Kational Bureau of Standard*

^ Library, N.W. Bldg -

NBS MONOGRAPH 41

Theory and Methods of

Optical Pyrometry

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
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UNITED STATES DEPARTMENT OF COMMERCE • Luther H. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

Theory and Methods of

Optical Pyrometry

H. J. Kostkowski and R. D. Lee

National Bureau of Standards Monograph 41

Issued March 1, 1962

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington 25, D.C. - Price 25 cents

Contents

Page

Introduction 1

1. Theory 1 1.1. The Planck radiation equation 1 1.2. The International Practical Temperature Scale 1

1.3. The primary calibration at the gold point 2

1.4. The primary calibration above the gold point 2

1.5. The absorbing glasses 3

1.6. The relation between effective and mean effective wavelengths 4

1.7. The use of non-blackbody sources in a primary caHbration__ 5

2. Optical pyrometers 6

2.1. General characteristics of optical pyrometers 6

a. Pyrometer lamp 7

b. Apertures and filters 7

c. Fairchild's criterion 8

2.2. The NBS optical pyrometer 8

a. Objective lens assembly 8

b. Absorbing glasses, pyrometer lamp, and red filter 9

c. Microscope assembly 10

d. The electrical circuit 10

3. Sources 10

3.1. Blackbodies 10

a. Gold-point blackbodies 11

b. Lesser quality blackbodies 12

3.2. Tungsten strip lamps 13

a. Types of strip lamps 13

b. Factors affecting the reproducibility of strip lamps 13

3.3. Other sources 14

a. The carbon arc 14

b. High-pressure arcs 14

4. Primary caUbration 15

4.1. Calibration at the gold point 15

4.2. Calibration above the gold point 16

4.3. Estimated accuracy 18

5. Secondary calibrations 19

5.1. Optical pyrometers 19

a. Inspection and cleaning 19

b. Determination of the effective wavelengths 19

c. Calibration procedure 20

d. Low-range calibration 21

e. High-range calibrations 21

5.2. Tungsten strip lamps 22

a. Calibration range 22

b. Mounting and orientation 22

c. The electrical system 23

d. Calibration 23

5.3. Precision and accuracy 23

a. Definition of precision and accuracy 23

b. Statistical model for calibration errors 24

c. Uncertainties on certificates 24

d. Differences between the IPTS and TTS 25

6. Applications 25

6.1. Temperature measurements 25

6.2. Spectrical radiance calibrations using strip lamps 25

6.3. Secondary standards 26

6.4. Recommendations for achieving high accuracy and precision 26

6.5. Fundamental limitations 27

6.6. Photoelectric optical pyrometers 27

7. References 28

iii

li

II Theory and Methods of Optical Pyrometry*

H. J. Kostkowski and R. D. Lee

A detailed review of the theoretical methods of optical pyrometry and the application of

these methods at the National Bureau of Standards in realizing, maintaining and distributing

the International Practical Temperature Scale above 1063 °C is presented. In the theoretical

presentation, the concepts of effective and mean effective wavelengths are introduced, and

various equations relating these parameters to each other and other physical quantities

are derived. The important features of precision visual optical pyrometers are discussed

and a number of blackbody sources and tungsten strip lamps described. Detailed experimental procedures and results of primary and secondary calibrations of optical pyrometers

at NBS are given. Finally, recommendations for achieving high precision and accuracy and

the fundamental limitations in visual optical pyrometry are presented.

Introduction

The quantity and quality of technical and scientific investigations using optical pyrometry have

been increasing steadily during the past 5 years.

This has resulted in the need for an improvement

in the efficiency and accuracy of optical pyrometer measurements. The National Bureau of

Standards (NBS) has tried to meet its responsibihties in this area by developing new instruments

such as the photoelectric pjrrometer [1] ^ and by

re-evaluating the theory and methods of optical

pyrometry.

The current paper is an attempt to make the

theory of optical pyrometry and the application

of this theory at NBS readily accessible. Most

of the theory presented is not new or original with

the authors. However, much of it is scattered

throughout the technical hterature, and to the

best of our knowledge, a detailed review of the

theory in English does not exist. In addition to

the general theory of optical pyrometry, the cur- rent paper presents the instrumentation and

methods currently used at NBS to realize the International Practical Temperature Scale ^ above

1063 °C and to transfer this scale to instruments

submitted for calibration.

No attempt has been made to present a complete bibliography on optical pjrrometry. References to other papers are given only when a more

detailed account than is given here is thought to

be helpful to the reader.

1. Theory

1.1. The Planck Radiation Equation

The measurement of temperature utilizing

optical pyrometry is based on the fact that the

*This paper was presented at the Fourth Symposium on Temperature,

Its Measurement and Control in Science and Industry; Columbus, Ohio; March 27-31, 1961; sponsored by the American Institute of Physics, the Instrument Society of America, and the National Bureau of Standards. The proceedings will be published in book form by the Reinhold Publishing

Corporation, New York, N.Y.

' Figures in brackets indicate the literature references at the end of this Monograph.

2 Prior to 1960, this scale was called the International Temperature Scale. The new name, International Practical Temperature Scale, was adopted in October 1960 by the Eleventh General Conference on Weights and Measures.

spectral radiance ^ from an incandescent body is a function of temperature. In particular, if the

body is black, i.e. can absorb all the radiation that

might be incident on it, the Planck radiation

equation

relates the spectral radiance to the temperature.

In eq (1-1) N^x is the spectral radiance at the

wavelength X of a blackbody at a thermodynamic

temperature T, and Ci and C2 are the first and

second radiation constants. Thus it is possible

to determine the thermodynamic temperature of a blackbody through the measurement of N^x

provided the other parameters in eq (1-1) are known. Absolute measurements of radiation,

however, are very tedious and usually not very

precise. To overcome these obstacles one could

measure Nix relative to some standard spectral

radiance; thus defining a temperature scale based

on the ratio of two spectral radiances, one of

which is selected as a standard. This is the

procedure adopted in the International Practical

Temperature Scale (IPTS).

1.2. The International Practical Temperature

Scale

The International Practical Temperature Scale

of 1948 [2] defines the temperature, t, above the

temperature of equilibrium between solid and

liquid gold (gold point), ^au, by the equation

Nt>xit) _e^('Au+^o)-i

N,x{t^,)- (1-2)

where C2 and the gold point, ^au, are defined to be

1.438 centimeter degrees and 1063 °C, respectively,

' Spectral radiance is defined as the energy radiated by a body in a partic- ular direction per unit time, per unit wavelength, per unit projected area of the body and per unit solid angle. Radiance is the integral with respect to wavelength of the spectral radiance. The American Standards Association has adopted the symbol, N\, for spectral radiance and this notation will be adhered to in this paper. The text of the International Practical Temperature Scale, however, utiUzes the symbol J.

1
and Tq is 273.15 degrees. Temperature-measuring instruments calibrated at the National

Bureau of Standards are calibrated in terms of

the IPTS, and therefore, temperature calibrations

above the gold point are based on eq (1-2).

If it were possible to use eq (1-2) directly,

little more would be required concerning the

basic theory of optical pyrometry. However,

this cannot be done because any observable radiation consists of a finite spectral band, and the

question arises as to the wavelength to use in

eq (1-2). In fact, most instruments used for

this purpose at the present time use the eye as a detector and require a large spectral bandwidth *

in order to have sufficient energy for the eye to

see. Thus a major part of the theory to be presented is concerned with determining the wavelength to be used in eq (1-2). Since it is simpler

to discuss this in terms of a particular instrument,

the main features of the instrument commonly

used will be given at this time. Nevertheless,

the presentation will be sufficiently general to

apply with minor modification to any such instrument, visual or photoelectric.

The instrument that is usually used to realize

the IPTS above the gold point is the disappearing

filament optical pyrometer. A schematic diagram

of this instrument is shown in figure 1. The

instrument is operated by imaging the blackbody

or source whose temperature is to be determined

onto the filament of the small pyrometer lamp

and varying the current in this lamp until its

filament disappears into the background of the

source. At this time the photometric brightness ^ of the body and the pyrometer lamp filament as seen through the optical pyrometer are the same.

< Photoelectric instraments which are now being developed have smalle- bandwidths but still sufficiently large for the wavelength question to be sigJ

nificant.

' Photometric brightness of a surface is the radiance of the surface evaluated

according to its capacity to produce visual sensation. In this paper, as elsewhere, the adjective photometric will often be omitted. The term lumi- nance is also used sometimes in place of the term photometric brightness.

fgh I

A. SOURCE

B. OBJECTIVE LENS

C. OBJECTIVE APERTURE

D- ABSORPTION FILTER

(Used for temp, above 1300 °C)

E, PYROMETER LAMP

F RED FILTER

G. MICROSCOPE OBJECTIVE LENS

H. MICROSCOPE APERTURE

STOP

I. MICROSCOPE OCULAR

J. EYE

K. CURRENT MEASURING

INSTRUMENT

If the instrument has been calibrated and the

source is a blackbody, this brightness match will

result in a temperature determination on the

IPTS. The calibration of an optical pyrometer

in which an attempt is made to realize the IPTS:

directly rather than from a calibrated pyrometer!

or source is termed a primary calibration. The

remainder of this section will describe the theory

required in order to perform a primary calibration

on an optical pyrometer.

1.3. The Primary Calibration at the Gold Point

The first step in the primary calibration of an

optical pyrometer is a brightness match of a blackbody at the gold point. A mathematical

description of this match, i.e., the brightness of

the blackbody being equal to the brightness of

the p3'rometer lamp, as seen through the instrument, is given by

r* CO N,,{t^;)Tirr^r'^V^d\= N,it:)TryT'^V,d\ (1-3)

where Nj,\{tAu) is the spectral radiance of the

blackbody at the temperature ^au, the gold point,

Tx is the spectral transmittance of all the optical

components preceding the pyrometer filament, rr\

that of the red ffiter, t^' that of all optical components following the pyrometer filament except

the red glass, T\ tlie relative luminosity factor of

the observer'''^ and iVx(^i) * is the spectral radi- ance of the pyrometer lamp ffiament at temperature ti. Ni,},(tAu) as well as typical curves for

and Tr\ are slaown in figure 2. The transmittances

Tx and are usually constant and equal to

about 0.8 and 0.7, respectively, in the -wavelength

range of interest. The spectral brightness of a

gold-point blackbody, /3x(fAu), as seen through such

a typical optical pyrometer, is also shown in

figure 2. The area under j8x is equal to the bright- ness and to the integrals in eq (1-3). When the

brightness match is made, measurement of the

current in the pyrometer lamp realizes the primary

calibration at the gold point. It should be emphasized that the temperature of the pyrometer

lamp ti or the lamp current at the match depends

on the particular transmittances and the observer's

relative luminosity factor. Changing any of these

will, in general, change the calibration.

1.4. The Primary Calibration Above the Gold

Point

To perform a primary calibration above the

gold point, a procedure simdar to that at the gold

FiGUKE 1. Schematic diagram of an optical pyrometer.

' The relative luminosity factor at a particular wavelength or relative

visibility function, as it is sometimes called, is the ratio of the luminous flux at that wavelength to the maximum luminous flux, maximum with respect

to wavelength. . ? K. S. Gibson and E. P. T. Tyndall, Visibility of radiant energy, BS Sci. Pap., No. 475 (1923).

8 Since N\(U) is, in general, a function of direction or angle with respect

to the tungsten filament surface, N\(ti) in eq (1-3) is an average over the range of angles involved. However, it will be seen later that only NbX will be used quantitatively, and this is independent of direction.

2
Figure 2. The spectral brightness of a gold-point blackbody

/3x(^Au) as observed by an observer with a relative luminosity

function V), through an optical pyrometer having spectral

transmittances Tr\ for the red glass and Ti = 0.8 and

t'x' =0.7 for all the optical elements preceding and following

the pyrometer lamp filament respectively, excluding the red

glass.

point is followed except that the higher temperature, say t, must be determined. To obtain the

temperature t a brightness match is made on the

blackbody as seen through a device whose transmittance is constant with wavelength and of such

value as to require the same pyrometer filament

current as that used in the gold point blackbody

match. Mathematically,

03 CO

Jo Jo

Jo Jo

CO -J^

i3x(^Au)c^A (1-4)

where R is the constant transmittance as a function of wavelength of the device, say a

sectored disk. From the nature of the various functions in the integrands, a plot of the

spectral brightnesses (xiSO and jSx^^au) together

with R^\{t) as a function of wavelength would

result in curves similar to those shown in figure 3. The wavelength at which /3x(<au) and R^\{t) are equal is called the mean effective wavelength between the temperature ^au and t and is denoted

by Xt^^-t. At this wavelength

i?iV.x,,,-,(^)=iV*x,^„-,(^0. (1-5)

.62 .64 A .66 .68 .70 .72

WAVELENGTH

Figure 3. Approximate spectral brightness as observed

through an optical pyrometer of a blackbody at the temperature <Au and a blackbody of temperature t such that the brightness of the <au blackbody equals that of the t blackbody

when the latter is observed through a sectored disk of trans- mittance R.

^'au"' ^'^^ mean effective wavelength between the temperature <au and t.

Thus the desired blackbody temperature t satisfies

the defining equation for the IPTS and can be

obtained by solving (usually numerical solutions are necessary) the integral equation represented

by the first and fourth integrals in eq (1-4), provided all the transmittances and the relative

luminosity function are known. In this manner

a primary calibration could be performed at a temperature t greater than the gold point and re- peated (with different sectored disks) for as many

temperatures as necessary in order to obtain a smooth curve of blackbody temperature versus pyrometer-lamp current.

1.5. Absorbing Glasses

In order to have a very stable pyrometer lamp

a vacuum lamp is usually used.^ However, to assure long-term stability, a timgsten vacuum

lamp is usually not used above a brightness temperature ^° of about 1350 °C. Thus, using the

method just described, an optical pyrometer

could only be calibrated to about 1350 °C. Higher

temperature calibrations could be attained, however, by using the sectored disks as part of the

calibrated instrument. For example, a 2280 °C

blackbody appears, as seen through a sectored disk

having a transmittance of 0.7 percent, to have the

brightness at 6500 A of a 1350 °C blackbody.

Therefore an optical pyrometer calibrated from

' This is discussed in detail in section 2 of this paper.

1" The brightness temperature of a source is defined as the temperature of a blackbody which has the same spectral radiance at a particular wavelength

as the source. Mathematically \lN\'{t) =Nb\'{t'), V is the brightness temperature of the source at the wavelength X'. Generally, the brightness temperature is different for different wavelengths.

3
1063 to 1350 °C together with sectored disks can be used to measure temperatures higher than 1350

°C. Equation (1-4) would be used to determine

this higher temperature t where ^au in eq (1-4) is replaced with a temperature below 1350 °C

already realized. There are two disadvantages,

however, in doing this. One is the inconvenience

of using sectored disks routinely. The other is that one cannot reahze temperatures much higher

than the 2280 °C without incurring large errors from the uncertainty of the sectored disk transmittance. Though it might be possible to design

and construct sectored disks for which the angular

opening of the disk can be determined to better

than 1 min of arc, this has not yet been done.

For a 0.007 transmittance which is necessary to

achieve 2280 °C an uncertainty of 1 min of arc amounts to an uncertainty of 2.0 deg C.

A means out of this dUemma is the use of a

filter rather than a sectored disk to reduce the

brightness of the source. Such a filter is called

an absorbing glass and is usually inserted between

the objective lens and the pjrrometer lamp. The

primary calibration of the pyrometer for temperature ranges using an absorbing glass would proceed as follows. The temperature i of a blackbody above 1350 °C but below 2280 °C would

be determined as described in the last paragraph.

Next the sectored disk would be removed, the

absorbing glass inserted, and a brightness match

made. The cm-rent in the pyrometer lamp at the

match together with the absorbing glass constitutes a calibration point at the temperature t. Now one is able to proceed to even higher temperatures than 2280 °C because with each absorbing

glass one can again use a sectored disk and need

not use a disk with a very small transmittance.

There are other advantages in using an absorbing glass, particularly if its spectral transmittance

is given by =e (1-6)

where k is a constant with respect to wavelength.

Suppose ts is a blackbody temperature above 1350

°C obtained by using eq (1^). Looking at such

a blackbody without a sectored disk but through

an absorbing glass, and using Wien's radiation

equation " rather than Planck's equation, we have

for the integrated brightness

a\-^e ^ c,),'^,^y^'v^dX (1-7)

•1 Wien's radiation equation states Ni\—(Ci\-^lir) exp (—CilXT) and for a temperature of 5000 °K and a wavelength of 7500 A (approximately the longest

wavelength required in eq (1-4)) it is about 2 percent smaller than the Planck

equation, while at 2500 °K and 7500 A it is only 0.05 percent smaller.

where ^3=^3+273.15.^2 Tj^^g ^ blackbody at the

temperature appears through the absorbing

glass as another blackbody at a temperature T2

where

2 -^3 ^2 -Lz (1-8)

Since klC2, the so-called "A" value of the absorbing

glass, is a constant, any blackbody whose temperature is Ti will appear through the absorbing glass as another blackbody at a lower temperature Tj

where

1 _J.

frT..

(1-9)

The apparent temperature Tj can always be made

less than 1350 °C by making the A value sufficiently large. Thus with an absorbing glass with

this type transmittance, the A value is a constant

and once obtained can be used together with eq

(1-9) and a lower range cahbration to calibrate

the upper range. In addition, such an absorbing

glass insures a close color match between the pyrometer lamp and the source. This is helpful for

precise brightness matching. Furthermore, from

eqs (1-7) and (1-8), the A value of two or more

absorbing glasses used together is the sum of the

individual A values. Therefore, since the A

values are also independent of the blackbody temperature, a high-temperatiu-e calibration can be

obtained without actually making observations at

the high temperature but simply by determining

the individual A values at some low temperature

and adding them together for the high temperature.

1.6. The Relation Between Effective and

Mean Effective Wavelengths

The basic principles involved in the primary

calibration of an optical pyrometer at any temperature above the gold point have been described. In this method, sectored disks and absorption filters are used, and eq (1-4) is solved

numerically for any pair of temperatures represented by t and txu- However, the amount of

tedious calculation can be greatly reduced by introducing and utilizing the concept of effective

wavelength.

If Wien's radiation equation rather than

Planck's equation is used and ^au and t are generalized to any two temperatures ti and ^2, one obtains

by using eqs (1-4) and (1-5)

j; =e

(1-10)

12 Ti= (,-1-273.15 °C is called the International Practical Kelvin temperature.

4
Designating the integrals in the numerator and.

denominator of eq (1-10) as Bi and B2, respectively, and taking the natural logarithm of both

sides of eq (1-10) leads to

1 ^In ^i-ln B2

(1-11)

The effective wavelength X^'^ at T'i = ris defined

as hm -A.

Xr Ti^T Xr- 1'2 (1-12)

Through the use of this definition and eq (1-11)

one obtains

1^1 djlnB)

or

In 52-ln Bi

(1-13)

(1-14)

and if eq (1-11) is substituted into eq (1-14)

Hence the reciprocal of the mean effective wavelength between two temperatures is the center of

gravity of the reciprocal of the effective wavelength with respect to and between the reciprocal

temperatures

An expression useful for computing the reciprocal effective wavelength can be derived as follows.

From eq (1-10) and the definition of /3 and mean

effective wavelength, one obtains

B,

B V/3 /Xr-r,

Then

(B-B2\l_J( \t-tJb Wt-T:

(1-16)

(1-17)

and

lim — 4= liTM

or 1 ^=fl

BdT-\l3dTj.

(1-18)

(1-19)

w In some references, the effective wavelength is called the limiting effec- tive wavelength and the mean effective wavelength is called the effective wavelength.

Substituting for /3 and B, differentiating and

solving for 1/Xr leads to

(1-20)

By numerical integration of eq (1-20), the

effective wavelength can be determined for any

temperature T. Doing this for 5 or 6 temperatures in a particular range of a pyrometer is usually sufficient to enable one to plot an acciirate curve of X^ versus T for that range. Moreover,

it turns out that l/Xy is, to a good approximation,

a linear function of 1/T and therefore

X

This approximation is usually correct to about

five significant figures. Therefore from the Xr

versus T or I/X7. versus l/T curves and eq (1-21),

the mean effective wavelength between any two

temperatures can be obtained. When one of the

temperatures is not known initially, such as in a primary calibration, the mean effective wavelength

is assumed to be 0.65 and the unknown temperature computed from eq (1-5). Using this first

approximation of the temperature, a second

approximation of the mean effective wavelength

can be determined from the effective wavelength

curve and eq (1-21) and a second approximation of

the temperature obtained from eq (1-5). One or two such successive approximations are usually

sufficient. Hence, through the use of effective

wavelengths, integral equations need be solved

only when initially determining the effective

wavelength versus temperature curves.

1.7. The Use of Non-blackbody Sources in a Primary Calibration

All that has been presented so far has required

a blackbody source, not only at the gold point

but at higher temperatures. However, it is possible to use any stable source (excluding, of

course, the gold-point blackbody) without error, when absorbing glasses are not used, and a tungsten strip lamp with only small errors «1°),

when absorbing glasses are used. This is easily

verified from the integrated brightness equations.

For example, suppose instead of looking at a blackbody of temperature ti through a sectored

disk of such transmittance that the blackbody's

integrated brightness appeared to be equal to

that of a gold-point blackbody, a tungsten strip

lamp was used and adjusted until through the

619082—62 2 5
1 same sectored disk, it matched the gold point.

Mathematically,

where 12 is the temperature of the tungsten,

ex (^2) its spectral emittance, and the spectral

and effective transmittance of the glass envelope

of the tungsten lamp, tc{t-i) is the color emissivity

and t\ is the color temperature for tungsten at a temperature ^2- From the second and fourth

integrals in eq (1-22) and the definition of mean

effective wavelength, one notes that the tungsten

as seen through the lamp envelope has a bright- ness temperature U at the mean effective wavelength X(j_,^. If an absorbing glass is inserted in

the optical path of the pyrometer when the sec- tored disk is removed, this mean effective

wavelength changes. Mathematically,

CO

=ec(i52)r J A''6x('f2)^ax^l^rxrx' V^dX

=£N,xit'r)raxriT,xr'x'l\d\. (1-23)

In addition as seen from eq (1-23) the brightness

temperature will, in general, also change from ti to some temperature t'l. A relationship between

t'l and ti can be obtained as follows. From eqs

(1-22) and (1-23) and the definition of mean

effective wavelength, one obtains

(1-24)

Then, using Wien's equation

^2 / 1 (^2 /I ]_\ e Tl^=e h[-f^T[ T?J (1-25)

and

" The color temperature of a source in a particular wavelength region is here defined as that temperature at which a blackbody has in this spectral region the same relative spectral radiance as the source. Mathematically,

e\(t)Ni,\(t) = ec(t)Nb\(t'') for all wavelengths where (c is the color emissivity

and a constant with respect to wavelength.

Rearranging and subtracting l/TiX(^_(^ from each

side of eq (1-26) gives

Combining the term on the left of eq (1-27) and

the first term on the right, multiplying through

by Xjj_tC, and solving for 1/T[ results in

• (1-28)

In practice T'l, the brightness temperature with

the absorbing glass inserted, is only a degree or 1 two different from Ti and very insensitive to T2. ' The correction of a degree or two can usually be i made sufficiently accurate so that the resulting

error is less than one degree.

It has been shown .that a blackbody source

is not needed for a primary calibration above the

gold point of an optical pja'ometer. When absorbing glasses are used, however, a source for I which a color temperature exists, at least in the

spectral bandwidth of the pyrometer, and which is

approximately known as a function of brightness

temperature is required.

The basic theory of optical pyrometry has been

developed. The application of this theory at

j NBS to actual calibrations of optical pyrometers 1

is given in sections 4 and 5. The basic charac-

| teristics of optical pyrometers and the sources of

| radiation commonly used in optical pyrometry 1 will be presented in sections 2 and 3.

j

2. Optical Pyrometers

In this section, some of the more important ; general characteristics of optical pjrrometers as

well as a detailed description of the NBS pyrom- i eter will be presented. Detailed accounts of the

j commercially available instruments are given in

instruction manuals issued by the manufacturers I

or, for the noncommercial instruments, in pub- ' hshed research papers [3-6].

2.1. General Characteristics of Optical

Pyrometers

The visual optical pyrometer, the schematic

diagram of which is shown in figure 1, is an instrument of surprisingi}" high precision and ac- curacy. This is mainly the result of the high

stability of the pyrometer lamp and the proper

selection of apertures and filters.

6
a. The Pyrometer Lamp

The pyrometer lamp is probably the most

important element in the optical pjrrometer.

It serves as the instrument's reference standard

for radiance. Most p3rrometer lamps used today

consist of a round or flat highly pure tungsten

filament in an evacuated small (dimensions of a few centimeters) glass envelope. The envelope

has plane windows of good optical quahty which

are sometimes oriented so as to avoid troublesome

reflections. A vacuum rather than gas lamp is preferred because the elimination of convective

and reduction of conductive heat transfer make

the lamp's radiance less dependent on its orientation or ambient temperature [5]. Typical dimensions of lamp filaments are 0.03

to 0.05 mm diameter for round filaments and

0.05 to 0.1 mm by 0.005 mm for ribbon filaments.

Lengths vary from 20 to about 40 mm. The small

cross-sectional area and relatively long length

keep the current and voltage requirements low

(30 to 200 ma, which is obtained with less than 6 v)

and reduce the heat losses through lead conduction, thus further reducing the effect of ambient

temperature on lamp radiance. These filament

dimensions also make the time constant of the

lamp short. For example, pyrometer lamps

of the type described reach within 2 deg C of

their final temperature within 5 to 60 sec from the

initial turn-on time, the exact time depending

on the particular filament dimensions and the

final temperature.

Pyrometer lamps are usually calibrated using

electrical current as the parameter to which the

brightness temperature is related. Current is a more convenient parameter to use than lamp

resistance or power input and appears to be a

sufficiently stable function of brightness temperature, at least to the extent of requirements in

visual optical pyrometry. Dii-ect current is used so that a potentiometer may be utilized for

determining the current. It is important that the

direction of current in the filament during use be the same as that for which the lamp was cahbrated. Due to the Thompson effect, a reversal

of the current will modify the temperature distribution along the filament and therefore change

the radiance at the sighting area. Most commercial p3rrometer lamps have a rate of change

of current with brightness temperature varying

from about 0.05 ma per degree at 800 °C to 0.1

ma per degree at 1350 °C. Corresponding figures

for higher source temperatures when using absorbing glasses can be determined by using

eq (1-9).

New p3T:ometer lamps are extensively annealed

or aged before being calibrated. The purpose of

the annealing is to complete the recrystalhzation

of the tungsten which occurs when the metal is subjected to high temperature. Since the re- crystallization modifies the resistivity and omittance of the tungsten, the calibration of the pyrometer lamp will change during this time.

Usually, the lamps in commercial pyrometers are annealed by the manufacturer. For lamps made

at NBS, an anneal of several thousand hours at

about 1800 °K (approximately 1400 °C brightness

temperature at 0.65 m) has been adequate for

visual optical p3a"ometry. However, recently,

using the new NBS photoelectric pyrometer [1] several NBS and commercial lamps were observed

to change in brightness temperature (for a fixed

current) from )^ to 1 °C in 300 hr in the vicinity of

1063 °C after having been annealed for 2000 hr at

1800 °K. On the other hand, one NBS constructed p3T:ometer lamp has been used for about

4000 hr without changing this much. At the

present time, the difference in the two results is not understood. Thus, unless the stabihty of a

particular pyrometer lamp has been established,

it is recommended that for accurate work a lamp

be compared with other lamps or recalibrated

after being used for 200 hr. As a corollary to this, an optical pyrometer lamp after being calibrated

should be left off except when brightness matches

are actually being made, keeping in mind of course

the time required for the lamp to reach

equilibrium.

b. Apertures and Filters

In addition to the stability of the p3T:ometer

lamp, two characteristics which are required for

an acciu-ate optical pjTometer are that the ratio

of the brightness of the pyrometer filament to

that of the source be independent of the source

distance and that there be a highly reproducible

means for realizing this ratio.

The first characteristic is largely achieved

through the microscope and objective apertures.

The microscope aperture is the aperture stop for

the entire optical system, and from a geometrical

optics viewpoint is adequate to maintain the

ratio of the source to the filament brightness independent of source distance. However, due to

the diffraction pattern of the source being partially

obscured by the filament, the radiance of the source image, particularly in the vicinity of the

pyrometer filament, depends on the angular size

of the cone of radiation incident on the p3a-ometer

filament. By adding the objective aperture, this cone is kept constant regardless of soiirce distance.

In most optical pyrometers, the test that the

observer uses to determine the existence of the

brightness ratio or match is the disappearance of

the pjTometer filament into the source image.

For this to occur the color of the incandescent

filament must be (visually) the same as that of the source image. For temperatures below which

absorbing glasses are used, this is achieved fairly

well by using a sharp cut-off red filter with a transmittance curve such as that shown in figm'e

2. This filter, cutting off the shorter wavelengths,

and the visibiUty function of the eye, cutting off

the longer wavelengths, produce a sufficiently

narrow spectral bandwidth so that an adequate

color match exists for most sources. However,

7
Lovejoy has shown [7] that greater precision can be obtained for brightness temperatures below

850 °C by removing the red glass. This is a con- sequence of increasing the apparent brightness of

the source and the pyrometer filament and therefore decreasing the eye's threshold contrast or contrast hmen.^^

Where sector disks or neutral absorbing glasses are used or where a non-blackbody source has a much higher color temperature than its brightness

temperatm"e, a noticeable color mismatch may

exist. The spectral distribution of the source is characteristic of a high temperatm-e whUe that of

the filament of a low temperatxu-e, giving the source image a more orange like color relative to

the filament. An observer will probably be aware

of a difficulty in brightness matching or disappear- ance before he is aware of the color mismatch.

This effect is minimized, at least for blackbody

and tungsten sources, by the use of absorbing

glasses which have the previously described ex- ponential transmittance. Most high-precision

optical p3rrometers use such absorbing glasses.

c. Fairchild's Criterion

Even when a color match exists, a complete

visual disappearance is not possible in some optical

P3nrometers. As a brightness match or disappear- ance is approached, a thin dark line appears outside the edge of the filament, and/or a bright fine

appears inside the edge. The origin of these Hnes

has not been definitely estabhshed. However,

Cunnold [8] develops a rather strong case that the

bright line is caused by deviations from Lambert's

cosine law, particularly for round filaments, and

that the dark line is caused by diffraction effects

at the edge of the pyrometer filament. Fairchild

and Hoover [3] experimentally determined how to

avoid the appearance of these effects and obtain

complete visual disappearance. They found that

if the ratio of the exit angle to the entrance angle

at the p3T:-ometer filament, aj^, as shown in figure

4 is sufficiently small, the dark or bright lines are not observed. The required ratio for disappear- ance is a function of the width and shape (round

or flat) of the pyrometer filament [3] and has

become known as Fairchild's criterion. It should

be pointed out, however, that Cunnold [8] contends that complete disappearance is not the most

precise condition for determining a brightness

match and that the apertures can be selected such

that the resulting enhanced variation of brightness

across a round filament permits a more precise

match than can be obtained by disappearance.

Moreover, under these conditions, the exit angle

may be made considerably larger and since the

pyrometer's transmittance is greater, lower bright- ness temperatures can be measured or a narrower

15 Contrast limen is defined as I (Bt—R,)IB,\ where B, is the brightness of a background reference source and Bt is the brightness of a test area for which

there is a 60 percent probability of an observer's detecting it from the back- ground. The contrast hmen is a function of B, and increases rapidly for brightness lower than those associated with optical pyrometer observations below about 1000 °C.

a EXIT ANGLE

/3 ENTRANCE ANGLE

/3

/3

B ^

\ ^

A

A OBJECTIVE APERTURE STOP

B PYROMETER LAMP FILAMENT

C MICROSCOPE APERTURE STOP

Figure 4. Schematic diagram showing the entrance and

exit angles at the optical pyrometer filament.

spectral bandwidth can be used. The latter would

allow a more acciu-ate determination of mean

effective wavelength. In spite of Cxmnold's convincing arguments, httle effort has been made in

this direction, and complete disappearance is still used to determine a brightness match in most

visual optical p3Tometers.

Optical p5T:ometer design has not been carried

to its ultimate but only to the extent that the

major hmitation in precision and accuracy is the

observer. The more important general characteristics and requirements of this design have been

presented. Their integration into an actual instrument will be illustrated through a detailed

description of the NBS optical pjnrometer.

2.2. The NBS Optical Pyrometer

The National Bureau of Standards maintains a

specially designed visual optical pyrometer for

realizing the International Practical Temperature

Scale above 1063 °C and for distributing this scale

throughout the United States by the calibration

of pyrometers and tungsten strip lamps. The

NBS pyrometer is based on the design of FairchUd and Hoover [3] and, to the best of our

knowledge, has been in use since about 1923;

It is described here in order to clarify the pyrometer design characteristics already discussed and

to prepare the reader for sections 4 and 5 on

calibrations.

a. Objective Lens Assembly

Figure 5 is a cross section of the NBS optical

pyrometer. The objective lens is a plano-convex

achromatic doublet with a clear aperture of 4.3 cm

and a focal length of about 13.6 cm. The source

is generally positioned about 65 cm from the

pyrometer filament and the objective lens adjusted

through a rack and pinion gear assembly until

the source image is at the filament. At this position the objective lens is about 45 cm from the source and 20 cm from the source image. The

objective aperture is 1 cm in diameter and 10.8

cm from the filament, forming a fixed centrance

angle of about 0.093 radian, independent of the

position of the objective lens.

8
A OBJECTIVE LENS F RED FILTER

B OBJECTIVE APERTURE q MICROSCOPE OBJECTIVE LENS

C ABSORBING GLASSES H MICROSCOPE APERTURE

D ADJUSTABLE LAMP MOUNT (Aperture stop)

E PYROMETER LAMP I HUYGENS OCULAR

Figure 5. Sketch of the NBS visual optical pyrometer.

In the construction of the NBS pyrometer, provision was made for inserting sectored disks

between the objective aperture and the pyrometer

lamp. Though this position is still used occasionally for routine work, it is no longer used in primary

calibrations because of vibrations being set up in

the pyrometer filament and because of the sectored

disks of low transmittance acting as objective

apertures. The alternate position for the sectored

disks that is usually used is at the source. This is accomplished by forming with an auxiliary lens an

image of the source at the distance from the fila- ment that the source itself is normally positioned

and placing the sectored disk there.

b. Absorbing Glasses, Pyrometer Lamp and Red Filter

The absorbing glasses, p3rrometer lamp, and red

filter are contained in a box in which the temperature can be accurately controlled. Thermostating this box, however, was foimd unnecessary and

has not been done for years. Nevertheless, as a precautionary measure, the temperature of the

room in which the pyrometer is used is controlled

to within ±1.5 deg C.

The absorbing glasses are mounted on a disk

which can be rotated into any of four positions

representing four of the instrument's five ranges.

These are designated as Ag 0 (no absorbing glass),

AG 1, AG 2, and AG 3, and are used for temperar

tures from 800 to 1350 °C, 1300 to 1750 °C, 1700

to 2050 °C, and 2000 to 2400 °C, respectively.

Their spectral transmittances are given in table 1

.

The fifth range is selected by placing another absorption glass called the extension glass in front

of the objective lens and using it in series with

AG 3. The instrument can be used up to 4000 °C

in this manner. AG 1 and the extension glass are

Corning pyrometer brown glasses and have a constant A value at least within the precision of

the measurements. Ag 2 and 3 are composite

glasses. Before the advent of the Corning pyrometer brown glass, a constant A value was

achieved by combining two or more glass filters.

Only the red portion of the spectrum needed to be

considered, and these glasses appear magenta to

the unaided eye.

The pyrometer lamp is mechanically mounted

with sufficient degrees of freedom to permit precise

alinement. The lamp, now in use, is designated

Ll and has been used in the pyrometer since 1953.

It is a vacuum lamp with a round filament 0.035

mm in diameter and about 40 mm long. The

filament contains a number of small coils which

increase the length of the filament possible and

decrease the effect of ambient temperature. The

coils also reduce temperature gradients by radiation exchange. The central part of the filament

is horizontal except for a slight dip at the center

which serves to indicate the portion used in bright- ness matches. The lamp envelope is Pyrex and

has plane windows inclined about 10 deg from the

normal to the optical axis as shown in figure 5. The previous gold-point primary calibrations of

Ll indicate that it has not changed by more than

1.5 deg C at 1063 °C since 1953 and has not

changed at all within the experimental error since

1957.

Following the pyrometer lamp in the optical

train is the red glass whose spectral transmittance

is given in table 1. It is located 4.0 cm from the

pyrometer filament and is moimted on a rotatable

disk similar to that containing the absorbing

glasses. The disk has open areas in which red

glasses from optical pyrometers being calibrated

may be mounted and compared to the NBS red

glass.

Table 1. Spectral transmittances of the absorbing glasses

and the red Alter in the NBS visual optical pyrometer and

the CIE standard relative luminosity factors

Wavelength

Spectral transmittances Luminosity

factors (CIE)

Agl Ag2 Ag3 Red filter

jnfi 600 0. 043 0. 009 0. 003 0. 000 0. 631 610 .048 .010 .003 .001 .503 620 .052 .011 .004 .019 .381 630 .056 .011 .004 .292 .265 640 .059 .012 .005 .078 .175

660 .062 .014 .005 .800 . 107 660 .065 .015 .006 .830 .061 670 .067 .017 .006 .841 .032 680 .069 .019 .007 .847 .017 690 .070 .022 .009 .850 .0082

700 .070 .025 .010 .850 .0041

710 .070 .028 .011 .849 .0021

720 .070 .031 .012 .846 .00105

730 .069 .034 .014 .844 . 00052

740 .068 .037 .015 .839 . 00025

730 .066 .040 .017 .836 .00012

760 .065 .044 .018 .830 . 00006

770 .063 .048 .020 .826 . 00003

780 .060 .051 .022 .821 . 000015

AO
c. Microscope Assembly

Beyond the red glass is a lens assembly similar

in design to a low-power microscope. The objective lens of the microscope is 0.7 cm in diameter,

has a focal length of about 4.0 cm and is momited

about 6.3 cm from the pjo-ometer filament. At a

distance of 4.0 cm from the microscope objective

is the microscope aperture which is the aperture

stop for the entire pyrometer. For brightness

temperatures above 1050 °C, the apert;ire stop is 0.16 cm in diameter, producing an exit angle at the

pjTometer lamp of about 0.04 radian. This, in

conjunction with the 0.093-radian entrance angle,

satisfies Fairchild's criterion for visual disappear- ance for the round filament used. At brightness

temperatures between 950 and 1050 °C an aperture stop of 0.24 cm is used, from 850 to 950 °C an

apertiu-e stop of 0.32 cm is used and below 850 °C

a stop of 0.40 om is used. With these larger stops

Fairchild's criterion is not satisfied, being sacrificed

in order to increase the apparent brightness '® and reduce the contrast limen. However, the

apparent brightness is now low enough so that the

edge efl^ects are not visible to the eye, i.e., disappearance still exists.

A 10-power Hu3'gens ocular completes the

microscope assembly and the optics of the optical

pyrometer. The microscope assembly thus magnifies the pyrometer filament by a factor of about 17,

and since the source observed by the pyrometer

objective is magnified by 0.5, the overall magnification of the source by the pyrometer is about 8.5.

With the 0.16 cm aperture stop, the exit pupil,

which is the image of the aperture stop formed by

the ocular, is about 0.07 cm. When compared to

the eye pupil diameter of 0.3 to 0.5 cm for the

brightness encountered with this aperture stop,

one is led to postulate that disappearance of the

pyrometer filament is achieved to some extent by

insufficient resolving power, fine details at the

edge of the filament being washed out.

d. The Electrical Circuit

The electrical current measuring apparatus used

with the NBS pyrometer is rather straightforward. The pyrometer lamp is connected in series

with a resistance box, a multitum rheostat, a 6v lead storage battery, a milliammeter, and a

0.1 -ohm standard resistor. A high-precision

potentiometer, standardized by a temperature

stabilized saturated electrical cell, determines the

filament cmrent by measuring the voltage drop

across the 0.1 -ohm standard resistor.

The Ll current ranging from 65 to 160 ma is usually determined to the nearest 0.01 ma. Values

of current corresponding to 1 deg C change in

brightness temperature are 0.12 ma at 800 °C,

0.17 ma at 1063 °C, and 0.20 ma at 1350 °C. It

" The apparent brightness is proportional to the retinal illumination and

the exit pupil of the pyrometer is generally smaller than the pupil of the eye. Therefore by Increasing the aperture stop diameter, the illumination and the apparent brightness can be increased.

has been a relatively simple matter, using the?

above described electrical equipment, to attain a jj long-term reproducibility in p3rrometer lamp cur-^

rent measurements of better than 1 part in 10,000 [ which is more than adequate for visual optical

pyrometry. ,

3. Sources

The two major types of sources used in optical 1 pyrometry are blackbodies and tungsten strip i lamps. The blackbody is the most fimdamental | source of radiation because it is generally accepted ; that the Planck radiation equation exactly describes the spectral radiation from a blackbody as a function of temperature and wavelength. However, highly stable blackbodies are not convenient

to use, particularly at high temperatures. Moreover, blackbodies for temperatures much higher

than 1000 °C are not readily available commercially (as of 1961). On the other hand, tungsten i strip lamps are highly stable, easy to use, and | commercially available. As a result, when very ' accurate knowledge of the spectral distribution of

radiation from a source is not as important as high | stability and convenience, tungsten strip lamps I are used. | In this section some of the general principles of

the design and use of blackbodies, tungsten strip I lamps, and other sources will be presented, with i particular emphasis on those used at NBS.

3.1. Blackbodies | A blackbody is a substance or object which I completely absorbs any radiation that is incident

j on it. If such a substance or object has a uniform I temperature, it will emit radiation as determined

j by its temperature and by Planck's radiation

j equation. Lampblack is an example of a substance J that approaches a blackbody, at least in the j visible spectral region," to within about 1 percent,

i.e., it absorbs about 99 percent of the visible

radiation falling on it. ! A hollow, opaque body containing a small hole

j can be made to approximate a blackbody ex-

| tremely weU, and sources used as blackbodies are usually of this type. In such bodies, the smaller i the area of the hole relative to the area of the j walls of the cavity, the higher the emittance or !' blacker the body. For a particular geometry, the ! blackness of a hollow body also depends on the , reflectivity of the inner surface of the cavity,

including how diffuse or specular it is. As an

" It is possible for a substance or object to have an absorptance of unity in some wavelength region or regions but not in all. Such a body is not, strictly I speaking, a blackbody; but radiates as a blackbody in the regions where its absorptance is unity. From Kirchoff's law, which states that the ratio of the i spectral radiance of a body at a uniform temperattn-e to its spectral absorptance is equal to the spectral radiance of a blackbody, and from the definition , of spectral emittance given in section 1, the spectral absorptance of a body is equal to its spectral emittance. i

10
example, the radiation emitted from the bottom of a hollow cylinder of which one end is closed and

the other open and whose inner walls are at a uniform temperature is about 0.99 that of a blackbody provided the ratio of the depth of the cylinder

to its radius is 10, its normal reflectivity is 0.2,

and it is diffuse [9]. If the same conditions

existed except for the reflectivity being largely

specular, the effective emittance of the cylinder

would be about 0.90 [9]. Calculations of the

effective emittance of hollow bodies of various

shapes, sizes, and reflectivities can be found in the

literature [9-11].

a. Gold-Point Blackbodies

The hollow bodies used as gold-point blackbodies for reahzing the IPTS are probably the

closest approximation to blackbody radiators cur- rently in existence. Figures 6 and 7 show two

such "blackbodies,"^^ with vertical and horizontal axes respectively, which were designed and constructed at NBS. The gold used to surround the

cavities is 0.99999 pure. In both cases the sighting tubes and the crucibles for the gold are made

of the highest purity graphite available so that

" For convenience, a hollow body used to approximate a blackbody will be

referred to as a "blackbody."

18.6 cm

-6.8 cm

GOLD

GRAPHITE

l°o°o°l CARBON BLACK

DEPTH OF CAVITY

RADIUS OF CAVITY OPENING

•POWDERED GRAPHITE

-MULLITE

=60

Figure 6. Cross section of the NBS vertical gold-point

blackbody.

QUARTZ WOOL

GOLD

GRAPHITE

SILOCEL POWDER

DEPTH OF CAVITY

RADIUS OF CAVITY OPENING = 72

-COPPER COOLING COILS

45 cm

QUARTZ CYLINDERS 1

I I

ALUMINA CONE

ARGON

METAL COVER

HIGH TEMPERATURE CEMENT

CAVITY BRACE NICHROME WINDINGS

IN ALUMINA TUBES

FiGUKE 7. Cross section of the NBS horizontal gold-point blackbody and furnace.

11
the gold remains uncontaminated. The graphite

used is reported by the manufacturer to contain

impurities not exceeding 20 parts per miUion. In

addition, the graphite has a high emittance, a

fairly high thermal conductivity, and is easy to

machine. The latter factor has made possible the

construction of sight tubes of }4-mm wall thiclmess

for the vertical "blackbody" and ji mm for the

horizontal type. The thinner the walls and the

higher their thermal conductivity, the closer the

inside temperature of the walls will be to that of

the freezing gold.

The vertical "blackbody" assembly is heated in a wire-woimd muffle furnace or in the coils of an

RF generator. It is estimated, using the calculations of Gouffe [11] that the emittance of the

vertical "blackbody," assuming the walls are at a uniform temperature, is 0.999. A partial confirmation of this emittance was obtained experimentally in the following manner. The region above

the diaphragm in the sight tube (see fig. 6) itself

approximates a blackbody, but of lesser quality

than the main "blackbody." The depth of this

"blackbody" is somewhat greater than the height

of the gold above the diaphragm and its base is the diaphragm of the primary enclosure. Optical

pyrometer measurements made on this base during

a gold-point freeze resulted in a brightness temperature 0.6 °C less than that obtained from the

primary enclosure. A calculation of the relative

emittance of these two "blackbodies" is compatible

with the 0.6 °C observed, and increases one's

confidence in the estimate of the emittance of the

main sight tube.

Though the vertical "blackbody" is easier to

construct, its use required that the axis of the

optical pyrometer be vertical or that a reflector

be used in conjunction with the "blackbody."

For many years, a 45-degree prism was used at

NBS for this purpose. Its A value was determined sufl&ciently weU so that it introduced an

imcertainty of the gold-point radiance of no more

than the equivalent of 0.1 or 0.2 °C. However,

in order to avoid this additional imcertainty and

in order to have as black a "blackbody" as possible

to be used with the recently developed NBS

photoelectric pyrometer, the horizontal "blackbody" and furnace shown in figure 7 were

developed.

In the design of the horizontal "blackbody"

and furnace, attention was placed on achieving a uniform temperature over the inner walls of the

sight tube. The crucible containing the gold is shaped so that the mass of gold per unit length

of the crucible is about constant for the crucible's

entire length. The furnace has three independently controlled heater windings which are embedded longitudinally in cylindrical graphite

muffles. The graphite, having a high thermal

conductivity, tends to reduce longitudinal temperature gradients. The power inputs to the two

end windings are adjusted to maintain the two

end sections at 1063 °C as determined by two

thermocouples positioned near the inner surface!

of these sections. The center winding is used toi

control the rate of heat loss by the gold during an

freeze. With this design, it is expected that the I gold will freeze more uniformly over the entire p sight tube than in the vertical blackbody. \ It has not been possible to detect in gold-point o freezes differences between the vertical and hori- \ zontal "blackbodies" using a visual optical pyro- n meter. Such differences that may exist are so small they wiU require the photoelectric pyrometer

for detection. The detailed results of using these

gold point "blackbodies" will be given in the

Primary Calibration section.

b. Lesser Quality "Blackbodies"

Lesser quality "blackbodies," particularly at

temperatures much higher than the gold point, I are required occasionally in optical pyrometer | calibrations.^^ In addition, they are preferred for

j accurate spectral calibrations of monochromators

and spectrographs. One such "blackbody" that I has been used at NBS up to temperatm-es of

3000 °C consists of a graphite cylindrical tube

resistively heated in an argon atmosphere and [ surrounded by a number of graphite radiation

shields. The tube is about 200 mm long, has a wall thickness of about 3 mm, and an inside

diameter of about 9 mm. A small hole in the I center of the tube and correspondingly larger I holes in the shields permit the radiation to exit.

A current of about 800 amp is required to reach a | temperature of 2800 °C. The tube can be used j for about 50 hr at this temperature and the j radiance stabiUzed for several hours to better

than 1 percent by automatically controlling the

current in the tube. The effective emittance of

this "blackbody" is currently (1961) being investigated.

"Blackbodies" are sometimes built into an i experimental apparatus so that the temperature

j in an experiment can be determined with an

optical pjTometer. For example, to determine

the surface temperature of an incandescent I material whose spectral emittance at 0.65 is not known, a small hole could be made in the

j material and optical pyrometer observations

j made on this "blackbody." The depth to diameter ratio of the hole will usually be a compromise ' between that required for an adequate absorptance

and that insuring a uniform temperature throughout the hole which is equal to the temperature

| at the surface. In general, even when blackbody

conditions cannot be met weU, temperature

measurements on a poor "blackbody" with estimated corrections often may be more accurate

than utilizing the brightness temperature of the

surface and a poor estimate of the emittance.

" Tungsten strip lamps usually are adequate for this purpose, as discussed

in section 1, Theory.

12
3.2. Tungsten Strip Lamps

The most stable lamp currently available is the small vacuum pyrometer lamp described in

the Optical Pyrometer section Though excellent

as a reference standard in optical pyrometers, its

smallness makes this lamp unsuitable for use in

checking or calibrating optical pyrometers, or for

spectral-radiance calibrations of monochromators

or spectrographs. For these purposes a larger

type tungsten lamp called a strip or ribbon

lament lamp is often used. A variety of these

lamps is commercially available from the General

Electric Company in the United States (to the

best of our knowledge the sole supplier in the

U.S.), General Electric Co., Ltd., in England, and

Philips' Lamp works in the Netherlands.

a. Types of Strip Lamps

In the United States, the tungsten strip lamp

most commonly used for optical p3rrometer

applications is the General Electric Company

type 30A/6V/T24 ribbon filament lamp. The

first two numbers in the type designation mean

that if 6 V is applied to the lamp, the resulting

current is about 30 amp. This lamp has a glass

envelope about 75 mm in diameter and 300 mm

long and a tungsten ribbon filament about

0.075 mm thick, 3 mm wide, and 50 mm long.

In order to increase the reproducibility of observing the same point or area of the filament,

the filament is notched on one edge at about the

midpoint of its length. A V bend toward one

end of the ribbon allows it to expand or contract

without twisting or bending when its temperature

is changed. The envelope contains, according

to the manufacturer, argon at a pressure of about

Yz atm at room temperature. The filament is approximately parallel to the axis of the envelope.

Its exact position varies, but it is preferable that

the filament be situated off the axis of the envelope

and that it be oriented so that the normal to

its surface is not on a radius of the cylindrical

envelope.^" There is sufficient volume in the

envelope above the filament to allow convective

gas currents to flow smoothly upward from the

filament and thus allow any tungsten vapor to

condense on the upper portion of the relatively

cool envelope.

The 30A/6V/T24 lamp requires a current of

about 14 amp for a brightness temperature of

1000 °C and about 45 amp for 2300 °C. The

change of ciu-rent per degree change in brightness

temperature varies from about 0.010 to 0.030 amp

per degree from 800 to 2300 °C, respectively.

Direct current is usually used so that standard

potentiometric measurement methods can be

employed. When a sufficiently high-current

source is not available, some of the lower current

lamps should be considered. However, their

2" Reasons for this will be given later in this section.

narrower filament makes brightness matching

more difficult with optical pyrometers having a low magnification.

A strip lamp that is especially useful when a higher brightness temperature is required is the

the General Electric 75A/T24. The filament and

filament supports for this lamp are designed to

permit the lamp to be used up to a brightness

temperature of about 2800 °K. In addition,

the lamp may be obtained with a plane quartz

window so that it can be used in the ultraviolet

spectral region. However, these lamps require

about twice the ctirrent of the 30A/6V/T24 lamp

and have no notch.

The General Electric Co., Ltd., in England

manufactures a vacuum tungsten strip lamp

which is highly recommended for use below 1400

°C. It is called a secondary standard tungsten

strip vacuum p3rrometer lamp and requires only

about 7 amp to achieve a 1400 °C brightness

temperature. This lamp has been used at NBS

up to 1750 °C, but if high stability is required, it

is recommended that the lamp not be used above

about 1400 °C.

The High Temperature Measurements Laboratory at NBS has had very little experience with

Phillips' tungsten lamps made in the Netherlands.

Lamps made in this country have usually been

adequate. However, with the increased stability

required of tungsten sources in photoelectric pyrometry, this will probably not continue to be the

case and tungsten strip lamps from essentially

every source will have to be investigated in the near future.

b. Factors Affecting the Reproducibility of Strip Lamps

There are a number of factors which must be

considered in order to obtain the optimum reproducibility and stabiUty with tungsten strip lamps.

Many of these have been investigated by Barber

[5], DeVos [6], and by the High Temperature

Measm-ements Laboratory at NBS. The following is a brief summary of the factors considered

to be of major importance.

Tungsten strip lamps possess a temperature

gradient along the length of the strip with a maximum temperature at or near the notch. In T24

type lamps the brightness temperature gradient

at the notch may vary from zero to 5 deg C per

millimeter, depending on the particular lamp, its

temperature, and orientation. The direction of

the current also has an efl^ect. The ciirrent direction is important because when direct current exists in a region of a temperature gradient, heat is absorbed or generated (in addition to the "Joule

heating") depending on the direction of the cur- rent relative to the gradient. This is called the

Thompson effect ; and in tungsten, if the current

direction is from hot to cold, heat is absorbed.

When the direction is from cold to hot, heat is generated. Thus in order to obtain reproducible

brightness temperatures from a strip lamp, care must be taken to sight at the same point or region.

This is usually the notch.

13
I

Another factor important in obtaining reproducibility with a strip lamp is the room or ambient

temperature, particularly for brightness temperatures below 1500 °C for gas-filled lamps and 900

°C for vacuum lamps. The convective and con- ductive heat losses depend on the ambient temperature, and if the ambient temperature changes,

the resulting temperatme at the notch will change.

For example. Barber [5] observed a variation of

brightness temperature of 0.3 deg C per 1 deg C

change of ambient temperature for a gas-filled

lamp at a brightness temperatm"e of 1050 °C.

At the very high filament temperatures, the energy

loss from a filament is largely radiative, and the

room temperatm-e has much less effect.

The temperature at the notch for gas lamps is also a function of the lamp orientation. This is caused by gas convection currents in the lamps,

and Barber [5] shows the effect to be about }^ deg

C for a forward tilt of the filament of an angle of

1 deg. At NBS, gas lamp strip filaments are adjusted with the aid of a plumb line to be vertical

at the notch.

In general, the radiance or brightness temperature of a tungsten strip lamp depends on the direction of observation. This is due to the fact that

the emittance of tungsten is a function of the angle

of emission. It is also caused by reflections.

Radiation from the filament may be reflected by

the envelope onto the tungsten strip and then into

the pyrometer's field of view. The emittance

variation as a function of angle of emission is very

small near normal emission and can usually be

neglected. This is not the case for the reflection

effect, and it is desirable to orient the lamp with

respect to the optical pyrometer to avoid these

reflections. Figure 8 shows several examples of

the reflection under discussion. It can be seen

that the nature of the reflection depends on the

position of the fllament relative to the axis of the

envelope and on the orientation of the plane of

the filament. Case c is the preferred positioning

and orientation of the filament. In this case the

Figure 8. Examples of reflections in a cylindrical envelope

tungsten strip lamp for three different positions and

orientations of the strip.

filament may be observed normally without any

contribution from reflections. It is desirable to

view a fllament normally because of the small

emittance variation stated above, and because at

normal emission the radiation will not be polarized.

In case a when the filament is on the axis of the

lamp, it is impossible to avoid reflections. In ! case b, reflections can be avoided but observations

must be made off the normal. In using lamps in I position b, one should keep in mind that the radiation is partially polarized.^^ When lamps are used 1 or calibrated at NBS, the best direction of sight- j ing is decided on, and an arrow is etched on the \ glass envelope such that a line extending from ! the head of the arrow through the notch defines ] the desired direction.

In order to achieve stabiUty, a tungsten strip

lamp should be extensively aged or annealed.

Some of the details concerning annealing were

discussed previously in connection with the small

P3Tometer lamps. DeVos [6] claims that after

anneaUng a tungsten strip for 100 hr at 2400 °K,

20 hr at 2600 °K, or 2 hr at 2800 °K, no further

change in its radiance (at constant current) was

observed. At NBS, gas-filled strip lamps are annealed at between 2325 and 2350 °C brightness

temperature (a tungsten temperature of about

2625 °C) for 2 hr. After such an anneahng and

after taking the necessary precautions with the

various factors discussed in this section, 30A/6V/

T24 gas lamps have been used as high as 2200 °C

for 50 hr and as high as 2380 °C for 20 hr without

any change in their radiance being detectable.

The precision of these measurements was about 2

deg C. It should be emphasized, however, that

all gas-filled strip lamps may not possess this kind

of stabihty; and at present, very httle statistical

information on their stability is available.

3.3. Other Sources

a. The Carbon Arc

At brightness temperatures higher than about

3000 °C, no convenient, stable sources are at

present (1961) available. The positive crater of a carbon arc has been recommended and used as a

radiation standard [12-14] at the subhmation

temperature of carbon. At this temperature the

brightness temperature of the crater corresponds

to about 3527 °C at 0.65 n. However, the carbon

arc is not as convenient to use as a lamp and is highly stable only at the one temperature.

b. High-Pressure Arc

At brightness temperatures above 3000 °C,

gaseous soiirces probably are the greatest hope for

the future. Xenon high pressure arcs have been

21 This is probably important only in using strip lamps to calibrate an

optical system containing mirrors. Such a system may have a transmittance which depends strongly on the polarization of the radiation.

22 This presumably means no change within the long-term precision of his measurements which appears to be about 1 percent in spectral radiance.

14
studied extensively [15] and are available commercially. Their usefulness in optical pjo-ometry,

however, has not yet been established.

4. Primary Calibration

The temperature scale above 1063 °C that is maintained at the National Bureau of Standards

is the result of attempting to reahze the International Practical Temperature Scale using the

methods of optical pyrometry. The experimental

attempt to reahze any portion of this scale without comparison with previously cahbrated pyrometers or sources is called a primary calibration. In the previous sections of this paper, the

IPTS above 1063 °C was defined and the theory

and instruments used in optical p3rrometry described. This section presents the results of the

1958 primary cahbration of the NBS visual optical

pyrometer.

4.1. Calibration at the Gold Point

The initial step in the primary calibration at the

gold point was the optical ahnement of the "blackbody" and the pyrometer. The optical axis of the

NBS pyrometer was positioned on the axis of the

vertical "blackbody," and the pyrometer focused

on the "blackbody" diaphragm. The "blackbody" was slowly heated until the gold was melted

and brought to a temperature estimated at 5 to 10

deg C above the melting point. It was then

allowed to cool, and brightness matches were made

as a function of time. The pyrometer lamp current, corresponding to these brightness matches,

plotted against time constituted the gold-point

"blackbody" coohng curve. As the "blackbody"

cooled, its brightness decreased rather rapidly,

and then increased slightly. This dip, seen on the

typical cooling curve in figure 9, is called the under105.00

I

1 1 1 1 1 1 1 1

1 1 1 11

oH - I

Q. 104.60 -

o

o:>

a. 104.20 -

J I I I

I I I I I

I L_ 0 10 TIME, min

FiGUHE 9. A typical cooling curve obtained during a goldpoint calibration with the NBS visual optical pyrometer

and the vertical gold-point "blackbody."

cool. After the imdercool, the brightness re- mained constant within the reproducibility of the

determinations, and matches were made about

every 15 sec alternating between a bright pyrometer filament to disappearance and a dark filament

to disappearance. The average of two such

matches was considered one observation. The

brightness remained constant from 5 to 8 min,

allowing 10 to 16 observations. This plateau

represented the freezing-point temperature of the

gold.

In the primary calibration of 1958, about 50

such plateaus were taken on the vertical "blackbody" over a 2-month period by 3 experienced

observers using both an RF generator and a

muffle furnace for heating. Though the muffle

furnace system had a larger heat capacity and

freezes lasted 2 to 3 times longer, the lamp cur- rents corresponding to the plateaus of the cooling curves were the same to better than the standard

deviation of an observer's brightness matches, or the equivalent of about 0.2 deg C.

Heating or melting curves were also obtained.

When inductively heating, the brightness matches

corresponding to the melts were almost 1 deg

higher than those obtained during the freezes ; but

in the muffle furnace, they were only a few tenths

of a degree higher.^^ The large difference in the

case of the RF melt is attributed to a less uniform

heat input and to the background conditions in

the pyrometer field of view affecting one's judgment of the match. In the case of freezes, the

cooling is more uniform and the brightness of the

region which surrounds the smaU sighting hole or diaphragm is negligibly different from the bright- ness of the sighting hole. Only the freezes were

used for the actual calculation of the gold-point

calibration.

The results of the 1958 gold-point determination

are given in table 2. In addition, data obtained

in 1957 and 1960 are included. The observations

in 1957 were made using a vertical "blackbody"

similar to that in 1958, but the horizontal "blackbody" of figure 7 was used in 1960. The 1957 and

1958 results include the effect of a 45° right-angle

prism and represent a temperature lower than the

gold point due to the prism absorption and reflection. This apparent gold-point temperature

was calculated from eq (1 —9) where Ti=To-\-

1063 = 1336.15 °K and ^=6.92 mureds 2* resulting

in T'app= 1323.9 °K. The A value of the

prism was determined independently using a strip

lamp and data from the previous primary calibration. The standard deviation of the A value of

each of three observers about their grand mean was

equivalent to about 0.1 deg C. Since only relatively smaU differences of temperature near the

gold point were required to determine A, use of the

28 Observations made in 1960 on the horizontal "blackbody" resulted in melts only 0.1 deg C higher than the freezes.

2* The unit in which A values are usually reported is the mired. One mired

is equal to 10-8 (<>K)-i.

15
Table 2. NBS primary optical pyrometer calibrations at the gold point using a glass prism and an apparent temperature of

1323.9 °K

Observer

1957 1958 1960 »

LI

Pyrometer

lamp

current >'

Number

of

freezes

Standard

deviation " LI

PjTometer

lamp

current

Number

of

freezes

Standard

deviation ° LI

Pyrometer

lamp

current''

Number

of freezes

Standard

deviation"

Si Si Si Si Si Sz

flDL

RCH

RCG

HJK

EL _ ATH

Mean of all observers

ma

104. 465 9 ma0. 023 ma ma104. 450

104. 426

104. 522

17

16

12

ma

0.019

.036

.042

ma ma

104, 484

104.457

104. 427

104.410

104. 573

3

12

12

ma

0. 029

.028

.018

ma

104. 465 104. 466 0.049 104, 470 0.059

"The 1960 data were obtained using a horizontal "blackbody," and therefore the glass prism used with the vertical "blackbody" was not required. As a result,

for comparison purposes, the 1960 data were normahzed to 1323.9 °K.

''0.05 ma is equivalent to 0.3 °C.

° Si is the sample standard deviation of an individual's freezing point determinations about his own mean. Sj is the sample standard deviation of individual

observers' mean determinations about the mean of the determinations of all observers.

former calibration data did not significantly affect

the accuracy of A. If no previous calibration had

existed, a sectored disk and strip lamp woidd have

been used to determine the A value of the prism.

The horizontal "blackbody" constructed after

1958 and used in 1960 did not require the use of a prism. For comparison in table 2, the 1960 data

were adjusted to the apparent temperature of

1323.9 °K or 1050.7 °C using the completed

calibration.

Table 2 shows that the standard deviation of an

individual's single freeze varied from about 0.1 to

0.25 deg C about his own mean. The difference

between observers was as large as 1 deg when only

a few freezes were taken. Even the means of 16

freezes of RCG and 12 freezes of ATH differed by

0.6 deg C, though the sum of the standard deviation of the two means was about 0.13 deg C.

These differences can not be accounted for by relative luminosity factor differences. The differ- ences in the measured relative luminosity factors

would account for only about 0.1 deg C. Moreover, the observer differences would be less when

using a tungsten strip lamp; but the observers

maintained the same differences in this case. When observations were made on tungsten strip

lamps through sectored disks with an apparent

temperature near the gold point, the same differ- ences still remained. These differences between

observers at the gold point were attributed to their

matching technique and to psychological factors,

and the only way of reducing their effect on the

accuracy is to use a number of observers. The

observer effect may be indicated quantitatively by

the standard deviation of an observer about the

mean of all observers. In the 1960 data, where

five observers were used, this standard deviation

was estimated to be 0.4 deg C.

4.2. Calibration Above the Gold Point

To extend the cahbration to temperatures above

and below the gold point, timgsten strip lamps

2= Even thoush the International Practical Temperature Scale is defined by

Planck's radiation equation only above 1063 "C, optical pyrometers are fre- quently required at lower temperatures.

were matched through sectored disks and eq (1-5)

used to calculate the new temperature t. Then

the sectored disk was removed and the strip lamp

matched to obtain the p37rometer current corre- sponding to the new temperature. The transmittances, R, of the sectored disks were determined

in the Metrology Division of NBS and the mean

effective wavelength, X, _,, were obtained from

eq (1-21) using the effective wavelengths shown in

figure 10. The latter were calculated with eq

(1-20) using spectral transmittance functions of

the pjTometer elements determined at NBS and

the CIE standard relative luminosity factors.

However, it was found from independent measurements that the relative luminosity factors of the

observers were shghtly different from the CIE

factors. This produced an average change in the

2» Commission Internationale de I'Eclairage. " I.E.S. General Guide to Photometry, Illuminating Engineering Society,

New York, N.Y. (1954).

a.

0,650

> No Ag

1 t

1

1

\Ag 2

1 1 1 1 1 1

. Ag 1

1000 2000 3000

TEMPERATURE,°K

Figure 10. Effective wavelengths for the NBS visual optical

pyrometer using the CIE standard relative luminosity

factors.

16
mean effective wavelengths of about 7 A, and re- quired a correction from about —0.2 deg C at 800

°C to about +3.2 deg C at 2400 °C;

For observations using sectored disks, the disks were positioned at the tungsten-strip image which

was produced by a lens corrected for spherical

aberration and coma. The strip-lamp current was

continually monitored to insure constancy of lamp

brightness. Using 7 sectored disks ranging in

transmittance from 0.35 to 0.007, three observers

made 50 sets of observations for the low range from

800 to 1300 °C, 42 for the range 1300 to 1750 °C

using absorbing glass number one (AG 1), and 30

sets each for AG 2 and AG 3 covering 1750 to

2050 °C and 2050 to 2400 °C, respectively. Each

set of observations consisted of 4 brightness

matches with the sector, 6 without, and 4 more

with the sector. Again, matches were made by

approaching the disappearance alternately from

the dark and bright side. Each observer used his

own gold-point or low-range cahbration to obtain

the apparent temperature.

In the low-range cahbration above 1051 °C, the

lamp brightness through the sectored disks was

maintained close to that of the gold "blackbody"

as seen through the glass prism, i.e., 1051 °C. For

temperatures less than 1051 °C, the lamp bright- ness was adjusted to about 1051 °C when not looking through the sector. Figure 11 shows the re- sults of the low-range calibration for the thi-ee

observers. Itabie in figure 11 was obtained from

the original (1952) calibration for this pyrometer

lamp. If a previous cahbration had not been

available, a 3d- or 4th-order pol3momial approximately fitting the new calibration could have been

used to obtain an Itabie as a function of temperature. For the low-range cahbration the standard

deviation of an observer about his own mean was

approximately 0.35 °C.

.24 -

e .16

.08 oH

800°C 1350°C

For the higher ranges where AG 1,2, and 3 are

used, brightness temperatures of the source as seen through the sectored disks were not maintained

at the gold point alone, but also at other points

already calibrated in the low range. A values

were calculated from eq (1-9) for each set of observations where Ti was the apparent temperature

as seen through the absorbing glass and Tj the

brightness temperature of the strip lamp obtained

from a sectored disk calculation. It should be

emphasized that the brightness temperature of the

tungsten strip lamp Tj must correspond to the

mean effective wavelength for the absorbing glass

used. Figures 12, 13, and 14 show the A values

obtained for each of the absorbing glasses. The

standard deviation of an observer's A value about

his own mean varied by an equivalent of 1.0 to

2.0 deg C.

128.20

127.80

127.40

=< 127.00

126.60

126.20

PREVIOUSV—>^ X

I 2°C X ATH V RDL 9 RCG

1300° C 1750°

C

105 115 125 135 145 PYROMETER LAMP CURRENT, ma

155 165

Figure 12. The 1958 determination of the A value of absorbing glass 1 of the NBS visual optical pyrometer.

194.20

193.80

E 193.40

tJ3

_I<

192.60

192.20

X

1 1

ATH

1 1 1

V RDL • RCG

Si l.4°C

V V

PREVIOUS_ _ _X

X

X •

•

1700°C

1 1 1 1 2050° C

1

75 95 115 135 PYROMETER LAMP CURRENT, ma

155 120 130 140 150 160 PYROMETER LAMP CURRENT, ma

170

Figure 11. The 1958 primary calibration of the low range

of the NBS visual optical pyrometer.

Figure 13. The 1958 determination of the A vahie of

absorbing glass 2 of the NBS visual optical pyrometer.

17
244.90

244.50

E 244.10

V 243.70

243.30

242.90

X

1

ATH

1

1 1

ROL

RCG l.9°C

-SZ—

: ^Evipys-

- X

- •

•

2000°

C

1 2400°

C

125 135 145 155 PYROMETER LAMP CURRENT, mO

65

Figure 14. The 1958 determination of the A value of

absorbing glass 3 of the NBS visual optical pyrometer.

An analysis of the data obtained for the lowrange calibration reveals that the observers continue to read strip lamps with about the same

difference throughout the low range, except for a

slight trend of observer RDL indicated by the

crossover of his calibration with that of observer

RCG. Thus the observer differences throughout

the low range also appear to be the result of judgment or psychological factors. Therefore it was

decided to take the mean of three observers and

apply an average relative luminosity factor correction to the mean. The 1958 low-range calibration,

including luminosity corrections, is 0.8 deg C

lower than the 1956 calibration at 800 °C and

0.9 °C higher at 1350 °C.

The A values for all the absorbing glasses are, within the experimental error, constant with source temperature, thus supporting an exp[— /c/X] transmittance. Except for AG 1, differences continue

to exist between observers that have no adequate

explanation. In analyzing the data, it is seen that

ATH and RCG have the same differences in

temperature when matching with or without

sectors, and this is independent of current. However, ATH and RDL match differently through

sectors when the apparent temperature is changed.

When matching through absorbing glasses, ATH

and RDL maintain the same difference that exists

between them at the gold point but ATH and RCG

change by C.6 °C. The mean of the A value curves

for the three observers was corrected for the

average relative luminosity factor of the three

observers and used in conjunction with the average

low-range calibration to obtain calibrations for the

high ranges. The 1958 calibration of the upper

ranges is about equal to the 1956 calibration at

1400° C, 0.6 deg higher than the 1956 calibration

at 1700 °C, and 2.4 deg C higher at 2000 and

2400 °C. Part of these differences is attributed

to the relative luminosity factor corrections which

were made in 1958 but not in 1956.

4.3. Estimated Accuracy

An estimate of the accuracy of this primary

calibration can be made by comparing it with the

mean of similar calibrations from other national

laboratories throughout the world. In fact, to the

best of our knowledge, this is the only way of

quantitatively estimating the accuracy. Fortunately this can be done through the international

comparison of strip lamps completed in 1958.

Figure 15 shows the difference as a function of

temperature between the strip lamp calibration at

NBS using six observers and using the 1958 primary calibration and the mean of the strip-lamp

calibrations of three other national laboratories.

These are the Deutsches Amt fiir Mass und

Gewicht, German Democratic Republic, the

National Research Council, Canada, and the

Physikalisch-Teclmische Bundesanstalt, Federal

Republic of Germany. The standard deviation

of all four national laboratories about their grand

mean is also given in figure 15. This serves as an indication of how Avell the IPTS above 1063 °C

has been realized.

It is felt that the results of the 1958 primary

calibration at NBS is about the best one can expect

from visual optical pyrometry. The major limitations are the sensitivity of the eye to differences in

brightness and the knowledge of the mean effective

wavelengths.

2.0

-~-t>

-LO

2.0

O ESTIMATED STANDARD DEVIATION OF THE MEANS

OF FOUR NATIONAL STANDARDS LABORATORIES

(DAMG, NBS, NHC, PTB) ABOUT THEIR GRAND MEAN.

A NBS MEAN USING SIX OBSERVERS AND 1958 PRIMARY CALIBRATION MINUS MEAN OF DAMG. NRC, PTB

1000 1400 1800

TEMPERATURE, °C

2200

Figure 15. The international comparison of strip lamp

calibrations completed in 1958 betiveen Deutsches Amt fiir Mass und Gewicht {DAMG) of the German Democratic

Republic, NBS of the United States, National Research

Council (NRC) of Canada, and Physikalisch-Technische

Bundesanstalt (PTB) of the Federal Republic of Germany.

The dashed curve represents a resrion in which the estimated standard

deviations are somewhat less reliable due to the fact that the laboratories rounded oft their data to the nearest degree.

18
5. Secondary Calibrations

The International Practical Temperature Scale

that is realized and maintained at the National

Bureau of Standards is distributed throughout

the United States through the NBS calibration

and test services. The fees and instructions for

utilizing these services are listed in the Federal

Register. The present section describes in detail

the procedures used in calibrating optical pyrometers and tungsten strip lamps.

5.1. Optical Pyrometers

a. Inspection and Cleaning

The initial step after receiving an optical

pyrometer submitted for calibration is the general

inspection of the instrument to confirm that it is in good operating condition. If it passes this

test, the optical elements of the mstrument are

cleaned, using lens tissue and distilled water.

The surfaces of the objective lens, absorbing

glasses, and the window of the pyrometer lamp,

which is located between the source and the

pyrometer lamp filament, are the most important

surfaces to clean. A reminder is given on optical

pyrometer certificates that the optical surfaces

should be kept clean in order for the calibration

to be applicable.

b. Determination of the Effective Wavelengths

Since optical pyrometers are usually calibrated

by comparison with the NBS pyrometer using a tungsten strip lamp and not a blackbody as a

transfer source,^^ differences between the mean

effective wavelengths of the test and the NBS

instrument are required. These differences are used to calculate from eq (1-28) the brightness

temperature T{ that the test pyrometer should

indicate when the NBS pyrometer indicates T^.

Even though both instruments are observing the

same tungsten lamp, the brightness temperature

obtained by the two should be different if their

effective wavelengths are different. If a blackbody were used, this would not be the case. Thus

T[ — Ti must be determined as a function of

temperature and added as a correction to each

brightness temperature determined by the NBS

pyrometer during the calibration.

The differences in mean effective wavelengths

required for the above temperature corrections

are obtained by either of two methods. The first

method is to determine the spectral transmittances

of the red filter and the absorbing glasses of the

test pyrometer and to calculate the effective and

mean effective wavelengths as outlined in sections

1 and 4. Effective wavelengths have been deter2' However, a resistively healed graphite tube "blackbody" similar to that

described in section 3.2 is being investigated at NBS for use as a transfer source in the calibration of optical pyrometers up to 2800 °C. Using a black- body would eliminate the need for determining the differences in effective wavelength.

mined for the NBS pyrometer for the primary

calibration, and therefore differences between

mean effective wavelengths for the NBS instrument and the test instrument can be computed.

The second method, though simpler to use when

established is not quite so straightforward, and

therefore a detailed description will be given.

The second method consists of determining the

brightness temperatures with the NBS pyrometer

using its own red filter and the test pjrrometer red

filter for a series of sources for which the brightness

temperatures are the same when using the NBS

red filter but for which the color temperatures

vary from values very large compared to the

brightness temperature to values close to it. Such sources can be obtained by using a strip

lamp in conjunction with a number of sectored

disks. With each of the sectored disks the lamp

brightness is adjusted so that when observed

through the disk, the lamp has the same brightness

temperature. Using eq (1-28), the differences

between the mean effective wavelengths are

calculated. The limit of the mean effective

wavelengths for the test red filter as the disks are changed and the color temperature approaches

the brightness temperature is the effective wavelength for that red filter at the limiting brightness

temperature. This is repeated for a sufficient

number of brightness temperatures in the low

range, in order to determine by curve fitting the

effective wavelength as a function of temperature

for the entire range. The resulting wavelengths,

however, represent only a first approximation to

the effective wavelengths required. The reason is that the calibration of the NBS pjTometer using

the test red filter is slightly different from that

using its own red filter. A closer approximation

can be obtained by correcting the primary calibration of the NBS pyrometer with the first

approximation of the effective wavelength for

the test red glass. The improved calibration for

the NBS pyrometer when using the test red

filter will usually modify the temperature differ- ences determined initially for the series of sources by about 25 percent and permit a second approximation to the determination of the test instrument

effective wavelength. This second approximation

is usually adequate.

Since the spectral transmittance curves of most

red filters used in optical pyrometers have the

same general shape, their efl'ective wavelength

versus temperature curves are approximately

parallel. Therefore, usually one effective wavelength determination is sufficient. Moreover, at

NBS the actual temperature corrections to be

applied to the test pyrometer have been determined as a function of the temperature dift'erence

observed using a particular strip-lamp brightness

and sectored disk and the uncorrected NBS

primary calibration. Such a set of curves need

be computed only once and, thereafter, a single

observation through each of the two red filters,

using one lamp brightness and sectored disk, is

19
sufficient to determine the correction to be applied

at every temperatiire of the cahbration.

For optical pyrometers which have absorbing

glasses with a constant A value, the effective

wavelengths of the higher ranges are approximately equal to the effective wavelengths of the

low range for corresponding pyrometer lamp

currents. In these cases the effective wavelengths

determined for the low range also suffice for the

higher ranges. When the type of absorbing

glass used is not of the constant A value type or

is not known, effective wavelengths for the higher

ranges are calculated from experimentally determined transmittances.

Most of the visual optical pjrrometers received

for cahbration that have been manufactxu-ed

since about 1959 appear to have mean effective

wavelengths negligibly different from those of

the NBS instrument. However, this is not the

case for the older instruments. Some of these

have had differences as large as O.Ol/x, corresponding to about a 5 deg C correction at a timgsten

brightness temperature of 2400 °C and to about

a 1 deg C correction at 1063 °C.

c. Calibration Procedure

After determining the effective wavelength

and/or corresponding tungsten brightness temperature correction as a function of temperature

for the test optical pyrometer, the test pyrometer

is carefully mounted alongside of the NBS

instrument so that their optical axes are parallel

and in the same horizontal plane. A GE tungsten

strip lamp, 30A/6V/T24, is oriented as described

in section 3, on a large lathe serving as an optical

bench so that it can be easily and accurately

translated in a direction perpendicular to the

optical axes of the pyrometers. Surplus lathes

have been found quite adequate for such purposes.

For convenience, micro-switches are positioned on

the lathe bed so that the lamp may be stopped

exactly on the optical axis of each pj^rometer.

The tungsten strip lamp is specially selected

to have its filament positioned olf the lamp axis,

and therefoi-e the filament plane can be made

perpendicular to the p^Tometer axis without

detrimental reflection effects. The brightness

temperature of the lamp as a function of distance

from the pjTometer is also determined; and, if large, the lamp is not used. As a result of this

careful arrangement of the pyrometer and lamp,

the orientation of the lamp with respect to each

pyrometer is the same within the experimental

errors of the alinement.

The test optical pyrometer could be compared

to the NBS instrument in the same manner in

which it is used; that is, a brightness match

made with the test instrument and the scale on

this instrument read. However, a different procedure has been found to be more accurate and

convenient. The calibration is performed in

2« By neglieible is meant an effective wavelength for which the temperature

correction when observing strip lamps is about 1/10 of the other uncertainties

in a calibration.

two parts, the first being a lamp calibration wherej

the brightness temperature indicated by the'

instrument is determined as a function of thef

test pyrometer lamp current. The second part is a f scale calibration where the instrument scale is' calibrated as a function of pyrometer lamp;

current. When combined, these two parts result

in the calibration of the instrument scale as a! function of the brightness or blackbody tempera-'

ture of the source being observed.

In order to perform the calibration as described,

the p3rrometer lamp current must be measured

to at least 1 part in 1 thousand and preferably to

1 part in 10 thousand. A potentiometer and

standard resistor are used for this purpose. An

electrical series circuit is set up containing the

test pyrometer lamp, resistors or meters normally

in the test pyrometer lamp circuit, a continuously

variable resistor, a standard resistor, and a lead

storage battery. The pyrometer lamp current is controlled with the variable resistor and determined with the potentiometer by measuring the

voltage drop across the standard resistor.

Two observers perform the first part or lamp

calibration of the test instrument; one observer

makes the brightness match while the other

determines the lamp current with the potentiometer. One point on the brightness calibration is obtained as follows. The strip-lamp current is determined. Then one observer makes two

brightness matches on the strip lamp using

the NBS instrument, the first approaching the

match with the filament initially darker than the

strip and the second with the filament initially

brighter. These matches will be designated as dark to bright and bright to dark respectively.

After each match, the current in the pyrometer

filament is determined. Next the observer shifts

himself and the strip lamp to the test instrument

and makes 4 matches, dark to bright, bright to

dark, bright to dark, and dark to bright. Returning to the NBS instrument, two more matches,

bright to dark and then dark to bright, are made; and the strip-lamp current again determined. Bracketing the eight brightness matches

with two strip-current determinations serves as a check on any drift of the strip-lamp current and

therefore the brightness temperature. The drift

is usually negligible. The data for this one

calibration point for the pyrometer lamp are completed after the observers switch roles (bright- ness matching and current measuring) and the

process repeated. In summary, the brightness

comparison of the test and NBS pyrometer at a given temperature consists of four matches on

the NBS instrument and four on the test instrument by each of two individuals.

The data obtained by the two individuals are separately averaged, each of the average NBS

pyrometer lamp currents are converted to bright- ness temperatures through the primary calibration, and finally these temperatures are corrected

for any mean effective wavelength differences

20
between the NBS and test instruments. Thus a lamp-cahbration point consists of two test pyrometer lamp currents and corresponding bright- ness temperatures of the tungsten strip lamp

determined by two observers at the mean effective

wavelength of the test instrument.

d. Low-Range Calibration

The brightness calibrations are performed range

by range. The low range is calibrated first,

because its calibration is used in the calibration

of the other ranges. Six calibration points

similar to that described in section 5.1.C are obtained for the low range, about 800 to 1250 °C.

Other points in the low range are obtained by

interpolation. For one class of optical pjo-ometers, calibrated at NBS for a number of years, a

table of current versus temperature representing

an average smoothed low-i'ange calibration has

been obtained. Temperature differences between

this table and the six calibrated points are plotted

as a function of current, and a curve best fitting

these points is drawn. This is similar to the

M curve obtained for the low range of the NBS

primary calibration. A typical example is shown

in figure 16. For instruments for which an aver- age calibration does not exist, eight calibration

points are obtained at equal current intervals in

the low range and a 4th- or 5th-degree equation is fitted to the eight points by the method of or- thogonal polynomials [16, 17].

The low-range calibration is completed by

determining the current corresponding to the

cardinal readings on the p3rrometer scale or meter

for which a temperature is to be reported. This,

together with the curve and the table or the

4th- or 5th-degree equation, permits a blackbody

temperature to be obtained for each of these

cardinal points.

10

1 \ \ 1 [ V

A OBSERVER 1 X OBSERVER 2 /

X

V

X

. X

800 'C

1

1

, 1225 °C 30 34 38 42 46 50 54

TEST PYROMETER LAMP CURRENT, mo

e. High-Range Calibrations

The high ranges of an optical pjrrometer are calibrated by determining the A value for each

of the absorbing glasses as a function of blackbody

temperature. The A value is calculated using

eq (1-9) in which Tj is the apparent temperature

determined from the low-range calibration using

the current corresponding to a brightness match,

through the absorbing glass, of a source having a

brightness temperature Ti. The temperature

is determined by the NBS instrument and must

be corrected for the mean effective wavelength of

the test pyrometer.

Observations at a particular temperature are taken in a manner similar to that described for

the low range. Since A values are usually linear

functions of temperature, observations are limited

to three temperatures in a range. However,

each observer takes two sets of observations at

each point to improve the precision of the mean.

A values for each range are plotted as a function of pyrometer lamp current or source temperature. As in the low-range calibration, pyrometer

lamp currents corresponding to the cardinal points

to be reported are determined. Apparent temperatures are obtained for these currents using the

low range curve. The Tapp together with the

corresponding A values are then used in eq (1-9)

to obtain a temperature calibration. Mathematically

-A=yp '

Itjt, ttt ) (5—1) T Tapp app app i/

where the apparent temperature associated with

the A value is primed to emphasize that its value

depends on how the A value curve is drawn and

may be different from Tapp- Since unexplainable

observer differences exist in brightness matches, a compromise is made when drawing the A value curve—-a compromise between completely smoothing, the data with the theoretically predicted curve and exactly following the experimentally determined A values. Figure 17 is a typical example

of an A value curve.

344.4 1

1 1 1

1

344.0

-

xx

343.6

V

343.2

l°C

342.8 X

V OBSERVER 1 X OBSERVER 2

342.4

1550 °C

, 1 ,2400 °C

, ,2800 °C

32 36 40 44 48 52 56 TEST PYROMETER LAMP CURRENT, ma

Figure 16. A typical low-range At calibration curve for a commercial optical pyrometer

.

Figure 17. A typical A value determination for an upper

range of a commercial optical pyrometer.

21
I

Optical pyrometers are calibrated up to 2400 °C

(as of May 1961) using tungsten strip lamp

sources. Usually for instruments used to 2800 or 3200 °C actual observations are not made above

2400 °C. The A value is extrapolated above 2400

°C using the theoretically predicted shape, which

is usually a constant. For ranges which extend

to about 4200 °C, in addition to using a tungsten

strip lamp up to 2400 °C, the positive crater of a carbon arc, at a brightness temperature of about

3530 °C with spectrographically pure graphite

electrodes or between about 3630 and 3800 °C

with projector pregraphited carbons, is also used

to obtain the A value. Since the carbon arc is not

as stable as a strip lamp, observations are often

made simultaneously with two observers making

brightness matches with the NBS p3a-ometer and

the test pyrometer simultaneously.

Changes in the brightness temperature with

wavelength in the case of carbon arcs are sufficiently small so that effective wavelength corrections can be neglected. This is because the positive crater of a carbon arc is very close to a gray

body with an emittance of about 0.77 in the visible

spectral region [14]. Thus the color temperature

in this case is the temperature; and for a bright- ness temperature of 3800 °C, the temperature

would be about 4000 °C. Such a range of bright- ness to color temperature is not sufficient to produce a significant change in brightness temperature for a 0.01 n wavelength shift, the maximum

normally observed.

In some optical pyi-ometers the range to 4200 °C

is reached by using two absorbing glasses in series.

These ma}^ be calibrated at lower temperatures

and the A values added. When this is possible

the uncertainty of the calibration is often less.

5.2. Tungsten Strip Lamps

a. Calibration Range

Gas-filled tungsten strip lamps are normally

calibrated at NBS at brightness temperatures

from 800 to 2300 °C. The lower limit is set by

the fact that very few calibrations are ever re- quested below this temperature and because the

eye's contrast limen^^ is already quite high at

800 °C . However, Lovejoy [7] , by removing the red

glass, has used a conventional laboratory optical

pyrometer to brightness temperatures as low as 590 °C with a standard deviation of about 7 °C.

The upper brightness temperature limit of 2300 °C

has evolved from years of experience of how well

the lamps withstand deterioration at high temperatures. Obviously, the limit is somewhat ar- bitrary. One can operate a lamp above a 2400 °C

brightness temperature; but on the other hand,

one should not leave a lamp at even a 2300 °C

brightness temperature needlessly. Though lamps

are usually calibrated at intervals of 100 deg C,

a calibration at any temperatures from 800 to

2300 °C will be supplied if requested.

2» See footnote on p. 19.

'5 See footnote on p. 8.

b. Mounting and Orientation

The first step in the calibration of a tungsten

strip lamp of the T24 type at NBS is to determine

the orientation for which the lamp is to be calibrated. The lamp is mounted on the optical axis

of the NBS pyrometer about 60 cm from the pyrometer lamp with the tungsten strip approximately vertical. With the strip at a brightness

temperature of about 1600 °C, the lamp is rotated

about the axis of its envelope so that radiation

reflected from the lamp envelope onto the tungsten

strip and then reflected by the strip does not

enter the pyrometer. This condition is determined

in the following manner. The reflection of the

strip from the glass envelope is observed from the

side of the cylindrical envelope away from the

pyrometer and the eye moved until the image

appears to be in line with the filament. This

determines the direction of the rays which are

reflected from the envelope and then reflected

from the strip. The direction of the secondary

reflection from the strip is obtained by looking

down from above the strip. If possible, the lamp

is oriented so that the pyrometer axis is normal to

the strip. If it is found that a reflection into the

pyrometer occm-s when the pyrometer optical

axis is normal to the filament, a suitable position

of the lamp close to this normal is selected.

Finally the lamp is adjusted so that the tungsten

strip at the notch is vertical as determined by a plumb line.

With the optical pyrometer axis horizontal and

aimed at the filament notch, a small ink mark is made on the envelope of the lamp at the position

where the optic axis strikes the envelope on the

side away from the pyrometer. The lamp is taken down and a small arrow etched on the glass

such that the head of the arrow just touches the

ink spot.

The etching is performed using hydrofluoric

acid (48 percent) and a wax protective coating

commonly referred to as a resist. Resist formula

P-1 described in NBS Circular 565 [18] is used.

A large needle is used to inscribe the arrow on the

resist and beeswax is placed on and around the

resist in the form of a small cup to keep the

hydrofluoric acid from coming in contact with any

glass not protected with the resist. A 3 min

etch appears to be quite satisfactory. After this

period of time, the acid is washed off with water,

the lamp is cleaned with xylene, then soap and

water, and finally dried with a nonabrasive tissue

paper.

The lamp is now remounted for final adjustment

prior to the actual calibration. With the strip

incandescent and some background illumination

on the arrow, the latter can be seen in the field of

view of the pyrometer; and the lamp is oriented

so that the arrowhead appears at the notch. This

orientation is checked and maintained throughout

the entire calibration.

22
At the normal distance at which lamps are calibrated, the angle subtended at the strip by the

entrance pupil of the pyrometer varies from about

0.02 radian in the range 1100 to 2300 °C to about

0.05 radian at 800 °C. A detailed description of

the lamp orientation, direction of sighting,

entrance angle, and room temperature is given in

each certificate of calibration so that these conditions can be duplicated by the lamp user.

c. The Electrical System

The source of electric current for the lamps is a bank of storage batteries having a 1600 amp-hr

capacity and an emf of 120 v. Coarse control of

the lamp current is obtained with an NBSconstructed air-ventilated resistor made of coils

of chromel A and nichrome wive connected in

parallel through knife smtches. In parallel with

this arrangement are two slide-wire reostats for

fine control permitting changes of a few parts in

10,000. The polarity of the electrical connection

to the lamp is identified on the certificate. Depending on the lamp, currents from a few amperes

to 75 amp are required. These are determined to

an accuracy of about 1 part in 10,000 with a potentiometer by measuring the potential difl'er- ence across a 0.001-ohm calibrated shunt resistor

placed in series with the lamp. The current drift

during the time required to make a set of 4 bright- ness matches is usuaUy less than the equivalent of

1 deg C.

d. Calibration

Gas-filled lamps are annealed at a brightness

temperature between 2325 and 2350 °C for 2 hr

just prior to the calibration. The first temperature

calibrated is the highest point requested. Observations are made using a procedm-e similar

to that used in calibrating optical pyrometers.

Two observers each make four matches (bright to

dark, two dark to bright, bright to dark) at each

of the temperatures to be reported. In the usual

case of calibrating at 100 deg C intervals, the

observers wait 10 min between points (after the

initial 2 hr anneal) to allow the lamp to reach

equilibrium after each temperature change. However, at 1000 and 900 °C, a 15 min wait is employed

and at 800 °C, 20 min. For temperature changes

greater than 100 °C even longer waiting periods

are used.

The brightness temperatures of tungsten strip

lamps calibrated at NBS are reported to corre- spond to a wavelength of 0.653 /x- The actual

wavelength for the observations between 800 and

2300 °C varies from 0.657 to 0.653 m with abrupt

changes in wavelength whenever the range of the

pyrometer is changed. However the greatest

difference in the actual wavelength and that re- ported only amounts to an error in brightness

temperature of about one-seventh the uncertainty

stated.

5.3. Precision and Accuracy^"

a. Definition of Precision and Accuracy

By the precision of a measurement, one usually

means how well the measurement is reproduced.

More specifically, if NBS calibrates an optical

pyrometer a number of times and if the pyrometer

is stable, a measure of the precision of the cahbration or calibrations is the standard deviation of

the entire population comprising the calibrations.

If the entire population is not available, the

standard deviation of the population is estimated

by the standard deviation of a sample of the

population, and it should be kept in mind that

such estimates are subject to considerable variation from sample to sample when the size of the

sample is small [19].

The concept of accuracy refers to how well a

particular value agrees with the correct value.

However, except in a situation where a material

standard defines a unit of measurement, such as the meter bar previous to 1960, the correct value

is not known and the accuracy of a particular

result can never be exactly determined. An

experimenter can make an estimate of the constant

or systematic errors of a measurement, and this

information is certainly useful. However, since

such estimates are a matter of judgment they

vary greatly from one individual to another, and

an objective interpretation on the meaning of the

errors is even more difficult if not impossible to

make.

There is a manner of obtaining an estimate of

accuracy, at least for temperature calibrations on

the IPTS, which does not possess these limitations.

The various national standards laboratories

throughout the world independently attempt to

experimentally realize the IPTS. Moreover, many

of these laboratories are continually trying to

improve their realization of the scale, and differ- ences among the laboratories are probably the best

indication available of how well the scale is being

realizied. Therefore, a very useful measure of the

accuracy of a temperature calibration relative to

the IPTS is the standard deviation of the population consisting of the means of the population of

the temperature calibrations performed in each of

the national laboratories. In practice numerical

results are usually not available from all the

national laboratories, and therefore only a sample

or estimated standard deviation can be determined. Of course, any constant systematic error that exists in all the national laboratories is not

revealed in this manner. But under these circumstances neither would it be accounted for in any

other way. Thus it is believed that the above

standard or sample standard deviation is the best

available estimate of the accuracy of realizing the

IPTS.

30 The authors thank C. Eiscnhart, H. U. Ku, and J. Mandel of the National Bureau of Standards for their interest and helpful discussions concerning this section.

23
b. A Statistical Model for Calibration Errors

There are a number of sources contributing to

the lack of precision and accuracy in optical pyrometer and tungsten strip lamp calibrations. These

have already been discussed in various parts of the

paper and are summarized in the following statistical model.

^i;ft =^int+e'+af +6j(+c&+(^ (5-2)

where t\jk represents the temperature obtained

from a single set of observations by a single individual with a particular apparatus in a particular

national laboratory. In eq (5-2) tint is the correct temperature on the IPTS, is the (random)

error of the ^th set of observations of an observer,^^

a, is the systematic error of the ith observer, hj is the systematic error of the jih. apparatus, Ct the

systematic error of the ^th national standards

laboratory and d is the constant systematic error common to all the laboratories. All the errors except d are assumed to be normally and independently distributed [19] with mean or expected

value zero and variances Vie), V{a), V{h), and

F(c). From theory of statistics, then, the vari- ance of t is equal to the sum of the variances of the

errors or

V{t)=V{e)+V{a)+V{h)+V{c). (5-3)

No statistical (or other type) information can be

obtained for d until it is discovered in one or more

laboratories, and then it becomes part of the c^'s of the remaining laboratories.

Estimates of the variances in eq (5-3) or their

square roots, i.e., the standard deviations, can be

obtained from the results of experiments by the

components of variance technique [20]. For ex- ample, if one observer performs many calibrations

at one temperature on the same instrument using

the same apparatus in the same standards laboratory, all the parameters on the right hand side of

eq (5-2) remain constant except eK Therefore the

variance of these individual temperature determinations is an estimate of V{e) . With V{e) determined, a large number of observers can be

used to obtain an estimate of V{a). Similarly

estimates of V(b) and V{c) can be obtained. This

involves a tremendous amount of work and in

addition is complicated by the fact that any

changes or drifts in the instruments must also be

taken into account. Nevertheless, an attempt has

been made at NBS to begin to determine the

variances in this model. Preliminary estimates

for the standard deviations of these errors are

'I For strip-lamp calibrations, a single set of observations means the 4 brightness matches (dark to bright, 2 bright to dark, dark to bright) and the

associated electrical current measurements. For optical pyrometer calibrations, a single set of observations means the 8 brightness matches of the NBS

and test pyrometers and associated electrical current measurements described m section ,'5.3. 32 For simplicity it has been assumed that the random error population for each observer is the same. This is only approximately true in practice.

Table 3. Preliminary estimates for the standard deviations]

in deg C of various errors associated with optical pyrometer]

and strip lamp calibrations on the IPTS \ e is the random error of a set of observations by a single observer and a, b, and c are systematic errors associated with the observers, the apparatus, and

the national standards laboratory, respectively.

Strip lamps Pyrometers

1063 "C 2300 °C 100)3 °C 2300 °C

s(e) 0.3 0.9 0.3 lA

s(a) 0.5 0.8 0.5 1.8

s(6) 0.3 0.6 0.3 1.4

s(c) <0. 5 <2.0 <0.5 <2.0

listed in table 3 for calibrations of optical pyrometers and tungsten strip lamps at 1063 and 2300

°C. Only an upper limit for the estimate of the

standard deviation of c could be determined be- cause of the incompleteness of the data from the

1957-58 international comparison of strip lamps

discussed in section 4. It is interesting to note that the estimated

standard deviations of the errors associated with

the calibration of pyrometers at 1063 °C turned

out to be the same as that for strip lamps. At

first this is surprising because twice as many

'

brightness matches are necessary for a pyrometer

calibration than for a strip-lamp calibration. I Analyzing the brightness matches more carefully,

however, one notes that when observers match

high or low with the NBS pyrometer, they also

match high or low respectively with the test py1

rometer. At 2300 °C the correlation does not

!

appear to exist, probably due to different pyrom-l

eter-lamp brightness temperatures in the test I (~1050 °C) and NBS instrument (~1300 °C).

|

c. Uncertainties on Certificates

j Ideally, the uncertainties stated on certificates

| of calibrations should be related to the estimated i standard deviation of t. Unfortunately, adequate • information has not yet been obtained to make

this sufficiently quantitative to be meaningful.

Thus, until sufficient data are obtained, prehmi- ! nary estimates of the type given in table 3 together : with the available data on the stability of strip

j lamps and pyrometers have been used to make i "judgement type" estimates of the sum of the : errors in eq (5-2), assuming the signs associated ! with the errors are the same. These are called !, maximum uncertainties on the calibration certifi- |, cates. For optical pyrometers they are usually f given as ±4 deg C at 800 °C, ±3 deg C at 1063 p °C, ±8 deg C at 2800 °C, and about ±40 deg C

at 4000 °C. For strip lamps thev are ±5 deg C I at 800 °C, ±3 deg C at 1000 and 1100 °C, and ±7 ! deg C at 2300 °C. It is presently (1961) felt that ' these errors are more conservative at the lower ' temperatures than at the high temperatures. It i should be emphasized that these uncertainties as , stated on the certificates do not represent a j 24
standard deviation or some multiple of a standard

deviation. It is hoped, however, that something

more statistically meaningful can be incorporated

in the certificates in the near future.

d. Differences Between the IPTS and TTS

When it is necessary for someone to obtain a temperature on the Thermodynamic Temperature

Scale (TTS) [21] with an instrument calibrated at

NBS on the IPTS, the estimated difference between the two scales is required. Above 1063 °C

this is relatively easy to obtain because the IPTS

would also be the TTS if the second radiation

constant C2 and the freezing point of gold t^xi were

correct. Thus, estimates of the correct values for

C2 and are sufficient to calculate estimated

differences between the two scales.

DuMond and Cohen [22] have reported a value

of 1.43884 ±0.00008 cm deg for C2, obtained from

their adjusted values of the atomic constants.

The freezing point of gold on the Thermod3niamic

Scale has been redetermined in a number of

laboratories during the past 6 years and three

independent groups have confirmed the value

1064.5 °C (therm.) [23]. Using these values for

C2 and i^Au, estimated differences between the TTS

and IPTS have been calculated and are presented

in figure 18. Also included in figure 18 is the error incurred in using the Wien equation at 0.65 ju as an

approximation for the Planck equation in the IPTS.

1 1 1

s' /

1

1 1000 2000 3000 4000 5000

TEMPERATURE,°K

Figure 18. Estimated difference between the Thermodynamic Temperature Scale and the International Practical

Temperature Scale, and the error incurred when using the Wien equation (at 0.65 n) as an approximation for the Planck equation in ike IPTS.

6. Applications

6.1. Temperature Measurements

An optical pyrometer determines the brightness

temperat\u"e of an incandescent body at the mean

effective wavelength between the brightness temperature and the color temperature of the body.

If the spectral eraittance of the particular part of

the body sighted on is known, the temperature of

the body may be determined from the following

equation

or r

^2 "1-1 r ^2 "1-1

(6-2)

where exr^-r^CT") is the spectral emittance at the

mean effective wavelength Xr^-^^, Tb is the bright- ness temperature of the body at this wavelength,

Tc the color temperature, and T the temperature.

When Wien's equation is an adequate approximation, eq (6-2) can be reduced to the simpler form

Spectral emittances are accurately known for

only a few substances and surface conditions.

Probably the most accurately known spectral

emittances are those for tungsten [6, 24, 25]. An

illuminating review of the principles, methods of

measurement and the results of investigations

on spectral emittances prior to 1939 has been

given by Worthing [26]. More recent contributions can be found in the proceedings [27] of the

Fourth Symposium on Temperature, Columbus,

Ohio (1961).

In the vicinity of the gold point and a wavelength of 6500 A an error of 1 percent in spectral

emittance results in an error of only 0.065

percent in temperature. More generally, using

Wien's approximation, assuming that the small

variation of spectral emittance with temperature

may be neglected, and differentiating the equation

iVx(r)=€x(r)CiX-^e-'^2/x^, (6-4)

one obtains

-T=c; w (6~^)

For the most accurate temperature determination with an optical p3n:-ometer, it is recommended

that a blackbody be built into the experimental

setup. Then, of course, the spectral emittance is unity and the temperature is equal to the bright- ness temperature. Often blackbody conditions can be approximated sufficiently well by simply

driUing a small hole into a solid or by inserting a

small cavity in a molten substance.

6.2. Spectral Radiance Calibrations Using

Strip Lamps

Tungsten strip lamps are often used to calibrate

the response of spectrographs and spectrometers

from about 2500 to 25,000 A. For this purpose,

25
the brightness temperature or spectral radiance

of the lamp as a function of wavelength is re- quired. Such a calibration is performed in the

Radiometry Section at NBS and is available to

the public. At present (1961) the maxiraum uncertainties repoited vary from 3 percent at 25000

A to 8 percent at 2500 A.

Another way of obtaining the spectral calibration of a strip lamp is to calculate it using the

brightness temperature from an optical pyrometer

determination and published values for the spectral omittance of tungsten. The spectral radiance

of a tungsten lamp is given by

Arx(T)=CiX-ne^2/x^B-l]-i

^e^{T)r,C,\-'[e^2'^^-l]-' (6-6)

where Tb is the brightness temperature of the

lamp at wavelength A, ex{T) is the spectral emittance of the tungsten, tx the spectral transmittance

of the lamp window or envelope, and T the strip

temperature. The procedure for determining

Nx(T) at any wavelength is to first solve for T

in eq (6-6) using the calibrated value of Tb and

the measured or assumed value for t\ and published value of ex, all at the mean effective wavelength associated with Tb. Then Nx(T) can be

calculated for any wavelength for which e\ and

TX are available. For the visible spectral region

and infrared to about 25000 A, it is usually adequate to assume rx is constant. If a quartz

envelope is used rather than glass, the constancy can be extended down to about 2800 A or less,

depending on the type of quartz. Several papers

have reported experimental determinations of ex for tungsten during the past 10 years [6, 24, 25].

One of the major limitations of this technique is the question of whether the emittance of the

tungsten in the lamp being used is the same as that reported in the literature. In addition, the

effect of internal reflections and knowledge of the

transmittance of the window will be somewhat

uncertain. On the other hand, all of these parameters are used in a relative manner, i.e., the spectral radiance is known at about 0.65 jtt, and one

merely has to compute values at other wavelengths

relative to it. As a result, the calculated spectral

radiances at wavelengths other than 0.65 n are usually only a few percent more uncertain than

the spectral radiance at 0.65 /x which is obtained

directly from the brightness temperature.

In using the tungsten lamp for spectral calibrations one should take the same precautions of

orientation and alinement described in sections \ 3 and 5. In particular, one should try to use the

strip lamp at the same entrance angle at which it was calibrated, especially when this angle is small

and the lamp envelope appears to be inhomogeneous in the region where the beam exits.

6.3. Secondary Standards

A laboratory or industrial group that requires

high accuracy in its optical pyrometry work or

that requires only moderate accuracy but uses many strip lamps or optical pyrometers should

consider maintaining its own secondary standards.

It is often asked which is preferable, a strip lamp

or optical pyrometer as a secondary standard to

ma,intain the IPTS above 1063 °C. There is no

unique answer to this question. It will depend

on some factors that only the user himself is aware of, factors such as the manner and frequency with which the secondary standards are used and the money and personnel available for

this work. Some of the factors that should be

considered are listed in table 4.

6.4. Recommendations for Achieving High

Accuracy and Precision

When high accuracy is the primary consideration in maintaining or making measurements on

the IPTS, a few procedures should be emphasized.

Both optical pyrometers and tungsten strip lamps

change with use. Therefore, in order to obtain

high accuracy, a laboratory should use one calibrated strip lamp or optical pyrometer infrequently and compare the strip lamps or pyrometers used regularly to it. As emphasized previously, great care should be taken concerning the

orientation and alinement of the strip lamps, and \ vacuum lamps should be used whenever possible. |

Table 4. Relative merits of strip lamps and optical pyrometers as secondary standards for the IPTS

Strip lamps Optical pyrometers Section

discussed

Stability

NBS calibration uncertainty

Brightness temperature range

Care necessary for orientation and ambient

temperature control.

Time to reach equilibrium

Cost of instrument

Cost of NBS calibration

Cost of additional apparatus for most ac- curate use.

800-2300 °C.

Considerable.

Somewhat better.

.At present (1961) about the same.

Minutes to an hour.

Considerably less Less

800-4000 °C, and higher.

Very little

Seconds to a minute.

Somewhat less.

2.1, 3.4

5.12

5.6 3.4

2.1, 5.9 I

26
For optimum precision and accuracy in the

use of pyrometers, laboratories should request

NBS to calibrate their pyrometer as a function of

pyrometer filament current. The laboratory

should then use a standard resistor and a sufficiently

accurate potentiometer to determine this current.

A multiturn smooth turning rheostat is highly

desirable for varying the filament current while

making the brightness matches. The precision

of matches can often be improved greatly by

having the pyrometer mounted rigidl}^ in a comfortable position for a sitting observer. A

black cloth thrown over the observer's head and

part of the optical pyrometer to shield the observer from any distracting or annoying light is helpful. Observations should always be made from

both a dark and a bright filament to a match or disappearance and the two results averaged.

If one or two individuals primarily use the pyrometer, make sure that their technique of matching

does not give results very different from the

average of 5 or 6 observers. In addition, if nonblackbodies are often used, it is well to use 5 or 6

observers to determine if any observer has a very

unusual relative luminosity curve. The standard

deviation of the mean effective wavelength due

to luminosity factor differences has been reported

[28] to be about 8 A, which in reading a strip

lamp at 2300 °C with a pyrometer having constant

A value absorbing glass, amounts to about 0.4

degree.^^ Of greater relative importance than the

relative Ixmiinosity factors for affecting the effective wavelengths are differences in spectral transmittance of the red glasses in pyrometers.

Methods for determining the effective wavelengths

of optical pyrometers were described in section 5. For convenience, table 5 summarizes the various

recommendations for the practice of precise and

accurate optical pyrometry.

^ However, in a primary calibration an error of 8 A in the mean effective wavelenith between 1063 and 2300 °C is equivalent to an error of about °C at 2300 °C.

Table 5. Recommendations for the precise and accurate

use of optical pyrometers and tungsten strip lamps

Recommendation

Use the instrument infrequently

Take the necessary precautions in orienting

and ahning strip lamps

Use a source whose image is large compared

to that of the pyrometer filament

Use several observers

The observer should be in a comfortable

position, have a hood, and have the pyrometer rigidly mounted

Determine the effective wavelength of the

pyrometer when observing non-black

sources

Use the pyrometer lamp current as the

parameter to relate the brightness match

Use a vacuum strip lamp for brightness

temperatures below 1400 °C

Section discussed

2.1, 6.4

3.4, 5.3, 5.7

3.3

5.11, 6.4

6.4

1.6, 1.7, 5.2, 6.4

5.3, 6.4

3.3

6.5. Fundamental Limitations

The fundamental limitation in visual optical

pyrometry is the sensitivity of the human eye.

Lovejoy [7], using the results of an investigation

of contrast thresholds or limens (see footnote 15)

reported by Blackwell [29], calculated the expected

observer standard deviation temperatures for

the mean of a set of matches consisting of a bright

filament to disappearance and a dark filament to

disappearance for a pyrometer having a 0.05

radian exit angle, a 0.7 mm exit pupil, and a 0.038

mm actual and 10 min apparent angular filament

width. The standard deviations ranged from 0.2

deg C at 1400 °C to 0.3 deg C at 1063 °C and

increased to 1.6 deg C at 800 °C,^* and agreed

well with his experimental values.

Another basic limitation in visual pyrometry is the uncertainty of the observer's relative luminosity function. This function is required in a primary calibration of optical pyrometers at

temperatures above the gold point, and its uncertainty corresponds to an equivalent uncertainty

of about 1 to V/i deg C in the primary calibration

at 2400 °C. The effect of the uncertainty in the

relative luminosity factors could be reduced by

using a narrower spectral bandwidth in optical

pyrometers. However, then one would begin to

be even more limited by the eye's contrast

sensitivity. Most optical pyrometers appear to

be designed so that the two limitations are about

equal at 2400 °C.

6.6. Photoelectric Optical Pyrometers

During the past 5 years, optical pyrometers

which employ a photomultiplier tube rather than

the eye as a detector have come into existence.

Such instruments have been developed in the

national standards laboratories of the U.S.S.R.

[30], Australia [31], and the United States [1]. They have considerably greater sensitivity and

precision (~0.01 deg) than the visual instruments

and can use a much smaller spectral bandwidth.

It is expected that photoelectric pyrometers will

make possible at least an order of magnitude

greater accuracy in optical pyrometry. However,

in order to achieve this a number of difficult

problems will have to be solved. Two of these

are obtaining a "blackbody" with an emittance

approaching 0.9999 and determining the ratio

of two beams of radiant energy with an accuracy

of 0.01 percent. These and other challenging

problems, and the promising increase in the

accuracy of high-temperature measurement if they

are solved, have stimulated a new and exciting

activity in the field of optical pyrometry.

31 Corresponding standard deviations for higher temperatures can be

obtained from the relation between two temperature differentials obtained from Wien's equation. This relation is dT={T/TA)^dTa where T represents the higher range temperature and Ta its corresponding apparent temperature

as seen through the absorbing glass. At 2400 °C the resulting standard

deviation is about 1 deg C.

27
7. References

[I] R. D. Lee, The NBS photoelectric pyrometer of 1961,

Temperature, Its Measurement and Control in

Science and Industry (to be published by Reinhold

Publishing Corp., New York, N.Y.).

[2] H. F. Stimson, The International Practical Temperature Scale of 1948, J. Research NBS 65A, 139 (1961) ; The International Temperature Scale of 1948, J. Research NBS 43, 209 (1949).

[3] C. O. Fairchild and W. H. Hoover, Disappearqnce of

the filament and diffraction effects in improved forms

of an optical pyrometer, J. Opt. Soc. Am. 7, 543

(1923).

[4] W. E. Forsythe, Optical pyrometry, Temperature,

Its Measurement and Control in Science and Industry

(Reinhold Publishing Corp., New York, 1941) p. 1115.

[5] C. R. Barber, Factors affecting the reproducibility of

brightness of tungsten strip lamps for pyrometer

standardization, J. Sci. Instr. 33, 238 (1946).

[6] J. C. DeVos, A new determination of the emissivity

of tungsten ribbon, Physica 20, 690 (1954).

[7] D. R. Lovejoy, Photometry of the optical pyrometer

and its use below 800°C, J. Opt. Soc. Am. 49, 249

(1959).

[8] F. A. Cunnold, The optical system of the disappearing

filament pyrometer, Proc. Roy. Soc. (London) 153A,

64 (1935).

[9] J. C. DeVos, Evaluation of the quality of a blackbody,

Physica 20, 669 (1954).

[10] J. Vollmer, Study of the effective thermal omittance

of cylindrical cavities, J. Opt. Soc. Am. 47, 926

(1957).

[II] A. Gouffe, Corrections d'ouverture des corps-noirs

artificiels compte tenu des diffusions multiples

internes. Revue d'optique 24, 1 (1945).

[12] H. G. MacPherson, The carbon arc as a radiation

standard. Temperature, Its Measurement and

Control in Science and Industry (Reinhold Publishing Corp., New York (1941) p. 1141.

[13] M. R. Null and W. W. Lozier, The carbon arc as a

radiation standard, Temperature, Its Measurement

and Control in Science and Industry (to be published by Reinhold Publishing Corp., New York,

N.Y.).

[14] J. Euler, The graphite carbon arc as a standard

source of intense radiation, Sitzber. Heidelberg

Akad. Wiss. 4, 418 (1956-57).

[15] A. Bauer and P. Sehultz, Eingeengte Xenon-Hochdruckentladungen hoher Stromdichte, Z. Physik

155, 614 (1959).

[16] R. A. Fisher, Statistical Methods for Research

Workers (Hafner Publishing Co., New York, 1954)

12th ed., p 147.

[17] R. L. Anderson and E. E. Houseman, Tables of

orthogonal polynomial values extended to A''= 104,

Iowa Agr. Exp. Sta. Research Bui. 297 (1942).

[18] R. Davis and C. I. Pope, Techniques for ruhng and

etching precise scales in glass and their reproduction

by photoetching with a new light-sensitive resist, NBS Circ. 565 (1955) p. 10. [19] For definitions and further discussions see J. M.

Cameron, Statistics, Fundamental Formulas of Physics, edited by D. H. Menzel (Dover PubHcations, Inc., New York, 1960) p. 107.

[20] F. A. Graybill, An Introduction to Linear Statistical

Models (McGraw-Hill Book Company, Inc., New

York, 1961), vol. I, ch. 6. [21] H. F. Stimson, Heat units and temperature scales for calorimetry. Am. J. Phys. 23, 615 (1955).

[22] J. W. DuMond and E. R. Cohen, Least squares

adjustment of the atomic constants, 1952, Revs.

Modern Phys. 25, 691 (1953).

[23] H. Moser, Review of recent determinations of thermodynamic temperatures of fixed points above 419°C,

Temperature, Its Measurement and Control in

Science and Industry (to be published by Reinhold

Pubhshing Corp., New York, N.Y.).

[24] R. D. Larrabee, The spectral emissivity and optical

properties of tungsten, J. Opt. Soc. Am. 49, 619

(1959).

[25] C. Tingwaldt, New optical methods for the determination of thermodynamic temperatures of glowing

metals, Temperature, Its Measurement and Control in Science and Industry (to be pubhshed by

Reinhold Publishing Corp., New York, N.Y.).

[26] A. G. Worthing, Temperature radiation emissivities

and emittances. Temperature, Its Measurement

and Control in Science and Industry (Reinhold

Publishing Corp., New York, 1941) p. 1164.

[27] Temperature, Its Measurement and Control in Science

and Industry (to be published by Reinhold Publishing Corp., New York, N.Y.).

[28] D. R. Lovejoy, Accuracy of optical pyrometry in the

range 800°C to 4000°C, Can. J. Phys. 36, 1397

(1958).

[29] H. R. Blackwell, Contrast thresholds of the human

eye, J. Opt. Soc. Am. 36, 624 (1946).

[30] V. V. Kandyba and V. A. Kovalevskii, A photoelectric spectropyrometer of high precision, Doklady

Akad. Nauk S.S.S.R. 108, 633 (1956).

[31] J. Middlehurst and T. P. Jones, A precision photoelectric optical pyrometer. Temperature, Its Measurement and Control in Science and Industry (to

be published by Reinhold Publishing Corp., New

York, N.Y.).

28

U.S. GOVERNMENT PRINTING OFFICE: 1362
U.S. DEPARTMENT OF COMMERCE

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NATIONAL BUREAU OF STANDARDS

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