Measurement of diffuse reflection factors, and a new reflectometer

NATL INST OF STANDARDS & jECH ".I.C.

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DEPARTMENT OF COMMERCE

Scientific Papers

OF THE

Bureau of Standards

S. W. STRATTON. Director

No. 391

MEASUREMENT OF DIFFUSE REFLECTION

FACTORS, AND A NEW ABSOLUTE

REFLECTOMETER

BY

A. H. TAYLOR, Associate Physicist

Bureau of Standards

JULY 28, 1920

PRICE, 5 CENTS

Sold only by the Superintendent of Documents, Government Printing Office,
Washington, D. C.

WASHINGTON

GOVERNMENT PRINTING OFFICE

1920

MEASUREMENT OF DIFFUSE REFLECTION FACTORS,
AND A NEW ABSOLUTE REFLECTOMETER

By A. H. Taylor

CONTENTS

Page

I. Introduction — Nature of reflection 42 1

II. Earlier reflectometers 422

III. The new absolute reflectometer 425

IV. Theory of reflectometer '. 426

V. Experimental results 429

VI. Effect of specular reflection from test surfaces 433

VII. Precautions in use of reflectometer 434

VIII. Conclusion 435

IX. Bibliography 436

I. INTRODUCTION— NATURE OF REFLECTION

The reflection factor of a surface is defined as the ratio of the
total luminous flux reflected by the surface to the total luminous
flux incident upon it.

The siu-face may be illtuninated by a narrow beam of light, by
light from several directions, by totally diffused light, or by some
combination of these. Reflection may take place in many ways —
e. g., specular reflection, in which case an incident cone of light is
reflected as a cone, the angles of incidence and reflection being
equal; perfectly diffused reflection, in which case the light is re-
flected in all directions in accordance with the ^ cosine law of emis-
sion ; mixed specular and diffused reflection, in all possible combi-
nations between the extremes.

No surface obeys the cosine law of emission perfectly, and most
surfaces are very far from being perfect diff users.

1 The cosine law of emission states in substance that the light is reflected from a perfectly dififusing stirface
in such a manner that the luminous intensity (expressed in candlepower or some similar tmit) of an element
of area at any angle of emission is equal to the intensity normal to the surface multipUed by the cosine
of the angle between the line of emission and the normal to the surface. This assumes that the intensity
at any angle is directly proportional to the projected area of the element of siuiace, hence that the surface
brightness (candles per ixnit area ) is constant at all angles.

This law has often been erroneously referred to as Lambert's cosine law. Mr. A. P. Trotter has recently
shown (see Bibliography, i) that Lambert's law refers to the incident light instead of the reflected light,
and that his law states that the intensity of illumination of any surface varies as the cosine of the angle
between the line of incidence and the normal to the surface. Hence it is seen that Lambert's cosine law
is rigidly correct. Mr. Trotter's article also gives much valuable ioformation regarding the characteristics
of reflected light.

421

422 Scientific Papers of the Bureau of Standards [Voi. i6

The numerical value of the reflection factor of a surface may
depend on the color of the incident light and the manner of its
incidence.

In the practical application of light and illumination it is often
desirable to be able to determine the reflection factors of various
surfaces. In the design of a lighting installation a knowledge of
the reflection factors of the walls and ceilings enables the illumi-
nating engineer, with the aid of prepared tables, to estimate the
size and number of lamps which will be required to produce the
desired illiunination. The determination of reflection factors with
precision is one of the most difficult feats in photometry, and pre-
vious to this time, so far as the author knows, no method has been
proposed which will give acciuate results and which may be ap-
plied to the measurement of surfaces in place. All previous
methods, with the exception of one, involve laboratory measure-
ments, and the one exception does not give correct results.

II. EARLIER REFLECTOMETERS

If one considers the way in which the light flux is reflected, it is
evident that in all cases except that of pure specular reflection
any method of measuring reflection factors must inevitably involve
an integration of the reflected flux. This practically limits the
method to some application of the integrating sphere.

A search of the scientific literature reveals only a few articles
on this subject. The information obtained shows that several
methods have been proposed, but apparently nothing has been
done as yet to standardize the method. In all except one of the
methods of which descriptions were found the test surface is com-
pared in some way with a standard surface, but little is said about
the initial standardization of the reference standard surface.
Even though the method of comparison may be faultless, the val-
ues obtained are merely relative to that of the standard stuface,
and if it is incorrectly evaluated they will evidently be subject to
the same error. A number of the methods which have been used
in the past have been seriously in error because of the assignment
of an incorrect value to the standard stuiace used. A few of the
methods used will be briefly described.

Apparently the first definite proposal of an instrument for the
measurement of diffuse-reflection factors was made in 191 2 by
Dr. Nutting. (See Bibliography, 2.) His instrument consists of
a highly polished nickeled ring 150 mm in diameter and 32 mm
high, through which projects the nose of a Konig-Martens polariza-

Taylor] Dlffusc RefLectometeY 423

tion photometer. An illtuninated diJBFusing glass plate is placed
on one side of the ring and the test surface on the other, and the
photometer is arranged to view the two surfaces at an angle of
about 75° from the normal. He describes it thus: "The principle
of the method is that of two parallel infinite planes, one of which
is a diffuse illuminator and the other the surface whose reflecting
power is to be determined. The relative brightness of the two
planes is then the reflecting power of the nonluminous plane."
Judging by the low value assigned to magnesium carbonate by this
instnmient, it apparently gives results which are very seriously in
error. Some of the factors which may contribute to this error are
as follows :

(a) The instrument is based on the principle of parallel infinite
planes, whereas it employs planes of very limited area, bounded
by a nickeled ring which is far from a perfect reflector.

(6) The distribution of illumination over the two planes is
seriously disturbed by the presence of the nose piece of the polari-
zation photometer and does not have the ideal distribution which
is assumed.

(c) No surface obeys the cosine law of emission perfectly, and
the brightness of the surface at a very oblique angle is usually very
appreciably lower than that of a perfect diffuser emitting the same
total flux.

A method devised and used by Mr. W. F. Little (see Bibliog-
raphy, 3) at the Electrical Testing Laboratories consists in the
projection of a beam of light through a small hole in the wall of
an integrating sphere onto the test surface, placed near the center
of the sphere. In this method the brightness of the observation
window when the test surface is in place, compared with that when
the standard surface is used, is substantially the same as the ratio
of the reflection factors of the two surfaces. Evidently this
method is limited by the accuracy of the value assigned to the
standard surface, but a slight modification would make it an abso-
lute method. If the light beam is first projected onto the sphere
wall at a point unscreened from the observation window, and is
next projected onto the test surface, screened from the window,
the ratio of the brightness of the window in the second case to that
in the first case is the numerical value of the reflection factor of
the test siuiace. In this method the area of the test surface
should be small with respect to the sphere surface. Another
method of using the sphere would be to determine the reflection
factor of its surface by a method which will presently be described,

424 Scientific Papers of the Bureau of Standards [Voi. 16

then to determine the relative values of test and sphere surface by
projecting the beam first on one, then on the other, the illuminated
spot being screened from the observation window in each case.
The greatest practical difficulty in the application of any one of
these 'three methods of using the sphere is the realization of a
narrow beam of light which is of a sufficiently high intensity and
at the same time is so concentrated that none of it is incident any-
where except on the test surface. The two modifications of Mr.
Little's methods pointed out by the author require the sphere
surface to be uniform in reflecting power.

In 19 1 6 Dr. Rosa (see Bibliography, 4) and the present author
described and applied a method of measuring the reflection factor
of the surface of an integrating sphere. In consists in the deter-
mination of the ratio of the average illumination received by the
sphere surface from the test lamp to the total illumination of the
sphere surface by both direct and reflected light, the numerical
value of this ratio being the absorption factor of the sphere siu-f ace.
The absorption factor of an 88-inch sphere at the Bureau of Stand-
ards, when the surface was fresh, was found to be 7.5 per cent.
Since magnesiiun oxide and carbonate have long been considered,
and probably are, the whitest substances in existence, this test set
the lowest possible limit for their reflection factors, and definitely
established the fact that the value of 88 per cent, given by Dr. Nut-
ting's reflectometer, was considerably in error. This sphere
method of determining the reflection factor of the sphere sinrface
is by far the most precise method which it is possible to devise, but
it is evidently very limited in its application.

In 191 7 Mr. M. Luckiesh (see Bibliography, 5) described a new
relative method for measuring reflection factors. An opal glass
globe, such as is used in lighting fixtures, is moimted in a white
box. The globe is surrounded by fotir or more lamps, symmetri-
cally placed. The globe has an opening at the bottom, against
which is placed the object to be tested. A brightness photometer
views the test object, its brightness being compared with that of
a standard surface of known reflection factor. The results of tests
with this instriunent may be in error because of the fact that the
photometer views the test object at a fixed angle, and that the
brightness at that angle may depend very largely on the amount
of specular reflection of the object, but it is probable that this error
would not be very large. The instrument will, however, give
incorrect results if the standard surface is incorrectly evaluated.

Taylor]

Diffuse Reftectometer

425

III. THE NEW ABSOLUTE REFLECTOMETER

In 191 6 the author worked out the complete theory of a reflec-
tometer which was to be an absolute instrument, and shortly there-
after the experimental instrument used in these tests was con-
structed. The few tests which were made gave good results, but
for lack of time very little more work was done with the instru-
ment until within the past few months. No publication of the
theory was made because insufficient work had been done to com-
pletely verify it, but it has now been verified by extensive experi-
ments, as will be shown later.

At the convention of the Illuminating Engineering Society in
Chicago, in October, 19 19, in the discussion of two of the papers
presented, the author called attention to the fact that the value of
88 per cent for magnesium carbonate was much too low, and also

Q}lamp

Test Su,yftic&.

Fiq. ih.

Fig. I. — The new type "absolute^' refiectometer

briefly described the instrument which it is the object of this paper
to describe more fully. * (See Bibliography, 6.) In a revision of
his discussion, prepared shortly after the convention, the author
stated that the reflection factor of magnesium carbonate was
approximately 96 per cent, that being slightly lower than a
value which he obtained by one measurement by point-by-point
methods.^

The reflectometer consists of a small sphere arranged as shown
in Fig. I. Light from a small lamp is projected through tube A

2 The absolute method for the determination of the reflection factor of magnesium carbonate which was
described by another author in a recent publication is merely a modification of the method which the
present author described in Chicago, and describes more fully here, and is strictly limited to the deter-
mination of the reflection factor of any surface which can be embodied in a hollow sphere. His method
uses an incomplete sphere divisible into two fractional parts, whereas the author described the used of the
complete sphere and one fractional part.

426 Scientific Papers of the Bureau of Standards [Voi. 16

onto the inner sphere wall. At 5 is a small hole through which
the opposite wall can be viewed by a brightness photometer. The
segment of sphere surface c' is cut off by a plane, leaving the
opening c" . The test surface is placed over this opening, and
the direct light is projected onto the sphere wall or the test sur-
face, depending on whether the lighting tube is placed at A or C.
The attachments are so constructed that their positions are inter-
changeable. In the experimental instrument constructed and
used in the tests the area c\ the portion cut off, was 10 per cent of
the total sphere area.

IV. THEORY OF REFLECTOMETER

If a plane siu-face is illuminated by an infinite plane of uniform
brightness h (candles per unit area) , the flux received by unit area
of the illuminated plane is irh lumens. (See Bibliography, 7.)

A perfect diffuser of imiform brightness h emits irh lumens per
unit area.

The interior illumination of a hollow sphere with diffusely
reflecting walls may be considered as composed of two parts:
(a) The light received directly from the light source, and (6) the
illiunination made up of light diffusely reflected from the sphere
walls. The part {h) is the same in value at all points in an empty
sphere, in accordance with the theory of the integrating sphere.

Assume the hollow sphere arranged as shown in Fig. la. Let
the area of the complete sphere be unity.

Let c' = ratio of sphere area cut off to total sphere area.

Let c" = ratio of area of hole to total sphere area.

Let a = I — c' = fraction of total sphere area which remains.

Let m = diffuse reflection factor of sphere surface.

Let mx = diffuse reflection factor of test surface.

Let F = total light flux (lumens) received from lamp.

Let 60 = average brightness (candles per unit area) of sphere
wall due to reflected light only when hole is imcovered.

Let 6x = brightness when hole is covered with a flat test surface
having a diffuse reflection factor Mx.

Let h = brightness when test surface has reflection factor m.

When the hole is imcovered, the escaping light flux may be
considered as composed of two parts. The portion of first reflected
flux which escapes through the hole is c'mF, since it is the once
reflected flux which would ordinarily be received by the portion
of the stuface which has been removed. The second part is the

Taylor] Diffuse Reflectometev 427

flux due to the average brightness bo of the sphere walls, which
in turn is due to reflected light only. Its effect in the plane c'' is
equivalent to that of an infinite luminous plane of brightness 60.
Hence, this second part is irboC^', and the total flux escaping
through the hole is

F'=c'mF + 7rboC'\ (i)

The total flux received by the remaining portion of the sphere
stirface is

irbod

m
the amoiuit absorbed being

+ F,

|_ m J

Neglecting the small amount of light flux lost through the
lighting and observing windows, the sum of (j) and (2) must be
equal to the total flux received, since it all escapes through the
opening or is absorbed. Therefore we have

wboc'' -hr/mF + {1 -m^"^ +f] = F. (3)

Solving (3) for bo,

m'^F{i—c') _ m^Fa .

°^7r[mc''+a(i -m)]^ Tr[mc'' +a{i -m)] ^^^

If the hole is covered with a flat surface having a reflection
factor my,, then (i — m^) times the flux incident on the test surface
will be absorbed. In that case we find that

(i —m:^)['rrbj,c"-^c'mF] + (l — m)
Solving for 6x we have

'^'^%f]=F. (5)

m

h m^F(a+c'm^)

"" Tr[c'^m(i—m^)+a{i—m)] ^ ^

If my: = m — that is, if the test surface has the same reflection
factor as the sphere surface — then (6) becomes

m^F{a + c^ni)
182802°— 20 2

428 Scientific Papers of the Bureau of Standards iVoi.16

It is possible to measure the relative brightness of the sphere
wall under the various conditions, and from these m and Wx can
be computed.

Let

r-=X and r^ = Xx.
bo bo

Then

m^F(a-\-c'm)

7r(i — -m) {c^^m+a (mc^ + a)[mc^ ' + a(i —m)] ,.

~ m^Fa a{mc'' +a){i —m)

7r[wc" +a(i — m)]

Clearing of fractions and collecting,

m'[c'{c^'-a) +Kac'']+ma[c' + W -a) (i -K)] + a\i -K) =0. (9)

Since c', c", and a are dimensional constants of the sphere and
K can be measured, m, the reflection factor of the sphere surface,
can be evaluated from this equation.

nt^F^a + c'rU:^

j^ _7r[<:"m(i — Mx) +a(i — 'm)]_ (a + c''mx)[twc" +a(i — m)] , .
^ m^Fa . a[mc"(i — Wx) +a(i — w)]

x(mc'' + a(i — m)]

^a{K^-i)[c"m+a{i-m)]
^" ac\i-m)+mc'\c'+K^a) ^^^^

The above equations have been derived for the case where the
direct light from the lamp is incident on the sphere wall. While
it is possible to use the reflectometer with that arrangement, it is
much more sensitive to changes of reflection factor of the test
surface, and therefore more acciurate, if it is arranged so that the
direct light is incident on the test surface. The most convenient
method is to use the former arrangement and determine the value
of m from equation (9), then arrange the instrument so that the
light is incident directly on the test surface, as shown in Fig. i&.
By using for a reference standard a surface painted with the sphere
paint it is then possible to evaluate in absolute measure the
reflection factor of any test surface. In practical work, however,
it is preferable to use a less perishable reference standard. A
rough-surface milk glass makes a satisfactory reference standard,
as it is easily restored by washing. It can be standardized by

Taylor] Diffuse Reflectometer 429

means of observations and use of equations (11) and (17). The

theory of the instrument when so used is as follows :

Let c', c" , a, m, m^, and F have the same meaning as before.

Let 6'= brightness of sphere surface when the hole is covered

with a test surface of factor m^.

value of V when hole is covered with surface m"

value of h' when hole is covered with surface m'

Since imit area of the sphere surface of brightness h' emits 7r6'

-Kh'
lumens, it must be receiving — lumens. Hence the sphere area a

absorbs (i— m) — - lumens. The test surface receives F + c^irh'
m

and absorbs (i-m^) {F + c"W) lumens. Hence, since all the

light is absorbed except that negligible amount which escapes

through the lighting and observing holes, we have

(i -fn)— + (i -m^)(F + c''W) =F. (13)

Solving for 6',

7r[a(i — -m) +c"m(i — Mx)]'

mm^F

(15)

7r[a(i —m) -\-c'^m{i — m' ')] _m"[a{i —m) +c"m(i —m' )]

mm'F m' [a{i—m) +c"m{i—m^')'\

7r[a(i — -m) +c"w(i — -m')]

Solving for m" ,

•m = — ^ -^ (16)

a(i —m) -\-c"m{\ —m'-^Rm')

In the special case where m' =m, we have

,,_ _ Rm[a{i —m) +mc^^] . .

^ ~^"~[(i -m)(a+c''m) -¥Rw?c''i ^^^^

V. EXPERIMENTAL RESULTS

In order to verify the theory of this instrument a graded series
of test objects was made up. Neutral gray objects were obtained
by mixing black drawing ink and lampblack with a white cement
(Keene's Fine). They were surfaced with coarse sandpaper,
resulting in fairly good diff users. Those having reflection factors
below 50 per cent were better diffusers than those above that value.

430

Scientific Papers of the Bureau of Standards

{Vol. i6

This appears to be characteristic of this material and possibly of
others, and may be treated more fully in a future paper. The gray
objects, after having been made up for about four or five months,
were found to have faded somewhat, and hence are not satisfactory
for permanent reflection factor standards.

The test objects were next tested for reflection factors by means
of the apparatus shown in Fig. 2. The objects were illuminated
normally by a 60-watt vacuum timgsten lamp, and the surface
brightness was measiured by point-by-point observations. The
amount of flux reflected was then calculated by applying the
proper factors, and since the incident flux was known, the ratio

m

I i I

Sur/Vice-Br'tjTttness Sto-ndord
ppcd QlassJ

Test Suy*fa.ces vVedjed Jl^ainst
these Sty*ips.

^. )

0

o

Fig.

Appar^atus Mounted on Ba.r*
Thotometer*, u/ith Stationar>if
Photometer' Head and Mov-
able Compa-rtson Lamp.

-Apparatus used in determining reflection factors by measurements of surface
brightness at io° intervals

of the reflected to the incident flux gave the reflection factors of the
test surfaces. The greatest difficulty in that method of measure-
ment is the standardization of the apparatus to read surface
brightness, as it involves very considerable practical difficulties,
chief among which is the great intensity step which must be taken.
Much work was done on this part of the problem, and it is believed
that the uncertainty in that standardization was not very large.

A number of the cement standards and a block of magnesium
carbonate were measured by both methods of using the instrument
as described above. By the use of equation (9) the reflection
factor of the sphere surface was found to be 88.3 per cent. This
value was then substituted in the equation and the reflection
factors of the various test objects were computed. The results
of the measurements in the three different ways are shown in
Table i.

Taylor] Diffuse Reflectometer

TABLE 1. — Reflection Factors by Three Methods of Measurement

431

Test object

Point-
by-point
measure-
ment

Sphere reflectometer
measurements

Direct

light

on test

objects

Direct

light

on sphere

wall

Cement Standard 1 . . .
Cement Standard 2. ■ ■
Cement Standard 3. . ■
Cement Standard 4. . .
Cement Standard 5. ■ •
Cement Standard 6. . .
Cement Standard 7. . .
Cjement Standard 8. . .
Cement Standard 9. ■ ■
Cement Standard 10. .
Magnesium carbonate

Per cent
17.7
23.7
31.5
36.3
42.9
60.0
67.4
81.9
86.5
90.8
99.3

Per cent

18.4

23.95

31.6

37.1

42.9

60.7

67.3

81.4

85.5

90.4

99.1

Per cent

21.9
28.2
35.2
39.6
46.4
62.8
70.2
82.7
86.8
89.6
98.7

It will be noted that the agreement between columns 2 and 3
is almost perfect, and that for reflection factors above 80 per cent
the fourth column is in satisfactory agreement. For factors
below 80 per cent the method represented by the fourth column
is rather insensitive, the error in the result being larger than the
error of the photometer reading with the actual conditions existing
in the experimental instrument. This is clearly shown by the
curves in Fig. 3. When the direct light is incident on the test
surface the error in the factor is always less than the error of the
reading. Hence it may safely be stated that at least a part of the
discrepancy between columns 2 and 4 may be attributed to
experimental error. The fact that the differences are all in the
same direction for the objects having low reflection factors might
lead to the belief that not all the discrepancy could be explained
this way, and that it might be necessary to look farther for an
additional reason. It is quite probable that the reflection factor
actually is greater when an object is diffusely illuminated than
when the light is incident normally, since some of the incident rays
strike the surface at very oblique angles and do not penetrate the
surface. If this explanation is correct, it naturally follows that
the effect would be greater the lower the reflection factor of the
surface. The sensitivity of the instnunent when used with diffused
illumination of the test surfaces would be greatly increased if the
reflectometer were painted with a paint having a higher reflecting
power, and it might then be possible to determine whether this is

432

Scientific Papers of the Bureau of Standards

[Vol. i6

a real departure from the theory as developed. The author has
made up paints having a factor of about 94 per cent, which would
be much better for this application.

It will be noted that the measurements by the three methods
give about 99 per cent for magnesium carbonate, whereas the
previously accepted value was only 88 per cent It did not seem
possible that its value could be so high, and the author was
reluctant to accept that value as reliable in spite of the agreement
of the three methods, unless verified by still another method.
Hence steps were taken to verify it by a fourth absolute method,

.X .3 ^ ^ j6 .7 .8

7?ejPlection Factor 0/ Test du^'Tface. (m,,)

Fig. 3. — Curves showing how the precision of determinations with the new rejiectometer
varies with different conditions

which was described above as a modification of the sphere method
used by Mr. Little. For this purpose a small disk of magnesium
carbonate wS,s made up from the block previously tested. It was
placed in a sphere and a very narrow beam of light was projected
through a small hole in the sphere wall onto the sphere surface at a
point imscreened from the observation window, then onto the
magnesium-carbonate disk so placed that none of the first reflected
light from it could reach the observation window. The ratio of
the brightness of the window in the second case to that in the first
case is the reflection factor of the test surface. This measurement
gave a factor of 98.9 per cent which, on the basis of the consistency
of the photometric readings, appeared to be thoroughly reliable.

Taylor] Diffusc ReflectometeY 433

Hence it appears that the reflection factor of this particular block
of magnesium carbonate is 99 per cent. Another block, obtained
about three weeks later from the same source, has a factor of
approximately 98 per cent while another block which has been
in the laboratory for about two or three years is appreciably
darker than either of these. No investigation has baen made of
the reproducibility of such surfaces for precision standards.

It should be pointed out that magnesium carbonate is not a
perfect diffuser, hence this must be taken into account if it is
desired to use it as a standard of surface brightness. The block
which was tested by point-by-point measurements was surfaced
by scraping with a sharp glass edge. When illuminated normally
its brightness at about 50° from the normal to the surface was the
same as that of a theoretically perfect diffuser emitting the same
total flux.

VI. EFFECT OF SPECULAR REFLECTION FROM TEST

SURFACES ' '

As mentioned above, the surfaces with which these tests were
carried out were fairly good diff users. Some other surfaces which
have been examined by point-by-point measurements have been
ordinary semimat surfaces. An examination of these data shows
that when the light is incident normally the angle at which the
surface has the same brightness as a perfect diffuser emitting the
same total flux is usually about 50°, which is also approximately
the angle between the normal and the line joining the observation
window and the center of the test surface. The difference between
the surface brightness of the test surface at 50° and a perfect
diffuser emitting the same total flux rarely exceeds 3 to 5 per cent
and is usually below 3 per cent. The effect of a deviation of 5
per cent from perfect diffusion at 50° for a stirface of reflection
factor 80 per cent has been calculated for a reflectometer having
10 per cent of its area cut off, and painted with a paint having a
reflection factor of 90 per cent. The calculation shows that the
error of the determination would be less than 0.5 per cent. Hence
it appears safe to state that the error of determination due to
specular reflection will not exceed 2 per cent in a reflectometer
having these dimensions, imless an excessive amount of the specu-
lar reflection of direct light is incident on the observation window.
This will not hold true unless the specular reflection takes place
only at the first surface.

434 Scientific Papers of the Bureau of Standards [Voi. i6

If it is desired to determine the reflection factor of a mirror,
this may be done by first directing a narrow beam of light into the
opening of the reflectometer, then let the same beam be reflected
from the mirror and be directed into the reflectometer when the
mirror is placed at an appreciable distance from the reflectometer.
The ratio of the brightness of the observation window in the second
case to that in the first will be the reflection factor of the mirror.

VII. PRECAUTIONS IN USE OF REFLECTOMETER

In the use of the reflectometer as described above certain pre-
cautions are necessary. Some of them are as follows:

(a) The dimensions should be precisely determined in order to
fix the values of the constants c', c", and a.

(b) In painting the sphere and the flat surface by means of
which its reflection factor is determined, care must be taken to
make the flat surface as nearly as possible the same in reflecting
power as the sphere surface.

(c) When calculating the reflection factor of the sphere surface
by the use of the equation (9), the figures should be carried out
as far as possible, as it involves differences of numbers which are
nearly equal, and a small error in calculation may make an appre-
ciable error in the result. The use of logarithms for this step is
recommended, though slide-rule calculations are sufficiently accu-
rate in working up test data for observations taken with direct
light on the test surfaces.

(d) When the direct light is incident on the sphere wall, care
must be taken to prevent any direct light from escaping through
the large opening c".

(e) Few, if any, paints will remain absolutely constant in
reflecting power, hence the reflection factor of the sphere surface,
when once determined, should not be assumed constant thereafter
but should be checked frequently. This can be done by means of
test objects standardized when the paint in the sphere is fresh.
Depohshed milk glass is excellent for this purpose, and white
blotting paper would probably be satisfactory, too. If a sufficient
number of such objects, covering a wide range of reflection factors,
were standardized very carefully when the siurface was fresh, they
could be used to establish an empirical calibration of the reflecto-
meter at any time, without the necessity of solving the mathe-
matical equations. Two standards having reflection factors of
about 90 and 50 per cent could be used to determine the reflection

Taylor] Diffusc ReflectometeY 435

factor of the reflectometer surface at any time by the use of equa-
tion (15), and the caHbration cirrve could then be calculated and
plotted for ready reference. An oil paint is not satisfactory for
painting the reflectometer on account of its change with time.
If the paint used is fairly constant, the method first described in
the theory of the reflectometer for determining its reflection factor
would be entirely satisfactory, but with any paint which changes
very much there is the danger that the reflectometer surface and
the flat siuiace painted with the same paint would not change at
the same rate.

The most symmetrical arrangement of the reflectometer is
obtained if the observation hole and side lighting hole are about
90° from the center of the portion cut off, and 90° from each
other. This is the arrangement shown in Fig. la.

VIII. CONCLUSION

In conclusion the most important points brought out by this
paper may be summarized as follows:

1. Five "absolute" methods of measuring reflection factors
are described, at least three of which are apparently new. Meas-
urements on magnesium carbonate by four of these methods give
values which are in excellent agreement.

2. The numerical value of the reflection factor for manesium
carbon^e which has been in use for many years — viz, 88 per
cent — is in error. This fact was first publicly pointed out by the
author at Chicago in October, 191 9. The actual value of its
diffuse reflection factor is approximately 99 per cent, but the
degree of reproducibility of this value with materials from differ-
ent sources is unknown.

3. The method described above for the use of an incomplete
sphere as a reflectometer furnishes two new absolute methods for
the determination of diffuse reflection factors. The determina-
tion of the reflection factor of the sphere sinf ace is only an inci-
dental step in the use of the instrument, and is not its principal
object.

4. The instrument just described should find a large field of
usefulness in photometry and illuminating engineering, and
furnishes a method of measuring the reflection factors of surfaces
in situ. Apparently no other instrument has been proposed for
this purpose which is accurate and portable. It can be adapted
for use with any good type of portable photometer. ,

436 Scientific Papers of the Bureau of Standards \voi. 16

5. It should be strongly emphasized that the reflection factor
of any colored surface is dependent on the color of the incident
light and that measurements by this or any other. method will
give its reflection factor only imder the particular conditions of
the test. Hence under such conditions the principal value of
the measurement is to indicate the approximate value of the
factor, but this is all that is usually required.

IX. BIBLIOGRAPHY

(i) A. P. Trotter, Diffused Reflection and Transmission of Light, Illuminating
Engineer, London, pp. 243-267; September, 1919.

(2) P. G. Nutting, A New Method and Instrument for Determining the Reflecting

Power of Opaque Bodies, Trans, Ilium. Eng. Soc, 7, p. 412; 1912.

(3) Henry A. Gardner, The Light-Reflecting Values of White and Colored Paints,

Jour. Franklin Institute, 181, p. 99; 191 6.

(4) E. B. Rosa and A. H. Taylor, The Integrating Photometric Sphere; its Construc-

tion and Use, Trans. Ilium. Eng. Soc, 11, p. 453; 1916.
5) M. Luckiesh, Measurement of Reflection Factor, Elec. World, 69, p. 958; 1917.
Journal of Optical Society of America; January-March, 19 19.

(6) Discussion by A. H. Taylor, Trans. Ilium. Eng. Soc, 15, p, 132, March 20, 1920.

(7) E. B. Rosa, Photometric Units and Nomenclature, B. S. Bulletin, 6, p. 543;

1909-10. Also B. S. Sci. Paper No. 141.

Washington, March 11, 1920.