# ASTM E308-17

Designation: E308 − 17Standard Practice forComputing the Colors of Objects by Using the CIE System1This standard is issued under the fixed designation E308; 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.This standard has been approved for use by agencies of the U.S. Department of Defense.INTRODUCTIONStandard tables (Tables 1–4) of color matching functions and illuminant spectral power distributionshave since 1931 been defined by the CIE, but the CIE has eschewed the role of preparing tables oftristimulus weighting factors for the convenient calculation of tristimulus values. There havesubsequently appeared numerous compilations of tristimulus weighting factors in the literature withdisparity of data resulting from, for example, different selections of wavelength intervals and methodsof truncating abbreviated wavelength ranges. In 1970, Foster et al. (1)2proposed conventions tostandardize these two features, and Stearns (2) published a more complete set of tables. Stearns’ workand later publications such as the 1985 revision of E308 have greatly reduced the substantial variationsin methods for tristimulus computation that existed several decades ago.The disparities among earlier tables were largely caused by the introduction of computations basedon 20-nm wavelength intervals. With the increasing precision of modern instruments, there is alikelihood of a need for tables for narrower wavelength intervals. Stearns’ tables, based on a 10-nminterval, did not allow the derivation of consistent tables with wavelength intervals less than 10 nm.The 1-nm table must be designated the basic table if others with greater wavelength intervals are tohave the same white point, and this was the reason for the 1985 revision of E308, resulting in tablesthat are included in the present revision as Tables 5.The 1994 revision was made in order to introduce to the user a method of reducing the dependenceof the computed tristimulus values on the bandpass of the measuring instrument, using methods thatare detailed in this practice.1. Scope1.1 This practice provides the values and practical compu-tation procedures needed to obtain CIE tristimulus values fromspectral reflectance, transmittance, or radiance data for object-color specimens.1.2 Procedures and tables of standard values are given forcomputing from spectral measurements the CIE tristimulusvalues X, Y, Z, and chromaticity coordinates x, y for the CIE1931 standard observer and X10,Y10,Z10and x10.y10for theCIE 1964 supplementary standard observer.1.3 Standard values are included for the spectral power ofsix CIE standard illuminants and three CIE recommendedfluorescent illuminants.1.4 Procedures are included for cases in which data areavailable only in more limited wavelength ranges than thoserecommended, or for a measurement interval wider than thatrecommended by the CIE. This practice is applicable tospectral data obtained in accordance with Practice E1164 with1-, 5-, 10-, or 20-nm measurement interval.1.5 Procedures are included for cases in which the spectraldata are, and those in which they are not, corrected forbandpass dependence. For the uncorrected cases, it is assumedthat the spectral bandpass of the instrument used to obtain thedata was approximately equal to the measurement interval and1This practice is under the jurisdiction of ASTM Committee E12 on Color andAppearance and is the direct responsibility of Subcommittee E12.04 on Color andAppearance Analysis.Current edition approved May 1, 2017. Published August 2017. Originallyapproved in 1966. Last previous edition approved in 2015 as E308 – 15. DOI:10.1520/E0308-17.2The boldface numbers in parentheses refer to the list of references at the end ofthis practice.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.1was triangular in shape. These choices are believed to corre-spond to the most widely used industrial practice.1.6 This practice includes procedures for conversion ofresults to color spaces that are part of the CIE system, such asCIELAB and CIELUV (3). Equations for calculating colordifferences in these and other systems are given in PracticeD2244.1.7 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.8 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.1.9 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:3D2244 Practice for Calculation of Color Tolerances andColor Differences from Instrumentally Measured ColorCoordinatesE284 Terminology of AppearanceE313 Practice for Calculating Yellowness and WhitenessIndices from Instrumentally Measured Color CoordinatesE1164 Practice for Obtaining Spectrometric Data for Object-Color EvaluationE2022 Practice for Calculation of Weighting Factors forTristimulus IntegrationE2729 Practice for Rectification of SpectrophotometricBandpass Differences2.2 ANSI Standard:PH2.23 Lighting Conditions for Viewing PhotographicColor Prints and Transparencies42.3 CIE/ISO Standards:ISO Standard 11664-1:2007(E)/CIE S 013-1/E:2006 Stan-dard Colorimetric Observers4,5ISO Standard 11664-2:2007(E)/CIE S 014-2/E:2006 Colori-metric Illuminants4,5CIE Standard D 001 Colorimetric Illuminants and Observers(Disk)52.4 ASTM Adjuncts:Computer disk containing Tables 5 and 663. Terminology3.1 Definitions of terms in Terminology E284 are applicableto this practice (see also Ref (4)).3.2 Definitions:3.2.1 bandpass, adj—having to do with a passband.3.2.2 bandwidth, n—the width of a passband at its half-peaktransmittance.3.2.3 chromaticity, n—the color quality of a color stimulusdefinable by its chromaticity coordinates.3.2.4 chromaticity coordinates, n—the ratio of each of thetristimulus values of a psychophysical color (see section3.2.7.11) to the sum of the tristimulus values.3.2.4.1 Discussion—In the CIE 1931 standard colorimetricsystem, the chromaticity coordinates are: x = X/(X+Y+Z),y=Y/(X+Y+Z), z=Z/(X+Y+Z); in the CIE 1964 supple-mentary colorimetric system, the same equations apply with allsymbols having the subscript 10 (see 3.2.7).3.2.5 CIE, n—the abbreviation for the French title of theInternational Commission on Illumination, Commission Inter-nationale de l’Éclairage.3.2.6 CIE 1931 (x, y) chromaticity diagram,n—chromaticity diagram for the CIE 1931 standard observer,in which the CIE 1931 chromaticity coordinates are plotted,with x as abscissa and y as ordinate.3.2.7 CIE 1964 (x10,y10) chromaticity diagram,n—chromaticity diagram for the CIE 1964 supplementarystandard observer, in which the CIE 1964 chromaticity coor-dinates are plotted, with x10as abscissa and y10as ordinate.3.2.7.1 Discussion—Fig. 1 shows the CIE 1931 and 1964chromaticity diagrams, including the locations of the spectrumlocus and the connecting purple boundary.3.2.8 CIE 1976 (u , v ) or (u 10,v 10) chromaticity diagram,n—chromaticity diagram in which the CIE 1976 L* u* v*(CIELUV) chromaticity coordinates are plotted, with u (oru 10) as abscissa and v (or v 10) as ordinate.3.2.9 CIE 1931 standard colorimetric system, n—a systemfor determining the tristimulus values of any spectral powerdistribution using the set of reference color stimuli, X, Y, Z andthe three CIE color–matching functions x¯(λ), y¯(λ), z¯(λ) adoptedby the CIE in 1931.3.2.10 CIE 1964 supplementary standard colorimetricsystem, n—a system for determining the tristimulus values ofany spectral power distribution using the set of reference colorstimuli X10, Y10, Z10and the three CIE color-matching func-tions x¯10(λ), y¯10(λ), z¯10(λ) adopted by the CIE in 1964 (see Note1).NOTE 1—Users should be aware that the CIE 1964 (10°) supplementarysystem and standard observer assume no contribution or constant contri-bution of rods to vision. Under some circumstances, such as in viewinghighly metameric pairs in very low light levels (where the rods areunsaturated), the amount of rod participation can vary between themembers of the pair. This is not accounted for by any trichromatic systemof colorimetry. The 10° system and observer should be used with cautionin such circumstances.3.2.11 color, n—of an object, aspect of object appearancedistinct from form, shape, size, position or gloss that depends3For 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.4Available from American National Standards Institute (ANSI), 25 W. 43rd St.,4th Floor, New York, NY 10036, http://www.ansi.org.5Available from CIE (International Commission on Illumination), http://www.cie.co.at or http://www.techstreet.com.6Computer disk of 72 tables is available from ASTM Headquarters. RequestAdjunct No. ADJE0308A. Originally approved in 1994.E308 − 172upon the spectral composition of the incident light, the spectralreflectance, transmittance, or radiance of the object, and thespectral response of the observer, as well as the illuminatingand viewing geometry.3.2.12 color, n—psychophysical, characteristics of a colorstimulus (that is, light producing a visual sensation of color)denoted by a colorimetric specification with three values, suchas tristimulus values.3.2.13 color–matching functions, n—the amounts, in anytrichromatic system, of three reference color stimuli needed tomatch, by additive mixing, monochromatic components of anequal–energy spectrum.3.2.14 fluorescent illuminant, n—illuminant representingthe spectral distribution of the radiation from a specified typeof fluorescent lamp.3.2.15 CIE recommended fluorescent illuminants, n—a setof spectral power distributions of 12 types of fluorescentlamps, the most important of which are FL2, representing acool white fluorescent lamp with correlated color temperature4200 K, FL7, a broad-band (continuous-spectrum) daylightlamp (6500 K), and FL11, a narrow-band (line-spectrum) whitefluorescent lamp (4000 K).3.2.16 luminous, adj—weighted according to the spectralluminous efficiency function V(λ) of the CIE.3.2.17 opponent-color scales, n—scales that denote onecolor by positive scale values, the neutral axis by zero value,and an approximately complementary color by negative scalevalues, common examples being scales that are positive in thered direction and negative in the green direction, and those thatare positive in the yellow direction and negative in the bluedirection.3.2.18 CIELAB color scales, n—CIE 1976 L*, a*, b*opponent-color scales, in which a* is positive in the reddirection and negative in the green direction, and b* is positivein the yellow direction and negative in the blue direction.3.2.19 CIELUV color scales, n—CIE 1976 L*, u*, v*opponent-color scales, in which u* is positive in the reddirection and negative in the green direction, and v* is positivein the yellow direction and negative in the blue direction.3.2.20 passband, n—a contiguous band of wavelengths inwhich at least a fraction of the incident light is selectivelytransmitted by a light-modulating device or medium.3.2.21 spectral, adj—for radiometric quantities, pertainingto monochromatic radiation at a specified wavelength or, byextension, to radiation within a narrow wavelength band abouta specified wavelength.3.2.22 standard illuminant, n—a luminous flux, specified byits spectral distribution, meeting specifications adopted by astandardizing organization.3.2.23 CIE standard illuminant A, n—colorimetricilluminant, representing the full radiator at 2855.6 K, definedby the CIE in terms of a relative spectral power distribution.3.2.24 CIE standard illuminant C, n—colorimetricilluminant, representing daylight with a correlated color tem-perature of 6774 K, defined by the CIE in terms of a relativespectral power distribution.FIG. 1 The CIE 1931 x, y and 1964 x10,y10Chromaticity Diagrams Ref (5) (see Note 2)E308 − 1733.2.25 CIE standard illuminant D65,n—colorimetricilluminant, representing daylight with a correlated color tem-perature of 6504 K, defined by the CIE in terms of a relativespectral power distribution.3.2.25.1 Discussion—Other illuminants of importance de-fined by the CIE include the daylight illuminants D50, D55, andD75. Illuminant D50is used by the graphic arts industry forviewing colored transparencies and prints (see ANSI PH2.23).3.2.26 standard observer, n—an ideal observer having vi-sual response described by the CIE color-matching functions(see CIE S 013 and Ref (3)).3.2.27 CIE 1931 standard observer, n—ideal colorimetricobserver with color-matching functions x¯(λ), y¯(λ), z¯(λ) corre-sponding to a field of view subtending a 2° angle on the retina;commonly called the “2° standard observer.”3.2.28 CIE 1964 supplementary standard observer, n—idealcolorimetric observer with color-matching functions x¯10(λ),y¯10(λ), z¯10(λ) corresponding to a field of view subtending a 10°angle on the retina; commonly called the “10° standardobserver” (see Note 1).3.2.29 tristimulus values, n—see 3.2.9 and 3.2.10.3.2.30 tristimulus weighting factors, Sx¯, Sy¯, Sz¯, n—factorsobtained from products of the spectral power S of an illuminantand the spectral color-matching functions x¯, y¯, z¯ (or x¯10, y¯10,z¯10) of an observer, usually tabulated at wavelength intervals of10 or 20 nm, used to compute tristimulus values by multipli-cation by the spectral reflectance, transmittance, or radiance (orthe corresponding factors) and summation.3.2.30.1 Discussion—Proper account should be taken of thespectral bandpass of the measuring instrument.4. Summary of Practice4.1 Selection of Parameters—The user of this practice mustselect values of the following parameters:4.1.1 Observer—Select either the CIE 1931 standard colo-rimetric observer (2° observer) or the CIE 1964 supplementarystandard observer (10° observer), tabulated in this practice,CIE Standard S 013 or D 001, or Ref (3) (see 3.2.26 and Note1).