ASTM E1767-11(2022)

Standard Practice for Specifying the Geometries of Observation and Measurement to Characterize the Appearance of Materials

SIGNIFICANCE AND USE
5.1 This practice is for the use of manufacturers and users of equipment for visual appraisal or measurement of appearance, those writing standards related to such equipment, and others who wish to specify precisely conditions of viewing or measuring attributes of appearance. The use of this practice makes such specifications concise and unambiguous. The functional notation facilitates direct comparisons of the geometric specifications of viewing situations and measuring instruments.
SCOPE
1.1 This practice describes the geometry of illuminating and viewing specimens and the corresponding geometry of optical measurements to characterize the appearance of materials. It establishes terms, symbols, a coordinate system, and functional notation to describe the geometric orientation of a specimen, the geometry of the illumination (or optical irradiation) of a specimen, and the geometry of collection of flux reflected or transmitted by the specimen, by a measurement standard, or by the open sampling aperture.  
1.2 Optical measurements to characterize the appearance of retroreflective materials are of such a special nature that they are treated in other ASTM standards and are excluded from the scope of this practice.  
1.3 The measurement of transmitted or reflected light from areas less than 0.5 mm in diameter may be affected by optical coherence, so measurements on such small areas are excluded from consideration in this practice, although the basic concepts described in this practice have been adopted in that field of measurement.  
1.4 The specification of a method of measuring the reflecting or transmitting properties of specimens, for the purpose of characterizing appearance, is incomplete without a full description of the spectral nature of the system, but spectral conditions are not within the scope of this practice. The use of functional notation to specify spectral conditions is described in ISO 5/1.  
1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.6 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

General Information

• Status: Published
• Publication Date: 30-Sep-2022
• ICS: 17.180.30 - Optical measuring instruments
• Technical Committee: E12 - Color and Appearance
• Drafting Committee: E12.03 - Geometry

Relations

• Refers: ASTM E284-13b - Standard Terminology of Appearance
• Effective Date: 01-Nov-2013
• Refers: ASTM E284-13a - Standard Terminology of Appearance
• Effective Date: 01-Jun-2013
• Refers: ASTM E284-13 - Standard Terminology of Appearance
• Effective Date: 01-Jan-2013
• Refers: ASTM E284-12 - Standard Terminology of Appearance
• Effective Date: 01-Jul-2012
• Refers: ASTM E284-09a - Standard Terminology of Appearance
• Effective Date: 01-Jun-2009
• Refers: ASTM E284-09 - Standard Terminology of Appearance
• Effective Date: 01-Jan-2009
• Refers: ASTM E284-08 - Standard Terminology of Appearance
• Effective Date: 01-Aug-2008
• Refers: ASTM E284-07 - Standard Terminology of Appearance
• Effective Date: 15-Jul-2007
• Refers: ASTM E284-06b - Standard Terminology of Appearance
• Effective Date: 01-Dec-2006
• Refers: ASTM E284-06a - Standard Terminology of Appearance
• Effective Date: 15-Jul-2006
• Refers: ASTM E284-06 - Standard Terminology of Appearance
• Effective Date: 15-Feb-2006
• Refers: ASTM E284-05a - Standard Terminology of Appearance
• Effective Date: 15-Jun-2005
• Refers: ASTM E284-05 - Standard Terminology of Appearance
• Effective Date: 01-Feb-2005
• Refers: ASTM E284-04 - Standard Terminology of Appearance
• Effective Date: 01-Jun-2004
• Refers: ASTM E284-03a - Standard Terminology of Appearance
• Effective Date: 10-Jul-2003

Overview

ASTM E1767-11(2022), titled Standard Practice for Specifying the Geometries of Observation and Measurement to Characterize the Appearance of Materials, establishes standardized methods to define and communicate the geometric conditions under which the visual and instrumental assessment of material appearance takes place. This standard, maintained by ASTM International, is crucial for manufacturers, equipment users, and standard developers to precisely specify the observation and measurement conditions for material appearance attributes like color and gloss.

The standard provides concise, unambiguous notation for describing the geometry involved in illuminating and viewing specimens. It introduces a unified coordinate system, symbols, and functional notation to communicate the setup of light sources and detectors relative to a material sample. This approach ensures that appearance measurements are both consistent and directly comparable across different laboratory setups and industries.

Key Topics

• Geometric Specification: Defines the orientation of the specimen, illumination angles, and viewing/detection angles using a standardized rectangular coordinate system and associated notation.
• Functional Notation: Introduces mathematical functional notation (e.g., R(G:g)) to precisely define the relationship between influx (illumination) and efflux (detection) geometries, promoting concise specification of measurement conditions.
• Terminology and Symbols: Establishes a set of terms (such as efflux, influx, specular direction, anormal angle) and symbols for describing the geometric configuration in both transmission and reflection measurements.
• Types of Distributions: Details the description of influx and efflux distributions, including conical, annular, and pyramidal geometries commonly used in appearance measurement instruments.
• Sampling Aperture: Specifies how the region of measurement (sampling aperture) should be defined and considered when characterizing specimen appearance, especially for textured or non-uniform samples.
• Tolerances and Uniformity: Addresses the need for tolerances in geometric setup to ensure measurement reliability, such as the angular spread and uniformity of light and detector response.
• Reversibility Principle: Recognizes the reversibility of geometry, stating that swapping the positions of illuminator and detector in many cases will yield comparable results.

Applications

ASTM E1767-11(2022) is widely applicable in industries where precise quantification and communication of material appearance is essential, including:

• Coatings, Paints, and Plastics: Ensures standardized assessment of color, gloss, and other visual properties for quality control and R&D.
• Textiles and Fabrics: Enables consistent evaluations across batches or when comparing materials with unique surface textures or finishes.
• Automotive and Consumer Electronics: Facilitates agreement between suppliers and manufacturers on the visual standards of components and finishes.
• Optical Instrumentation Development: Guides the design and calibration of appearance measurement instruments (e.g., spectrophotometers, glossmeters) so that results are comparable across different brands and models.
• Standardization and Certification: Assists organizations in developing appearance-related specifications that are clear, concise, and compatible with international requirements.

Note: Retroreflective materials and optical measurements on areas smaller than 0.5 mm in diameter are not covered by this standard; other ASTM standards apply for those specialized situations.

Related Standards

For more comprehensive or specific applications, ASTM E1767-11(2022) references and should be used in conjunction with:

• ASTM E284:Terminology of Appearance - Provides foundational definitions for terms related to material appearance.
• ISO 5/1:Photography-Density Measurements-Part 1: Terms, Symbols, and Notations - Details functional notation principles for optical measurement, especially regarding spectral conditions.
• ANSI PH2.36: Terms, symbols, and notations for optical transmission and reflection measurements.
• Additional ASTM standards developed under Committee E12 on Color and Appearance, particularly for spectral or retroreflective material assessment.

By implementing ASTM E1767-11(2022), organizations achieve greater clarity and comparability in the specification, measurement, and communication of materials’ visual attributes, supporting high standards in product quality and industry collaboration.

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: E1767 − 11 (Reapproved 2022)
Standard Practice for
Specifying the Geometries of Observation and Measurement
to Characterize the Appearance of Materials
This standard is issued under the fixed designation E1767; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
INTRODUCTION
The appearance of objects depends on how they are illuminated and viewed. When measurements
are made to characterize appearance attributes such as color or gloss, the measured values depend on
the geometry of the illumination and the instrumentation receiving light from the specimen. This
practice for specifying the geometry in such applications is largely based on an international standard
ISO 5/1, dealing with the precise measurement of optical density in photographic science, based on
2,3
an earlier American National Standard.
1. Scope are not within the scope of this practice. The use of functional
notation to specify spectral conditions is described in ISO 5/1.
1.1 This practice describes the geometry of illuminating and
1.5 This standard does not purport to address all of the
viewing specimens and the corresponding geometry of optical
safety concerns, if any, associated with its use. It is the
measurements to characterize the appearance of materials. It
responsibility of the user of this standard to establish appro-
establishes terms, symbols, a coordinate system, and functional
priate safety, health, and environmental practices and deter-
notation to describe the geometric orientation of a specimen,
mine the applicability of regulatory limitations prior to use.
the geometry of the illumination (or optical irradiation) of a
1.6 This international standard was developed in accor-
specimen, and the geometry of collection of flux reflected or
dance with internationally recognized principles on standard-
transmitted by the specimen, by a measurement standard, or by
ization established in the Decision on Principles for the
the open sampling aperture.
Development of International Standards, Guides and Recom-
1.2 Optical measurements to characterize the appearance of
mendations issued by the World Trade Organization Technical
retroreflective materials are of such a special nature that they
Barriers to Trade (TBT) Committee.
are treated in otherASTM standards and are excluded from the
scope of this practice.
2. Referenced Documents
1.3 The measurement of transmitted or reflected light from
2.1 ASTM Standards:
areas less than 0.5 mm in diameter may be affected by optical
E284 Terminology of Appearance
coherence, so measurements on such small areas are excluded
2.2 Other Standard:
from consideration in this practice, although the basic concepts
ISO 5/1 Photography—Density Measurements—Part 1:
described in this practice have been adopted in that field of
Terms, Symbols and Notations
measurement.
1.4 The specification of a method of measuring the reflect-
3. Terminology
ing or transmitting properties of specimens, for the purpose of
3.1 Definitions:
characterizingappearance,isincompletewithoutafulldescrip-
3.1.1 The terminology used in this practice is in accordance
tion of the spectral nature of the system, but spectral conditions
with Terminology E284.
3.2 Definitions of Terms Specific to This Standard:
This practice is under the jurisdiction of ASTM Committee E12 on Color and
Appearance and is the direct responsibility of Subcommittee E12.03 on Geometry.
Current edition approved Oct. 1, 2022. Published November 2022. Originally
approved in 1995. Last previous edition approved in 2017 as E1767 – 11 (2017). For referenced ASTM standards, visit the ASTM website, www.astm.org, or
DOI: 10.1520/E1767-11R22. contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
ISO1/5 Photography — Density Measurements — Part 1: Terms, symbols, and Standards volume information, refer to the standard’s Document Summary page on
notations. the ASTM website.
3 5
ANSIPH2.36–1974AmericanNationalStandardsterms,symbols,andnotation Available from American National Standards Institute (ANSI), 25 W. 43rd St.,
for optical transmission and reflection measurements. 4th Floor, New York, NY 10036, http://www.ansi.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E1767 − 11 (2022)
3.2.1 anormal angle, n—an angle measured from the 3.2.16 uniplanar geometry, n—geometry in which the re-
normal, toward the reference plane, to the central axis of a ceiver is in the plane of incidence.
distribution, which may be an angular distribution of flux in an
3.3 Symbols:
incident beam or distribution of sensitivity of a receiver.
3.2.2 aspecular angle, n—the angle subtended at the origin
de = general symbol for diffuse geometry with specular
by the specular axis and the axis of the receiver, the positive
component excluded.
direction being away from the specular axis.
di = general symbol for diffuse geometry with specular
3.2.3 aspecular azimuthal angle, n—the angle subtended, at
component included.
the specular axis in a plane normal to the specular axis, by the
E = identifies the direction of the axis of an efflux
projection of the axis of the receiver and the projection of the
distribution on a diagram.
x-axis on that plane, measured from the projection of the x-axis
g = general symbol, in functional notation, for efflux
in a right-handed sense with respect to the specular axis.
geometry.
3.2.4 efflux, n—radiant flux reflected by a specimen or G = general symbol, in functional notation, for influx
geometry.
reflection standard, in the case of reflection observations or
i = subscript for incident.
measurements, or transmitted by a specimen or open sampling
I = identifies the direction of the axis of an influx
aperture, in the case of transmission observations or
distribution on a diagram.
measurements, in the direction of the receiver.
m = subscript for half cone angle subtended by the
3.2.5 efflux, adj—associated with the radiant flux reflected
entrance pupil of a test photometer.
by a specimen or reflection standard, in the case of reflection
M = optical modulation.
observations or measurements, or transmitted by a specimen or
n = subscript for half cone angle subtended by a test
open sampling aperture, in the case of transmission observa-
source.
tions or measurements, in the direction of the receiver.
N = identifies the direction of the normal to the reference
3.2.6 efflux region, n—region in the reference plane from
plane on a diagram.
o = point of origin of a rectangular coordinate system, in
which flux is sensed by the observer.
the reference plane, at the center or centroid of the
3.2.7 influx, n—radiant flux received from the illuminator at
sampling aperture.
a specimen, a reflection standard, or open sampling aperture.
r = subscript for reflected.
3.2.8 influx, adj—associated with radiant flux received from
S = identifies the specular direction on a diagram.
the illuminator at a specimen, a reflection standard, or open
t = subscript for transmitted.
sampling aperture.
x = distance from the origin, along the x-axis, in the
reference plane, passing through point o.
3.2.9 influx region, n—region in the reference plane on
y = distance from the origin, along the y-axis, in the
which flux is incident.
reference plane, passing through point o, and normal
3.2.10 optical modulation, n—a ratio indicating the magni-
to the x-axis.
tude of the propagation by a specimen of radiant flux from a
z = distance from the origin, along the z-axis, normal to
specified illuminator or irradiator to a specified receiver, a
the reference plane, passing through point o, and
general term for reflectance, transmittance, reflectance factor,
having its positive direction in the direction of the
transmittance factor, or radiance factor.
vector component of incident flux normal to the
3.2.11 plane of incidence, n—the plane containing the axis
reference plane.
of the incident beam and the normal to the reference plane.
α = aspecular angle.
3.2.11.1 Discussion—This plane is not defined if the axis of
β = aspecular azimuthal angle.
the incident beam is normal to the reference plane. δ = in a pyramidal distribution, the half-angle measured
in the direction normal to the plane of incidence.
3.2.12 reference plane, n—the plane in which the surface of
ε = in a pyramidal distribution, the half-angle measured
a plane specimen is placed for observation or measurement, or
in the plane of incidence.
in the case of a nonplanar specimen, the plane with respect to
η = azimuthal angle, measured in the reference plane,
which the measurement is made.
from the positive x-axis, in the direction of the
3.2.13 sampling aperture, n—the region in the reference
positive y-axis.
plane on which a measurement is made, the intersection of the
θ = anormal angle.
influx region and the efflux region.
κ = half cone angle of a conical flux distribution.
Φ = radiant flux.
3.2.14 specular axis, n—the ray resulting from specular
45°a = general symbol for 45° annular geometry.
reflection at an ideal plane mirror in the reference plane, of the
45°c = general symbol for 45° circumferential geometry.
ray at the geometric axis of the incident beam.
3.2.14.1 Discussion—This term is applied to an incident
4. Summary of Practice
beam subtending a small angle at the origin, not to diffuse or
annular illuminators.
4.1 This practice provides a method of specifying the
3.2.15 specular direction, n—the direction of the specular geometry of illuminating and viewing a material or the
axis, the positive direction being away from the origin. geometry of instrumentation for measuring an attribute of
E1767 − 11 (2022)
appearance. In general, for measured values to correlate well to the following rules, intended to place the positive x-axis in
with appearance, the geometric conditions of measurement the azimuthal direction for which the product of illumination
must simulate the conditions of viewing. and receiver sensitivity is a minimum.
6.2.1 For an integrating-sphere instrument with diffuse
5. Significance and Use
illumination, the positive x-axis is directed toward the projec-
5.1 Thispracticeisfortheuseofmanufacturersandusersof tion of the center of the exit port on the reference plane.
equipment for visual appraisal or measurement of appearance, 6.2.2 For an integrating-sphere instrument with diffuse
those writing standards related to such equipment, and others
collection, the positive x-axis is directed toward the projection
who wish to specify precisely conditions of viewing or of the center of the entrance port on the reference plane.
measuring attributes of appearance. The use of this practice
6.2.3 For an instrument with annular (circumferential)
makes such specifications concise and unambiguous. The
45°:0° or 0°:45° geometry, the positive x-axis is in the
functional notation facilitates direct comparisons of the geo-
azimuthal direction for which the product of illumination and
metric specifications of viewing situations and measuring
receiver sensitivity is a minimum.
instruments.
6.2.4 For an instrument with highly directional illumination,
off the normal, such as is used in the measurement of gloss or
6. Coordinate System
goniochromatism, the positive x-axis is directed along the
6.1 The standard coordinate system is illustrated in Fig. 1.It
projection of the specular direction on the reference plane.
is a left-handed rectangular coordinate system, following the
6.3 Anormal angles are specified with respect to rays
usual optical convention of incident and transmitted flux in the
passing through the origin. (In a later section of this standard,
positive direction and the usual convention for the orientation
allowance is made for the size of the sampling aperture by the
of x and y for the reflection case. The coordinates are related to
tolerances on the influx and efflux angles.) Anormal angles of
a reference plane in which the first surface of the specimen is
incident and reflected rays are measured from the negative
placed for observation or measurement. The origin is in the
z-axis. Anormal angles of transmitted rays are measured from
reference plane at the center or centroid of the sampling
the positive z-axis.
aperture.
6.4 The azimuthal angle of a ray is the angle η, measured in
6.2 Instruments are usually designed to minimize the varia-
the reference plane from the positive x-axis in the direction of
tion of the product of illumination and receiver sensitivity, as a
the positive y-axis, to the projection of the ray on the reference
function of the azimuthal direction. That practice minimizes
plane. The direction of a ray is given by θ and η, in that order.
the variation in modulation as the specimen is rotated in its
Angleη is less than 360° andθ is 180° or less, and usually less
own plane. Even in instruments with an integrating sphere,
than 90°.
residualvariationoftheproduct,knownas“directionality,”can
cause variations in measurements of textured specimens ro- 6.5 In gonioradiometry and goniospectrometry, the efflux
tated in their plane. To minimize variation among routine angle θ or θ may be measured from the normal, but for
r t
product measurements due to this effect, the “warp,” “grain,” reflection measurements to characterize goniochromatism, it is
orother“machinedirection”ofspecimensmustbeconsistently
often measured from the specular axis. The aspecular angle α
oriented with respect to the x-axis, which is directed according is the angle subtended at the origin by the specular axis and the
FIG. 1 Coordinate System for Describing the Geometric Factors Affecting Transmission and Reflection Measures
E1767 − 11 (2022)
axis of the receiver. In most gonioradiometric measurements, may be very complicated. Fortunately, most such distributions
the axis of the receiver is in the plane of incidence and the in instruments used to measure appearance can be approxi-
aspecular angle is measured in that plane. In that case, the mated by uniform pencils bounded by right circular cones. The
positive direction ofα is from the specular direction toward the eye, the receiver in the case of visual observation, may be
normal. described in this way. In such cases, the description can be
relatively simple. For this purpose, the direction of the axis of
6.6 Iftheaxisofthereceiverisnotintheplaneofincidence,
the cone is given by θ and η and the half cone angle is given
the direction of the axis may be described in terms of anormal
the symbol κ. This method of description is illustrated in Fig.
and azimuthal angles, as defined in 6.5, but an aspecular
3. Annular distributions, such as those often used in reflection
azimuthal angle β may be useful. The aspecular azimuthal
measurements, can be described by the rays between two
angle is a special kind of azimuthal angle, measured in a plane
cones. In that case the numbers 1, for the smaller, and 2, for the
normal to the specular axis, with positive direction in the
larger, are added to the subscripts, as shown in Fig. 3.
right-handed sense. (With the right thumb along the specular
axis and directed away from the origin, the right hand fingers
8. Pyramidal Description
point in the positive direction of β.) See Fig. 2. The aspecular
8.1 In some instruments, influx or efflux distributions are of
azimuthal angle is measured from the projection of the x-axis
pyramidal rather than conical form. For a pyramidal influx
on the plane normal to the specular axis, to the direction of the
distribution, flux incident on the origin comes from an area of
axis of the receiver.As the angle of incidence approaches zero
a directional illuminator uniformly filling a rectangle on a
(near normal to the specimen), the aspecular azimuthal angle
plane normal to the beam, with two sides parallel to the plane
approaches the azimuthal angle. Aspecular angular excursions
of incidence. For a pyramidal efflu
...