ASTM E2387-05(2011)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: E2387 − 05 (Reapproved 2011)
Standard Practice for
Goniometric Optical Scatter Measurements
This standard is issued under the fixed designation E2387; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope an appropriate sample coordinate system to specify the mea-
surement location on the sample surface and appropriate beam
1.1 This practice describes procedures for determining the
properties for samples that are not flat.
amount and angular distribution of optical scatter from a
surface. In particular it focuses on measurement of the bidi-
1.8 This practice does not provide a method for ascribing
rectional scattering distribution function (BSDF). BSDF is a
the measured BSDF to any scattering mechanism or source.
convenient and well accepted means of expressing optical
1.9 This practice does not provide a method to extrapolate
scatter levels for many purposes. It is often referred to as the
data from one wavelength, scattering geometry, sample
bidirectional reflectance distribution function (BRDF) when
location, or polarization to any other wavelength, scattering
considering reflective scatter or the bidirectional transmittance
distribution function (BTDF) when considering transmissive geometry,samplelocation,orpolarization.Theusermustmake
scatter. measurements at the wavelengths, scattering geometries,
sample locations, and polarizations that are of interest to his or
1.2 The BSDF is a fundamental description of the appear-
her application.
ance of a sample, and many other appearance attributes (such
as gloss, haze, and color) can be represented in terms of
1.10 Any parameter can be varied in a measurement se-
integrals of the BSDF over specific geometric and spectral
quence.Parametersthatremainconstantduringameasurement
conditions.
sequence are reported as either header information in the
1.3 This practice also presents alternative ways of present- tabulated data set or in an associated document.
ing angle-resolved optical scatter results, including directional
1.11 Theapparatusandmeasurementprocedurearegeneric,
reflectance factor, directional transmittance factor, and differ-
sothatspecificinstrumentsareneitherexcludednorimpliedin
ential scattering function.
the use of this practice.
1.4 ThispracticeappliestoBSDFmeasurementsonopaque,
1.12 For measurements performed for the semiconductor
translucent, or transparent samples.
industry, the operator should consult Practice SEMI ME 1392.
1.5 The wavelengths for which this practice applies include
the ultraviolet, visible, and infrared regions. Difficulty in 1.13 This standard does not purport to address all of the
obtainingappropriatesources,detectors,andlowscatteroptics
safety concerns, if any, associated with its use. It is the
complicates its practical application at wavelengths less than responsibility of the user of this standard to establish appro-
about 0.2 µm (200 nm). Diffraction effects start to become
priate safety and health practices and determine the applica-
important for wavelengths greater than 15 µm (15000 nm),
bility of regulatory limitations prior to use.
which complicate its practical application at longer wave-
lengths. Measurements pertaining to visual appearance are
2. Referenced Documents
restricted to the visible wavelength region.
2.1 ASTM Standards:
1.6 This practice does not apply to materials exhibiting
E284Terminology of Appearance
significant fluorescence.
E308PracticeforComputingtheColorsofObjectsbyUsing
1.7 This practice applies to flat or curved samples of
the CIE System
arbitraryshape.However,onlyaflatsampleisaddressedinthe
E1331Test Method for Reflectance Factor and Color by
discussionandexamples.Itistheuser’sresponsibilitytodefine
Spectrophotometry Using Hemispherical Geometry
This practice is under the jurisdiction ofASTM Committee E12 on Color and
Appearance and is the direct responsibility of Subcommittee E12.03 on Geometry. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
CurrenteditionapprovedJuly1,2011.PublishedJuly2011.Originallyapproved contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
in 2005. Last previous edition approved in 2005 as E2387–05. DOI: 10.1520/ Standards volume information, refer to the standard’s Document Summary page on
E2387-05R11. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2387 − 05 (2011)
FIG. 1 Angle Conversions
2.2 ISO Standard: α 5θ 2θ (1)
i s
ISO 13696Optics and Optical Instruments—Test Methods
A more general expression for the aspecular angle, valid
for Radiation Scattered by Optical Components
for all incident and scattering directions, is given by:
2.3 Semiconductor Equipment and Materials International
α 5 cos @ cosθ cosθ 2 sinθ sinθ cos~φ 2φ !# (2)
i s i s s i
(SEMI) Standard:
ME 1392Practice forAngle Resolved Optical Scatter Mea-
Since the arccosine of a value is always positive, the sign
surements on Specular and Diffuse Surfaces
must be separately chosen so that it is positive when the
scattering direction is behind the specular direction and
3. Terminology
negative when the scattering direction is forward of the
3.1 Definitions:
specular direction. The convention adopted here is that it is
3.1.1 Definitionsoftermsnotincludedherewillbefoundin
positive if:
Terminology E284.
sinθ cos φ 2φ . sinθ (3)
~ !
s s i i
3.2 Definitions of Terms Specific to This Standard:
and negative otherwise. Fig. 2 illustrates the regions of posi-
3.2.1 absolute normalization method, n—a method of per-
tive and negative aspecular angles.
forming a scattering measurement in which the incident power
3.2.4 beam coordinate system, n—a coordinate system par-
is measured directly with the same receiver system as is used
allel to the sample coordinate system, whose origin is the
for the scattering measurement.
geometric center of the sampling region, used to define the
3.2.2 angle of incidence, θi, n—polar angle of the source
angle of incidence, the scatter angle, the incident azimuth
direction, given by the angle between the source direction and
angle, and the scatter azimuth angle.
the surface normal; see Fig. 1.
3.2.2.1 Discussion—See Discussion of scatter polar angle.
3.2.5 bidirectional reflectance distribution function, BRDF,
3.2.3 aspecular angle, α,n—the angle between the specular n—the sample BSDF measured in a reflective geometry.
directionandthescatterdirection,thesignofwhichispositive
3.2.6 bidirectional scattering distribution function BSDF,
for backward scattering and negative for forward scattering.
n—the sample radiance L divided by the sample irradiance E
e e
3.2.3.1 Discussion—For scatter directions in the plane of
for a uniformly-illuminated and uniform sample:
incidence (with φ =0 and φi=180°), the aspecular angle is
s
L
given by:
e
BSDF 5 @sr # (4)
E
e
3.2.6.1 Discussion—BSDF is a differential function depen-
Available from International Organization for Standardization (ISO), 1, ch. de dent on the wavelength, incident direction, scatter direction,
la Voie-Creuse, Case postale 56, CH-1211, Geneva 20, Switzerland, http://
andpolarizationstatesoftheincidentandscatteredfluxes.The
www.iso.ch.
4 BSDFisequivalenttothefractionoftheincidentfluxscattered
Available from Semiconductor Equipment and Materials International (SEMI),
3081 Zanker Rd., San Jose, CA 95134, http://www.semi.org. per unit projected solid angle:
E2387 − 05 (2011)
FIG. 2 Definition of the Sign of the Aspecular Angle
P CIE 1931 Standard Colorimetric Observer), and the color
lim s
BSDF 5 sr (5)
@ #
Ω→0 PΩ cosθ system(forexample,CIELAB)mustbespecifiedandincluded
i s
with any data.
The BSDF of a lambertian surface is independent of scat-
3.2.10 differential scattering function, DSF, n—the fraction
ter direction. The BSDF of a specularly reflecting surface
of incident light scattered per unit solid angle, given by:
has a sharp peak in the specular direction. If a surface scat-
ters non-uniformly from one position to another then a series
P
lim s
DSF 5 5BSDFcosθ (6)
of measurements over the sample surface must be averaged s
Ω→0 PΩ
i
to obtain suitable statistical uncertainty.
3.2.11 directional transmittance factor, T,n—the ratio of
d
3.2.7 bidirectional transmittance distribution function,
the BTDF to that for a perfectly transmitting diffuser (defined
BTDF, n—the sample BSDF measured in a transmissive
as 1/π), given by:
geometry.
T 5π BTDF (7)
d
3.2.8 BSDF instrument signature, n—the mean scatter level
3.2.12 directional reflectance factor, R,n—the ratio of the
d
detected when there is no sample scatter present expressed as
BRDF to that for a perfect reflecting diffuser (defined as 1/π),
BSDF.
given by:
3.2.8.1 Discussion—The BSDF instrument signature is
R 5π BRDF (8)
given by the DSF instrument signature divided by cosθ . The
d
s
BSDF instrument signature depends upon scattering angle.
3.2.13 DSF instrument signature, n—the mean scatter level
Because of the factor cosθ , if it is not below the noise
s detected when there is no sample scatter present expressed as
equivalent BSDF, it diverges to infinity at θ =90°.
s a DSF.
3.2.9 colorimetric BSDF, n—the angle-resolved multi- 3.2.13.1 Discussion—The DSF instrument signature pro-
parameter color specification function which is scaled so that vides an equivalent DSF for a perfectly reflecting specular
the luminance factor Y corresponds to the photometric BSDF. surface as measured by the instrument. The instrument signa-
3.2.9.1 Discussion—The colorimetric BSDF consists of ture includes contributions from the size of the incident light
threecolorcoordinatesasafunctionofthescatteringgeometry. beam at the receiver aperture, the diffraction of that beam, and
Oneofcolorcoordinatescorrespondstotheluminancefactor Y stray scatter from instrument components. For high-sensitivity
and is usually expressed as the ratio of the luminance of a systems (those whose NEDSF strives for levels below about
-6 -1
specimen to that of a perfect diffuser. For the colorimetric 10 sr ), the limitation on instrument signature is normally
BSDF, this color coordinate is replaced by the photometric Rayleigh scatter from molecules within the volume of the
BSDF. The specific illuminant (for example, CIE Standard incident light beam that is sampled by the receiver field of
Illuminant D65), set of color matching functions (for example, view. The instrument signature can be measured by removing
E2387 − 05 (2011)
thesampleandscanningthereceiverthroughtheincidentbeam 3.2.19 photometric BSDF, n—thesampleluminancedivided
in a transmission configuration. The signature can also be by the sample illuminance for a uniformly-illuminated and
measured by scanning a reference sample, whose scatter is uniform sample.
expected to be significantly lower than that of the specimen
3.2.20 plane of incidence, PLIN, n—the plane containing
being studied, in which case the signature is adjusted by
the sample normal and central ray of the incident flux.
dividing by the reference sample reflectance. It is necessary to
3.2.21 relative normalization method, n—a method for per-
furnish the instrument signature when reporting BSDF data so
forming a scattering measurement in which a diffusely reflect-
that the user can decide at what scatter direction the measured
ing sample of known BRDF is used as a reference.
sample BSDF or DSF is lost in the signature. Preferably the
signature is at least a few decades below the sample data and
3.2.22 receiver, n—a system that generally contains
can be ignored. The DSF instrument signature depends upon
apertures, filters, focusing optics, and a detector element that
the receiver solid angle and the receiver field of view.
gathers the scatter flux over a known solid angle and provides
a measured signal.
3.2.14 incident azimuth angle,φ,n—the angle from the XB
i
axis to the projection of the source direction onto the X-Y
3.2.23 receiver solid angle,Ω,n—thesolidanglesubtended
plane;whennotspecified,thisangleisassumedtobe180°;see
by the receiver aperture stop from the center of the sampling
Fig. 1.
aperture.
3.2.14.1 Discussion—See Discussion for scatter polar
3.2.24 sample coordinate system, n—a coordinate system
angle.
fixed to the sample and used to specify position on the sample
3.2.15 incident direction, n—the central ray of the incident
surface.
flux specified by θ and φ in the beam coordinate system,
i i
3.2.24.1 Discussion—The sample coordinate system (X, Y,
pointing from the illumination to the sample.
Z) is application and sample specific. The cartesian coordinate
3.2.15.1 Discussion—The incident direction is the opposite
system shown in Fig. 3 is recommended for flat samples. The
of the source direction.
origin is at the geometric center of the sample face with the Z
3.2.16 incident power, P,n—theradiantfluxincidentonthe
i axis normal to the sample. A fiducial mark must be shown at
sample.
the periphery of the sample; it is most conveniently placed
3.2.16.1 Discussion—For relative BSDF measurements, the
along either the X or Y axes. If the sample fiducial mark is not
incident power is not measured directly. For absolute BSDF
an X axis mark, the intended value should be indicated on the
measurements it is important to verify the linearity, and if
sample.Theincidentandscatterdirectionsaremeasuredinthe
necessary correct for any nonlinearity, of the detector system
beam coordinate system (XB, YB, ZB). The Z and ZB axes are
over the range from the incident power level down to the
always the local normal to the sample face.
scatter level which may be as many as 13 to 15 orders of
3.2.25 sample irradiance, E,n—theradiantfluxincidenton
e
magnitude lower. If the same detector is used to measure the
the sample surface per unit area.
incidentpowerandthescatteredflux,thenitisnotnecessaryto
3.2.25.1 Discussion—In practice, E is an average calcu-
e
correctforthedetectorresponsivity;otherwise,thesignalfrom
lated from the incident power, P, divided by the illuminated
i
each detector must be normalized by its responsivity. In all
area, A.Theincidentfluxshouldarrivefromasingledirection;
cases, the absolute power is not needed, so long as the unit of
however, the acceptable degree of collimation or amount of
power is the same as that used to measure the scattered power
convergence is application specific and should be reported.
P .
s
3.2.26 sample radiance, L,n—adifferentialquantitythatis
3.2.17 noise equivalent BSDF, NEBSDF, n
...