# ASTM E1767-11 (Reapproved 2017)

Designation: E1767 − 11 (Reapproved 2017)Standard Practice forSpecifying the Geometries of Observation and Measurementto Characterize the Appearance of Materials1This standard is issued under the fixed designation E1767; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.INTRODUCTIONThe appearance of objects depends on how they are illuminated and viewed. When measurementsare made to characterize appearance attributes such as color or gloss, the measured values depend onthe geometry of the illumination and the instrumentation receiving light from the specimen. Thispractice for specifying the geometry in such applications is largely based on an international standardISO 5/1, dealing with the precise measurement of optical density in photographic science, based onan earlier American National Standard.2,31. Scope1.1 This practice describes the geometry of illuminating andviewing specimens and the corresponding geometry of opticalmeasurements to characterize the appearance of materials. Itestablishes terms, symbols, a coordinate system, and functionalnotation to describe the geometric orientation of a specimen,the geometry of the illumination (or optical irradiation) of aspecimen, and the geometry of collection of flux reflected ortransmitted by the specimen, by a measurement standard, or bythe open sampling aperture.1.2 Optical measurements to characterize the appearance ofretroreflective materials are of such a special nature that theyare treated in other ASTM standards and are excluded from thescope of this practice.1.3 The measurement of transmitted or reflected light fromareas less than 0.5 mm in diameter may be affected by opticalcoherence, so measurements on such small areas are excludedfrom consideration in this practice, although the basic conceptsdescribed in this practice have been adopted in that field ofmeasurement.1.4 The specification of a method of measuring the reflect-ing or transmitting properties of specimens, for the purpose ofcharacterizing appearance, is incomplete without a full descrip-tion of the spectral nature of the system, but spectral conditionsare not within the scope of this practice. The use of functionalnotation to specify spectral conditions is described in ISO 5/1.1.5 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety, health, and environmental practices and deter-mine the applicability of regulatory limitations prior to use.1.6 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recom-mendations issued by the World Trade Organization TechnicalBarriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:4E284 Terminology of Appearance2.2 Other Standard:ISO 5/1 Photography—Density Measurements—Part 1:Terms, Symbols and Notations53. Terminology3.1 Definitions:3.1.1 The terminology used in this practice is in accordancewith Terminology E284.3.2 Definitions of Terms Specific to This Standard:1This practice is under the jurisdiction of ASTM Committee E12 on Color andAppearance and is the direct responsibility of Subcommittee E12.03 on Geometry.Current edition approved Nov. 1, 2017. Published November 2017. Originallyapproved in 1995. Last previous edition approved in 2011 as E1767 – 11. DOI:10.1520/E1767-11R17.2ISO1/5 Photograhpy — Density Measurements — Part 1: Terms, symbols, andnotations.3ANSI PH2.36–1974American National Standards terms, symbols, and notationfor optical transmission and reflection measurements.4For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.5Available from American National Standards Institute (ANSI), 25 W. 43rd St.,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 StatesThis international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.13.2.1 anormal angle, n—an angle measured from thenormal, toward the reference plane, to the central axis of adistribution, which may be an angular distribution of flux in anincident beam or distribution of sensitivity of a receiver.3.2.2 aspecular angle, n—the angle subtended at the originby the specular axis and the axis of the receiver, the positivedirection being away from the specular axis.3.2.3 aspecular azimuthal angle, n—the angle subtended, atthe specular axis in a plane normal to the specular axis, by theprojection of the axis of the receiver and the projection of thex-axis on that plane, measured from the projection of the x-axisin a right-handed sense with respect to the specular axis.3.2.4 efflux, n—radiant flux reflected by a specimen orreflection standard, in the case of reflection observations ormeasurements, or transmitted by a specimen or open samplingaperture, in the case of transmission observations ormeasurements, in the direction of the receiver.3.2.5 efflux, adj—associated with the radiant flux reflectedby a specimen or reflection standard, in the case of reflectionobservations or measurements, or transmitted by a specimen oropen sampling aperture, in the case of transmission observa-tions or measurements, in the direction of the receiver.3.2.6 efflux region, n—region in the reference plane fromwhich flux is sensed by the observer.3.2.7 influx, n—radiant flux received from the illuminator ata specimen, a reflection standard, or open sampling aperture.3.2.8 influx, adj—associated with radiant flux received fromthe illuminator at a specimen, a reflection standard, or opensampling aperture.3.2.9 influx region, n—region in the reference plane onwhich flux is incident.3.2.10 optical modulation, n—a ratio indicating the magni-tude of the propagation by a specimen of radiant flux from aspecified illuminator or irradiator to a specified receiver, ageneral term for reflectance, transmittance, reflectance factor,transmittance factor, or radiance factor.3.2.11 plane of incidence, n—the plane containing the axisof the incident beam and the normal to the reference plane.3.2.11.1 Discussion—This plane is not defined if the axis ofthe incident beam is normal to the reference plane.3.2.12 reference plane, n—the plane in which the surface ofa plane specimen is placed for observation or measurement, orin the case of a nonplanar specimen, the plane with respect towhich the measurement is made.3.2.13 sampling aperture, n—the region in the referenceplane on which a measurement is made, the intersection of theinflux region and the efflux region.3.2.14 specular axis, n—the ray resulting from specularreflection at an ideal plane mirror in the reference plane, of theray at the geometric axis of the incident beam.3.2.14.1 Discussion—This term is applied to an incidentbeam subtending a small angle at the origin, not to diffuse orannular illuminators.3.2.15 specular direction, n—the direction of the specularaxis, the positive direction being away from the origin.3.2.16 uniplanar geometry, n—geometry in which the re-ceiver is in the plane of incidence.3.3 Symbols:de = general symbol for diffuse geometry with specularcomponent excluded.di = general symbol for diffuse geometry with specularcomponent included.E = identifies the direction of the axis of an effluxdistribution on a diagram.g = general symbol, in functional notation, for effluxgeometry.G = general symbol, in functional notation, for influxgeometry.i = subscript for incident.I = identifies the direction of the axis of an influxdistribution on a diagram.m = subscript for half cone angle subtended by theentrance pupil of a test photometer.M = optical modulation.n = subscript for half cone angle subtended by a testsource.N = identifies the direction of the normal to the referenceplane on a diagram.o = point of origin of a rectangular coordinate system, inthe reference plane, at the center or centroid of thesampling aperture.r = subscript for reflected.S = identifies the specular direction on a diagram.t = subscript for transmitted.x = distance from the origin, along the x-axis, in thereference plane, passing through point o.y = distance from the origin, along the y-axis, in thereference plane, passing through point o, and normalto the x-axis.z = distance from the origin, along the z-axis, normal tothe reference plane, passing through point o, andhaving its positive direction in the direction of thevector component of incident flux normal to thereference plane.α = aspecular angle.β = aspecular azimuthal angle.δ = in a pyramidal distribution, the half-angle measuredin the direction normal to the plane of incidence.ε = in a pyramidal distribution, the half-angle measuredin the plane of incidence.η = azimuthal angle, measured in the reference plane,from the positive x-axis, in the direction of thepositive y-axis.θ = anormal angle.κ = half cone angle of a conical flux distribution.Φ = radiant flux45°a = general symbol for 45° annular geometry45°c = general symbol for 45° circumferential geometry4. Summary of Practice4.1 This practice provides a method of specifying thegeometry of illuminating and viewing a material or thegeometry of instrumentation for measuring an attribute ofE1767 − 11 (2017)2appearance. In general, for measured values to correlate wellwith appearance, the geometric conditions of measurementmust simulate the conditions of viewing.5. Significance and Use5.1 This practice is for the use of manufacturers and users ofequipment for visual appraisal or measurement of appearance,those writing standards related to such equipment, and otherswho wish to specify precisely conditions of viewing ormeasuring attributes of appearance. The use of this practicemakes such specifications concise and unambiguous. Thefunctional notation facilitates direct comparisons of the geo-metric specifications of viewing situations and measuringinstruments.6. Coordinate System6.1 The standard coordinate system is illustrated in Fig. 1.Itis a left-handed rectangular coordinate system, following theusual optical convention of incident and transmitted flux in thepositive direction and the usual convention for the orientationof x and y for the reflection case. The coordinates are related toa reference plane in which the first surface of the specimen isplaced for observation or measurement. The origin is in thereference plane at the center or centroid of the samplingaperture.6.2 Instruments are usually designed to minimize the varia-tion of the product of illumination and receiver sensitivity, as afunction of the azimuthal direction. That practice minimizesthe variation in modulation as the specimen is rotated in itsown plane. Even in instruments with an integrating sphere,residual variation of the product, known as “directionality,” cancause variations in measurements of textured specimens ro-tated in their plane. To minimize variation among routineproduct measurements due to this effect, the “warp,” “grain,”or other “machine direction” of specimens must be consistentlyoriented with respect to the x-axis, which is directed accordingto the following rules, intended to place the positive x-axis inthe azimuthal direction for which the product of illuminationand receiver sensitivity is a minimum.6.2.1 For an integrating-sphere instrument with diffuseillumination, the positive x-axis is directed toward the projec-tion of the center of the exit port on the reference plane.6.2.2 For an integrating-sphere instrument with diffusecollection, the positive x-axis is directed toward the projectionof the center of the entrance port on the reference plane.6.2.3 For an instrument with annular (circumferential)45°:0° or 0°:45° geometry, the positive x-axis is in theazimuthal direction for which the product of illumination andreceiver sensitivity is a minimum.6.2.4 For an instrument with highly directional illumination,off the normal, such as is used in the measurement of gloss orgoniochromatism, the positive x-axis is directed along theprojection of the specular direction on the reference plane.6.3 Anormal angles are specified with respect to rayspassing through the origin. (In a later section of this standard,allowance is made for the size of the sampling aperture by thetolerances on the influx and efflux angles.) Anormal angles ofincident and reflected rays are measured from the negativez-axis. Anormal angles of transmitted rays are measured fromthe positive z-axis.6.4 The azimuthal angle of a ray is the angle η, measured inthe reference plane from the positive x-axis in the direction ofthe positive y-axis, to the projection of the ray on the referenceplane. The direction of a ray is given by θ and η, in that order.Angle η is less than 360° and θ is 180° or less, and usually lessthan 90°.6.5 In gonioradiometry and goniospectrometry, the effluxangle θror θtmay be measured from the normal, but forreflection measurements to characterize goniochromatism, it isoften measured from the specular axis. The aspecular angle αis the angle subtended at the origin by the specular axis and theFIG. 1 Coordinate System for Describing the Geometric Factors Affecting Transmission and Reflection MeasuresE1767 − 11 (2017)3axis of the receiver. In most gonioradiometric measurements,the axis of the receiver is in the plane of incidence and theaspecular angle is measured in that plane. In that case, thepositive direction of α is from the specular direction toward thenormal.6.6 If the axis of the receiver is not in the plane of incidence,the direction of the axis may be described in terms of anormaland azimuthal angles, as defined in 6.5, but an aspecularazimuthal angle β may be useful. The aspecular azimuthalangle is a special kind of azimuthal angle, measured in a planenormal to the specular axis, with positive direction in theright-handed sense. (With the right thumb along the specularaxis and directed away from the origin, the right hand fingerspoint in the positive direction of β.) See Fig. 2. The aspecularazimuthal angle is measured from the projection of the x-axison the plane normal to the specular axis, to the direction of theaxis of the receiver. As the angle of incidence approaches zero(near normal to the specimen), the aspecular