A Lambertian reference standard for uniformly scattering a beam of light is constructed of a plate having a planar surface with a layer of glue disposed on the surface. An evenly packed layer of monodisperse spheres is set in the layer, and when the standard is used for bi-directional (BRDF) measurements, the spheres are coated with a layer of highly relective substance, such as gold or silver. When the standard is used for bi-directional transmittance distribution function (BTDF) measurements, the spheres are of a transparent material and are provided with a roughened surface, as by acid etching. In this case, the layer of glue is an optical cement, and the plate is of glass, with the spheres, the layer, and the plate all possessing a similar refractive index

Witherow, William K.

English

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NASA CASE NO. 0 3 / 2 5-- y
PRINT FIGURE _
NOTICE
The invention disclosed in this document resulted from
research in aeronautical and space activities performed under
programs of the National Aeronautics and Space Administration.
The invention is owned by NASA and is, therefore, available for
licensing in accordance with the NASA Patent Licensing
Regulation (14 Code of Federal Regulations 1245.2).
To encourage commercial utilization of NASA-owned inventions,
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Address inquiries and all applications for license for this
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Mail Code CCOI, Huntsville, AL 35812. Approved NASA forms for
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from the above address.
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TECHNICAL ABSTRACT
REFERENCE STANDARD FOR BI-DIRECTIONAL REFLECTION
DISTRIBUTION FUNCTION AND BI-DIRECTIONAL TRANSMISSION
DISTRIBUTION FUNCTION MEASUREMENTS
Thls invention relates generally to Lambertlan reflectors and
refractors and more particularly to reference standards for bl-
dJrectlona] reflection and refractive distribution function
measurements.
A Lambertian reference standard Is constructed by affixing an
even layer of llke-slzed monodlsperse spheres in a thin layer of
bonding agent on a flat surface of a plate. In the instance where
a reflective standard is constructed, the plate and spheres are
coated, as by vapor deposition, with a reflective material, such
as gold or silver. In the instance where a refractive standard is
constructed, the spheres are of a transparent material, such as
glass, and have an irregular surface created by a process such as
acid etching. The refractive embodiment includes a bonding agent
- and plate having refractive indexes which matches that of the
spheres.
The novelty of thls Invention particularly lles in
constructing these reference standards with monodlsperse spheres,
and in the case of a refractive standard, matching the refractive
index of the plate and bonding agent to that of the spheres.
Inventor: William K. Witherow
Employer :
Serial Number :
Date Filed:
NASA/MSFC
244,367
September 15, 1988
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NASA Case No. MFS-28183-I ] PATENT
A REFERENCE STANDARD FOR BI-D[RECTIONAL REFLECTION
DISTRIBUTION FUNCTION AND BI-DIRECTIONAL TRANSMISSION
DISTRIBUTION FUNCT[ON MEASUREMENTS
Origin of the Invention
The invention de.scribed herein was made by
employees of the United States Government and may be
manufactured and used by or for the Government for
Government purposes without the payment of any royalties
thereon or therefor.
i0
15
Technical Field
This invention relates generally to Lambertian
reference standards used in bi-directional reflectance
and transmission distribution function (BRDF and BTDF)
comparisons and calibrations, and more particularly to
a standard wherein an evenly packed layer of similarly
sized monodisperse spheres are fixed on a planar
surface of a flat plate.
20
25
30
Background of the Invention
In the field of optics relating to the visible and
long-wavelength (infrared) spectrums, it is necessary
to evaluate stray light rejection systems, laser back
scatter, reflective characteristics of materials, and
coated or polished surfaces. This is generally done
by shining _ incident beam of light on a coating or
surface being evaluated and measuring light which is
scattered or reflected therefrom. These measurements
of reflected or scattered light are known as
hi-directional reflection distribution function (BRDF)
when obtained from a reflective surface, and
bi-directional transmission distribution function
(BTDF) when obtained from transparent or translucent
materials. BRDF/BTDF is mathematically defined as
being:
-2-
i0
15
20
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35
where _ and _ are angles in spherical coordinates, i and
r refer to incident and reflected quantities,
respectively, Lr is reflected radiance, and Ei is
incident irradiance. This formula is a solid geometric
"" t
representation of a- ratio of incident light to reflected
light and is helpful in determining characteristics of
light reflective/transm ssiv_ surfaces.
In practice, measuring scattered light is done by
mounting a sample of the surface being evaluated on a
rotating turntable. This turntable is angularly
positionable from 0 ° to 90 ° in any plane with respect
to an incident beam of light directed onto the sample.
A sensitive photovoltaic detector is mounted a fixed
distance from the sample on an arm that can be rotated
in a horizontal plane about the sample. The horizontal_
plane includes the incident beam. The detector records
reflected light levels at points of interest and
converts this reflected or scattered light to voltage
levels, which are recorded. Next the sample surface is
removed from the turntable, and a reference standard is
similarly mounted on the turntable, with a photovoltaic
detector being positioned to measure scattered light
at the identical points of interest that were measured
from the sample. This reference standard is constructed
to scatter a beam of light perpendicularly striking the
reference sample uniformly and in an even distribution
360 ° around the point where the incident beam of light
impinges on the standard, and in an even distribution
from 0 ° to 90 ° with respect to the beam. Additionally,
the reference standard must absorb as little as possible
of the incident beam of light. This type of reflector
is known as a Lambertian reflector, and when compared
as described to a surface being evaluated for light
scattering properties, establishes a baseline reference
for scattered light. Accordingly, and since the
aforementioned formula defining BRDF/BTDF is cumbersome
to use and difficult to implement when there are
nllm_rnll_ nN_nt_ _f interest at which it is desirable to
"3"-
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know the degree of ]ight scattered thereto, measurements
of light scattered by the sample and the reference
standard may be compared to find the BRDF/BTDF of a
sample by using the simplified formula:
p,
f°' >
where VUN K and VRE F are the photovoltaic voltage levels
from the surface to be eval'uated (VuN K) and the
reference standard (VREF), with BRDF/REF being
approximately 0.318, a constant representative of a
Lambertian reflector or transmitter.
Problems with these BRDF comparative methods are
that, to date, a suitable reference standard has yet to
be found. Some of the materials used in attempts to
duplicate a Lambertian reflector are magnesium oxide
(Mg0), halon, sintered bronze, and flowers of sulfur.
These materials are deposited, typically by vapor
deposition, on a planar surface which is then used as
a reference as described. However, Mg0 and halon
possess a physical structure which is too fine to behave
as a Lambertian reflector in the long wavelength
infrared spectrum, while flowers of sulfur are not
sufficiently durable to survive handling. Sintered
bronze only approximates a Lambertian reflector because
of surface irregularities which scatter light in a non-
uniform manner. This has led researchers to use a fine
grade (600 grit) sandpaper which is coated with gold to
approximate a Lambertian reflector. Problems with using
gold-plated sandpaper are that, like sintered bronze,
gold-plated sandpaper has irregularities which scatter
light in a non-uniform manner. Further, gold-plated
sandpaper is not sufficiently durable and degrades over
time. Additionally, gold-plated sandpaper is not
consistent enough between different sheets to be used
as a reference standard. Still further, it was
discovered that gold-plated sandpaper is a fairly good
approximation of a Lambertian surface when the anqle of
4-
5
incidence of the beam of light is small, but not when
the angle of incidence is as large as 60 ° . For more
information on the BRDF of gold-plated sandpaper, see
"Applied Optics," Vol. 20, No. 15, August I, 1981,
Bi-directional Reflectance!Distribution Function of
I0
Gold-plated Sandpape% by T.W. Stuhlinger, E.L.
Dereniak, and F.O. Bartell. " _
Accordingly, it is an object of this invention to
provide a BRDF reference standard which is durable and
which more closely approximates a Lambertian reflector
than any of the substances priorly used.
15
Summary of the Invention
In accordance with this invention, a Lambertian
reference standard for uniformly scattering light is
constructed having a plate with a planar surface, with
a layer of similarly sized spheres disposed thereupon.
20
25
30
Brief Description of the Drawings
Fig. 1 is a sectional view of a Lambertian
reflector of the present invention.
Fig. 2 is a sectional view of a Lambertian
transmitter of the present invention.
Fig. 3 is a diagrammatic illustration of a light
scattering apparatus.
Fig. 4 is a diagrammatic illustration of a
Cassegrainian reflecting telescope.
Fig. 5 is a diagrammatic view of the light
scattering apparatus as generally used to evaluate
light absorbing coatings.
Fig. 6 is a diagrammatic view of a refracting
telescope.
Fig. 7 is a diagrammatic view of the light
scattering apparatus as generally used to evaluate
light transmissive coatings.
35
Description of the Preferred Embodiment
A reference standard for bi-directional reflectance
-5-
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and transmittance distribution function (BRDF and BTDF)
measurements consists of similarly sized monodispersed
spheres disposed on a planar surface and appropriately
treated to behave either as a Lambertian reflector or a
Lambertian transmitter. , '
Referring to Fig. i, a BRDF.re_erence standard i0
is constructed as shown of a _late 12 having a planar
surface 14. Surface 14 is evenly coated with a layer
16 of bonding agent, such as an epoxy resin, and into
this layer 16 is pressed an evenly packed layer of
like-sized monodisperse spheres 18. Spheres 18 are
constructed of material such as glass or latex and,
depending on the wavelength of light to be studied, can
range in size from 0.I to 500 microns between different
standards. Spheres 18 are coated, as by vapor
deposition, with a highly reflective substance, such as
gold or silver, to minimize light absorption by spheres
18.
When an incident beam of light 20 is directed onto
reference standard I0 (Fig. I), individual beams of
light are reflected in directions depending on where
the light strikes a discrete coated sphere 18. Thus,
light impinging at a point on a sphere which is closest
to a light source is generally reflected back toward the
source, while light striking sides of a sphere 18 may be
directed almost 90 ° with respect to beam of light 20.
This evenly distributes the beam of light 360 ° around
the point where the beam impinges on the sample and from
0 ° to 90 ° with respect to the beam. Light which is
thusly diffused is used as a baseline for comparing
reflective characteristics of surfaces to be evaluated
thereto.
In the instance where a reference standard is to
be used in bi-directional transmission distribution
function (BTDF) measurements (Fig. 2), a standard 22 is
constructed having glass spheres 24 constructed with a
slightly roughened surface. This is achieved as by acid
etching, with spheres 24 being evenly pressed in an even
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35
layer into a layer 26 of optical cement selected to
have a refractive index similar to that of spheres 24
and a transparent glass plate 28. Optical cement is
used to reduce refraction of light is it passes first
through glass plate, 28, th4n through layer 26 of optical
cement, and finally through ispheres-_24. "_
In this case, the incident beam of light is
directed onto side 30 of standard 22, with the light
passing through transparent plate 28 as described and
into spheres 24. Because of the roughened surface on
spheres 24, the individual beams of light are then
reflected within discrete spheres until encountering an
irregularity which is generally perpendicular to the
direction of the reflected beam. When this occurs, the
beam exits the sphere. Very fine irregularities on
surfaces of spheres 24 are more associated with
Lambertian surfaces, while coarse irregularities tend
to scatter light in a non-uniform manner. As with the
aforementioned standard 10, light passing through
standard 22 is evenly diffused 360 ° around the point
where beam 20 passes therethrough and from 0 ° to 90 °
with respect to beam 20. This also establishes a
baseline against which light transmissive coatings may
be compared.
In use, and referring to Fig. 3, a light scattering
apparatus 32 is diagrammatically shown which is
typically used to measure scattered light. A sample 34
having a surface 36 to be evaluated is mounted on a
rotating turntable 40, with this turntable in turn
being mounted to an angularly positionable gimbal 42.
Turntable 40 is rotated at a predetermined speed to
average out effects of speckle. A pair of detector arms
44 and 46 are mounted to be rotated about gimbal 42 and
are used to mount photovoltaic detectors 48 thereupon.
These photovoltaic detectors convert light reflected
from light source 49 to voltage levels, with these
voltage levels obtained from the sample being compared
to vo]taoe levels obt_ine_ hv a rpfer_nc_ _n_
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similarly positioned on turntable 40.
One illustration of this procedure is shown in
Fig. 4 and, by way of example, diagrammatically shows
a Cassegrainian reflecting telescope 50. In this type
of telescope, a concave przmary mirror 52 having a
central viewing aperture 54 is mounted at one end 56
of a housing 58. A secondary°convex mirror 60 is
mounted to reflect light from primary mirror 52 through
aperture 54. As the clarity and resolution of the
viewed image is largely dependent on the precision of
mirrors 52 and 60, and to the extent that unwanted
light 70 can be prevented from reaching mirrors 52
60, it is crucial that factors such as these be
accurately evaluated. In the instance where a light
absorbingcoating 62 on interior wall 64 of telescope
housing 58 is to be evaluated, a sample 66 of coating
is deposited on a planar surface and mounted on
turntable 40 of light scattering apparatus 32. An
incident beam of light 68 from light source 49 is
directed onto sampie 66 in a similar angular relation
to the incident unwanted light 70 (Fig. 4) entering
telescope 50 and impinging on coating 62, with
detector 48 being positioned where aperture 54 would
be. The voltage level is recorded, and for purposes
of illustration, it is assumed that this voltage
level is 0°05 my. Next, reference standard I0 is
mounted on turntable 40, and beam 68 is directed
thereupon in the same angular relation as the unwanted
light 70 in telescope 50. Detector 48 is again
positioned where aperture 54 would be, and for
purposes of illustration, it is assumed that it
records 0.50 my. In accordance with the formula
earlier set forth:
BRDFuNK = BRDFREF (VuNK)/(VRE F)
_GI_AI: PAGEIS
©? pC,OR .,_U.<!,PFY
or
BRDFuN K = 0.318 (0.05/50).
It is seen that the light absorbing sampie 66 has a
BRDF value of 0.000318, mea_ing_'that_sample 66 is a
5 good medium for absorbing unwanted reflected light.
When apparatus 32 is to be used to evaluate BTDF
(bi-directional transmission distribution function) of
a transparent sample, such as when compound lenses are
coated with a light transmitting coating, such as zinc
I0 selenide, operation is as follows. By way of example,
Fig_ 6 diagrammatically illustrates a refractive
telescope 71. Telescope 71 is constructed having
compound lenses 72 and 74, which refract light entering
objective lens 72 to focus it on eyepiece lens 74. In
15 this case, the clarity of the viewed image is dependent
on the quality of lenses 72 and 74 and the degree they
accurately refract the available light to the viewer.
Obviously, it is crucial that the coatings on lenses
72 and 74, such as the aforementioned zinc selenide,
20 accurately transmits this light with as little
scattering as possible.
To evaluate lens coatings of the refractive
telescope shown in Fig. 6, a transparent sample plate
76 (Fig. 7) is constructed having the light
25 transmissive coating 78 deposited on a surface 80,
which is furthest away from source 49 of incident
light 68. This sample is mounted over a window 38 in
turntable 40. Detector 48 is positioned on arm 46, _
which in turn is positioned to allow detector 48 to
30 measure light scattered in planes other than the focal
plane of incident light from light source 49. This
allows researchers to determine the degree of light
scattered by coating 78 by comparing the voltage levels
produced by sample 76 to the voltage levels obtained
35 from the Lambertian refractor priorly described. As
an example, it is assumed that sample 76 produces a
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voltage level of 0.02 mv., while, as stated, reference
standard 22 (Fig. 2) produces a voltage level of 50 my.
By using the formula:
which becomes
BTDFuNK ..= BTDFRE F (VuNK/VRE F)
BTDFuN K = 0.318 (0.02/50)
meaning that the BTDFuN K is 0.0001272. Thus, it is
seen that coating 78 is a good light transmitting
coating which results in little scattering.
In addition to the aforementioned uses of the
Lambertian reflector I0 and refractor 22 in evaluating
surfaces, reflector I0 and refractor 22 may be used to
calibrate BRDF/BTDF facilities. This would be done by
simply mounting reflective reference standard I0 or
transmitting reference standard 22 in window 38 of
turntable 40 (Fig. 3) and appropriately positioning one
of detectors 48 at various points of interest around
the reference standard. Detector 48 may then be
calibrated to provide a voltage level which is
consistent with similar facilities elsewhere, thus
bringing all such facilities into an aligned relation.
From the foregoing, it is apparent that the
applicant has provided a Lambertian reflector and
Lambertian refractor to be used as a reference standard
for comparative studies of materials to be evaluated
and which can be used as a Standard for calibrating
BRDF/BTDF facilities. Further, this standard is both
durable and long-lived and can be constructed with
little variation between discrete standards.
A REFERENCESTANDARDFOR BI-DIRECTIONAL REFLECTION
DISTRIBUTION FUNCTION AND BI-DIRECTIONAL TRANSMISSION
DISTRIBUTION FUNCTION MEASUREMENTS
I0
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Abstract of the Disclosure
A Lambertian r gference standard (i0) for uniformly
scattering a beam of light {s constructed of a plate
(12) having a planar surface (14) with a layer (16) of
glue disposed on the surface (14). An evenly packed
layer of monodisperse spheres (18) is set in the layer
(16), and when the standard (i0) is used for
hi-directional (BRDF) measurements, the spheres (18)
are coated with a layer of highly reflective substance,
such as gold or silver. When the standard (22) is used
for hi-directional transmittance distribution function
(BTDF) measurements, the spheres (24) are of a
transparent material and are provided with a roughened
surface, as by acid etching. In this case, the layer
(26) of glue is an optical cement, and the plate (28)
is of glass, with the spheres (24), the layer (26), and
the plate (28) all possessing a similar refractive
index.


A reference standard for bidirectional reflection distribution function and bidirectional transmission distribution function measurement

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