) = } j i=n+l

where f(j) = j-2, and j = 1,3

2 V .(0,f(j)y)

V

i,2 ( °' 0) + V

i,U (0 ' 0)

(77)

(78)

During the above described measurements the radiometer did not have a window over its

receiver in order to avoid any errors due to scattering by the window. Consequently, the

radiometer was not well shielded from atmospheric micro-turbulence, and the data was subject

to considerable noise from this source. Since long measurement periods of between eight to sixteen hours were required to obtain the desired signal to noise ratio in the calculated

quantities, R(x,y;0,y) and R(0,y,0,0), the entire apparatus was automated. Now we discuss

how these quantities were used to calculate the relative responsivity of the receiver.

Let P be the power within a 3 mm diameter circle concentric with the image, let S(x,y)

be the relative responsivity of the receiver at the point (x,y), let P'(x,y) be the power

incident on the receiver outside of the 3 mm diameter circle_concentric with the image,

when the center of the image is at the point (x,y) , and let S'(x,y) be the average relative

responsivity of the receiver to P'(x,y). Thus, using the techniques developed in section

k.l to express the thermopile voltage in terms of responsivities

and

R(x,y;0,y) -

R(0,y;0,0)

PS(x,y) + P'(x,y) S'(x,y)

PS(0,y) + P'(0,y) s'(0,y)

PS(0,y) + P'(0,y) S'(0,y)

PS(0,0) + P'(0,0) s'(o,o)

(79)

(80)

where S(0,0) is arbitrarily chosen to be unity. _Next multiply eq. (79)_by eq. (80), expand

the result in a binomial series and approximate S'(0,0) and S'(x,y) by S(x,y) to obtain

R(x,y;0,y) R(0,y;0,0) - S(x,y) [l + (P'(x,y) - P'(0,0))/P] (81)

36
The approximations are justified because it will turn out that P'(0,0) and P' (x,y) are small

compared to P, and that S(x,y) varies less than one percent over the surface of the receiver.

In order to determine the quantity, (P 1 (x,y)-P' (0,0) )/P in eq. (8l), which is a scattering correction, we must measure the irradiance as a function of position in the image plane.

The apparatus was modified to do this. Two different detectors were employed. A vacuum

thermopile detector with a CaF window and a 0.2 x 2 mm receiver (stopped down to 0.2 x 1 mm) was used to map out a relative distribution of scattered flux, and a windowless thermopile

detector with a 3 mm diameter receiver of fairly uniform sensitivity over its surface was used to determine the constant by which the relative distribution should be multiplied to obtain the distribution of scattered flux as a percent of the power contained in a 3 mm

diameter circle surrounding the image. The nanovoltmeter in the apparatus was replaced by

a lock-in amplifier, and a chopper was inserted into the radiation beam between the lamp

and aperture when using the vacuum thermopile.

The points at which measurements were made with the different detectors are shown in

figure 21. A number of different functions were fit to the vacuum thermopile data using a non-linear fitting routine, in an attempt to find a simple function, f (x,y) , which represented

the data fairly well.

4-

3-

2-

I - oI - 2-

3-

4-

i

i i

i

i

i i

i

I 2 3 4 5 6 7

Figure 21. The points in the plane of the image of the aperture

at which the flux scattered outside of the area of the

image was measured. The scale is millimeters and the

origin is the center of the image. The circles represent the positions of the large detector (3 mm diameter)

and the rectangles represent the positions of the small

detector (0.2 x 1 mm).

37
The function finally chosen was normalized in the following manner. Let

1(A) = f Jf(x5y) dxdy, (82)

where A is the surface in the (x,y) plane over which the integration is to be performed.

For the normalization procedure, the surface A was a 3 mm diameter circle with its center

displaced k.5 mm from the center of the image of the aperture. It was required that l(A)

be equal to the output voltage of the 3 mm diameter detector when displaced 1+.5 mm from the

center of the image, divided by the output voltage of the same detector when at the center

of the image. In this way l(A) was made equal to the ratio of the power incident on surface

A to that incident on a 3 mm diameter region concentric with the center of the image. Thus

P'(0,0) = P I (A n00'J, (83)

and

P'(x,y) = P I (A ), (8U)

where A is the surface in the plane of the image that is occupied by the receiver of the

electrically claibrated radiometer when the center of the image is located at the point

(x,y) of the receiver, minus the 3 mm diameter circular area surrounding the image, and

AQ q is similarly defined.

Substituting eqs . (83) and (8*+) into eq. (8l), and using the first two terms of a binomial expansion results in an approximate expression for the relative responsivity,

S(x,y) = R(x,y;0,y) R(0,y;0,0) (l + l(AQQ ) - KA^)), (85)

in terms of quantities based upon measurements. In evaluating l(A ) - l(AQ0 ), it is not necessary to integrate over all of A and AQ0 . All that is necessary is to integrate over

the areas where Axy

. and AQ0 do not overlap. Thus

l(Axy ) - I(A0Q ) = iCAj) - I(A

2 ), :86)

where A, and A2 are defined in figure 22. This is the reason that measurements were performed only at the points shown in figure 21, when determining f(x,y). These were the only

points for which the values of f(x,y) would affect the final result. (Spot checks that had

been conducted previous to the measurement showed that f(x,y) was symmetric about the image

to within ±10$).

Table 1: The values of the scattering correction for the points (x,y)* at which

the responsivity as a function of position was measured.

y/x -100 -50 50 100

100

50

-50

-100

0.0011+ 0.0011 0.001*+

0.0010 0.0006 0.0003 0.0006 0.0010

0.0011 0.0007 0.0003 0.0000 0.0003 0.0007

0.0010 0.0006 0.0003 0.0006 0.0010

0.001U 0.0011 0.0011+

0.0011

*The distances x and y are measured in thousandths of an inch from the center of receiver.

38
Figure 22. The definition of the areas, Aj and A z

. 2 - the area of the receiver disk when concentric with

3 - the image of the aperture. 1 - the area of

the receiver disk when displaced from area 2. Aj and A2 are the portions of 1 and 2 that do

not intersect.

The values of the scattering correction, l(AQ0 ) - l(A ) , computed from eq. (86) are listed in table 1, for the points (x,y) shown in figure 20. The principal sources of error affecting these values are the residuals of the fit of f(x,y) (including the ±10$

deviations from symmetry about the image of the aperture), and the three-sigma uncertainty

in the normalization of l(A) due to the poor signal-to-noise ratio in the measurements made

with the 3 mm diameter detector. This uncertainty was ±66$ of l(A). The values of S(x,y)

calculated according to eq. (85) are tabulated in table 2.

Table 2: The measured values of the relative responsivity, S(x,y) as a function

of position* over the surface of the receiver of ECR f/10.

y/x -

' -80 -50 50 80 100

100

50

-50

-100

1.0010

0.9969 0.999 1* 0.9986

1.0006 0.9998 1.0000 0.999^ l.OOOU

1.0002 0.9981 1.0000 0.9998 1.0008

1.0022 0.9997 1.0005 1.0000 1.0016

1.0000 1.0003 0.9993

.

*The distances x and y are measured in thousandths of an inch from the center of receiver.

39
The three-sigma uncertainties associated with the R(x,y;0,y) and R(0,y;0,o) data

ranged about 0.03%. The estimated limit of error in the S(x,y) data is ±0.2% for the points

on outer edge of the measured area, decreasing to zero at the center.

The areas on the receiver's surface that absorb the electrical pover from the heater

and the radiant power from the sun were shown in figure 21. The power density within these

areas is quite uniform in both cases, so the average responsivity for the case of electrical

heating was calculated as

SE

= E S(x,y)

xe{-50, 0, 50}

ye {-50, 0, 50)

+ 0.5 2_j S(x,y)>/l2

xej-50, 0, 50}

xej-100, 100}

(87)

and the average responsivity for the case of solar heating was calculated as

S s

= |s(0,0) + 0.25[s(-50,0) + S(0, -50) + S(0,50) + S(50,0)]l/2

where_ x and y are measured in thousandths of an inch, are S = 0.9995 and S = 0.9998.

The values computed in this fashion

The_correction for the variations in responsivity over the receiver of ECR #10 at Davos

is just S /S - 1 = -0.0003 with an estimated limit of error of ±0.0010.

e s A measurement was also performed on ECR #10 to determine the responsivity of the cavity

top relative to that of the center of its receiver disk. This was done after construction

of the detector was completed, by covering the ring on the cavity top that surrounds the

aperture with a ring of one thousandth inch thick transparent tape, and painting a heater

onto this ring. The heater configuration is shown in figure 23. Nearly equal quantities

Figure 23. The configuration of the heater on the cavity top for

the measurement of the responsivity of the cavity top

relative to the center of receiver disk. 3 - the

receiver disk, 2 - the cavity top, 1 - the heater on the cavity top, k - heater leads.

U0
of power were alternately dissipated in each heater. These quantities of power were adjusted

so that the steady state voltage across the thermopile was independent of which heater the

power was dissipated in. The ratio of the responsivity of the cavity top to that of the

center of the receiver disk was calculated as the reciprocal of the ratio of the power

dissipated in the cavity top heater to that dissipated in the receiver disk heater. This

ratio was 0.9699 with a three sigma uncertainty of ±0.0020.

In order to calculate an exact correction for this effect it is necessary to know the

responsivity as a function of position over the cavity top, and the quantities of flux

reflected from the coating of the receiver disk to different parts of the cavity top. However, we can calculate an approximate correction and a limit of error from the data that we

do have. The relative responsivity of the cavity top that we have measured is a lower limit,

due to the fact that it was measured at the point most remote from the thermocouple, and due

to the fact that the thermal resistance of the tape reduced the measured value from the true

value. Similarly we do not know the exact reflectance of the coating of Eppley-Parsons

Optical Black Lacquer on the receiver disk, but we do know that it can range from less tnan

two percent up to about five percent [2U]. An upper limit for the correction for this effect

is obtained by assuming that the reflectance of the coating is five percent, and that all

of the reflected flux is detected with the lower limit of responsivity. In this case, the

receiver would detect 95$ + 5% of the flux as 95$ + ^.85$, so the maximum correction factor

for this effect would be 1.0015- We assumed a correction of 0.0008 with an estimated limit

of error of ±0.0008.

-h-d

Figure 2k. The spherical mirror used in the reflectance plus

excess emittance apparatus. 9, - 2.8°, 6g = 1*5.0°,

d = 7.0".

l4l
Now we will describe the measurements of the reflectance plus excess emittance correc- tion for ECR #10. An apparatus similar to that described, in section U.3 was used. The

dimensions of the spherical mirror (not a full hemisphere) are shown in figure 2k. This

type of mirror was used because it was felt that a full hemisphere would prevent adequate

observation of the alignment of the receiver relative to the mirror. Ideally, separate

measurements would also be made on the same apparatus using a mirror which formed the other

half of the hemisphere. However, for the receiver of ECR #10, these measurements were not necessary. Since its interior was coated with Eppley-Parsons Optical Black Lacquer [23],

which tends to be a retor-reflector for normally incident radiation [25], almost all of the

reflected and excess emitted flux leaves the receiver after but one reflection. This flux

is confined to a solid angle much smaller than that collected by the mirror. Of course a small correction has to be applied, as does a correction for the flux which passes through

the hole in the mirror. Both of these corrections, the sum of which is equal to 0.10$ with

an estimated limit of error of ±0.10$, were based upon the data in reference 25.

The image of the aperture was nominally 2 mm in diameter. It is important that a negligible amount of flux fall outside an area 5 mm in diameter centered on the image. Any

flux outside this region would be incident on the cavity top, and would cause the apparatus

to measure a linear combination of the reflectance plus excess emittance of the cavity

aperture and top instead of just that of the aperture. In order to measure a correction for

this effect, a detector with a flat, ring shaped receiver of 5-0 mm ID and 10 mm 0D was constructed. First the detector was aligned so that the image of the aperture was incident

on the ring, and then the thermopile voltage with the shutter opened, v, , and with the

shutter colosed, vQ

, was recorded. Next the detector was aligned so that the image passed

through the hole in its center. Again the thermopile voltage with the shutter opened, v1

'

and with it closed, v

Q

' , was recorded. The detector had no window, and was not shielded

from the air currents in the room for the same reasons mentioned in the description of the

responsivity as a function of position measurements. So again signal to noise was a problem,

and the apparatus was automated and let to run overnight.

The percentage of flux scattered out of the image into a ring with a 5-0 mm ID and

10.0 mm OD is given by (vj ' - Vq')/(v, - v ). This ratio was 0.1$ with a three sigma un- certainty of 0.3$. Since the cavity top ring that surrounds the receiver aperture was

coated with a specular black paint of about 3$ reflectance, the correction for the scattered

flux reflected by the cavity top is 0.00$ with an estimated limit of error of ±0.01$.

Once the scattered flux correction was measured, ECR #10 was aligned in the apparatus

and measurements were performed in accordance with the discussion in section H.3. Since

no measurements were made to determine 6 and 6 r , it was assumed that & = 6 + 0.1$ ± 0.1$.

In this case, eq. ( 71 ) can be approximated by

? e

- E' (1 - 5 r

- 0.001)/(1 - E'), (89)

where

E ' = ( B

e " Ae )/( Ae " e e ) ' (90)

and where £ is given by eq. (TO).

Again it was necessary to run the apparatus overnight in order to achieve a satisfactory

signal-to-noise ratio. Seven separate measurement runs were performed, yielding the seven mean values, 0.26$, 0.26$, 0.39$, 0.26$, 0.23$, 0.30$, and 0.26$ for ? r

- £ e

. The standard

deviations of these seven mean values ranged from 0.02$ to 0.0^$. A number of different

statistical tests on this data show that it is very likely that a variable systematic

error that has not been taken into account is present in the data [26]. Under these

circumstances, the recommended estimate of the population mean is the simple average of

the mean values of the seven runs. This average, 0.28$, is used as the correction for the

reflectance plus excess emittance error. Since the calculated three-sigma interval

(0.28$ ± 0.06$), does not span the range of the seven mean values, we will use ± 0.11$ as an estimated limit of error for the correction.

U2
The receiver thermal environment heating and lead heating corrections were measured

in accordance with the procedures described in section h.^. The dummy aperture holder

that was used is shown in figure 25. A high intensity total irradiance lamp [27] was used

to irradiate the detector during the dummy aperture holder and lead heating measurements.

Since the plane of the aperture was only i+0 cm away from the lamp, almost twice as much

irradiance was incident on the view limiting aperture as on the plane of the aperture,

whereas for solar irradiance measurements the same irradiance is incident on both surfaces.

To check for errors from this effect , the dummy aperture heating measurement was run with

and without the view limiting aperture affixed to the detector. The result was the same in

both cases, indicating that all of the effect arises in the aperture holder, probably in

the thin ring surrounding the aperture. The correction for this effect is -0.33% with a three sigma uncertainty of ± 0.02%. The lead heating correction was measured to be 0.02%

with a three sigma uncertainty of ± O.OW.

2r?,

Figure 25. The dummy aperture holder. 1 - black coating on interior of dummy aperture holder (also on interior

of aperture holder), 2 - 1*5° half-angle polished

aluminum core to simulate the effect of the hole

on emitted flux.

To summarize the corrections, we can rewrite eq. (56) as

P ,P r/ e

6 -

' [l +(^r " r .) + ( Ze) + (

+ p' s'/s P - p' S'/P s 1 e e' r e r r' e r

S -

e •)/

£

(91)

The right side of eq. (91) is the correction factor by which the power measured during

electrical heating must be multiplied to obtain the power incident on the receiver during

radiant heating, once it has been adjusted so that the thermopile voltage is the same during both radiant and electrical heating.

Table 3 contains a summary of each of the corrections that contribute to the correction factor, and the estimated limits of error (three sigma limits in some cases)

associated with them.

I»3
Table 3: A Summary of the Corrections for the Various Sources of Error for ECR #10.

Component of Error Correction Limit of Error

Uniformity of Responsivity

(S - S )/S

e r r

a) receiver disk

b) cavity top

Reflectance Plus Excess Emittance

Ue - cp>

a) collected by mirror

b) lost by mirror

Air Conduction Non-equivalence

(6 - 6 ) e r

Case Heating

-P 'S '/PS

r r e e

Lead Heating

P 'S '/PS

e e r r

-0.0003

+0.0008

±0.0010

±0.0008

+0.0028

+0.0010

+0.0010*

-0.0033

+0.0002

±0.0011

±0.0010

±0.0010

±0.0002

±0.000U

*Estimated

In obtaining these corrections, P

e and P , and S and S r have been interchanged in the last

tvo terms of eq. (9l)- Since these corrections are small, this introduces negligible

error. The value of the correction factor calculated according to eq. (9 ) from the values

in table 3 is 1.0022 with an estimated limit of error of ± 0.0055.

5.3 The Participation of ECR #10 in the

Third International Pyrheliometric

Comparisons

In this section we describe the data obtained from ECR #10 during the Third International

Pyrheiometer Comparisons at Davos, Switzerland.

Tables k and 5 contain data taken on September 11, 1970 as a check on the linearity of

the radiometer. Kendall's electronics were used. The receiver of the radiometer was heated

electrically with quantities of power corresponding to 113 mw/cm2 and 78 mw/cm2 irradiance,

respectively. The calibration constant*, K, of the radiometer at these two levels of

irradiance was 0.550 w/cm2 mv ± 0.002 w/cm2 mv. Notice that the quantity C f

= 18.682 cm 2

,

*that is, the number of watts/cm2 per millivolt of thermopile output.

kh
which is used in calculating K, is the product of the reciprocal area of the detector

aperture and the correction factor' for the detector.

Experiments were conducted on September l6, in order to calibrate the span of the

strip chart recorder that was used to record the thermopile voltage in millivolts per

chart division. A schematic diagram of the experiment is shown in figure 26. A computer

program was written to perform a least squares fit of a quadratic equation to this data.

The data itself, the coefficients of the linear and quadratic terms in the equation, and a comparison between the experimental values and the values computed from the quadratic

equation are all contained in table 6.

£

4- <2

Figure 26. Schematic diagram of strip chart recorder

linearity calibration. 1 - battery, 2 - variable

resistor, 3 - Fluke Differential Voltmeter,

h - Keithley Microvolt Ammeter, 5 - strip chart

recorder.

The solar irradiance measurements were taken in the following manner: During the

periods when the Angstrom 210 pyrheliometer was taking data, the receiver of the NBS

instrument was continuously heated by insolation. During the rest periods, the view

limiting aperture was closed and the receiver was heated electrically for calibration

purposes. Thus, a continuous strip chart recording of alternate periods of electrical and

radiant heating was obtained; each period of radiant heating lasting about thirteen minutes.

During the periods of electrical heating of the receiver, the voltage across the heater and

the voltage across a 1000 ohm standard resistor in series with the heater were read on the

Fluke Differential Voltmeter [23] and written in pen on the strip chart next to the trace. During the periods of radiant heating of the receiver, the time at which the strip chart

pen crossed one of the time scale divisions on the strip chart was written on the chart next to that division, and the division was marked.

The data reduction technique is the following: The average value of the strip chart trace is calculated for each period of electrical heating and for the last twelve or twelve

and one-half minutes of each period of radiant heating. For the periods of electrical

heating, the equivalent irradiance of the electrical power is calculated as 18.682 cm 2 times the product of the voltages across the receiver heater and the standard resistor

divided by 1000 ohms. This quantity is the value of irradiance which would result in the same strip chart recorder value during a period of insolation of the receiver as was recorded during the period of electrical heating of the receiver. For a period of

insolation, the irradiance is calculated as the sum of the equivalent irradiance for an

The correction factor that was applied at Davos was 1.0035-

the value obtained in section 5.2.

b5

Later measurements yielded
adjacent period of electrical heating of the receiver and the value of the irradiance

difference, AE, which corresponds to these adjacent periods of electrical and radiant

heating. The irradiance difference was calculated from tables k and 5 as 0.55 mw/cm2 mv

times the difference in voltage which corresponds to the two different strip chart recorder

values. And of course, the difference in voltage, corresponding to two different strip

chart recorder values, is calculated from the quadratic equation which was fit to the

voltage as a function of strip chart recorder value data taken on September l6 , and described in table 6.

Table 7 summarizes the reduction of the strip chart calibration and solar irradiance

data to yield average values for the insolation during each of the twelve-minute measurements periods , during which the NBS instrument was running. The first four columns of this

table are taken from the strip chart recordings. The numbers in the first column are ones to twos, depending upon whether the data on the line on which the number appears is for a period of electrical or a period of solar heating of the receiver. If the data on the line

is for a period of solar heating, the computer time at the beginning of the period is re- corded in the second column. If the data on the line is for a period of electrical heating,

the equivalent irradiance of the electrical power is recorded in the fourth column. In either case, the average value of the strip chart trace for the period is recorded in the

third column. The values of AE, which correspond to the average values of the strip chart

trace for adjacent periods of electrical and radiant heating, are tabulated in the fifth

column on the line between the lines on which the data for the adjacent periods of electrical

and radiant heating is tabulated. The sum of AE and the corresponding equivalent irradiance

are tabulated in the sixth column on the same line as AE. The average value of the two values so obtained for each period of insolation is tabulated in the seventh column on the

line on which the computer time of the beginning of that period of isolation is tabulated.

Table 8 summarizes the relation of the NBS instrument and Angstrom 210 on September ik.

Tables 9 and 10 are similar to tables 7 and 8, respectively, except they contain the

data taken on September 15-

The difference between the means of the ratios, %bs/e210' obtained on September ll+ , 1970

and September 15, 1970 is statistically significant and disturbing. None of the other

radiometers at Davos showed this behavior relative to Angstrom 210. But unfortunately this

discrepancy was not discovered until after I returned from Davos (since I did not reduce

the data in Switzerland once I discovered that the strip chart recorder that I borrowed

was nonlinear.) Then it was too late to definitively analyze the discrepancy. However,

there is much circumstantial evidence that this discrepancy was caused by a misalignment

of ECR #10 relative to the PACRAD in the equitorial mount that supported both detectors.

Consequently, I prefer to reject the September 15 data.

In view of the preceding discussion and in view of the new correction factor assigned

to ECR #10 in section 5-2, the ratio of the irradiance incident on ECR #10 to that reported

by Angstrom 210 is given by 1.0193 * 1.0022/1.0035 = 1.0180 with an estimated limit of

error of ±0.0063.

U6
Table h: Data Taken on September 11, 1970 to Check the Linearity of the ECR #10.

Compare with Table 5-

V E I E/I E x I C f

x e x I/V

Time mV volts amps R ohms watts K

1020 .li+191 5.0017 .833U7 6001.1 .001+169 .5^88

1023 .lklk9 5.0013 .833U0 6001.1 .001+168 • 5503

1030 .1^159 5.0010 .833U7 6000.2 .001+168 • 5500

1033 .11*160 5.0001+ .833I+6 5999-6 .001+168 • 5^99

1036 .11+183 5.0035 .83398 5999-5 .001+173 .51+96 ioUo .11+183 5.00>+0 .83392 6000.6 .001+173 • 5^97

101+5 . 1I+161 5.001+8 .83380 6000.2 .001+173 • 5505

101+8 .11+161 5. 00U5 .83390 6001.3 .001+173 • 5506

1052 .lUiUlj 5-003 .8339 5999-5 .001+172 .5510

1055 .1U153 5-003 .8339 5999-5 .001+172 • 5507

R = .55011

St. Dev. of Single Meas . = .12$

St. Dev. of Mean = ,0k% Max. Dev. from Mean = .2k%

Table 5: Data Taken on September 11, 1970 to Check the Linearity of ECR #10.

Compare with Table h.

VmV

E voltsI amps

E/I

R ohms

E x I watts

C

f

x E x i/v

913 .20561 6.0085 1.0066 5969.1 .00601+8 • 5l»95 925 .201+91 6.0102 1.0062 5973.1 .00601+7 5511* 930 .20515 6.0088 i.oo6i+ 5970.6 .00601+7 • 5507

931* .20516 6.0097 1.0062 5972.7 .00601+7 .5506

937 .20518 6.0092 1.0062 5972.2 .00601+1+ .5501+

9l+l .201+97 6.0090 1.0063 5971.3 .00601+7 • 5511

91+5 .201+88 6.0088 1.0063 5971.2 .00601+7 • 5511* 950 .20531* 6.0090 1.0063 5971.1* .00601+7 • 5501

95 1

* .20523 6.0088 i.oo6i» 5970.6 .OO60I47 .5505

957 .20512 6.0090 1.0063 5971.1* .00601+7 • 5507

K = .55061+ St. Dev. of Single Meas. = . lljt St. Dev. of Mean = .03* Max. Dev. from Mean = .21*

1+7
Table 6: The data taken on September 16 to calibrate the span of the strip chart

recorder and a least squares fit of the data to W = D+EC+FC 2

.

C(N)' V(N)'

1 20.50

2 30.00

3 38.00

1+ 1*2.00

5 1+9.00

6 52.50

7 57.50

8 57-50

9 62.00

10 70.50

11 71.50

12 76.50

13 83.00

lit 83.50

15 91.00

16 92.00

E

-.31+1 + 00

175.00

172.00

170.00

169.00

166.00

166.00

161+.00

161+.00 163.00

161.00

160.00

159.00

158.00

158.00

156.00

155.00

F In Least Squares Fit of

.601 - 03 Above Data to W = D+EC+FC2

DV(N) DW(N)

1 .00 .00

2 3.00 2.95

3 5.00 5.36

1+ 6.00 6.53

5 9.00 8.53

6 9.00 9.51

7 11.00 10.89

8 11.00 10.89

9 12.00 12.10

10 li+.oo 1U.33

11 15.00 1U.58

12 16.00 15. 81+ 13 17.00 17. 1+1+ lU 17.00 17.56

15 19.00 19.33

16 20.00 19.56

a) C(N) = strip chart reading

b) V(N) = microvolts out of differential voltmeter

c) DV(N) = V(l) - V(N) and

d) DW(N) is the prediction of this quantity by the equation

1+8
Table 7: Summary of Data Reduction for September lU, 1970,

Type Time

Chart Equiveading Irradiance V

X(N) E

l AE E

X +AE

73.36

UU 68.05

73. k2

93.97

93.98

0.75 9^.72

0.76 9^.lh

9^.73

10:06 61.U0

75-50

10:28 59-22

U5.83

10:50 57-90

U6.29

11:12 58.9^

1*7.72

11:3*4 58.

1*

U8.50

11:56 59.

1*9. 61»

12:19 63. 0U

50.77

12:U5 68.68

1 extrapo- (51-90)

lated

93.99

98.87

98.85

98. 8U

98.86

98.85

> .

(98.86)

1.72 95.70

95.85

2.01 96.00

2.33 96.32

96.57

-2.05 96.82

-1.85 97.02

97. ou -1.78 97.07

-1.93 96.92

97.02

-1.71 97.13

-1.71 97.13

97.20

-1.59 97.27

-1.73 97.13

97.22

-1.55 97.30

-2.02 96.83

96.92

-1.8U 97-02

-2.65 96.21

96.30

-2.U8 96.38

(continued)

h9
Table 7 (continued)

Chart EquivReading Irradiance E„=

Type Time X(N) Ej AE Ej+AE E

2 1 extrapo- (62.78) (88.67)

lated

lH:15 62.06

6k. ih

0.11 88.78

0.30

-3.05 85.63

Ik: 31 86.25 85 -TU -2.85 85.81+ 65.50

Table 8: Comparison of Xngstrom 210 and NBS on September lU, 1970.

Time ENBS E210

ENBS^E210

9:1+U 9^. 73* 92.93

+ 1.0191+ 10: 06 95.85 9^.05 1.0191

10:28 96.57 9I+.81 1.0186

10:50 97.01+ 95-18 1.0195

11:12 97.02 95.35 1.0175

11:31+ 97.20 95-37 1.0192

11:56 97.22 95. lU 1.0219

12:19 96.92 9k. 91 1.0212

12:1+5 96.30 9^.39 1.0202

ll+:15 88.88 87.18 1.0195

1^:37 85.7>+ 81+. 33 1.0167

Unweighted Mean = 1.0193

Std. Dev. of a Single Meas. = 0.0015

Std. Dev. of the Mean = 0.000U

*Based on last 6 minutes of run Based on first, third, and fourth measurement during run

50
Table 9- Summary of Data Reduction for September 15, 1970.

Type Time X(N) AE

10:13

10:U3

11:28

11:50

89-99

72.50

66.93

5^.70

U7.50

6l.0l+

70.50

7I+.I+8

70.68

83.9!+

86.99

90.25

73

i.71

2. 3U 86.28

0.79 86.20

1.80 88.79

1.11 89. lit

2.06 88.19

1.36 88.09

O.56 86.17

0.53 86.18

86.2>+

88.96

l.lU

86.18

Table 10: Comparison of Angstrom 210 and NBS on September 15, 1970.

Time ENB3

E210

ENBS/E210

10:13 86. 2U 8I4.96 1.0151

10:U3 88.96 87. h3 1.0175

11:28 88. lU 86.60 1.0178

11:50 86.18 814.82 1.0160

Unweighted Mean = 1.0166

Std. Dev. of a Single Meas. = 0.0013

Std. Dev. of the Mean = 0.0006

51
6. Conclusion

This report has described the theory of the errors affecting electrically calibrated

detectors in considerable detail, and has presented an illustrative example of the application of this theory to the testing and use of a detector to measure solar irradiance

during the Third International pyrheliometer comparisons at Davos, Switzerland in

September 1970. The main purpose of the theory developed here is to provide insight into

the way various sources of error affect this type of detector, and more importantly to

allow the design of experiments to accurately measure corrections for each of these

sources of errors. This part of the program is pretty well completed. However, most of

the experiments described here were the first of this nature that we had ever performed,

and it is clear in retrospect how many of them could be improved. Furthermore, the results

of these experiments also suggest that the design of the detector could be improved in many

ways. This is most evident in the cavity receiver and the aperture holder. The cavity

receiver should be redesigned for a specular, high-absorptance coating, and the aperture

holder should be redesigned to reduce the effect of case heating. It is estimated that with

a considerable expenditure of time and money, the estimated limits of error for this type

of detector can be reduced from the 0.6% obtained at Davos to about 0.1$.

The author gratefully acknowledges the valuable assistance of Alfred W. Crigler

in the design and construction of the radiometer and the instrumentation used to characterize it.

52
7. References

IlJ Birge, R. T. , Phys . Rev. Supplement, 1, % (1929).

12] Coblentz, W. W. , Bur. Standards, Bull. 12, 553 (1916).

13] Mttller, C. , Zeits. f. Physik, 82, 1 (1933).

[k] Eppley, M. , and Karoli , A. R. , J. Opt. Soc. Am., kj_, ikQ (1957).

1 5

Stair, R. , Schneider, W. E. , and Fussell, W. B. , Appl. Opt., 6, 101 (1967).

[6] This was the state of affairs in January 1968; however, two measurements of a have

recently been conducted and are in agreement with the value calculated from atomic

constants to within the estimated experimental uncertainties , which are on the order

of a few tenths of a percent in both cases. See references 11 and 17.

[7] Guild, J., Proc. Roy. Soc. A, l6l , 1 (1937).

[8] Gillham, E. J., Proc. Roy. Soc. A, 26£, 2U9 (1962).

[9] Blevin, W. R. , and Brown, W. J., Aust. J. Phys., 20, 567 (1967).

[10] Bischoff, K. , Optik, 28, 183 (1968).

[11] Kendall, J. M. , Sr. , and Berdahl , C. M. , Appl. Opt., 9, 1082 (1970).

[12] Carslaw, H. S. , and Jaeger, J. C. , Conduction of Heat in Solids (University Press,

Oxford, 1959), 2nd ed. , p. 10.

[13] Jakob, M. , Heat Transfer, Vol. 1 (John Wiley and Sons, New York, 1962) , p. 8.

[lk] Mathews, J., and Walker, R. L. , Mathematical Methods of Physics (W. A. Benjamin, N.Y.,

1965), p. 255.

[15] Watson, G. N. , Theory of Bessel Functions (University Press, Cambridge, 19^8), 2nd ed.

p. 367.

[16] Reference 15, eq. 20, p. 80.

[17] Blevin, W. R. , and Brown, W. J., Metrologia, 7, 15 (1971).

[18] Reference 3, p. 18.

[19] Gillham, E. J., Brit. J. Appl. Phys., U, 151 (1953).

[20] Reference 8, p. 257.

[21] Reference 8, p. 272.

[22] Frohlich, C. , Geist, J., Kendall, J., and Marchgraber, R. M. , to be published in the

Proceedings of the International Solar Energy Society Conference 1971 — Goddard

Space Flight Center, Greenbelt , Md. , April 1971.

[23] It is the policy of the National Bureau of Standards to avoid mentioning trade names

in publications, whenever possible. However, in this case, the use of a trade name

is necessary to the proper identification of the material or instrument. This by no means implies an endorsement by the National Bureau of Standards.

[2h] Reference 19, p. 155.

53
{25] Geist, J. C. , and Richmond, J. C. , On the Absorptance of Cavity-Type Receivers , Nat. Bur. Stand. (U.S.) Tech. Note 575, 38 pages (July 1971).

[26] I would like to acknowledge the assistance of J. J. Filliben of the Statistical

Engineering Section of NBS in the statistical analysis of this data.

[27] Schneider, W. E. , Appl. Opt. £, 1^10 (1970).

5U
FORM NBS-114A (1-71) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

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1. PUBLICATION OR REPORT NO.

NBS TN-594-1

2. Gov't Accession No.3. Recipient's Accession No.

4. TITLE AND SUBTITLE

OPTICAL RADIATION MEASUREMENTS:

Fundamental Principles of Absolute Radiometry and the

Philosophy of This NBS Program (1968 to 1971)

5. Publication Date June 1972

6. Performing Organization Code

7. AUTHOR(S) Jon Geist

8. Performing Organization

10. Project/Task/Work Unit No. 9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

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16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

The philosophy of the present NBS program in realizing a scale of total

irradiance with electrically calibrated (absolute) detectors, a theoretical analysis

of the sources of error in such a scale realization, a description of the electrically calibrated detector developed from 1968 to 1971, and participation in the Third

International Pyrheliometer Comparison are presented.

17. KEY WORDS (Alphabetical order, separated by semicolons)

Absolute detector radiometry; electrically calibrated detectors; International

Pyrheliometric Scale; irradiance; radiometry.

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