1、Designation: E 2175 01 (Reapproved 2008)Standard Practice forSpecifying the Geometry of Multiangle Spectrophotometers1This standard is issued under the fixed designation E 2175; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the y
2、ear of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.INTRODUCTIONThe appearance of metallic coatings and plastics usually depends on the directions of illuminationand viewing,
3、 a phenomenon called “gonioappearance.” This phenomenon is also observed with othermaterials, such as lustrous textiles and materials containing pearlescent or interference pigments. Thecharacteristic appearance of most such materials is accentuated by directional illumination, such asthat provided
4、by the sun on a clear day or a small lamp at night. The variation in color, as a functionof geometry, is usually measured by spectrophotometry with several specified sets of geometricconditions. Measurement of this kind, at a few selected angles, is called “multiangle spectrophotom-etry,” as disting
5、uished from measurement over a broad range of angles, which is called“ goniospec-trophotometry.” Spectrophotometric aspects of these measurements, including spectral resolution andlinearity of photometric scales, are treated in other standards, including Practice E 308 and PracticeE 1164. Practice E
6、 1767 provides practice for specifying the geometry of measurements. Retroreflec-tors exhibit a special kind of gonioappearance, which is treated in other ASTM documents. Thepresent document provides standard practice for specifying influx and efflux angles, angularselectivity, spatial distributions
7、 of illuminators and receivers, and angular aspects of standardizing thephotometric scale, that are peculiar to multiangle spectrophotometry. Directional illuminationemphasizes the gonioappearance of most materials, but when interference pigments are used, such asthose used in ink to mark paper curr
8、ency, the effect is observed with diffuse illumination and varyingangles of viewing, so these materials are also measured with diffuse illumination.1. Scope1.1 This practice provides a way of specifying the angularand spatial conditions of measurement and angular selectivityof a method of measuring
9、the spectral reflectance factors ofopaque gonioapparent materials, for a small number of sets ofgeometric conditions.1.2 Measurements to characterize the appearance of retrore-flective materials are of such a special nature that they aretreated in other ASTM documents and are not included in thescop
10、e of this standard.1.3 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 and health practices and determine the applica-bility of regulatory limitations prior to
11、use.2. Referenced Documents2.1 ASTM Standards:2E 284 Terminology of AppearanceE 308 Practice for Computing the Colors of Objects byUsing the CIE SystemE 1164 Practice for Obtaining Spectrometric Data forObject-Color EvaluationE 1767 Practice for Specifying the Geometries of Observa-tion and Measurem
12、ent to Characterize the Appearance ofMaterials1This 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 Jan. 1, 2008. Published January 2008. Originallyapproved in 2001. Last prev
13、ious edition approved in 2001 as E 2175 - 01.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.1Copyright ASTM
14、International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3. Terminology3.1 For definitions of appearance terms used in this practice,refer to Terminology E 284.4. Significance and Use4.1 This practice is for the use of manufacturers and users ofinstruments t
15、o measure the appearance of gonioapparent ma-terials, those writing standard specifications for such instru-ments, and others who wish to specify precisely the geometricconditions of multiangle spectrophotometry. A prominent ex-ample of industrial usage is the routine application of suchmeasurements
16、 by material suppliers and automobile manufac-turers to measure the colors of metallic paints and plastics.5. Components of Apparatus5.1 The apparatus shall consist of one or more illuminatorsand one or more spectrometric receivers at fixed or adjustableangles with respect to a reference plane, a me
17、ans of positioningspecimens in a reference plane, a means of indicating the areaon the specimen to be measured, shielding to avoid stray light,and a means of displaying spectral or colorimetric data and/orcommunicating such data to a data-recorder or computer. (Theterms“ light,” “illuminator,” “illu
18、mination,” and “illuminance”are used here for simplicity, though the corresponding terms“radiant power,” “irradiator,” “irradiation,” and “irradiance”would be more accurate when the incident flux includesultraviolet flux, as is necessary if the appearance of a fluores-cent material is measured.)6. G
19、eometric Types of Apparatus6.1 The geometric configuration of the instrument may beuniplanar, annular, circumferential, or diffuse. In all cases, thespecimen is taken to be a flat surface lying in a plane called the“reference plane,” which is designated the x, y plane. Whenthere is a single directio
20、nal illuminator, the x direction is thedirection of the projection of the axis of the incident beam onthe reference plane. If there are several directional illuminatorsor a single diffuse illuminator, the direction of the x-axis mustbe selected and specified. The area of the reference plane onwhich
21、measurements are made is called the “sampling aper-ture” and the center of that area is designated the origin, o, ofthe geometric space used to specify the configuration. Thenormal to the sampling aperture, at the origin, is the -z-axis.Angles subtended at the origin and measured from that normalare
22、 called “anormal angles.” The specular direction is thedirection of the beam from a directional illuminator afterspecular reflection by an ideal plane mirror at the samplingaperture.Angles subtended at the origin and measured from thespecular direction are called“ aspecular angles” and are posi-tive
23、 in sign when measured in the direction toward the normal.The normal and the axis of a directional illuminator define aplane, known as the “plane of incidence.” The speculardirection necessarily lies in that plane.6.1.1 To facilitate simple and precise geometric specifica-tion of the sampling apertu
24、re, it shall be either circular orrectangular.6.1.2 To facilitate simple and precise geometric specifica-tion of directional influx or efflux distributions, they shall beeither conical or pyramidal. For purposes of describing geom-etry by functional notation, a diffuse distribution may beconsidered
25、a conical distribution centered on the normal andhaving a half angle of 90 degrees.6.1.3 In a uniplanar configuration, a directional illuminatoris used, the axes of the receivers lie in the plane of incidence,and their positions are specified by aspecular angles. Auniplanar configuration is illustra
26、ted in Fig. 1. To simplify thefigure, only one receiver is shown.6.1.3.1 For a conical influx distribution, the flux incident onthe origin comes from an area of a directional illuminatoruniformly filling a circle on a plane normal to the beam. For aconical efflux distribution, flux from the origin i
27、s uniformlycollected and evaluated over an area of the receiver that is acircle on a plane normal to the beam.Auniplanar configurationwith conical influx and efflux distributions is illustrated in Fig.2. To simplify the figure, only one receiver is shown.6.1.3.2 For a pyramidal influx distribution,
28、flux incident onthe origin comes from an area of a directional illuminatoruniformly filling a rectangle on a plane normal to the beam. Fora pyramidal efflux distribution, flux from the origin is uni-formly collected and evaluated over an area of the receiver thatis a rectangle on a plane normal to t
29、he beam. A pyramidalconfiguration can be used to subtend a small angle in the planeFIG. 1 Uniplanar ConfigurationE 2175 01 (2008)2of incidence, to enhance angular selectivity, but have a largeenough solid angle to provide adequate flux for reliablemeasurements.Auniplanar configuration with pyramidal
30、 influxand efflux distributions is illustrated in Fig. 3. To simplify thefigure, only one receiver is shown and the angles d and e areshown for the receiver, but not for the illuminator.6.1.4 In an annular configuration, the incident beam uni-formly fills the space between two right-circular cones,
31、withtheir axes on the normal and apices at the origin. An annularconfiguration can be used to provide a flux distribution with asmall range of anormal angles, to enhance anormal angularselectivity, but of large enough solid angle to provide adequateflux for reliable measurements. The nominal angle o
32、f anannular distribution is the average of the half-angles of the twodefining cones. For multiangle spectrophotometry, provisionmust be made for several annular distributions with differentnominal angles. The efflux distribution is a conical distributionwith its axis on the normal and its apex at th
33、e origin.6.1.5 A circumferential configuration approximates an an-nular configuration, except that flux incident on the origincomes from a ring of discrete directional illuminators, allhaving their axes at the same anormal angle, but arrayed atvarious azimuthal angles. The nominal angle of incidence
34、 ismeasured from the normal to the axes of the illuminators. Formultiangle spectrophotometry, provision must be made forilluminators at several different nominal angles. A circumfer-ential configuration with three illuminators is illustrated in Fig.4. To simplify the figure, the angles ki, ui, and h
35、iare shown forthe first illuminator only.6.1.5.1 The discrete illuminators shall all have the samenominal angle of incidence, for a given measurement.6.1.6 In a diffuse configuration, the incident flux is diffuse.Ideally, the illuminator illuminates the sampling aperture at allangles within the hemi
36、sphere on the -z side of the referenceplane, except those directions occupied by receivers. The useof an integrating sphere to produce uniform diffuse illumina-tion requires non-selective diffusing baffles to obscure theentrance port and the area on the sphere wall at which the fluxentering the sphe
37、re is first reflected. When diffuse illuminationis used, the receivers are all in one plane defined by the normaland having an arbitrarily designated x-axis. The positions ofthe receivers are specified by anormal angles.6.2 Given a geometric configuration, the reverse geometryis considered equivalen
38、t, if all other components of theinstrument design are equivalent.7. Nominal Geometric Specifications7.1 Angles for these specifications are customarily given indegrees.7.2 Uniplanar Geometry:FIG. 2 Uniplanar Configuration with Conical Influx and Efflux DistributionsFIG. 3 Uniplanar Configuration wi
39、th Pyramidal Influx and Efflux DistributionsE 2175 01 (2008)37.2.1 The direction of a conical distribution is specified bythe angle u subtended at the origin from the normal to the axisof the distribution or the angle a subtended at the origin fromthe specular direction to the axis of the distributi
40、on. The extentof a conical distribution is specified by the angle k subtendedat the origin by the radius of the circular distribution at theilluminator or receiver, with subscripts i and r indicatingilluminator and receiver, respectively. (See Fig. 2.) When morethan one illuminator or receiver is in
41、volved, they are distin-guished by alphabetic subscripts a, b, c, etc., the half-anglesbeing given symbols of the form kia, kib, kic, and kra, krb,krc.7.2.2 A pyramidal distribution is specified by anglesd and e,where d is the angle subtended at the origin from the centralaxis of the distribution to
42、 the edge, measured in the directionnormal to the plane of incidence, and e is the angle subtendedat the origin from the central axis of the distribution to theedge, measured in the plane of incidence. Subscript i and rdistinguish half-angles for the illuminator and receiver, respec-tively. Letter s
43、ubscripts are added to identify multiple distri-butions, as in the case of circular conical distributions. (SeeFig. 3.)7.3 An annular distribution is specified by a half-angleki1orkr1for the smaller of the two cones limiting the annulus and ki2or kr2for the larger of the two. Subscripts a,b,c, etc.
44、are usedto distinguish multiple distributions, as in the case of conicaldistributions, for example, ki1c. The nominal angle of incidenceor angle of reflection is given the same symbol without the 1 or2, for example kic. (See Fig. 4.)7.4 A circumferential distribution is specified by the anor-mal ang
45、le u of the axes of the discrete illuminators, the conicalor pyramidal description of the discrete illuminators, and theazimuthal positions of their axes with respect to some identi-fied direction, considered the x direction.7.5 A diffuse distribution is specified by specifying direc-tions, if any,
46、from which illumination is excluded, other thanthe obvious directions of receivers and necessary baffles.Excluded directions are specified in the same way as conical orpyramidal influx or efflux distributions.8. Angular Selectivity8.1 Angular selectivity is the degree to which the measuredspectral q
47、uantity approaches the ideal value for the nominalangular geometry. Precise characterization of the effectiveangular “slit-width” of the measurement system can be diffi-cult, but the fraction of the angular illumination distributionand the angular sensitivity distribution within specified anglescan
48、be determined by practical means.8.2 Ideally, flux incident on the origin should come from thenominal direction specified for the measurement. At leastDEa% of the incident flux shall come from angles within Da1degrees of the nominal direction. All of the incident flux shallcome from angles within Da
49、2degrees of the nominal direction.8.3 Ideally, the sensitivity of a receiver should be limited tothe nominal direction. A fraction DSa% of the angular sensi-tivity distribution shall be withinDa3degrees of the nominaldirection. All of the angular sensitivity distribution shall bewithin Da4degrees of the nominal direction.9. Tolerances9.1 The objective is to have the sampling aperture uniformlyilluminated. Tolerances are specified for the departure fromuniformity of the illuminance. The nominal specified angularextents of influx and efflux distributions should not be confusedwith t
