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NBS TECHNICAL NOTE 575

H^ns of •* ^M

U.S.

>ARTMENT

OF

OMMERCE

National ^ Bureau ° of

'^indards

11

On the Absorptance of

Cavity-Type Receivers

°
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7/

NBS TECHNICAL NOTE 575

ISSUED JULY 1971

Nat. Bur. Stand. (U.S.), Tech. Note 575, 38 pages (July 1971)

CODEN: NBTNA

On the Absorptance of Cavity-Type Receivers

Jon C. Geist and Joseph C. Richmond

Heat Division

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C, 20402.

(Order by SD Catalog No. C 13.46:575). Price 45 cents. Stock Number 0303-0881
Contents

Page

1. Introduction 2

2. Description of the Samples k

3. The Directional -Hemispherical Reflectance Measurements 6

3»1 The Experimental Apparatus 6

3.2 Tests of the Apparatus 7

3.3 Experimental Procedure and Results 10

k. The Retro-Reflectance Measurements 13

U.l Description of the Apparatus 13

k. 2 Tests of the Apparatus 15

k. 3 Experimental Procedures and Results 20

5. Conclusion 22

6. References 25
On the Absorptance of Cavity-Type Receivers

Jon C. Geist and Joseph C. Richmond

The directional-hemispherical reflectance of a number of

flat samples that had been coated with Parsons Optical Black

Lacquer procured from Thos. Parsons and Sons and The Eppley

Laboratory, respectively, was measured at 0.6328 and 1.15 ^m

with a laser-source integrating sphere reflectometer. The

reflectance varied significantly with method of application,

and was significantly higher for the Eppley lacquer than for

the Parsons lacquer. The reflectance of two cavity receivers,

one coated with each lacquer, was also measured. At 0.6328 jjjn

the reflectance of the Parsons cavity was higher, but at

1.1!? pm it was lower. The measured reflectance of the Parsons cavity was appreciably higher than that computed from

the measured reflectance of the lacquer and the geometry

of the cavity, assuming the coating to be a perfectly diffuse reflector. Retro-reflectance measurements revealed

that both lacquers reflected more radiant energy back into

directions near the direction of incidence than would a perfect diffuser of the same directional-hemispherical reflectance, but the Parsons lacquer was by far the more pronounced

retro-reflector. The principal conclusion is that the diffuse assumption can lead' to significant errors in computing

the absorptance of cavity-type receivers, when the cavity

coating is in fact not diffuse.

Key words: Absorptance; black coatings; cavity absorptance;

1
davity reflectance; laser-source reflectometer;

Parsons black; retro-reflectance.

1. INTRODUCTION

Within the last ten years, Gillham [1], Kendall and Berdahl [2]

and Willson [3] have each used absolute radiometers with cavity type receivors to realize a scale of irradiance based on electrical quantities.

Each of these investigators has calculated the absorptance of his cavity

receiver from the absorptance of the "black" lacquer with which the interior of the cavity was coated, under the assumption that the lacquer

reflects in a perfectly diffuse manner. Since the only justification

for this assumption is the matte appearance and low specular reflectance [U] of the lacquer, it is impossible to obtain an uncertainty or

error limit for cavity absorptances obtained in this manner.

Willson [5,6] has estimated that the uncertainty in absorptance is

reduced from ±2% for a flat receiver to ±0.3$ for the cavity receiver

which he describes, by the geometry of the cavity. Bat this estimate is

also based on the assumption that the coating of the cavity reflects in a

perfectly diffuse manner.. As a counter example, consider a cavity coated

with a perfect retro-reflector-x-. In this case there will be no "cavity

-x-A perfect retro-reflector is a sample for which all of the flux

which is not absorbed is reflected back along the path of the incident

rays. A perfect mirror is a perfect retro -reflector for a normally incident ray. A retro -reflector is a sample for which more flux is re- flected into a solid angle about the direction of incidence than would be

reflected into this solid angle by a perfect diffuser of the same directional-hemispherical reflectance.

2
enhancement" of the absorptance, because all of the flux which is reflected off of the interior surface of the cavity will be lost out the

hole in the cavity through which the incident flux entered. The cavity

receiver will have the same absorptance and the same uncertainty in

absorptance as a flat receiver coated with the same material.

The point is that if nothing quantitative is known about the geometric distribution of the flux reflected from the interior surfaces of

the cavity, nothing quantitative can be said about the increase in the

absorptance of the cavity over that of its interior surfaces. Consequently, nothing quantitative can be said about the decrease in the

uncertainty of the absorptance of the cavity from that of its interior

surfaces. This is very significant. After all, the principal reason

for using a cavity type receiver on an absolute radiometer is to decrease

the uncertainty in the absorptance of the receiver in order to decrease

the uncertainty in the scale of irradiance which is realized by the

radiometer.

In addition to the geometrical distribution of reflected flux there

is another important source of uncertainty in the absorptance of the

cavity receivers of Gillham, Kendall and Willson. This is the uncertainty in the absorptance of the black lacquer with which the cavities

were coated. It arises from two sources. The first of these is the

error inherent in the reflectance measurements from which the absorptance

is calculated. Such measurements are subject to systematic errors which

have not been well characterized. Thus it is impossible to estimate

limits of error for such measurements with great confidence; unless these

limits are left quite large. The second source of uncertainty is the

3
assumption that the reflectance of the lacquer coating on the interior of

any given cavity is the same as has been reported in the literature for

that particular lacquer. The effect of variations in painting

technique on the reflectance of these lacquers has not been investigated

so the samples on which the published reflectance measurements were made

might not be at all representative of the coating of the cavity.

Kendall and Berdahl [2] have calculated the reflectance of the cavity receiver of the Primary Cavity radiometer which they describe to be

0.1$. However, in order to better determine the reflectance of this type

of receiver, Kendall coated twenty flat samples and two cavities with

black lacquers. On these samples we made directional-hemispherical reflectance measurements at two wavelengths, and retro-reflectance measurements with broad band radiation from a tungsten strip lamp. The purpose

of this paper is to report the results of these measurements and to examine the suitibility of these lacquers for coating cavities in light of

these results. The next three sections of this report will describe the

samples, the directional-hemispherical reflectance measurements, and the

retro-reflectance measurements, respectively. The results will be discussed in the concluding section.

2. DESCRIPTION OF THE SAMPLES

Twenty flat aluminum disks, 1.0 cm. in diameter by 0.2 cm. thick,

were machined and marked with different letters to distinguish them.

Ten of these disks were sprayed with the Thos. Parsons and Sons Optical

h
Black Lacquer-x- undercoat. They were then sprayed with the Thos. Parsons

and Sons Optical Black Lacquer top coat until it appeared (to the unaided

eye) that continued spraying was not increasing the absorptance of the

coating. To see if this was true, five of the samples were then sprayed

with more of the top coat. The same procedure was followed in the case

of the remaining ten aluminum disks, except that the Eppley-Parsons

Optical Black Lacquer under and top coats were used. Table 1 summarizes

the preparation of the flat samples.

When the four groups of samples were viewed together, the samples

coated with the Eppley-Parsons lacquer seemed to have a less matte

appearance and a higher reflectance than the samples coated with the

Thos. Parsons and Sons lacquer. It is not known whether this was due

to a difference in the composition of the two lacquers, or a difference

in the techniques with which they are applied. The two lacquers are

supposed to be identical in composition, but the possibility of an improperly prepared batch or of an unknown difference in composition cannot be ruled out. The possibility that the Eppley-Parsons top coat was

not mixed well enough before application cannot be ruled out either.

•Kit is the policy of the National Bureau of Standards to avoid men- tioning trade names in publications whenever possible. However, in this case it is necessary to use trade names in order to properly identify

the materials of this investigation. These materials are of more than

passing interest since they are recommended by the World Meteorological

Organization for the coating of detectors employed in the measurement of

solar and terrestrial thermal radiation.
Completely characterizing the properties of these lacquers as a function

of the multitude of variables associated with spray painting techniques

is far beyond the scope of this investigation.

Two cavities of the same dimensions as the cavity receivers in the

Primary Cavity radiometers described by Kendall and Berdahl [2] were constructed. One was painted using a camels hair brush with the Thos.

Parsons and Sons Optical Black Lacquer under and top coats, while the

other was painted in the same way with the Eppley-Parsons Optical Black

Lacquer under and top coats. The Thos. Parsons and Sons Lacquer used in

this investigation was from the same batch and applied using the same

techniques as that which was used to coat the receivers of the Primary

Cavity Radiometers.

3. THE DIRECTIONAL-HEMISPHERICAL REFLECTANCE MEASUREMENTS

3.1 The Experimental Apparatus

A laser source, integrating sphere refleetometer, which has been

described previously [7] 5 was used to obtain the directional -hemispherical reflectance of the flat samples and the cavities at .6328 jjjn. and

1.13? |jm. This instrument has several noteworthy features. The integrating sphere itself is 35 cm in diameter. This large size minimizes the

errors caused by the entrance, sample, and detector ports disturbing the

geometry of the sphere. A He-Ne laser is the source of radiant flux for

this instrument, and by changing the mirrors at the ends of the laser

tube, radiation wavelengths of .6328 pjn, 1.15> \m9 or 3.39 p,m may be

selected. As might be expected, the radiant output of the laser is quite

unstable. However, a second detector, a second amplifier, a mirror

chopper, and a ratio multiplexer adequately compensate for this
instablility, and high precision results are obtainable.

Reference 7 presents a theoretical analysis of the instrument which

indicated that it should be capable of producing reflectance data which

are free from systematic error to within 1% of the measured reflectance

values. This reference also describes an experimental verification of

this analysis for high reflectance, specular samples. However, no experimental checks on the accuracy of the instrument in the low reflec-.

tance range were performed. In fact, this instrument had never been used

to measure reflectances lower than 10$ until the present work was begun.

Consequently, tests for systematic errors at low reflectances levels were

undertaken.

3.2 Tests of the Apparatus

Two tests for systematic error at low reflectance levels were

conducted. The first test verified that the detector -amplifier system

was linear in response. The second test determined that about 1% of the

power in the incident beam missed the sample entirely and was incident

instead on the highly reflective interior walls of the sphere. Obviously, this is a very serious source of systematic error at low reflectance

levels. It turned out that the magnitude of this effect was variable,

depending perhaps upon the mode structure of the laser, and it was

necessary to measure the effect at set intervals during the directionalhemispherical reflectance measurements. Consequently, this test will be

described in conjunction with the reflectance measurements in the next

section.

In order to verify that the detector-amplifier system was linear in

its response, the transmittance of a neutral density filter was first
measured using a recently calibrated optical pyrometer. Then the trans

mittance of the filter was measured with the integrating sphere reflectometer and its associated detector amplifier system. Anv cummulative

non-linearity in the response of the detector amplifier system would manifest itself as a difference between the transmittance values obtained

using the two different techniques.

In calibrating the transmittance of the neutral density filter, the

filament of a strip lamp was viewed through an optical pyrometer. Brightness matches with the filament of the lamp were made when it was viewed

through the filter and when it was viewed directly. Thus the radiance

transmitted by the filter was equal to the black-body radiance at the

mean effective wavelength of the pyrometer defined by the brightness

temperature of the filament when viewed through the filter. Likewise,

the radiance incident on the filter was equal to the blackbody radiance

at the mean effective wavelength defined by the brightness temperature of

the filament when viewed directly. The transmittance of the filter was

calculated as the ratio of the transmitted radiance to the incident

radiance. Data supplied by the manufacturer of the filter indicated that

o its transmittance at 7000 A was about 1.03 times as high as its transo mittance at 6000 A. Thus, the mean effective wavelength of the pyrometer was not modified significantly by the filter, and it was assumed

o to be 6550 A in both cases.

Three determinations of the transmittance of the filter were made

using an optical pyrometer in the manner described above. The average

value of the three determinations was 1,1+0$. The estimated limit of

systematic error in this average is ±0,03$. It arises from the

8
uncertainty in the calibration of the pyrometer and the scatter in the

brightness matches made with the pyrometer.

In order to measure the tranmittance of the neutral density filter

with the integrating sphere reflee tome ter, the response of the detectoramplifier system to .6328 ^m radiation was recorded both with the filter

attenuating the laser beam between the chopper and the sphere, and with

it removed. A zero level signal was also recorded when the laser beam

was blocked off near the end of the laser, to correct for any zero offset in the apparatus. The zero level signal was subtracted from both

the signal obtained when the beam is attenuated by the filter and the

signal obtained with the beam unattenuated. The ratio of the resulting

zero corrected signals was taken as the transmittance of the filter

as measured with the integrating sphere reflectometer.

Six separate determinations of the transmittance of the filter were

obtained in this manner. The average of the six determinations was

l.UO$. The maximum deviation of a single determination from the average, the estimated standard deviation of a single determination, and the

estimated standard deviation of the mean were 0.17$, 0.09%, and 0.0U$,

respectively.

Thus the detector-amplifier system is probably linear in response to

within a few percent from the highest flux level encountered in the

directional -hemispherical reflectance measurements down to flux levels

at least as low as one seventieth of this value. It is reasonable to

assume that any cummulative non-linearities in the detector-amplifier

system response will be largest for large fluxes and large electric

signals, so no further linearity tests were made at lower flux levels.

9
3.3 Experimental Procedures and Results

In this section the directional -hemispherical reflectance measurements, which were made on the flat samples and the cavities, will be

described.

The fraction of the incident beam that missed the sample and was

incident on the sphere wall was evaluated as follows. A high-quality

mirror was placed about 3 cm outside the sample aperture in the sphere,

in a position to direct the laser beam to a room-temperature blackbody

cavity lined with black velvet, that was located about 60 cm from the

sample aperture. Three measurements were required in the form of an

amplifier output in terms of a potential, which was read on a digital

voltmeter. These were (l) when the laser beam was blocked between the

chopper and the entrance aperture to the sphere (the zero reading, V ),

(2) when the laser beam was incident on the sphere wall (the 100$ reading, Vim) and (3) when the laser beam passed out the sample aperture

in the sphere (the scattered radiant energy reading, V ). The scattering correction factor, S, was computed as

V - V

o sc o ?

ioo " ?

o (i)

The directional-hemispherical reflectance of a sample also required

three measurements, in the form of an amplifier output, which was read

on the same digital voltmeter. These were V and V, ^„ as above, and the

o 100

sample measurement, V , obtained when the laser beam was incident on the

s sample near its center. The reflectance of the sample, p(l2°;2rr) was

then computed as

10
(¥100" V - (V100 - V S

(2)

Ten consecutive readings of the digital voltmeter, taken at uniform

time intervals of approximately six seconds, were added to obtain each

of the instrument values referred to above. Six replicate reflectance

determinations were made on each sample. The mean and the estimated

standard deviation of a single one of the six replicate reflectance

determinations are reported in Tables 2 and 3. In the instances where

two values of reflectance are reported for a single sample at a single

wavelength, they are the results of measurements taken about six months

apart. The cavity reflectance measurements were taken at various times

during the six month interval. The differences in reflectance obtained

on the same sample at different times during the six month period are in

many cases larger than can be accounted for by the observed statistical

scatter. The observed differences may be real, and is perhaps related

to some factor such as humidity of the laboratory atmosphere. On the

other hand, it may be due to some systematic error in the measurement

process that has not been identified and corrected for. It was noted

that the scattering error is variable, and that it does not drift

slowly with time, but changes abruptly by comparatively large amounts.

An unrecognized change in the scattering error might be responsible for

the observed differences. In any case, the results of these measurements

are still significant for the purpose of this paper.

Gillham [8] has published a curve for the spectral reflectivity of

samples of optical black lacquer manufactured by Thos. Parsons Ltd. He obtained a reflectance of approximately .010 at .63 pja and .016 at 1. 15> u,m 9 11
with an estimated accuracy of ±.0025. Whether the differences between

his values and the values reported in this paper are due to differences

in the formula for the lacquers } or to experimental errors in either

or both sets of data, or to some other cause is not known.

For a Primary Cavity Radiometer cavity coated with a perfect diffuser,

Kendall has prepared a graph of cavity absorptance as a function of

coating absorptance. In terms of reflectances , his graph shows that for

coating reflectances below 3%>

p c -0.07 p (3)

where p and p are the coating and cavity directional-hemispherical

reflectances, respectively. It is of interest to compare the minimum

and maximum measured values of the directional-hemispherical reflectance

of the cavities with the values calculated using Eq. 3 from the measured

directional hemispherical reflectance of the flat samples. This is

done in Table U. Each pair of entries in a box labeled "measured" consists of the smallest and largest cavity reflectance values reported in

Table 3 for a given type of lacquer at a given wavelength. Each pair

of entries in a box labeled "calculated" consists of values calculated

using Eq. 3 from the smallest and largest flat sample reflectance values

reported in Table 2 for a given type of lacquer at a given wavelength.

The poor agreement between the measured and calculated values for the

Thos. Parsons lacquer could arise from any of three sources. The

directional - hemispherical reflectance measurements might be in error;

the lacquer as applied to the flat samples might not be representative

of the lacquer as applied to the interior of the cavity; or the distribution of reflected flux from the lacquer might deviate significantly

from that of a perfect diffuser. Having attempted

12
to eliminate the first, possibility, the retro-reflectance measurements

described in the next section were undertaken to investigate the last

two possibilities.

k. THE RETRO-REFLECTANCE MEASUREMENTS

U.l Description of the Apparatus

Figure 1 is a schematic diagram of the apparatus which was used

to make the retro-reflectance measurements. The image of the filament

of a tungsten strip lamp was focused by a lens through a baffle onto a

small aperture in an opaque screen. The chopper for a synchronous

amplifier was so located that it chopped the beam from the lamp between

the lens and the baffle. The lamp, lens, chopper and baffle were all

enclosed in a box which was light tight except for one opening; the

aperture on which the image of the filament was focused. Through this

aperture the portion of the chopped beam from the lamp, which passed

through the baffle, emerged from the box. An image of the aperture was

focused through the opening in the box onto the sample to be measured

after reflection off a beam splitter, as shown in the figure. The portion

of the incident beam which was transmitted through the beam splitter was

collected on a high absorptance surface located a considerable distance

from the detector and out of its field of view. The flux reflected off

the sample into a cone centered about the incident beam was collected,

after transmission through the beam splitter, by a large spherical mirror

and focused onto a thermopile 'detector whose receiver was 3 mm on a side.

The solid angle subtended by the incident beam at the sample was approximately 0.001 tt steradians, and the solid angle over which the retroreflected flux was collected was O.OlIiii- it steradians. The estimated

13
limits of systematic error in the solid angle over which the flux was

collected is ±2%.

The sample holder had two rotational degrees of freedom which allowed the sample to be rotated about both horizontal and vertical axes

passing through the geometrical center of the front surface of the sample. For the remainder of this paper, the retro-reflectance of a sample

will be defined as the ratio of the flux reflected by the sample into a

conical solid angle of O.OII4I4. tt to the flux incident on the sample, where

the incident flux is confined to a solid angle of 0.001 rr symetrically

located within the solid angle of collection. Thus the directions of

incidence and reflectance are identical, and the retro-reflectance is a

function of only one direction in space.

The spectral composition of the flux used in the retro-reflectance

measurements is given by the product at each wavelength of the radiance

of the filament of the lamp, the transmittances of the lamp envelope and

the lens, the reflectance of the three aluminum coated mirrors, the

atmospheric transmittance of the optical path, the reflectance and trans

mittance of the beam splitter, and the responsivity of the detector. The

lamp had a tungsten ribbon filament and a lime glass envelope. The lens

was quartz. The spectral radiance of the filament was computed from the

measured brightness temperature of the lamp (2300 K) using the emissivity data of DeVos [9] and the envelope transmittance. The envelope

lU
transmittance as well as the transmittance of the lens were taken from

the AIP Handbook DlO] , and the spectral reflectance of the aluminum

mirrors was taken from the data of Bennett, et al. , [ll] and Twidle [12],

The spectral transmittance of the atmosphere over the approximately 500cm

path length was taken from the data of Wyatt, Stull and Plass [13] for

0.005 precipitable cm of water vapor (%0% relative humidity at 72 °F).

The relative spectral responsivity of the detector was measured between

0.1; p,m and 1.8 p,m by a modification of a technique which has been described previously [ill.]. It was found to be uniform to within i$% in

this spectral region. The spectral transmittance and reflectance of the

beam splitter were measured on commercial double beam spectrometers over

the spectral range from O.U pjm to 3.0 p,m. The approximate spectral composition of the flux as calculated from the above described data is

shown in Fig. 2.

A number of tests were performed on the apparatus to determine the

accuracy with which the retro-reflectance measurements could be made.

They are described in the next section.

k. 2 Tests of the Apparatus

In order to verify that the detector amplifier system which was used

in these measurements was linear in response, the transmittance of the

neutral density filter whose calibration was described in Section 3.2

was measured. Again the .6328 ^m radiation from the laser was used. The

response of the detector-amplifier system, which was used in the retroreflectance measurements, was recorded with the beam directly incident

on the detector; and when the beam was attenuated by the filter. A

zero-level signal was also recorded. The transmittance was calculated

15
from this data in the same manner as described in Section 3.2 in reference to the transmittance measurements made with the integrating sphere

reflectometer and its detector-amplifier system. It was necessary to use

the laser as a source in order to achieve the highest flux level which

was experienced in the retro-reflectance measurements, while at the same

time restricting the flux to the wavelength region which was effective

in the calibration of the transmittance of the filter using the optical

pyrometer.

The average of six measurements of the transmittance of the filter

by this technique is l.UW. The maximum deviation of a single measurement from the average , the estimated standard deviation of a single

measurement , and the estimated standard deviation of the mean are 0. 06%,

0.03$, and 0.01$, respectively.

This result requires that a correction factor of 0.97 be applied to

those values of retro-reflectance which are measured to be l.hh% with

this apparatus. The uncertainties associated with this correction factor are an estimated limit of systematic error of ±0.02 arising from

the uncertainty in the measurement of the transmittance of the filter

with the optical pyrometer which was described earlier, and a three

standard deviation uncertainty of ±0.02 arising from the random errors

in the measurement of the transmittance of the filter with the detector

amplifier system used for the retro-reflectance measurements-. The

measured retro-reflectance values reported in this paper for all of the

materials except the black electrical tape fall between 0. 02$ and 1. 6%.

It is reasonable to assume that any cummulative non-linearity in response

of the detector amplifier system will be largest for large fluxes and

16
large electrical signals. Thus, it is very likely that the errors from

non-linearity arising between 0.02% and 1.6$ retro-reflectance are less

than those arising between 1.6$ and 100$ retro -reflectance. Since no

other data on the linearity of response of the apparatus between 0.02$

and 1.6$ retro reflectance were available, it was subjectively decided

to apply a correction factor to 0.96 to all of the measured retroreflectance values reported in this paper. It is estimated that the

limit of error associated with this correction factor is ±0.06 for retroreflectance values between 0.02$ and 1.6$.

Ideally, the responsivity of the apparatus should be constant for

all directions of reflection from the samples which are collected by the

spherical mirror (11 ) in Figure 1, and zero for all other directions of

reflection. In order to investigate the actual responsivity of the

apparatus as a function of the direction of reflection from the sample,

a gold mirror was mounted in the sample holder. It was rotated about the

horizontal and vertical axes passing through the geometric center of its

front surface, and the output voltage of the detector was measured as a

function of the direction of the reflected beam. Since the incident

beam subtended a much smaller solid angle than that over which the retroreflected flux was collected, It was possible, using this technique, to

measure the responsivity of the apparatus for various portions of the

solid angle of collection. This was done by directing the beam reflected

from the gold mirror onto five different portions of the spherical mirror (11) as shown in Figure 3. The average responsivity over the surface

of the mirror was approximated by the average of the five measured values.

The ratio of the average responsivity over the surface of the mirror to

17
that of its central portion is 1.021. Thus a correction factor of 0.98

was applied to all of the measured retro-reflectance values reported in

this paper. The estimated limit of systematic error associated with this

correction factor is ±0.02 for all of the materials except the black

electrical tape for which it is ±0.0U.

The rest of the spherical solid angle centered on the sample-x- was

investigated in a manner similar to that used to investigate the solid

angle over which the retro-reflected flux was collected. However, the

emphasis here was on directing the beam onto other portions of the

apparatus which might scatter light into the field of view of the detector after only one or two reflections.

For the most part, the amount of flux getting to the detector

when the beam was directed anywhere except in the vicinity of the beam

s plitter was so small that it could not be detected. A few directions

were located in which measureable signals were produced. In each of

these cases judicious placement of highly absorbing cloth and baffles was

sufficient to reduce these signals to the point that they could not be

detected. Hhen the beam was directed into the immediate vicinity of the

beam splitter, non-negligible signals were recorded. It is not known

whether these were due to scattering at the surface of the gold mirror,

or scattering by portions of the beam splitter that were not being used,

or some other source. Due to this difficulty and to the rather poor

-x-That is, all of the spherical solid angle whose center is the

sample except for the solid angle over which the flux was collected.

18
angular resolution all that could be determined was that the correction

for this effect could not be less than 0% nor larger than 6%. So a

correction factor of 97% with an estimated limit of systematic error in

the correction of ±3% was employed.

All of the retro-reflectances described in this paper were measured

relative to the reflectance of a gold mirror. The data of Bennett and

Ashley [15] were used to calculate a reflectance of 0.965 for such a

mirror for the flux distribution shown in Figure 2. Thus a correction

factor of 1.036 was applied to all of the measured retro-reflectance

values to allow them to be reported on an absolute scale. The estimated

limit of uncertainty of this correction factor, ±0.03, reflects both the

uncertainties in the spectral flux distribution and in the spectral

reflectance of the mirror.

All of the correction factors and the estimated limits of uncertainty associated with them are summarized in Table 5. The product of all

of these correction factors is 0.9U5. The sum of the absolute values of

the estimated limits of certainty is O.lU and the square root of the sum

of the squares of the estimated limits of uncertainty is 0.08. Two comments about the significance of these cummulative estimated limits of

uncertainty are necessary. First, this uncertainty is associated with the

absolute error , that is, with the deviation of a reported value from the

true value on an absolute scale of reflectance. Notice that an error in

the reflectance of the gold mirror contributes the same percentage error

to all of the retro-reflectance values. Thus the ratio of the reported

retro-reflectance values of any two samples has no uncertainty arising

from this source of error. Likewise, all of the sources of error listed

19
in Table 5* contribute larger errors to the individual retro -reflectance

values of the different samples than they contribute to the ratios of

these retro-reflectance values. Thus the limit of uncertainty associated

with the relative errors in the reported values is smaller than that

associated with the absolute error in them. This limit of uncertainty

is estimated to ±$% of the reported value. Finally, these limits

of error do not reflect the uncertainty in the measurement of the solid

angle (estimated limit of uncertainty of ±2% of the solid angle), nor do

they reflect the uncertainty in the actual shape of the spectral distribution of flux used in these measurements, except in its effect on the

uncertainty in the reflectance of the gold mirror for this flux distribution.

U. 3 Experimental Procedures and Results

The sample holder had a flat surface against which the rear surface

of each sample was pressed when mounted in the holder. Thus the orientation of the normal to the front surface of a sample relative to the

holder was the same for all of the samples, except for small deviations

introduced by any lack of parallelism of the front and rear surfaces of

the sample. This fact was used to align the samples for the retroreflectance measurements. The experimental procedure was as follows.

A first- surface gold mirror of the same dimensions as the flat

samples coated with Parsons black lacquer was mounted In the sample

holder. The holder was then aligned so that the beam reflected off the

mirror was incident on the central portion of the spherical mirror (ll)

shown in Figure 1. When the room lights were turned off, the location

of this beam on the mirror could be observed visually due to the

20
scattering from dust particles on the mirror's surface. Hence , the normal to the surface of the gold mirror could be made to pass through the

approximate center of the spherical mirror. Mien properly aligned in

this manner the voltage output from the detector was recorded. After

the completion of this step the gold mirror was removed from the sample

holder and replaced by one of the samples of this investigation. Thus

this sample was aligned so that its normal passed through the approximate

center of the spherical mirror. This position of the sample holder was

taken as 0° of rotation about the vertical axis through the front surface

of the sample. The voltage output of the detector was then recorded for

the following rotations about the vertical axis: 0°, -2$° , -15% -5%

5% 0°, 15% 25% 35% U5% 0% 55% 65% 75% 0°. The repeated readings

taken at 0° were to check for instrument drifts during the measurement.

After each set of retro -reflectance measurements the gold mirror was

again placed in the sample holder, the alignment checked visually, and

the voltage output from the detector recorded.

The BaS04 was the first sample to be measured, then samples E, C, J,

N, and L in that order, and finally the black electrical tape. The

results are shown in Table 6 and Figure U. Since the solid angle of

collection was 0.01UU tt, the retro-reflectance of a perfect diffuser

whose directional-hemispherical reflectance was 100$, would be given by

O.OlUU cos 9, where 6 is the angle between the direction of incidence

(equals direction of exitence) and the normal to the perfect diffuser.

The retro -reflectance of the BaS04 sample was measured to be in excess

of 0.015 for small e. This is approximately 5$ higher than the retroreflectance of a 100$ reflectance perfect diffuser, but this difference

21
is relatively small compared to the ±lh% limit of uncertainty which must

be associated with the measurements on an absolute scale of reflectance.

However, the BaS04 does not have a 100% directional-hemispherical reflectance over the entire wavelength range of the flux distribution shown in

Figure 2 } so the measured difference probably is significant. The unbroken line in Figure h is a plot of O.Ol^Ol). cos 8 for comparison with

the measured curve for BaS04

. Since the ordinate in the figure is linear

with the log of the retro-reflectance, the cosine curve can be displaced

downward for comparison with any of the other curves. It is interesting

to notice that sample E, whose directional -hemispherical reflectance is

approximately 1.5%, has the same retro-reflectance at normal incidence

as a perfect diffuser whose reflectance is h%} and at 5>5>° as a perfect

diffuser whose reflectance is 6%. Also notice that a low reflectance

specularly reflecting material such as the black electrical tape would

be a better choice for coating the interior of a cavity receiver than

either type of Parsons Optical Black Lacquer, as long as the normal to

the bottom of the cavity were directed more than about 10° away from the

opening of the cavity.

5. CONCLUSION

Since the mean wavelength of the flux distribution of the retroreflectance measurements is close to l.l£ |im, it is of some interest to

compare the measured values of the directional-hemispherical reflectance

of the PACRAD cavities at 1.15 \m with values calculated from the broad

band retro-reflectance values of the flat samples coated with the same

lacquer. This is done in Table 7. Each pair of entries in a box labeled "calculated" consists of cavity reflectance values

22
calculated-x- from the smallest and largest flat sample retro-reflectance

values reported in Table 6 for a given type of lacquer at an angle of

incidence of 55 °« In Table h a similar comparison was made between the

measured valued of the directional-hemispherical reflectance of the

PACRAD cavities and the values calculated from the results of the directional-hemispherical reflectance measurements on the flat samples. The

data in both of these tables is summarized qualitatively in Table 8.

It seems unlikely that the inconsistencies in this table are due to

experimental errors in the reflectance measurements, since either the

directional-hemispherical or the retro -reflectance appartus would have

to measure too low for some of the samples and too high for others, and

a large amount of effort was expended looking for such effects. It seems

much more likely that the reflectance characteristics of the same type of

lacquer were different depending upon whether the coating was applied to

a flat sample or to a cavity. This conclusion is further supported by

the fact that the lacquers were sprayed onto the flat samples but were

brushed onto the cavities.

Other more significant conclusions can also be drawn from the data

in this paper. First, it appears that there can be considerable variation in the reflectance of samples of either of the two types of black

lacquers studied even when the samples are prepared at the same time

-X-In this case the values were calculated by multiplying the flat

sample retro-reflectance values by 9.1, the ratio of the solid angle

from the base of the PACRAD cavity to the opening, to the solid angle

of collection used in the retro -reflectance measurements.

23
according to the directions specified by the manufacturer. Thus in

order to determine the reflectance or absorptance of an object coated

with either of these lacquers, measurements must be made upon that object. Confidence cannot be put in values taken from the literature, nor

even in measurement taken on different samples of the lacquer prepared

at the same time as the object was coated. Secondly, in order to achieve

high absorptance, cavity recievers should have bottoms whose normals are

directed well away from the opening of the cavity and they should be

coated with a specular black material, even if its directional-hemispherical reflectance is higher than that of the available "matte" coatings.

2k
6. REFERENCES

1. Gillham, E. J., Proc. Roy. Soc. London, Ser. A 269, 2^9 (1962).

2. Kendall, J. M. , and Berdahl, C. M. , Appl. Opt. 9, 1082 (1970).

3. Will son, R. C. , Experimental and Theoretical Comparisons of the JPL

Active Cavity Radiometric Scale and the International Pyrheliometric

Scale, (TR 32-1365, Jet Propulsion Laboratory, Pasadena, Calif.

Feb. (1969).

1;. Eppley-Parsons Optical Black Lacquer, Advertising Brochure, Eppley

Laboratory, Inc., Newport, R.I.

5. Willson, R. C. , Experimental and Theoretical Comparisons of the JPL

Active Cavity Radiometric Scale and the International Pyrheliometric

Scale

,

(TR 32-1365, Jet Propulsion Laboratory, Pasadena, Calif.

Feb. (1969), p. Ik.

6. Willson, R. C. , private communication.

7. Kneissl, .G. J. , and Richmond, J. C. , A Laser-Source Integrating

Sphere Reflectometer, Nat. Bur. Stand. (U.S.), Tech. Note U39,

69 pages (February 1968).

8. Gillham, E. J., Brit. J. Appl. Phys. , k9 l5l (1953).

9. Devos, J. C. , Physica, 20, 690 (195U).

10. Gray, D. E. , Ed. , American Institute of Physics; Handbook (McGrawHill Book C. , New York, 1963), 2nd ed. , Chap. 6, p. 58.

11. Bennett, H. E. , Bennett, J. M. , and Ashley, E. J., J.O.S.A. 52,

12U7 (1962).

12. Twidle, G. G. , Brit. J. Appl. Phys. 8, 338, (1957).

13. Wyatt, P. J., Stull, V. R. , and Plass, G. N. , Appl. Opt. 3, 238

(196U).

25
liu Goebel, D. G. , Poole, E. W. , and Hartsock, R. G. , Appl. Opt. 8, 17L1.9

(1969).

15. Bennett, J. M. , and Ashley, E. J., Appl. Opt. k } 221 (1965).

26
TABLE 1

Thos. Parsons and Sons Eppley-Parsons

Ooatxng under Coat and Top Coat Under Coat and Top Coat

Samples ABCDE FGHIJ KLMNO PRSTU

Extra

yes N0 YES NO

Top Coat

27
TABLE 2

Reflectance of Flat Samples

Sample at 0.6328 ^m at l.l^m

o S.D. p

A 0.0153

B .0132

C .01U2

.0161

D .0161

E .0138

.0160

F .0187

G .0216

H .0213

I .0191

J .0171

.0196

K .03U8

L .03U6

.0375

M .0310

N .0331

.0372

.0333

P .03U0

.0359

R .03U1

S .03U2

T .0357

U .0380

S.D.

0.0005 n .0003 0.02U6 0.0002

.000U -02U2 .oooU

.0011 .0273 -OW

.0009

.0008 . .0016 .0279 ..0005

.0011 — —

,

.0013 .0328 -OOOU

.0011 .037U .°002

.ooo5

.0008 n .0008 .0305 -0001

.0013 .oU7U .0006

.0006 n .0012 .0512 .0002

.0012 .0UU8 -oooU

.0009

.001U .OU85 .0003

.0008

.0009

.0013

.0008

.0009

.0005

.0007

28
TABLE 3

Reflectance of HLackbody Cavities

at 0.6328 (jjn at 1.15 (j,m

Thos. Parsons

S.D. S.D.

.0031U .00028 . 00251 . 00019

.ool+oo .0007U .00292 . 00025

.00U36 .00017 .00276 .00018

.0033U . 00050

.00352 . 00056

.00208 . 000U2

Eppley-Parsons

.00366 . 00021 . 00367 .00023

.0021+3 .0010U .003U2 . 00016

.00301 .00039 .003U1 .00018

.00221; .0001+8

.002U7 .00019

.00199 .OOOI46

29
TABLE h

lacquer Thos. Pars ons Eppley--Parsons

wavelength measured calculated measured calculated

0.6328 um

0.0021

0.00UU

0. 0009

0.0015

0.0020

0. 0037

0.0023

0.0027

1.15 |j,m

0.0025

0.0029

0. 0017

0.0026

0. 003U

0. 0037

0.0031

0. 0036

Directional-Hemispherical Reflectances for PACRAD Cavities. Maximum

and minimum measured values vs. values calculated from the maximum

and minimum directional -hemispherical reflectance values measured for

flat samples.

Source of Error

TABLE 5

Correction Factor

Estimated Limit

of Uncertainty

non-linearity

of system

variations in

re sponsivity

over solid angle

of collection

O.96

0.98

0.06

0.02

responsivity to

flux reflected

into solid angles

other than that of

collection

0.97 0.03

reflectance of

gold mirror 1.036 0.03

30
TABLE 6

Retro-reflectance of the samples for a O.OlUU tt steradian solid angle of collection, in percent

Angle of

Incidence BaS04 C E j L N

Electric

Tape

-25° 1.325 o. 05U5 0.0529 0.0539 0. 0618 O.O6U8 0. 00U99

-15° 1.U37 .0558 .05U6 .0603 .0763 .083U .0105

-5° i.5oi .056U .0556 .067H .0895 .1028 .1U33

0° i.5oU .0571 .0562 .0699 .0913 .1081 2.222

5° 1.518 .0569 .0561 .0688 .0900 .IO6I4 0. 7111

15° 1.U71 .0560 .05U9 .0632 .078U .0888 .0153

25° 1.381 .05U9 .o5Uo .0576 .0632 .0687 . 00506

35° 1.25U .0538 .0531 .0527 .OU98 .0533 . 003U3

U5° 1.09k .0528 .0511 .oU97 .0U0U .0U3U . 002U2

55° 0.911 .0515 .0U89 .0I478 .0336 .0362 . 00175

65° 0.711 .OU97 .0U63 .0U67 .0296 .0327 .0019U

75° 0.523 .OU97 .0I4JU.6 .0U7U .0338 .0320 . 00101

TABLE 7

Thos. Pars ons Eppley Pars ons

measured calculated measured calculated

0. 0025

0.0029

0. 00U7

0. 0050

0. 003U

0. 0037

0. 002I4

0.0027

Directional-Hemispherical Reflectances at 1.15 p-m for PACRAD cavities.

Measured values vs. values calculated from broad band retro-reflectance

values measured for flat samples.

31
TABLE 8

Type of data used

Type of Lacquer

in calculation Thos. Parsons Eppley-Parsons

directionalq ^328 m much too low about right nemispnerica± _ _ ^ reflectance u ^ ^m a little too low about right

retro -reflectance much too high too low

A Qualitative Comparison of How Much Too Low or Too High the Calculated Directional -Hemispherical Reflectance Values Were Relative to

the Measured Directional-Hemispherical Reflectance Values for PACRAD

Cavities.

32^
1. TUNGSTEN STRIP LAMP

2. LENS

3. CHOPPER

4. BAFFLE

5. APERTURE

6. BLACK BOX

7 PLANE MIRROR

8. OFF AXIS ELLIPSOIDAL MIRROR

9. BEAM SPLITTER

10. SAMPLE 8 SAMPLE HOLDER

ON ROTARY TABLE

SPHERICAL MIRROR

12. THERMOPILE DETECTOR

13. BLACK CLOTH

Fig. 1. Schematic diagram of the retro-reflectance apparatus.

33
.8 1.0 .2 1.4 1.6 1.8 2.0 2.2

WAVELENGTH (/i m)

2.4 2.6 2.8

Fig. 2. The relative spectral distribution of the radiation used in the

retro-reflectance measurements.

3k
Fig. 3. The relative sensitivities of five portions of the solid angle

over which the retro-reflected flux was collected.

35
<

H

O

LU

I o

UJa:

i. .8

.6

.4

— .2 LU

O

.08

.06

.04

.02

.01 .008

.006

.004

.002

^•wrO-n cu.

*

<" »

1 ^

^

- <§J K

X

J I ^

-30 -20 -10 JO 20 30 40 50 60 70 80

ANGLE (DEGREES)

Fig. k» The variation of retro -reflectance with angle of incidence for

a perfect diffuser ( ), BaS04 (o ) 9 samples E (Cq« ),

and N (• ), and black electrical type (© )., The retroreflectances of samples C and L were very similar to those of E

and N, respectively, and are not shown there.

36
form NBS-114A (1-7D

1. PUBLICATION OR REPORT NO.

NBS - TN - 575

2. Gov't Accession No.

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEETS

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

On the Absorptance of Cavity-Type Receivers

5. Publication Date July 1971

(S. Performing Organization Code

7. AUTHOR(S)

Jon C. Geist and Joseph C. Richmond

8. Performing Organization

10. Project/Task/ Work Unit No. 2210127

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

11. Contract/Grant No.

12. Sponsoring Organization Name and Address 13. Type of Report & Period Covered

Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) The directional-hemispherical reflectance of a number of flat samples

that had been coated with Parsons Optical Black Lacquer procured from Thos. Parsons

and Sons and The Eppley Laboratory, respectively, was measured at 0.6328 and 1.15 wm with a laser-source integrating sphere reflectometer. The reflectance varied

significantly with method of application, and was significantly higher for the Eppley

lacquer than for the Parsons lacquer. The reflectance of two cavity receivers, one coated with each lacquer, was also measured. At 0.6328 urn the reflectance of the

Parsons cavity was higher, but at 1.15 urn it was lower. The measured reflectance of

the Parsons cavity was appreciably higher than that computed from the measured

reflectance of the lacquer and the geometry of the cavity, assuming the coating to be

a perfectly diffuse reflector. Retro-reflectance measurements revealed that both

lacquers reflected more radiant energy back into directions near the direction of

incidence than would a perfect diffuser of the same directional-hemispherical reflectance, but the Parsons lacquer was by far the more pronounced retro-reflector. The

principal conclusion is that the diffuse assumption can lead to significant errors

in computing the absorptance of cavity-type receivers, when the cavity coating is in

fact not diffuse.

17. KEY WORDS (Alphabetical order, separated by semicolons) absorptance; black coatings; cavity absorptance; cavity reflectance; laser-source reflectometer; Parsons black; retro-reflectance.

18. AVAILABILITY STATEMENT

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