NATIONAL BUREAU OF STANDARDS REPORT

9894

DEVELOPMENT OF A STABLE ULTRAVIOLET SOURCE

AND TECHNIQUES FOR ACCURATE RADIOMETRY

Final Report to the

National Aeronautics and Space Administration

Order Number C-91488-A

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
NATIONAL BUREAU OF STANDARDS

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NATIONAL BUREAU OF STANDARDS REPORT

NBS PROJECT

2210417 July 1, 1966 - June 30, 1968

NBS REPORT

9894

DEVELOPMENT OF A STABLE ULTRAVIOLET SOURCE

AND TECHNIQUES FOR ACCURATE RADIOMETRY

by

Henry J. Kostkowski

Albert T. H attenburg

Final Report to the

National Aeronautics and Space Administration

Order Number C-91488-A

IMPORTANT NOTICE NATIONAL BUREAU OF SI

for use within the Government, and review. For this reason, th whole or in part, is not autho Bureau of Standards, Washingt

the Report has been specifically

Approved for public release by the

Director of the National Institute of

Standards and Technology (NIST) on October 9, 2015

ss accounting documents intended

subjected to additional evaluation

listing of this Report, either in

e Office of the Director, National

)y the Government agency for which

opies for its own use.

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

PREFACE

The current report presents the work completed during the last

two years on the project entitled "Development of a Stable Ultraviolet

Radiant Source and Techniques for Accurate Radiometry".

Part I of the report is a tutorial paper on the calibration of a spectroradiometer for the purpose of measuring spectral radiance, spectral irradiance or spectral line intensities. The treatment includes

detailed discussions on the radiation parameters, the slit function,

available standards, and effects due to non-uniform targets, scattering

and polarization. Though rigorous, it is presented at a level that

requires only an elementary knowledge of optics and calculus.

t Part II presents the work completed during the last two years on

the use of the high pressure argon arc as a standard of ultraviolet

radiance and irradiance. Earlier NBS Reports, numbers 866U and 9099,

incorporate work performed from January I96U to December 1965 on the

design, construction and preliminary measurements of this arc. The

current report presents final results on the arc's operation, stability

and calibration in terms of spectral radiance. Though the arc appears

extremely useful as a spectral irradiance standard, only preliminary

measurements were possible on this radiation parameter. New techniques

and instrumentation are required before accurate (few percent) spectral

irradiance measurements between 300 and 210 nm can be made. Work in

this area will be initiated as soon as possible.

ii

TABLE OF CONTENTS

PAGE

PREFACE i

PART I: THE PRINCIPLES AND METHODS OF CALIBRATING

SPECTRORADIOMETERS , H. J. Kostkowski

Introduction 2

Spectral Radiance 3

Calibration Equation for a Monochromatic Source 8

The Slit Function 12

General Calibration Equation 17

Experimental Determination of the Slit Function

and the Effective Spectral Response 20

Specific Calibrations 27

a. Spectral radiance of a continuum 27

b. Intensity of a spectral line 33

c. Intensity of several spectral lines 40

d. Combination of a continuum and a spectral line 4l

Standards of Spectral Radiance 43

Higher Order Effects 46

a. Lack of uniformity in spectral radiance,

transmittance and response 46

b. Size of source effect 49

c. Polarization effect 51

d. Detector non-linearity and fatigue 53

Spectral Irradiance 55

a. Definition of spectral irradiance 56

b. Determination of spectral irradiance

using a spectral irradiance standard 57

c. Using a spectral radiance standard 6l

d. Standards of spectral irradiance 63

References 64

iii

Table of Contents, Continued

PAGE

PART II: OPERATION, STABILITY AND CALIBRATION OF

THE HIGH PRESSURE ARGON ARC, A. T. Hattenburg

Summary 66

Spectral Radiance of the Arc Source

a. Operating Parameters 66

b. Absolute Values 67

c. Short term stability and noise 68

d. Long term stability 69

e. Quartz window transmission 69

f. Geometric stability 69

g. Positioning sensitivity 70

h. Sensitivity to changes in operating

parameters 70

i. Suitability of the arc as a standard source ... 70

Operation of the Arc

a. Design changes 70

b. Alignment of the arc 72

c. Preliminary steps 72

d. Starting and stopping procedure 73

e. Operating procedures 7^

Calibration Methods

a. Details of the calibration 75

b. Calibration with graphite arc standard 76

c. Calibration with tungsten lamp and filters .... 78

d. Filter calibrations 79

Spectral Irradiance Evaluation 80

References 8l

Figures 82

Appendix

a. Fabrication of constriction plate sections .... 8U

IV

PART I

THE PRINCIPLES AND METHODS OF

CALIBRATING SPECTRORAD IOMETERS

H. J. Kostkowski

2

INTRODUCTION

This report introduces physical concepts and develops methods

useful for accurately calibrating spectroradiometers for the purpose

of determining the spectral radiance, irradiance or spectral line intensity of a source or beam of incoherent optical radiation. Though

very little of the report is new, a complete, detailed treatment of

this problem is not available in the literature, at least not to the

author 1 s knowledge. A spectroscopist or radiometrist is required to

develop much of this material himself. With the number of people active

in optical radiation measurements increasing and the number of graduate

students in optics decreasing, it was considered worthwhile to write a tutorial type report on this subject.

In order to reach as broad an audience as possible, the level and

pace of the presentation has been aimed at an individual familiar with

relatively simple optics and calculus. However, it is hoped that some

parts of the presentation will be sufficiently novel or thought provoking to also be of interest to the expert.

The approach and the methods described have evolved over a period

of time from attempts to perform various types of calibrations useful

in spectroscopy, pyrometry and radiometry. Discussions with colleagues

and perusal of the literature have certainly contributed to this evolution. When the origin of a particular idea is known, its source is

- 3 -

certainly given. However, no attempt has been made to provide a complete bibliography on the subject, and if proper credit is not given,

it is not intentional. Many of us have "invented" or "discovered"

things that we later find have been used, known or even published previously.

There are two concepts that are very useful in dealing with the

problems associated with accurate spectrometer calibrations. The first

is the characterization or association of an optical ray with a particular radiation parameter called spectral radiance. The second is

describing the spectral band pass of the spectrometer by the so-called

slit or apparatus function. In the first section of this report spectral

radiance is defined and the relation between the output and input of

the spectrometer developed. In doing this, the need for the slit function

arises and it is introduced and discussed in the second section. Applications of various types of calibrations when determining spectral

radiance, line intensities, or irradiance, are presented in the remaining

sections

SPECTRAL RADIANCE

In order to characterize an arbitrary distribution of radiation;

whether it is emanating from a source, propagating in space, or falling

on the surface of a detector; it is convenient to have a quantity which

describes the radiant power as a function of position and direction.

- k -

Since the radiant field is considered to he continuous in its distribution in space, a finite amount of radiant power cannot be propagated

through a point or in a particular direction. However, it is still

possible9 through the use of a limiting process 9 to associate a quantity

of radiant power with a point and a direction.

Consider an arbitrary incoherent radiant field represented in Fig. 1.

by optical rays making arbitrary angles with the plane areas AA and AA'

at the points (xyz) and (x’y* z ’) respectively . Call A^f the radiant energy

passing through AA per unit time, often referred to as the radiant flux

through AA, A^ f (A^<§) that portion of A^<| also passing through AA1 ; and

A^[ A.A, (A.A$) ] "kkat portion of A^,(A^$) contained in the wavelength

- 5 -

interval A A surrounding the wavelength A. The angle 0 is the angle

between the ray (x'y'z') -> (xyz) and the normal to the AA surface.

The limit of the ratio of the flux A^[ A^, (

A

<|) ] to the product of

AAcos0, Aft and AA, where Aft is the solid angle which is subtended by

AA* and has its apex at the point (xyz), as AA, Aft and AA approach 0

is the spectral radiance, L , at the point (xyz) in the direction

(x T y'z f ) (xyz) for the wavelength A. Symbolically

I iwit

°

o

o

A A asi aa cos e

L Cj ^ a)

where (0c})) represent the polar and azmuthal angles of a spherical coordinate system whose origin is at (xyz) and polar axis is in the direction

of the surface normal n. From calculus

u - —^

dX 3-T2- Cose

In addition, the radiant flux in a wavelength interval A 2 - Aj, propagating through an area A and solid angle ft, whose apex is at A, is

A?,

1 ^ d (\ co s & d X~L cl A (3

)

S2- ft

- 6 -

The common unit for spectral radiance is watts (centimeters) -2

(steradian)- 1 (centimeter) -1

.

Since spectral radiance is associated with a point and a direction,

it can be said to be associated with an optical ray through this point

and in this direction. One might guess that because of this association,

it should be possible to prove some sort of invariance between a ray

and the spectral radiance. Such an invariance can be proved (l). The

result is that, excluding losses due to reflection, scattering or

absorption, the ratio of the spectral radiance to the square of the

index of refraction of the medium along a ray is constant. Moreover,

these losses may be taken into account through the spectral transmittance or reflectance of the ray by the surface, medium or optical element

responsible for the loss. This spectral transmittance or reflectance,

defined as the ratio of the emerging spectral radiance to the incident

spectral radiance, may often be determined once and used thereafter.

Fig. 2, showing a familiar tungsten strip being imaged by a simple lens.

F.> 2.

- 7 -

illustrates this property of invariance. In this figure L , L' and

A A l" are the spectral radiances of the point 0]_ and 0 2 , in the direction

of the rays shown and t L , t’l' and t"l" are the spectral radiances

of the image points 1^ and I 2 in the respective ray directions. The

factors t , t’ and t" are the spectral transmittances of the lens at

A A A the position and direction of the rays shown. Except for the transmittances, the radiance along a ray remains constant as long as the

index of refraction does.

As indicated in Fig. 2 the spectral radiances associated with two

rays from the same point, and of course from different points, on a

source may be different. In general, the spectral radiance on a source

is a function of both position and direction. However, to obtain the

finite flux required for any actual measurements , a finite area and

solid angle must be observed, and only the average radiance for this

particular solid angle and area can be obtained. Moreover, as will be

shown later, this average may be unusually weighted and a function of

the particular spectroradiometer used. Thus care must be taken in

describing the results of radiance measurements and such a commonly

used phrase as the ’’spectral radiance of a source” should be avoided

or at least accompanied with an explanation.

- 8 -

CALIBRATION EQUATION FOR A MONOCHROMATIC SOURCE

The basic radiometric calibration of any spectroradiometer involves

the relationship between its electrical output and its radiant flux

input, the latter usually expressed in terms of spectral radiance. In

order to develop this relationship it is convenient to introduce the

coordinate systems illustrated in Fig. 3.

A cartesian coordinate system is selected such that its origin is on

the optic axis of the spectroradiometer and its (xy) plane is tangent

to the source at this point. For simplicity we will assume the source

is also a plane which is normal to the optic axis. Thus the z axis will

coincide with the optic axis and a point on the radiating surface of

the source can be represented by the coordinates (xy). At every point

- 9 -

(xy) on the source we consider another coordinate system, a spherical

system with the polar axis parallel to the optic axis. The angle

between any such polar axis (z axis) and the direction of the ray of

interest is designated 0 and the angle about the polar axis is called

<j>, as shown in Fig. 3. Using this coordinate system, the spectral

radiance from an arbitrary point (xy) on the source and in an arbitrary

direction (0(f)) can be denoted by the functional expression L = L (xy0<j>).

A A Fig. 1| is a schematic representation of a spectroradiometer . It includes

f

Fig. 4 SPrCTfcORADlOME'TE.R

10

source optics, a monochromator, a detector, and required electronics

and recorder or output meter. Let L^(xiy]_0i<J>i ) be the spectral radiance

of the point (x^y^) on the source and in the direction ( 6

q

<|> i ) corresponding to one of the rays in Fig. h. Since the medium in which the optical

elements are placed is the same throughout (usually air), the spectral

radiance associated with this ray following the source lens is

Mx iyi01<f>l) T

[ ( 1 0 1 4>i ) where t' (xiy^G^i ) is the spectral transmittance of the source lens for this particular ray. The spectral radiance

of the ray following the collimating lens is L ( x^y 1 6

<|> i ) t’ ( x^y

1 4>i

T "( x iyi0l4)l ) and continuing in this manner, L ( x^y 1 9 1 4> i ) x(xiyiis

A A

the spectral radiance of the ray falling on the detector where t ( x j_y 1 0 1 <|> i

is the product of the individual transmittances of each of the optical

components for this ray. In general t (xy0<J>) is the spectral transmitA tance of the entire spectroradiometer for the ray characterized by the

coordinates (xy0(j>) where (xy) is the point on the source where the ray

originates and (0<j>) is its initial direction.

The transmittance of an element may also depend on the polarization

associated with the spectral radiance or ray in question. Since most

sources of radiometric interest are either unpolarized or only slightly

polarized, we will assume, at least for the present, that the flux

incident on the spectroradiometer is unpolarized. Corrections for this

11 -

assumption not being valid will be considered in a later section.

If the source in Fig. U emits radiation at only one wavelength,

A , or more meaningfully emits radiation in a wavelength band, AX, which

is very small compared to the spectral band passed by the spectroradiometer

the total radiant flux which is emitted by the source and which will

enter the spectroradiometer is

Xu &<S> \J)

where sin0d0d<}) is the differential solid angle dft and dxdy is the dA

of Eq. (3). The limits of integration for x and y are determined by

the entrance window (2) or effective target area and for 0 and <J> by the

solid angle subtended by the entrance pupil (2) which is determined by

the aperture stop as indicated in Fig. k. If the spectroradiometer is

set on wavelength A , the corresponding radiant power reaching the

detector is

co$£ 5ln£ deci^j)

and the voltage output from the recorder is

VcM = M 5 L (X n

©4> \<) ~q(X H e <j> A

a(* L| e<f>A.)elxd<-| VnQ'd&df (L)

12

where (xy64>X ) is the spectral response of the detector* for the ray

A O

characterized by the coordinates (xy0<j>X ) and G* is the combined gain

and response of the amplifier and recorder.

Eq. (6) is the calibration equation desired for a "monochromatic"

source; that is, a source where the spectral radiance is constant within

a small spectral band AX, defined above, and zero elsewhere. For a more

general type source, the slit function concept is required as will be

shown in the next section.

THE SLIT FUNCTION

If the source or beam of radiation that one is observing is not a

narrow spectral line (monochromatic source), an integration relative to

wavelength must be performed. The question arises as to what the limits

of the wavelength integration should be. We shall try to answer this

question by considering a few simple examples.

One of the most common conditions when using a spectroradiometer

is that the entrance and exit slit widths are equal and the optical

magnification of the entrance slit in the plane of the exit slit is one.

Thus, the image of the entrance slit is the same size as the exit slit.

*For a photomultiplier tube the units for

A are amperes per watt.

In the present case the units for G are volts per ampere.

- 13 -

Let us assume that the entrance slit is irradiated by radiation for

which the spectral radiance is constant with both wavelength and with

position and direction of incidence on the entrance slit. Also, let

us assume that the spectral transmittance of the monochromator is

constant with respect to wavelength and that the spectroradiometer is

set for a wavelength Xo. The latter statement means that radiation of

wavelength Xo passing through an infinitesimal strip centered in the

entrance slit and through the monochromator will fall on a similarly

centered strip in the exit slit. Moreover, since the dispersion of

the monochromator will generally vary negligibly over the width of the

entrance or exit slit, all the rays corresponding to Xo incident on the

entrance slit and getting through the monochromator to the plane of the

exit slit will fall on and pass through the exit slit. This assumes

perfect (no aberrations) ray (no diffraction) imagery and is illustrated

in Fig. 5a

V\ZAV£ LENGTH

' }

/A

//0

a.

b. c

Ao+M

a.

%

V

A

\ m

e.

5 POSITION op IMA6,E of entrance

SUIT AS A FUNCTION OF WAVELENGTH

- Ik -

where the image of the entrance slit produced by radiation of wavelength

Ao is superimposed on the exit slit. Images corresponding to other

wavelengths will fall on either side of the Ao image. Thus, there will

be a wavelength, Ao + AA, such that its image will be sufficiently displaced to just miss getting through the exit slit (Fig. 5B). A similar

situation occurs on the other side of the exit slit for Ao - AA. For

wavelengths Ao + AA/2 and Ao - AA/2, half the image of the entrance slit

will pass through the exit slit. Fig. 6 is a plot of the fraction of

radiant flux of wavelength A relative to that of wavelength Ao which gets

through the exit slit when the spectroradiometer is set on wavelength Ao.

Such a plot or function is called a slit or apparatus function and will be

denoted by the symbol a(Ao A).

1.0 h

Ao

Fl'^. IDEALISED SLIT FUNCTION FOR

EQUAL entrance AND EX. IT SLITS

For the simple ideal case described, the slit function is an

isosceles triangle with its peak at Ao and the width of its base equal

- 15 -

to 2AX. The width at half-height, AX, sometimes referred to as the

spectral slit width, is approximated hy AS/(dx/dX) where AS is the slit

width and dx/dX is the linear dispersion of the monochromator. Fig. 7

Entrance

5Lit

ETtfiT Sut

Awb <3p

auce- suit

CoRRfS POWDiMtej

SUT FUNCriOMS

^ Hs >

1 1

1 1 1

1

1 1

1

1

1 r

•

Fl 5

7 | DEAL! EEb SLIT FUNCTIONS FOR.

UNEQUAL ENTRANCE AND EXIT SLITS

- 16 -

shows the perfect ray slit functions for cases when the entrance and

exit slit widths are not equal but at least one is large compared to

(Xo/w)f. The slit functions are either rectangular or trapezoidal and

their width at half-height is equal to the width of the wider of the

two slits divided by the dispersion.

For the real case, where diffraction and possibly optical aberrations or even imperfect optical adjustment is present, the slit functions

shown in Figs. 6 and 7 are only first approximations to the actual slit

functions. The approximations may be quite good when at least one of the

slits are wide compared to the distance between the peak and first minimum

of the diffraction pattern associated with the image of the entrance slit

in the plane of the exit slit. This distance is approximately equal to

(Xo/w)f where w is the diameter of the aperture stop and f is the focal

length of the focusing lens in Fig. k. Diffraction, aberrations, and

imperfect optical adjustment will tend to broaden, round off the corners

and extend the "wings" of the slit function as illustrated in Fig. 8.

1DFAL

n«. 8 TYPICAL RrAL SLIT FUNCTION

- IT -

In general, accurate slit functions must be obtained experimentally

and a technique for doing this will be presented later.

From the definition of the slit function, the radiant flux reaching

the detector in the spectroradiometer for an arbitrary spectral radiance

input is obtained by including the slit function in the integrand of

Eq. (5) and replacing AX with an integration relative to wavelength.

Denoting the slit function, when the spectroradiometer is set on Xo by

a(Xo X), the output signal from the recorder for an arbitrary input is

therefore given by

where the wavelength integration is over the wavelength range for which

the integrand is non-zero. These limits of integration for a continuous

source are usually determined by the extent of the slit function and

for a spectral line source by either the slit function or the spectral

GENERAL CALIBRATION EQUATION

<r(\o X) dxdy Cos 6

line

- 18 -

Eq. (T) emphasizes the many factors that can affect the output of

the spectroradiometer . Fortunately the equation can he simplified

significantly when the spectral radiance of all the rays incident on

the spectroradiometer are independent of all variables except wavelength.

For the most accurate radiometric measurements this is an important

requirement, and for some sources is realized by viewing a small enough

area and solid angle*. When this is not possible, an integrating sphere

may be used and this will be discussed later in the section on Spectral

Irradiance. In addition, a method for estimating the magnitude of the

error when L (xy0<}>A) / L (X) will be presented in the section on Higher

Order Effects.

Assuming that L is independent of (xy); i.e., a uniform target

A or source, and of (0cj>); i.e., a lambertian source, Eq. ( 7 ) may be written

*Generally the radiance associated with rays from different points vary

significantly more than that from the same point but a different

direction. Thus, usually the field stop must be reduced but not the

aperture stop. This can be confirmed by determining the radiance of

the target as a function of (xy0<J>) using a very small field and aperture

stop

- 19 -

VQo) - § ar(K>\) (^XxCXt)^A) d^(>< Lf -©-4>a)

dxdycosG- Si^yG'd^dcf) d\ ($)

\/(Xo] ~~ &} ^ LA (M &~C A° ^ (R^(M <A A

where ^

e (x) is the multiple integral in Eq. (8) and will he called

A the effective spectral response of the spectroradiometer . Thus, if

^ e (A) can be determined experimentally, the equation relating the

A spectral radiance incident on the spectroradiometer to the output signal

of the instrument can be simplified significantly. Fortunately it can,

as will be shown in the next section. It should be emphasized, however, that Eq. (9) applies only to the above described idealized source

and that $

e (x) changes if the field or aperture stop is modified. Also

A required in the derivation of the equation is the assumption that the

effective spectral response does not depend on the magnitude of the flux

incident on the detector and that the gain of the electronic system, G,

is independent of the magnitude of the electrical input signal.

- 20

EXPERIMENTAL DETERMINATION OF THE SLIT FUNCTION

AND THE EFFECTIVE SPECTRAL RESPONSE

For many calibration problems it is necessary to know the effective

radiometer. Therefore, this section will be devoted to the determination of these functions.

for a particular spectroradiometer by spectrally scanning a source whose

relative spectral distribution is known and doesn’t change significantly

over the wavelength range of the slit function. A blackbody, tungsten

strip lamp or the positive crater of a graphite arc are suitable for

this purpose if the spectral slit width is a few angstroms or less.

Under these conditions, Eq. (9) can be reduced to

The effective spectral response <^

e

( A) in Eq. (9) can be obtained

and

(ii)

21 -

V(M

£ <=

1— x^X A (X o )

0

Thus, by dividing, at each wavelength, the recorder output of the

spectral scan, V(Ao), by the product of the spectral radiance of the

source and the dispersion of the monochromator at that wavelength,

one obtains a function proportional to the effective spectral response.

As will be seen later, only the relative value of (R

e (A) is required.

A However, it is not uncommon over a wide spectral scan for the amplifier

gain to require change, and such changes in G must also be taken into

account

In this treatment it is required that e (\) not depend on the

A magnitude of the radiant flux passing through the monochromator or

striking the detector because ^

e

( A) will usually be determined using

a different a and G than when the spectroradiometer is calibrated.

Fortunately the requirement can be experimentally checked by simply

determining (R e

( A ) with a number of sources having significantly

A different radiances.

The slit function can be obtained, at least in principal, by setting

the spectroradiometer at the wavelength for which the slit function is

22

desired and filling the field and aperture stops with the flux from

a number of monochromator sources each having the same radiance but

slightly different wavelengths, all however falling within the wavelength range of the slit function. The spectroradiometer output for

each of these sources is proportional to the product of the effective

response of the spectroradiometer at the wavelength of the source and

the value of the slit function corresponding to the monochromator wavelength setting and for the wavelength of the source. Thus, dividing

this output at each wavelength by the effective response for that wavelength makes it possible to map out the slit function. However, this

straightforward approach is quite impractical because "monochromatic"

sources satisfying the above requirements are rarely if ever available.

In some situations, a second monochromator could be used as a source,

but this would require an extensive amount of work.

Fortunately, the slit function can be obtained, and rather simply,

by using one "monochromatic" source and a number of monochromator wavelength settings instead of a number of sources and one setting. That

is, the slit function can be obtained by a wavelength scan of a spectral

line which is very narrow compared to the spectral slit width. Actually

the spectral scan is not the slit function but its mirror image,

reflected about the wavelength of the source. Fig. 9 illustrates

- 23 -

entrance

A. SLIT IMAGES

SPfCTRORA&ioMnre \ f

£\ Ac-vSX

IfV AVE LENGTH SETT^ 8 \o Ac ~"$ ^ XcT^-^y

C d €

Ft*. °t Relation between spectral scam

•' OF marrow emission uns and

SLIT FUNCTION

- 2k -

why this is the case and why this method works. In Fig. 9A, the

image of the entrance slit, which is irradiated with virtually monochromatic radiation, Xo, is shown in the plane of the exit slit for

various wavelength settings of the spectroradiometer . It should be

noted that the irradiance of the images is not uniform, an effect that

could be caused by improper optical adjustment of the spectrometer.

Fig. 9B shows the recorder output for the spectral scan. Since the only

wavelength present is Xo, the value of the spectroradiometer effective

response does not change significantly* and from the definition of the

slit function, the recorder deflections are proportional to values of

the slit function. However, except for the result at Xo, the values

do not correspond to the slit function for a monochromator setting Xo.

The deflection at "a" is proportional to a(Xo+26X Xo) which is the value

of the slit function for the wavelength Xo when the monochromator is

set at Xo+26X. Similarly the deflection at b is proportional to

c(Xo+6X Xo), at c to a(Xo Xo), at d to a(Xo-6X Xo) and at e to

a(Xo-26X Xo). Fortunately, the slit function usually changes negligibly over a wavelength interval corresponding to its own range. For

7v 0 Slight changes ino^(X) might be expected due to very small changes in

the optical system resulting from the wavelength scan from Xo+26X to

Xo-2SX.

- 25 -

example, the value of the slit function for a wavelength Ao when

the monochromator is set on Ao+26 is equal to its value for a wavelength Ao-26 when set on Ao ; that is, a( Ao+26 Ao) = a(Ao Ao-26).

Similarly a(Ao+6 Ao) = a(Ao Ao-6), a( Ao-6 Ao) = a(Ao Ao+5) and

a( Ao-26 Ao) = a(Ao Ao+26). Thus, the slit function a(Ao A) is the

mirror image shown in Fig. 9C of the spectral scan of the line with

the plane of reflection being Ao.

The above result can also be obtained directly from Eq. (9).

Assume the monochromator is set at Ao+x. Since the narrow spectral

line is at Ao and the effective response and slit function is virtually

constant over the extent of the line,

V(a«i-x.) = <R

e

x

C\o) <r(Xotx , Ao') C L X (M d\ 0*)

Ime

As discussed in the previous paragraph

O^Aa-t-X AcT) - cr ( Ao Xo-k) 0*0

and

Vx) j" l x V(Ao^x) - (\) d\ Q*)

- 26 -

so that

V (

A 0 ^ £

Lfr) cl A

l»n'<

At the peak of the recorder trace, we have

VM = <R f(A«) cr(A 0 Ao) 5 LOO

ImC

and combining this with Eq. l6 results in

<r(A„ a.-*) =

^^

But from our definition of the slit function a(Ao , Ao) El and

fore

<r(Ao Ao-*)

V( Ao + *)

VM

0<0

(17)

0«)

there03)

- 27 -

SPECIFIC CALIBRATIONS

Spectroradiometers are usually calibrated by relating their output when observing an unknown source of spectral radiance to their output when observing a known or standard source of spectral radiance. The

basic equations for such calibrations are obtained by applying Eq. (9)

to both the standard and the unknown, i.e.

vIk)

vw

£|

5

f L^M Wa, \) dA

^ f L x

l\) x) <R/(X) dA

where the superscript s refers to the standard. In this section,

specific calibration equations for various types of spectral distributions will be derived and discussed.

a. Spectral radiance of a continuum

One of the most common type spectra of interest in radiometry is

that which excludes spectral lines. Such a spectrum is usually obtained

from the emission of solids and liquids and referred to as a continuum.

The common standards of spectral radiance such as tungsten strip lamps

or blackbodies have this type of spectrum.

The calibration equation for a continuum is very simple provided

- 28 -

the slit function or the effective spectral response of the spectroradiometer is such that the spectral radiance functions in Eq. (20)

may he taken outside the integral sign. Then

~ ^ L^(Ao) ^ ^ ^A

V (A o)

^

^ $\>(A) °^A

and

VO ^

V

?

0«) <=7

This can he done when neither the standard nor the unknown spectral

radiance changes significantly over the wavelength range for which the

integrands in Eq. (2l) are significant. In this case, it is not

necessary to know the slit function or effective response of the spectroradiometer. However, it is necessary to know that the above stated

condition prevails which usually means the distant wings of the slit

- 29 -

function are negligible. This is usually the case for a double monochromator*. Incidentally, Eq. (22) assumes that the field stop and

aperture stop is the same when viewing the unknown and standard. Otherwise, ^?

e (X), which is given by the multiple integral in Eq. (8) would

A not be the same for the two equations in Eq. (21). In addition, whenever possible the standard should be adjusted so that

^Xo) = hi- = | C23)

Then the accuracy of the measurement will not depend on the lack of

linearity in the detector or amplifier.

If L or L can not be removed from the integral sign in Eq. (20),

A A the calibration is considerably more difficult. Not only the slit

function and the effective spectral response of the spectroradiometer

are required but also the relative spectral distribution, f(X), of the

#

A double monochromator is the name of the instrument in which two

monochromators are used in series. The exit slit in Fig. U would

then be the entrance slit of another monochromator.

- 30 -

unknown where

LA

(») - c-fM

and C is a constant relative to wavelength. Fortunately, the relative

spectral distribution f(A) need not be known as accurately as L (A) is

A desired. The accuracy required will depend on the magnitude of

a(X X)

^

e (A) at wavelengths distant from Xo. This, of course,

means that C may vary with wavelength and should be determined at each

wavelength for which the spectral radiance is desired. Mathematically,

if measurements with the spectroradiometer result in

y(X„) = K(Xs) V

s(AO 0-*)

where K is the number relating the two outputs, then using Eq. (2U)

and Eq. ( 20

ecu

*&«•) [ Lx(>) r(X V>R fw dX

f-p(x) cr(A<> >) Rfb) ^X

which is the calibration equation for this case. If f(X) is not available, a zero order approximation, fo C X )

can be obtained by applying

Eq. (22) as a function of wavelength and assuming the resulting L^(X)

- 31 -

equals fo(X). A first order approximation of C ( X

obtained by using

these f o ( X ) in Eq. (26) can then be used for a first order approximation of f(X); that is, f i

( X ) = Ci(X) f(j(X) which in turn can be used

in Eq. (26) to obtain C 2 (X). This is repeated until C^ +1 (X) = Ch(X)

to well within the accuracy desired.

Eq. (26) rather than Eq. (22) may be required, even for moderate

accuracies of about 5%, when using a single monochromator (rather than

a double monochromator) in the situation when the spectral radiance

functions of the standard and unknown are significantly different and

when at least one of these functions has a very small value at the wavelength of interest relative to its value at other wavelengths. Fig. 10

|0

F 1 ^

10

32 -

illustrates this problem for the case of the argon arc in Part II.

It is assumed that the slit function has a constant value of 2 x 10“ 5

except for near 250 nm. As seen in the figure GL^ (250 nm) differs

from KG L (250 nm) by a factor of about two even though the simple

A calibration using Eq. (22) would indicate they are equal. The fact

that V(Ao) = K(Ao) V

S (Ao) or

^Lx00<K*o xK(>)dA - «(XA6j

V

\

l\(a) <r(Ao })(K

c

p) dA fr)

s s merely means that GL = KG L for at least one wavelength. This waveA A length need not be Ao. It can be obtained by combining its defining

equation

La

(A ') - K ) (?€)

with Eq. (27), resulting in

^ LyCA) <t(Ao A') >/ A) clX

0 x O) \) <AA

- 33 -

The wavelength X' has had extensive use in optical pyrometry and is

referred to as the mean effective wavelength (3) of the instrument

for the two radiance functions.

In any serious work, even with a double monochromator, one should

obtain estimates of a(Xo X)^6

and f(x) and determine how well the

effective wavelength, X’ , agrees with the wavelength setting of the

monochromator, Xo. If the agreement isn’t adequate, Eqs. (26) and

(29) must be used or a(Xo X) or <2? 6 improved by adding a filter or

A replacing the existing detector with one having a more appropriate

response

b. Intensity of a spectral line

When a spectrum of interest contains spectral emission lines, one

is radiometrically concerned with either the spectral radiance at each

wavelength of the line; that is, the shape of the line or the integral

with respect to wavelength of the spectral radiance of the line. The

latter is called the intensity of the line.

When determining the shape of a spectral line, the width of the

slit function must be significantly less than the width of the line.

Then the problem is equivalent to determining the spectral radiance of

a continuum which has been presented. When the spectral slit width is

approximately equal to the line width, determining the line shape or
'
- 3b -

width is very difficult, generally inaccurate, and essentially a research problem (U). It will not be considered in this report. When

the spectral line is much narrower than the spectral slit width, the

line intensity is usually all that can be determined. Fortunately, it

is often all that is required.

Fig. 11 shows a typical spectral line, a standard continuous source,

UKiCTlOM

L

Fifij. II

effective response and slit function. Since L

A

s and change negligibly

^ 35 -

over the slit function and a(Xo X) changes negligibly over the line,

Eq. (20) may be reduced to

V

s&*) = §

°r^ X)

(30

VW =

£, a-CA.X.

-) <R&.) f L k 00

\\At

where /

line

L (X) dX is the line intensity.*

A

* In terms of atomic parameters

1w

L .(x)olx

= h 21w An wY) Nivi A?

where h is the Planck constant, v the frequency of the line, A its

nm 5 nm

transitional probability, the volume density of the emitter in the

initial state of the transition and AZ the depth of the volume being

observed.

- 36 -

Since a(Xo Xo) = 1, combining Eqs. (30)

J

La(M*A =

^- 5- f^A)dA

V €> J

Thus, in this measurement, the integral of the slit function, some0 times called the effective spectral slit width, AX , is required and

g must be obtained experimentally. Note that V(Xo) and V (Xo) are outputs

corresponding to only one wavelength, Xo, of the spectroradiometer . In

the case of a line, V(Xo) will correspond to the peak of the wavelength

scan over the line.

Eq. (31) is the equation for determining the intensity of a line

in the case when the spectral line is completely contained within the

essentially constant portion of the slit function as shown in Fig. 11.

This never really occurs and some correction is required for that part

of the line outside this region. The correction will depend primarily

on the shape of the line in the distant wings. If this shape is known,

an estimate of the required correction can be obtained from the equation

oO

f

LOO dX

CoKftfcnoK) = &Xe/v

Ux) Ay

A<5

- 37 -

For a line with a shape proportional to 1 where a is the

(A-Ao) 2 + a

2

half-width (half the width of the line at its half radiance values) of

the line, the correction is about 0.13 when the ratio of half the

spectral slit width to line half width is 10 and about 0.01 when it is

100 .

If it is not desirable to make the spectral slit width considerably

greater than the line width, possibly because other spectral lines are

too near the particular line of interest, Eq. ( 31 ) can not be used to

obtain the line intensity. In this case, assuming the slit function

is approximately the same width as the line, as illustrated in Fig. 12a,

Fuwcnoto

b.

5P£CT£Al_ SCAN)

V(x)

F15. 12.

- 38 -

Eq. (20) becomes

V&o) = Q? $r(AoA) ^0

as before, but

\/(X 0

) — ^7

^

A CA^) ^

L-\C^) A)

^ ^ {$2-)

Since we are now allowing Ao to vary, let’s call it x. V(x) is the

spectroradiometer ’ s spectral scan over the line and is shown in Fig.

12b. The integral of this scan; that is, the area under the curve in

Fig. 12b is

§

VI) lx = &) f fcffr) ( j

/_*(>) <r(y >) 1a) <*U £

3)

J

y

x

>

Usually the effective response changes negligibly over the extent of

such an integration. Therefore

^ V(x) dx - Of

I* f L>00 cr(x >) 1A lx OO

* X

- 39 -

Interchanging the order of integration

jV(*)dU = ^

L*C» (f<r6< (?fj

A

Since the slit function is really a function of the difference of its

two variables, integration relative to either of its two variables

results in the same value, i.e., the area under the slit function.

Moreover, if the slit function does not change over the full extent of

the line, its area will not change and can be removed from within the

line integration. Thus

and using the above stated fact that /a(x A)dx = /a(x A)dA and Eq. (3l)

£ LM ~ <S,

s <4*

If one is concerned with the error associated with the variation

-Motion where the standard is a 2500 K blackbody . For this source, the

spectral radiance varies for a wavelength interval of one angstrom by

about 0.01? at 10 000 A and about 0.5? at 2500 A. As before, a correction

must be applied for not integrating the recorder trace over the distant

wings of the line.

It is not uncommon to have a spectrum in which there are a number

of spectral lines within the spectral slit width as shown in Fig. 13.

c

Intensity of several spectral lines

Slit fukjCTiokJ

Fi^. 13

These lines will not be seen individually and all one can determine is

the total intensity of all the lines. With the slit function shown in

Fig. 13 it is necessary to integrate the recorder trace and use Eq_. (37).

- hi -

The numerical integration involved can he avoided by using the rectangular slit function (one slit much wider than the other) shown in Fig. ih .

e

Then the total intensity of the lines can be obtained from Eq. (3l).

d. Combination of a continuum and a spectral line

This is a common occurrence when hot emitting gases are surrounding

a solid (positive crater of a graphite arc) or when a gas is sufficiently

hot to ionize some of the atoms (electrons and ions in a plasma emit a continuum while the atoms and ions also emit lines). In applying Eq.

(20) to a single line and continuum as shown in Fig. 15

- 1+2 -

F.&. ir

one can express the unknown spectral radiance as the sum of line and

continuum radiances resulting in

\ 0«)

Using the first of Eqs . (30), one obtains

line

+ L_ y

(A «)

Thus in this situation one can obtain the sum of the continuum radiance

plus the line intensity averaged over the effective spectral slit width.

Relative to the continuum, as before, this implies the distant wings of

the slit function are negligible and don’t contribute to the output.

- 1+3 -

The extension to several lines plus a continuum can be made in the same

manner as was done for several lines alone.

STANDARDS OF SPECTRAL RADIANCE

The most common standard of spectral radiance is the tungsten strip

lamp. The gas filled version of this lamp can be used at blackbody temperatures varying from about 2U00 K at 2500 nm to 2900 K at 210 nm. A

typical strip is 3 mm x U0 mm and has uniformity of 1 Jo over a central

area of about 0.5 mm by 1.0 mm. Currents varying from 18 to U 5 amps with

voltages up to 13 volts depending on the model lamp are required. A

current uncertainty of .

% corresponds to about .hf uncertainty in

spectral radiance at 650 nm and this varies roughly inversely with

wavelength (i.e., .Q% uncertainty at 325 nm) . Various models of the

lamps are available from General Electric, Inc. in the United States

and General Electric Limited in England. The lamps may be calibrated

using an optical pyrometer and published emissivities* (5,6). The

detailed procedure has been described in the literature (3). Calibrated

lamps may be obtained from commercial laboratories or from the National

Bureau of Standards. The estimated or reported uncertainties of these

*In our experience Larrabee’s emissivities are preferred from 650 nm

to 300 nm and Devos ' from 650 nm to 850 nm.

calibrations , the wavelength range available and the approximate cost

as of 1968 are given in Table 1.

Table 1

Source of Approximate

Calibration Uncertainty {%) Cost

2500 nm 850 650 300 250 210

Pyrometer

Calibration

Commercial 3

NBS

5 2 7

^ U 7 8

112 2

Cost of lamp,

provided calibrated

pyrometer available

$U50

h $1500

Another very useful standard of spectral radiance is the positive

crater of a low current graphite arc (7)- The spectral radiance of this

source is similar to that of a 3800 K blackbody for a wide range of

wavelengths in the visible and ultraviolet. In some wavelength regions

there are very strong emission lines or bands from the arc column and

below about 280 nm the arc column also contributes significantly to the

continuum. The arc has been calibrated and used with an uncertainty

(95% confidence) ranging from about 3% at 850 nm to 9 % at 210 nm. It

has a uniformity of about over a diameter of about one millimeter.

This arc, developed specifically as a radiometric source, is commercially

available from the Mole Richardson Co., Hollywood, California, for about

$1500 and $3000, without and with a power supply, respectively. The

major advantages of the graphite arc are its high radiance and the fact

that it does not require a calibration. Its radiance corresponds to

approximately the sublimation temperature of graphite. The disadvantages

of the arc are that it cannot be used in a number of wavelength regions

because of line emission, and it is less convenient to use than a strip

lamp

.

There are other sources that can be used as standards of spectral

radiance, but, at present, either less is known about them, or they are

not available commercially. Cavity radiators would be very useful

standards provided their blackbody quality were confirmed and an accurate

means of determining their temperature available. High temperature blackbodies are available commercially from a number of firms and, if

sufficiently stable, could be calibrated at KBS. To date, no requests

of this type have been received. The high pressure argon arc described

in Part II of this report is also a very useful standard of spectral

radiance between 200 nm and 300 nm but it is not currently available

commercially. For details about this source one is referred to Part II.

Relative to the future, NBS is currently trying to improve and

- U6 -

extend infrared calibrations and standards. An improvement at 2500 nm

to about 1% and an extension to 15 ym is contemplated within a year.

HIGHER ORDER EFFECTS

The general calibration equation, Eq. (9), requires that the

spectral radiance, L , be independent of (xy0cj)) over the entrance window

and pupil of the spectroraaiometer . In addition, the optical radiation

was represented by optical rays, assumed unpolarized, and the optical

components considered perfect; thereby ignoring diffraction, polarization

effects, and scattering and aberrations. The magnitude of the errors

resulting from these assumptions and the methods of correcting these

errors, if significant, will be presented in this section.

a. Lack of uniformity in spectral radiance,

transmittance and response

If the transmittance of the spectroradiometer and response of the

detector were uniform; i.e., constant for all rays passing through the

instrument, no error would result from the spectral radiance being nonuniform. In this case, the new calibration equation obtained from

Eq. ( 7 ) would be

V(\o) = <^Axl \ o-/ Ao x) dX Qfo)

- 1+7 -

where

T>

x c| &<$> X) d<dy cose d&d0

A

and

A rr_ cosG- st^-0 ded<$

6yVfra^ce

iVindo*/ pu pi |

L is the average radiance passing through the spe 2troradiometer as defined by Eq. (l+l). Thus, even if the source is non-uniform, the

average radiance can be obtained using the previous treatment if t and are uniform.

In order to estimate the error committed when using Eq. ( 9 ) or

Eq. (hO) when x and ^ are not uniform for all rays of interest, experimental measurements of the non-uniformities in L, t and ^ are required.

Using a very small target area, say 0.2 mm x 0.2 mm, and precisely

translating the unknown source and standard in the x and y directions,

it is possible to map the spectral radiance variations of the sources.

An adequate angular mapping can be obtained with a larger target area,

say 1 mm x 1 mm, but with an f/100 relative aperture. Typical maximum

variations for the tungsten strip lamps , referred to in the Standard

Sources section, are about 1% per millimeter and 1% per 6 degrees of

- 48 -

rotation. The variation in can he obtained by observing the output as

a function of position of a small (say f/100) aperture stop placed in

to 20% but can be greater for some monochromators and detectors. Thus,

f/10 (about 6 degrees entrance angle) relative aperture. The actual

error should be less than this maximum figure. Nevertheless, in any

serious effort, the variations for the particular source and spectroradiometer should be checked.

If the error is larger than desired, it can be decreased by various

means. If the error is due largely to the (xy) non- uniformity in the

target, a smaller target can be viewed, the detector more properly

positioned as shown in Fig. l6a, or a field lens used as illustrated in

Fig. l6b.

front of the source lens in Fig. 4. Typical variations of T^are 10

the maximum error [ AL x A(t $ )] caused by the non-uniformities assumed

A A A here in L , t, and $ is about . 2 % for a one millimeter target and an

A A A

fOCUSlNC, LjFKJS EfKiT SLIT DETECTOR,

f

t>E5 iRA BLt“

Posit

4

UNJ DESIRABLE

detector posmoisj

l

Fi^. i

&
m
- U9 -

The latter two approaches are designed so that each point of the target

irradiates a large and similar detector area. If the error is due

to large angular variations either in L or t , it can be reduced

A A A by decreasing the size of the aperture stop. These techniques are

usually adequate. If not, an integrating sphere should be used, and

its use will be discussed in the next section on Irradiance.

b. Size-of-source effect

The effects of scattering, diffraction and aberrations inside the

monochromator are taken into account by the slit function. However,

this is not the case for the source lens or any other optical elements

located ahead of the entrance slit. If the unknown and standard source

are identical in size, shape and non-uniformity, the effect of the above

factors on the output will be the same for both sources and cancel in

the comparison. Moreover, if the pre-monochromator optical system is

well designed and the optics of high quality, diffraction and aberration

effects will contribute less than 0.05% to this error (8) even when

significantly different sized sources are being compared. For the

standard sources referred to in this report, this can be realized if

the optical system produces images in which a resolution of about 0.1

mm exists. Therefore, scattering is usually the major factor in this

effect

.

- 50 -

The kind of scattering being referred to is illustrated in Fig. 17

.

In the figure, ray A would normally follow the path A* and not enter

the field stop or entrance slit. However, a portion of the radiance

associated with A is scattered into the monochromator. The amount

scattered into the monochromator will depend on the size of the source

and the condition of the optical element in question. We refer to it

as a size-of-source effect. The result of this type scattering is

that the larger of two sources will appear to have a greater radiance

even if the radiances of the two target areas are the same. Typical

increases vary, depending on the optical element, from 0.05% to 0.5%.

The size-of-source effect can be determined and corrected through

SouRCtr

UFVjS

F,,. 17

- 51 -

the use of a scattering function (9), a concept similar to that

associated with the slit function. However, a more direct and simpler

approach (8) is often adequate in radiometry. This involves observing

an irradiated diffuse reflector containing a hole slightly larger than

the target area. The hole, which emits no radiation, is imaged on the

field stop. The only radiation entering the system is that scattered.

By placing flock paper cut-outs simulating the size and shape of the

standard and unknown sources on the diffuse reflector, the difference

in the scattering for the two sources can be obtained. Corrections of

this type have been made (8) with an estimated uncertainty of a few

hundredths of a percent of the spectral radiance to be determined.

c. Polarization effect

Most spectroradiometers act as polarizers, or put in a different

manner, have a transmittance which is a function of the polarization

of an incident beam. The polarization in spectroradiometers varies

with wavelength and has been observed, when the instrument incorporates

a prism-grating double monochromator, to be as large as 0.2, where

/Vmax - Vmin polarization is defined as P = Vmax and Vmin refers

Vmax + Vmin

to the maximum and minimum outputs of the spectroradiometer relative

to the direction of polarization of a linearly polarized flux incident

on the instrument. Such a spectroradiometer polarization will result,

- 52 -

as will be shown below, in an error of 0.k% when an unknown source,

linearly polarized to only 2% is compared to an unpolarized standard.

A complete experimental investigation of this effect; that is,

determining the polarization properties of the spectroradiometer and

the polarization of the source for arbitrary types of polarization is

quite tedious and requires a quarter wave plate as well as a polarizer

for each wavelength of interest ( 10,11). Fortunately, strip lamp sources

and the prism and grating monochromators used by the author could be

characterized as a combination of linearly polarized and unpolarized

radiation, and therefore analyzed with only a polarizer.

The following method has been successfully used to accurately

correct for the polarization effect for sources and spectroradiometers

used by the author. The polarization of the unknown source is determined

by observing it at a wavelength for which the spectroradiometer is unpolarized. If such a wavelength doesn’t exist it can be realized by

mounting and properly orienting two or three plane parallel plates of

CaF 2 , or other optical material transmitting over the wavelength range

of interest, just beyond the exit slit of the monochromator. When the

spectroradiometer is unpolarized, a linear polarizer placed normal to

the optic axis and between a blackbody and the entrance slit will not

affect the spectroradiometer output as the polarizer is rotated about

- 53 -

the optic axis. The polarizer and blackbody can then be used in the

same manner at other wavelengths to determine the polarization of

the spectroradiometer as a function of wavelength. In addition, the

spectroradiometer can be used at its unpolarized wavelength, with the

polarizer to determine the polarization of the unknown source. In

each case, if the output varies with angle of rotation of the polarizer as Vo + Vp cos 2

0 the polarization is equivalent to an unpolarized

component, Vo, and a linearly polarized component, Vp. When this is

the case, one can use the simple vector representation and the calculations indicated in Table 2 on page 5 U to correct for the polarization effect. In the example used in Table 2, the unknown would be

corrected by increasing its spectral radiance by 0,h%.

d. Detector non-linearity and fatigue

In general, the response of detectors may vary with the magnitude

of the radiant flux incident on them. Errors caused by this effect

can be avoided if the standard is adjusted so that its monochromator

output is equal to that for the unknown source. When this is not

possible, the response of the detector should be experimentally

determined as a function of the incident flux. This can be accomplished

with a standard source whose radiance (and therefore the flux incident on

the detector) can be varied in a known manner. Such a test will also

require checking the response of the electronic system as a function

- 5U -

Table 2

Relative Effective

Response of Spectroradiometer

Spectral Radiance

of Sources

Unpolarized

os

^ 0.i>

A 0,5 048 L/z

Polarized 02.5

*0-5

L/^ * 0.02 L

0 g S 0 Assuming Y = KL and V = KL and using the unpolarized spectroradiometer to determine the L required in order for V = V"

+- L

+ -02l)+- 0S)(4S)L

ll

Similarly with the polarized spectroradiometer

(: 5r+.2s)(. < tf^ + .oil) + (.?)£

£i>.2s) -r L = .^Ls

Thus the spectral radiance determined with the polarized is found to

be 0.k% less.

- 55 -

of its input signal.

The response of a detector may also change with the time a constant

radiant flux is incident on it. In photomultipliers this effect is

referred to as fatigue and depends on the magnitude of the incident flux,

the anode current and the history of its exposure to radiant flux just

prior to the time of interest. The lower the flux and anode current

and the longer the period of irradiation, the smaller the fatigue rate.

In tubes having an S20 type relative response, a fatigue rate of 0.01$

per minute for an anode current of 10“ 8 amperes following a 30 minute

irradiance with a flux of 10" 10 watts is not uncommon. However, tubes

characterized with such low fatigue rates, often changed differently on

darkening for a minute or two following the 30 minute exposure. The

response of some tubes changed by less than 0.02$ while others changed

(usually increased) by a few tenths of a percent. For larger fluxes and

anode currents and shorter irradiation times, response changes of a few

percent have been observed. Thus, the characteristics of each individual

tube (or detector) should be investigated under the particular conditions

and variables with which it will be used.

SPECTRAL IRRADIANCE

In previous sections of this report, the concept of spectral radiance

and methods for determining it were developed. In this final section.

another useful radiation parameter, spectral irradiance, will be introduced

- 56 -

and methods of measuring it presented.

a. Definition of spectral irradiance

Spectral irradiance, denoted by E , is the radiant flux falling on

A a surface per unit area of the surface and per unit wavelength interval.

More exactly, it is the limit of the ratio of the flux falling on a surface to the product of the area of the surface and the wavelength

interval of the flux as the area and the wavelength interval are made

to approach zero, i.e.,

. = Limit Ai(aa $) = 3^

x ^ 4A-IO &X AA PA 3 a

A A

where represents the flux incident on an area AA surrounding the

point (xyz) and A (A <§) is that portion of this flux in the wavelength

interval AX surrounding the wavelength X. From the definitions of

spectral radiance and spectral irradiance (Eqs. (2) and (U3) respectively),

these two parameters are related by the equation

tA (xn?-X) ~ IA i_ A (* h

G<PX)coseSw\-ected(t> (h-m)

Solid

where L (xyz0cf>X) is the spectral radiance at a point (xyz) and in a direction (0$) and E (xyzX) is the spectral irradiance at that same point.

A

- 57 - source n

0/ \ 5URPACF

L x(k 4

^€>4> a)

^OLlH) /^N^Lb

18

Fig. 18 illustrates the geometry involved in Eq. (kb) for the case

of a source irradiating a surface where n is the normal to the surface

at the point (xyz). The coordinate system used is similar to that

employed previously with the polar axis coinciding with the surface

normal. The solid angle 0. is the angle at the point (xyz) subtended

by the source.

b. Determination of E using a spectral irradiance standard

A The simplest manner of determining spectral irradiance with a spectroradiometer is to consider the monochromator slit or field stop

as the surface being irradiated. This means optics prior to the entrance

slit of the spectroradiometer have to be removed. The output of the

modified spectroradiometer when observing an unknown source of spectral

- 58 -

irradiance would then be

- <S| LA

(v Lj

^6 d X d

y

Co s ^S, n Ga e a<p T(x ^

Cj 9

(p) otAo a)

Cis)

where zo refers to a point in the entrance slit or field stop, t now

excludes the preoptics, and the integrating limits, as before, cover

the entrance pupil, entrance window and slit function. If t and

are independent of (xy0<j>)

$ir»6 Q5S& dOdfpjdxdcl d.A

0 0

and if the solid angle subtended by the source at the slit is completely

included in the entrance pupil.

where E (xyz A) is the spectral irradiance at the point (xyz ) in the

A ° o entrance slit. Finally, if E is independent of x and y A A \ E

x (

A) T

a(\) IR x(x) <rC A) d\ (m?)

- 59 -

where A is the area of the entrance slit. Similarly, for the standard

same for the unknown and standard, the spectral irradiance can he obtained

in the same manner as developed for spectral radiance.

Unfortunately, t and are rarely, if ever, independent of (xy0<j>)

and it is not uncommon for an error of 20% to be realized if this condition is assumed. This error can be significantly reduced by placing

an optical element that diffuses the radiation in front of the detector

as shown in Fig. 19.

Eq. ( U8 and (1+9 ) are similar to Eqs. (20) and assuming t and ^ are the

txAMPLE i Ex Am p Le 1—

I S

- 6o -

This not only irradiates the entire receiving area of the detector hut

does this approximately uniformly tending to make ^ the same for both

source and standard. This still leaves the error due to a non-uniform

t which can be particularly significant when the unknown and standard

sources or beams are quite different.

A more accurate approach to a non-uniform t and £ is to make L in

A Eq. (U 5 ) independent of (xy0<|>). This can be accomplished by using an

integrating sphere in front of the entrance slit as shown in Fig. 20.

E> = K Lx

Ex -

(So)

Then

- 6l -

and Eq. (45) becomes for the unknown and standard

'/(>'«) = cr dX

(?>

sphere. If the interior of the sphere is a uniform diffuse reflector

and the sphere holes vanishingly small,

uniformity and diffuseness in the reflectance of the sphere wall as well as the vanishingly small sphere holes can be compensated for by

irradiating approximately the same area of the sphere wall by both

the unknown and standard. A major limitation in this approach is that

the sphere significantly reduces the flux incident on the monochromator

and the corresponding reduction of the signal to noise ratio becomes a problem, particularly at short wavelengths.

and Eq. (51) can be used to accurately determine E . Departures from

A

c. Using a spectral radiance standard

If one wishes to determine the spectral irradiance of a source or

- 62 -

beam and is required to use a radiance standard, an arrangement similar

to that shown in Fig. 20 is required when using the standard. The

spectral irradiance at a point on the sphere opening is

C* M ~ f f

s where L is now the spectral radiance at the sphere entrance. If

A L

S (xyz 0<J>A) is uniform relative to (xy0<Js),

A O

•rr i s 2

t y - L X

TT SM •&

and this can be used in Eq. (5l). Small variations in L relative to

A

(xy0(j>) can be taken care of by using an average spectral radiance,

determined by the spectrometer, for an image similar to that entering

the integrating sphere. To insure that Eq. (52) is valid, one should

use an angle 6 such that the sphere wall that is irradiated with the

standard is as close as possible to that irradiated with the unknown

irradiance. This can be checked experimentally by investigating the

g constancy of K as a function of 0 in the relationship (obtained from

Eqs. (50) and (5^)

CT ^ j S z * $ j

f tLy = L

x

TTsm a = K

- 63 -

where L* is the spectral radiance at the exit of the sphere.

A d. Standards of spectral irradiance

The standards of spectral irradiance presently available in the

U.S. are the 1000 watt General Electric Corporation type DXW or FBY

tungsten halogen lamps. They are approximately 1 cm by 7*5 cm in size,

are usually calibrated at 8.3 amperes, either AC or DC (approximately

110 volts), and are available from a number of commercial concerns with

calibrations traceable to NBS. At the above current the spectral

irradiance at 50 cm from the lamp is about U0 watts per cm3 at 2500 run, increases to about 250 at 1000 run, and decreases to about 0.2 at 250 nm.

The uncertainties currently assigned these lamps varies from about ±3%

in the infrared to about ±8% in the ultraviolet. Since their stability

for 100 hours of use is generally considerably better, an effort is

being planned at NBS to try to reduce these uncertainties.

Recently, the irradiance of these standards has been significantly

increased as a result of the development of a ceramic reflector to be

used with the lamp (12). The new higher irradiance reflector type

standards have an effective radiating surface of about 3 cm x 5 cm,

and when used at a distance of Uo cm have about four times the spectral

irradiance of the lamp (without a reflector) for wavelengths longer than

500 nm and about two times the irradiance at 300 nm. They are not calibrated below 300 nm because of the rapid change in the reflectance of

the reflector at these short wavelengths.

- 6k -

REFERENCES

1. F. E. Nicodemus, Am. J. Phys . 3^L, 368 (1963).

2. A. C. Hardy and F. H. Perrin, The Principles of Optics , 68

(McGraw-Hill, New York, 1932).

3. H. J. Kostkowski and R. D. Lee, Temperature, Its Measurement

and Control in Science and Industry, Volume Three, Part I , *+U9

(Reinhold Publishing Corp., New York, 1962).

*+. H. J. Kostkowski and A. M. Bass, J. Quant. Spectrosc. Radiat.

Transfer 1_, 177 (l96l).

5. J. C. DeVos, Physica 20_, 690 (195*0.

6. R. D. Larrabee, J. Opt. Soc. Am. *+9_, 619 (1959).

7. A. T. Hattenburg, Appl. Opt. 6^, 95 (1967).

8. H. J. Kostkowski, D. E. Erminy, and A. T. Hattenburg, (High

Accuracy Spectral Radiance Calibrations from 210 to 850 run)

In preparation. National Bureau of Standards, Washington, D.C. 2023*+.

9. W. H. Venable, Jr., (Effects upon Radiant Intensity Measurements

due to Scattering in the Optical System) In preparation. National

Bureau of Standards, Washington, D. C. 2023*+.

10. F. A. Jenkins and H. E. White, Fundamentals of Optics , 560

(McGraw-Hill, New York, 1957).

11. W. A. Shurcliff, Polarized Light , (Harvard University Press, Cambridge,

Massachusetts, 1966).

12. W. E. Schneider, NASA Report, (Development of a High- Intensity

Standard of Total and Spectral Irradiance) In preparation.

National Bureau of Standards, Washington, D. C. 2023*+.

PART II

OPERATION, STABILITY

AND CALIBRATION OF THE HIGH

PRESSURE ARGON ARC

A. T. Hattenburg

- 66 -

SUMMARY

The spectral radiance and stability of the high pressure argon

arc has been determined from 320 to 220 nm for the side-on, 50 ampere,

10 atmosphere pressure mode. The source produces a spectral radiance

of about 8 x 10 5 to 17 x 10 5 watts /cm 3 -sr over the wavelength region,

and exhibits a stability of about ±0 . 2 % per hour and 1% per 200 hours,

with a signal to noise ratio of at least 1000.

This report presents details relative to the above results, the

capabilities and limitations of the arc source, the methods of use and

maintenance found desirable, and the apparatus and techniques utilized

in this investigation. Also included is a preliminary study of the

spectral irradiance of the arc. SPECTRAL RADIANCE OF THE ARC SOURCE

a. Operating Parameters

The arc source is basically the same unit described in earlier

reports (1,2), and a schematic diagram of it is shown in Fig. 1.* It

was operated at a direct current of 50.15 amperes, an argon pressure

of 150 psia, and argon exhaust flow rates of ^.5, 0.U3, and 0.1

*The various components of the arc and auxiliary equipment discussed

throughout this report are identified in Figs. 1 and 2.

- 67 -

liters /minute from the cathode, anode, and middle sections respectively,

The argon was technical grade, quoted "by the manufacturer as 99*996%

pure. About nine liters /minute of 13 °C water was used for cooling.

The spacing of the central plates was 1.0 mm and the channel diameter

was 3.18 mm. For the major part of the investigation, the observed

radiation emanated from a 0.6 mm wide by 0.8 mm high section at the

center of the arc column, into a solid angle of 0.0028 sr. Earlier

efforts employed a 0.1 mm by 0.8 mm target area.

b. Absolute values

The spectral radiance of one arc unit was determined over a period

of 200 hours by comparison with a stable tungsten lamp, using the 0.6

by 0.8 mm target area. Values obtained at the seven chosen wavelengths

are given in Table 1, and represent the spectral radiance emerging from

a freshly cleaned quartz window.

Table 1. Spectral Radiance of Side-On 50 amp 150 psia Arc.

Wavelength

(nm)

320

300

280

260

2k0

225

Spectral Radiance

(w/cm3 - sr)

16.8 x 10 5

15.6

lk.2

12.6

10.5

8.5

7*6

Wo. of

Determinations

15

3

3

7

3

h

220 15

- 68 -

The radiation is unpolarized, and except for the carbon line at

2 U 7.8 nm, contains no spectral lines from 200 to 335 nm.

The estimated standard deviation uncertainties of these absolute

values are 2 1 at 320 nm increasing to b/o at 220 nm. Standard deviations of the individual measurements we re about 1% throughout the wavelength region.

Another set of determinations on another arc unit were obtained

earlier over a 100 hour period. In this case a graphite arc was used

as the reference standard (3) with a target area of 0.1 by 0.8 mm.

The observed values, when adjusted to the 0.6 mm target width, were

lower than those of Table 1 by about 6% throughout the wavelength

range. The estimated standard deviation uncertainties of these absolute

values are- 3% at 320 nm and 6% at 220 nm and standard deviations of the

individual measurements varied from about 2 % at the longer to b% at

the shorter wavelengths

.

c. Short term stability and noise

The spectral radiance of the arc typically varies by less than

0.2% over one hour periods, when operated from the constant current

power supply. The signal to noise ratio is about 1000, when measured

with a one second time constant system and the spectroradiometer described

in an earlier report (l).

- 69 -

d. Long term stability

The spectral radiance of the arc remained constant over the 200

hour period, within the 1fo precision of the measurements. About 15

determinations were made at both 320 and 220 nm. The same result is

obtained, within the 2 to h% precision, from the 100 hours of graphite

arc comparisons, when the data is adjusted for the estimated decrease

in transmittance of the undisturbed quartz window.

e. Quartz window transmission

The measured transmittance of the quartz window varied smoothly

from about 0.91 at 320 nm to 0.82 at 220 nm. The transmittance remained

constant, within the measurement precision, when the window was cleaned

daily. When used without cleaning for periods of about 50 hours, the

relative transmittance decreased by 0 .025% per hour at 320 nm and 0 .06%

per hour at 220 nm.

f. Geometric stability

Repeated observations on the selected volume of the arc stream

indicated that the arc column is spatially stable to better than 0.05

mm. Repeated scans over the column width and height (between the central

constricting plates) indicated a repeatability in position of the radiation peak of about 0.03 mm. Measurements of the radiation half-width

(width of the arc column at the half-radiance points) over the 200 hours

yielded values between 1.63 and 1.69 mm.

- TO -

g. Positioning sensitivity

The decrease in radiance output of the arc when moved from the

normal viewing position (radiation maximum) by 0.02 mm, either parallel

or normal to the column axis, is undetectable. Changes of 0.1 mm result

in a decrease of almost 1%.

h. Sensitivity to changes in operating parameters

The spectral radiance of the arc is most sensitive to changes in

the operating current and argon pressure. An increase or decrease of

0.5% (0.25 amperes) in current or 2 I in absolute pressure causes a corresponding increase or decrease of about if in spectral radiance.

The power supply typically holds the current to within ±0.05% of the

set value over an 8 hour period; the absolute pressure decreases about

0.5% per hour without adjustment.

The spectral radiance is at a minimum for the chosen argon flow

rate in the cathode region, so that either an increase or decrease of

2b% in this flow causes a 1% increase in radiance. The influence of

the exhaust flow rates from the middle and anode regions is negligible,

amounting to less than a 0.1% change in radiance for a 50% change in flow.

Raising the temperature of the cooling water from 13 °C to 25 °C

or lowering its flow rate from 9 to 5 liters /minute caused an increase

in spectral radiance of about 0.1%.

- 71 -

i. Suitability of the arc as a standard source

The results of this investigation establish the value of the arc

as a stable, intense standard source of spectral radiance in the near

ultraviolet, when the arc is calibrated as an individual unit. When

components are changed or a completely new unit is used (l) radiance

changes varying from zero to lk% have been observed. Thus, for optimum

results, each arc unit must be individually calibrated. However,

experience with the arc components fabricated with the most recent

vacuum brazing techniques (see appendix) suggests that a unit should

operate stably for at least a few hundred hours, and probably significantly longer, without requiring replacement of components and therefore recalibration.

OPERATION OF THE ARC

a. Design changes

The arc used in this investigation and shown in Fig. 1 is basically

the same model described earlier (1,2). Slight modifications which have

evolved during this study include the replacement of the electronic

ripple filter with a more simple filter composed of an array of inductors

and capacitors, a starting resistor used to prevent high transient currents

when striking the arc (see electrical circuit in Fig. 2), warning buzzers

which signal the absence of cooling water, an arc mount allowing more

- 72 -

precise orientation of the unit, and the improved method of vacuum

brazing the constriction plates (see appendix).

b. Alignment of the arc

Before initial operation of the arc, a mechanical alignment is

performed, utilizing small aperture inserts in place of the front and

rear windows. The apertures, consisting of a 2 mm hole in a circular

plate, are illuminated from the rear with a strong light, and the unit

is oriented until the images of the apertures are aligned on the entrance

slit. The inserts are then removed, a close-fitting rod is inserted in

the arc channel, and the arc translated until the edges of the rod are

focused and centered on the slit.

c. Preliminary steps

Before preparing to start the arc, the front quartz window should

be removed and cleaned.* The length of the tungsten cathode should be

measured, and adjusted if it has deviated by more than 0.3 mm from its

optimum length of 1.25 mm projection from the hollow graphite cathode

(see Fig. l). The resistances between the cathode, successive constriction plates and anode should be measured to detect any shorting in

* In this investigation the cleaning solutions employed were either

ethyl alcohol or aerosol soap, followed by distilled water rinsing

and drying.

- 73 -

the system, due to large water leaks or other causes. These measurements are made with cooling water applied, and typical values are 0.5

to 2.0 megohms.

d. Starting and stopping procedure

The cooling water is turned on, the argon exit flow valves are

opened slightly, and a slight flow of argon is induced in the arc "by

adjusting the inlet regulator pressure (large initial flows result in

formation of a plasma jet at the hollow cathode). The shorting switch

for the 3-5 £2 starting resistor is opened, and power applied to the

electric supply unit. The DC voltage is raised to about 150 volts, and

the arc is ignited with the brass starting rod. Starting current is about

20 amperes. The tungsten cathode is lowered into place and the cap

tightly fastened. The starting resistor is shorted, raising the current

to about i+0 amperes, the argon pressure brought to 150 psia, and the flow

rates adjusted. The DC voltage is raised and the bias control setting

adjusted until the arc has reached the operating current and the voltage

across the current regulator attains some selected value between 15 to

30 volts. After a short wait to allow all components to reach equilibrium (5-10 min.) the arc is ready for use.

When extinguishing the arc, the DC voltage is lowered to zero, input

power shut off, and water and argon supplies shut down. If immediate

adjustments or dissembly of the arc is attempted, the water and argon

- Ik -

should he bled from the system, and the residual charge on the capacitors removed.

If the flow rate valves and bias control setting are left undisturbed, only minor adjustments will be required for the flows in subsequent starts, while the electric current will be set by simply raising

the DC voltage until the chosen value appears across the current

regulator.

e. Operating procedures

With the arc operating under standard conditions, the final alignment procedure is undertaken. Radiometric scans through the rotational

degrees of freedom are made to insure that the peak radiance is being

observed. The arc is carefully adjusted in the directions parallel and

perpendicular to the column axis (leaving focus undisturbed), until the

maximum radiation output is also obtained relative to these degrees of

freedom. This procedure is repeated each time the arc is returned to

the viewing position after observations on another source. The argon

flow rates are set and the current measured at the time of each radiance

reading if optimum accuracy is desired.

The image of the arc column and surrounding constriction plates

should be examined periodically for any evidence of foreign material

in the chamber or spatial instability in the column. These problems

may often be cured by temporary large increases of argon flow in the

various sections. Instability of current or radiance output may often

- 75 -

be overcome by choosing a slightly different voltage drop across the

current regulator.

CALIBRATION METHODS

The high pressure arc was calibrated against known standards of

spectral radiance by means of the high accuracy spectroradiometer , utilizing the ratio of amplified output currents of the detector to obtain

radiance ratios. Two methods of calibration were employed. The first

consisted of a direct comparison of the high pressure arc with the low

current graphite arc (3) over a period of 100 hours of operation. The

limited precision of this method, due to short-term fluctuations in the

graphite arc, dictated a new approach. The second method consisted of

comparing the arc radiance, as viewed through a set of calibrated filters,

with that of a very stable quartz-windowed tungsten strip lamp. This

approach was employed during a 200-hour test to determine the long term

stability of the arc.

a. Details of the calibration

The calibration methods involved comparisons between sources of

different spectral distribution, size, strength, and uniformity. It was

therefore necessary to investigate the possible errors arising from these

factors, as described in Part I of this report, ’’The Principles and Methods

of Calibrating Spectroradiometers”

.

The spectroradiometer employs a double monochromator with a trialkali photomultiplier detector, equal entrance and exit slits, and an
*
optical magnification of one. For the 0.6 mm slits used here, the

measured slit function exhibits a transmission in the distant wings

on the order of 10“ 9

, with a resulting error of less than 0.1% due to

spectrally scattered light. The effective spectral response was found

to he independent of the flux magnitude. The "size of source" effect

was determined to he less than 0

.

1% for the sources employed here.

Placement of the detector 15 cm from the exit slit reduced the effect

of non-uniform source areas to negligible amounts. All sources used

here were found to he uniform over the solid angle utilized, and to

have negligible polarization. The detector-amplifier response was

calibrated for the range of signal ratios employed (3), and corrections

applied to each measured ratio.

b. Calibration with graphite arc standard

Comparisons with the graphite arc were made at five wavelengths

from 320 to 210 nm, over a period of 100 hours. From eleven to eighteen

determinations were made at each wavelength. The slit was set at 0.1 mm

width and a mask was used to obtain a 0.8 mm height, resulting in a spectral bandpass of 0.15 nm at 210 nm increasing to 0.25 nm at 320 nm.

The solid angle was restircted to 0.0028 sr by an external circular stop.

All comparisons were made at fixed wavelengths.

The low current graphite arc was operated in the standard manner

(3), with the current just below the overload point and the central
.

,
- 77 -

portion of the anode focused on the slit. Each anode was turned for

ten minutes before readings were taken, and five minutes was allowed

when anodes were reignited. Nine anodes were consumed during this

period, and comparisons at a given wavelength were repeated for a majority of the anodes.

The comparisons were made at each wavelength with the graphite

arc anode being centered on the slit, and the high pressure arc image

peaked for maximum signal. Checks and adjustments of the operating

parameters of each source were made while the other source was being

observed. A determination consisted of one or more readings of the

high pressure arc over a one minute time span, each surrounded by

similar readings of the graphite arc. The ratio of spectral radiance

at that wavelength was then derived from the output currents of the

photomultiplier, with appropriate corrections for non-linearity of the

detector-amplifier response. The quartz window was left undisturbed

for TO hours of operation, and cleaned frequently thereafter. Any

effect on the radiance output of the arc due to this cause was not

detectable within the precision of the method. During the latter part

of the 100 hour period, water leaks appeared in various sections of

the arc, necessitating replacement of these sections. This led to the

development of the vacuum brazing technique described in the appendix

for fabricating new components for the arc.
'
- 78 -

c. Calibration with tungsten strip lamp and filters

The high pressure arc was compared to the tungsten strip lamp

at seven wavelengths from 320 to 220 nm over a period of 200 hours.

About fifteen determinations were made at 320 and 220 nm, and three

to six at the remaining wavelengths . The slit was set for a 0.6 mm

width and masked to a 0.8 mm height, resulting in a spectral bandpass

of 1.0 nm at 220 nm and 1.5 nm at 320 nm. For the determination of

the radiance width of the arc, the slit was narrowed to 0.05 mm. The

solid angle remained at 0.0028 sr.

The spectral radiance of the tungsten lamp was determined during

the course of the arc studies to an estimated uncertainty of about

1.5 % (l). The orientation and positioning of the lamp is routinely

accomplished to a precision of about 0.1%.

The spectral radiance of the high pressure arc exceeded that of

the lamp by a factor varying from about 10 3 at 320 nm to 10 5 at 220 nm,

making direct comparisons of the two sources impractical. A set of

commercially available neutral transmission filters was used to attenuate

the arc output. The filters were composed of a sandwich of two pieces

of ultraviolet transmitting quartz, with an inconel metal film deposited

on the inner faces, and had nominal transmitt ances of 10%, 1%, and 0.1%.

Wedges were inserted between the edges of the quartz plates in order to

form a slight angle between the metallic surfaces , thereby diverting

- 79 -

from the optical path the secondary images which arose from internal

reflections. "When used with the arc in pairs, the filters were mounted

at a two degree angle from one another to avoid similar reflections.

The comparisons were made at each wavelength with the lamp image

"being precisely located on the slit, and the image of the arc, with

appropriate filters mounted, peaked for the maximum signal. The radiance

ratios were derived from the detector currents and the measured filter

transmitt an ces , with corrections for the non-linear response. The

radiance width of the arc was then determined at 320 nm. During the

last 150 hours, the filters were calibrated immediately after each set

of source comparisons.

d. Filter calibrations

The filters were calibrated in situ using the arc as reference

source. It was necessary to adjust the arc position for each filter

insertion, due to image shifting caused by mounting the filters at

angles to the normal. At each wavelength, the 10$ filter was calibrated

by alternately inserting and removing it from the output beam of the

arc, with appropriate changes in amplifier gain. The ratio of detector

currents, corrected for nonlinearity, yielded the transmittance. Filters

of lower transmittance were calibrated by comparison to the 10$ filter,

in order to avoid uncertainties from large ratios of detector current.

The effect of heating upon filter transmittance was investigated

by alternating nearly identical filters, with long exposures to allow

- 80 -

for any heating effects. Comparisons were also made between sets of

filters calibrated singly and used in pairs. In both cases no effects

were observed within the precision of the measurements.

The transmittance of the quartz window was determined by using a replacement window in the arc unit , and mounting the regular window as near as possible to its normal position in the arc beam.

SPECTRAL IRRADIANCE EVALUATION

A preliminary evaluation of the spectral irradiance of the 50 ampere

150 psia arc was obtained by comparison with a 1000 watt tungsten-iodide

quartz lamp (U) calibrated for spectral irradiance down to 250 nm. The

two sources were alternately positioned on the optic axis of the monochromator, about one meter from the 0.6 mm wide by 0.8 mm high entrance

slit. The spectral irradiance of the arc at one meter was found to be

4.3, 3*7 and 2.7 watts/cm3 at wavelengths of 320, 280, and 250 nm respectively, to an estimated accuracy of about 15 %. In the lower region where

no calibration was available, the arc spectral irradiance exceeded that

of the lamp by factors of 80 at 240 nm to 500 at 210 nm. The arc irradiance at 250 nm remained stable to about 0.2% over half-hour periods,

and repeated to better than 0.5% when extinguished and relit.

The present limitations in the wavelength and accuracy of currently

available spectral irradiance standards preclude a significantly more

accurate calibration of arc irradiance at this time. A major effort

- 81 -

to improve and extend (in wavelength) these standards is being undertaken, utilizing the existing high accuracy spectral radiance standards,

small-aperture integrating spheres (compatible with the small target

areas of these sources), and low-level detection techniques, required

because of the resulting low ultraviolet flux levels. When completed

this work is expected to permit a more accurate and extensive evaluation of the arc as a source of spectral irradiance.

REFERENCES

1. H. J. Kostkowski, C. R. Yokley, D. E. Erminy, and A. T. Hattenburg,

NBS Report 9099, (1965).

2. C. R. Yokley, Proceedings, International Symposium on Solar

Radiation Simulation, Jan. 18-20, 1965, Institute of Environmental

Sciences

.

3. A. T. Hattenburg, Appl. Opt. 6_, 95 (1967).

1+. R. Stair, W. E. Schneider, and J. K. Jackson, Appl. Opt. 2_,

1151 (1963).

-82 -

SeAuwcCAP

TUWCVT®*»

CATHO®*

Arson

Bxrr

VALVES

HOULOU) CfcTHOOg

CCNSTRtLTlOU

Platss

VlSvJINfr-

\XJ I N06M

FlC-.i. Arc Schematic.

- 83 -

- 81+ -

APPENDIX

a. Fabrication of constriction plates

An improved method of fabrication of the constriction plate

sections of the arc became necessary, due to frequent occurrence of

water leaks at the silver soldered copper-stainless steel joints.

Inspection of the defective components disclosed poor adherence of

the solder to the stainless steel surfaces, and presence of oxide

films in part of the joints. Efforts to repair the defective components by cleaning and resoldering the joints were unsuccessful.

Soldering in an inert atmosphere, with or without flux, also failed

to achieve tight joints.

A successful method of forming tight joints by vacuum brazing

was developed, and components fabricated by this method have remained

leak-proof for over a 100 hours of hydrostatic tests and 200 hours of

operation as arc components. The design of the units was altered to

increase the contact area between the stainless steel and copper by

about a factor of 5* After being machined, the parts are degreased

and electro-polished. Inserts of a special gold-nickel alloy* are

placed between the parts to be joined, and the unit is heated in a vacuum furnace at about 30 microns until the alloy melts.

*NI0R0 alloy. Western Gold & Platinum Company, Belmont, California.

USCOMM— DC— NBS


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