# ASTM E313-15e1

Designation: E313 − 15´1Standard Practice forCalculating Yellowness and Whiteness Indices fromInstrumentally Measured Color Coordinates1This standard is issued under the fixed designation E313; 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.ε1NOTE—Section 7 was corrected editorially in June 2015.1. Scope1.1 This practice provides numbers that correlate withvisual ratings of yellowness or whiteness of white and near-white or colorless object-color specimens, viewed in daylightby an observer with normal color vision. White textiles, paints,and plastics are a few of the materials that can be described bythe indices of yellowness or whiteness calculated by thispractice.1.2 For a complete analysis of object colors, by a specifiedobserver and under a specified illuminant, use of three param-eters is required. For near-white specimens, however, it is oftenuseful to calculate single-number scales of yellowness orwhiteness. This practice provides recommended equations forsuch scales and discusses their derivations and uses, and limitsto their applicability (see also Ref (1)2).1.3 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.4 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 use.2. Referenced Documents2.1 ASTM Standards:3D1535 Practice for Specifying Color by the Munsell SystemD1729 Practice for Visual Appraisal of Colors and ColorDifferences of Diffusely-Illuminated Opaque MaterialsD1925 Test Method for Yellowness Index of Plastics,4E284 Terminology of AppearanceE308 Practice for Computing the Colors of Objects by Usingthe CIE SystemE805 Practice for Identification of Instrumental Methods ofColor or Color-Difference Measurement of MaterialsE991 Practice for Color Measurement of Fluorescent Speci-mens Using the One-Monochromator MethodE1164 Practice for Obtaining Spectrometric Data for Object-Color EvaluationE1247 Practice for Detecting Fluorescence in Object-ColorSpecimens by SpectrophotometryE1331 Test Method for Reflectance Factor and Color bySpectrophotometry Using Hemispherical GeometryE1345 Practice for Reducing the Effect of Variability ofColor Measurement by Use of Multiple MeasurementsE1347 Test Method for Color and Color-Difference Mea-surement by Tristimulus ColorimetryE1348 Test Method for Transmittance and Color by Spec-trophotometry Using Hemispherical GeometryE1349 Test Method for Reflectance Factor and Color bySpectrophotometry Using Bidirectional (45°:0° or 0°:45°)GeometryE1360 Practice for Specifying Color by Using the OpticalSociety of America Uniform Color Scales SystemE1499 Guide for Selection, Evaluation, and Training ofObserversE1541 Practice for Specifying and Matching Color Usingthe Colorcurve System (Withdrawn 2007)53. Terminology3.1 Terms and definitions in Terminology E284 are appli-cable to this practice.3.2 Definitions:1This 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 Jan. 1, 2015. Published February 2015. Originallyapproved in 1967. Last previous edition approved in 2010 as E313 – 10. DOI:10.1520/E0313-15E01.2The boldface numbers in parentheses refer to the list of references at the end ofthis practice.3For 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.4The last approved version of this historical standard is referenced onwww.astm.org. Replaced by Section 6 of E313.5The last approved version of this historical standard is referenced onwww.astm.org.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.2.1 perfect reflecting diffuser, n—ideal reflecting surfacethat neither absorbs nor transmits light, but reflects diffusely,with the radiance of the reflecting surface being the same for allreflecting angles, regardless of the angular distribution of theincident light.3.2.2 whiteness, n—the attribute of color perception bywhich an object color is judged to approach the preferredwhite.3.2.3 whiteness index, WI, n—a number, computed by agiven procedure from colorimetric data, that indicates thedegree of departure of an object color from that of a preferredwhite.3.2.4 yellowness, n—the attribute of color perception bywhich an object color is judged to depart from colorless or apreferred white toward yellow.3.2.5 yellowness index, YI, n—a number, computed by agiven procedure from colorimetric or spectrophotometric data,that indicates the degree of departure of an object color fromcolorless or from a preferred white, toward yellow.3.2.5.1 Discussion—Negative values of YI denote departuretoward blue.3.3 Definitions of Terms Specific to This Standard:3.3.1 near white, n—a color having a Munsell value greaterthan 8.3 (luminous reflectance factor Y = 63) and Munsellchroma no greater than 0.5 for B hues, 0.8 for Y hues, and 0.3for all other hues.3.3.2 preferred white, n—color of a white standard used asthe basis for calculating indices of whiteness or yellowness asthe departure of the color of the specimen from that of thepreferred white; in this practice, the perfect reflecting diffuser.4. Summary of Practice4.1 The calculations described in this practice assume thatspecimens have been measured according to Practices E1164and E308 and one of the Test Methods E1331, E1347, E1348,or E1349, depending on the type of specimen and measuringinstrument used (see also Practice E805).4.2 This practice takes as a starting point for the calculationsCIE tristimulus values X, Y, and Z for one of the CIE standardobservers and one of the CIE standard or recommendedilluminants of daylight quality. Such tristimulus values areavailable by use of modern color measuring instruments.4.3 Equations for the preferred methods of calculating YIand WI are described in Sections 6 and 7, respectively.Equations for calculating other quantities used as indices ofyellowness or whiteness are given in Appendix X1 andAppendix X2, respectively.5. Significance and Use5.1 This practice should be used only to compare specimensof the same material and same general appearance. Forexample, a series of specimens to be compared should havegenerally similar gloss, texture, and (if not opaque) thickness,and translucency.5.2 For yellowness measurement, this practice is limited tospecimens having dominant wavelength in the range 570 to580 nm, or Munsell hue approximately 2.5GY to 2.5Y. Forwhiteness measurement, this practice is limited to specimenshaving Munsell value greater than 8.3 (CIE Y greater than 65)and Munsell chroma no greater than 0.5 for B hues, 0.8 for Yhues, and 0.3 for all other hues (see 3.3.1).5.3 The combination of measurement and calculation lead-ing to indices of yellowness or whiteness is a psychophysicalprocess, that is, the procedures specified are designed toprovide numbers correlating with visual estimates made underspecified typical observing conditions. Because visual observ-ing conditions can vary widely, users should compare calcu-lated indices with visual estimates to ensure applicability.Some standards addressing the visual estimation of color andcolor difference are Practices D1535, D1729, E1360, andE1541, and Guide E1499.5.4 This practice does not cover the preparation ofspecimens, a procedure that may affect significantly the quan-tities measured. In general, specimens should be prepared andpresented for measurement in the manner that is standard forthe test being performed. Select enough specimens or specimenareas to provide an average result that is representative of eachsample to be tested. See Practice E1345.6. Yellowness Index6.1 This section contains two main parts: 6.2 Historicalbackground and 6.3 Calculation of currently recommendedYellowness Index. If the user wants to calculate the currentlyrecommended Yellowness Index (YI), it is recommended toskip directly to 6.3.6.2 Background—The currently recommended equation forthe calculation of yellowness index is derived from an equationdue to Hunter (2) in 1942: YI =(A−B)/G, where A, B, and Gare, respectively, amber or red, blue, and green colorimeterreadings. Another version, used in the 1940s to 1960s fortransparent plastics (3, 4), was based on transmittances near theends of the visible wavelength region: YI = 100(T680− T420)/T560(with a factor of 100 introduced to give values of YI nearunity). This equation failed to account correctly for differencesin the spectral transmittance curves of such plastics, especiallyafter the adoption of ultraviolet light absorbers to improveweathering, and was soon abandoned. When, in 1957, ASTMsolicited new equations for calculating yellowness indices,Hunter’s equation was converted (5) into CIE tristimulus valueform by using Hunter’s approximate relations between colo-rimeter readings and those tristimulus values; the resultingequation, YI = 100(1.28X − 1.06Z)/Y, was adopted for use inTest Method D1925 in 1962.6.2.1 In the original form of Test Method E313, an alterna-tive equation was recommended for a yellowness index. Interms of colorimeter readings, it was YI = 100(1 − B/G). Itsderivation assumed that, because of the limitation of theconcept to yellow (or blue) colors, it was not necessary to takeaccount of variations in the amber or red colorimeter reading A.This equation is no longer recommended.6.2.2 Significant Digits and Precision—The coefficients ofTest Method D1925 equation were rounded to the number ofdigits shown, commensurate with the precision of then-existingE313 − 15´12color measurement instrumentation. It was not intended thatmore significance should be attributed to values of YI than thatimplicit in this number of digits. As instrumentation wasimproved, however, it was found that some instruments unex-pectedly gave nonzero values of YI for clear air or the perfectreflecting diffuser. One suggested ((1), p. 205) remedy for thispresumed failure of the equation was to increase the number ofdigits in the numerical coefficients from two to ten after thedecimal point, despite the obvious lack of significance of mostof these digits. With modern instrumentation, it is believed thattwo digits added to the coefficients in the original Test MethodD1925 equation suffice to bring the nonzero value of YI below0.0005 on average. The new coefficients are given to thisprecision in 6.2.3.6.2.3 Derivation of Equations—Several sets of coefficientsare involved in the derivation of the final equations recom-mended for calculating yellowness indices. With themevaluated, it is possible to derive highly precise equations forboth the CIE 1931 standard observer and the 1964 supplemen-tary standard observer, in combination with either CIE standardilluminant C or D65. The results are given in Table 1.6.2.3.1 The first set of coefficients required, consists of thetristimulus values Xn, Yn, and Znof the perfect reflectingdiffuser (or clear air) for the above observer-illuminant com-binations. These are established by the CIE, and for the presentderivation were taken from the tables of tristimulus weightingfactors in Practice E308.6.2.3.2 From these “white point” values, it is possible tocalculate the coefficients in Hunter’s equation relating tristimu-lus value X and colorimeter readings A and B: X=Xn-(FAA + FBB), thus improving on the approximation FA= 0.8and FB= 0.2 originally used.6.2.3.3 The coefficients in revised Test Method D1925equations for YI can be calculated, rounded, and adjusted in thelast retained significant digit to minimize the residual error inthe white point values. These coefficients are given in Table 1as CXand CZ. The tabulation of the residual white point errorcompletes the table.6.3 Calculation of Yellowness Index (YI)—YI can be calcu-lated for either illuminant C or D65, and either the CIE 1931standard colorimetric observer (2°), or the CIE 1964 standardcolorimetric observer (10°).6.3.1 Use Eq 1 to calculate Yellowness Index (YI):YI 5 100~CXX 2 CZZ!/Y (1)where X, Y, Z are the measured tristimulus values of thespecimen calculated for either Illuminant C or D65, and eitherthe CIE 1931 standard colorimetric observer (2°), or the CIE1964 standard colorimetric observer (10°); and coefficients Cxand Czare selected from Table 2 for the chosen illuminant andobserver.7. Whiteness Index7.1 Background—The earliest equation for whiteness indexWI appears to be due to MacAdam (6) and related WI toexcitation purity. This and other equations utilizing the purityhave largely been abandoned. Judd (7) appears to have been thefirst to recognize that a whiteness index should incorporate twoterms, one based on the lightness of the specimen relative tothat of a preferred white, and the other describing the differ-ence in chromaticity between the specimen and that preferredwhite. Much debate has arisen over the years as to the natureof the preferred white, but at the present time the perfectreflecting diffuser is almost always adopted as that reference.7.1.1 In the original form of Test Method E313, the equationfor WI was based on the above premise and the use ofcolorimeter readings G and B only. It was found that thechromaticity factor G−B required three to four times theweighting of the lightness factor G. Hence the equation waswritten WI=G−4(G−B)=4B −3G. This equation is nolonger recommended.7.2 CIE Equations—The equations for whiteness recom-mended in this practice were derived and published (8) by theCIE. Two equations are given, one for the whiteness index WIand another for a tint index T. Their coefficients are given inTable 3. The CIE gave coefficients for both standard observersand Ill. D65; those for the 1931 observer and Ill. C were takenfrom the American Association of Textile Chemists and Col-orists (AATCC) method for WI(9); and those for the 1964observer and Ill. C and Ill. D50were estimated by Subcommit-tee E12.04. Those for Ill. C and Ill. D50and both observers areunofficial and should be used for in-house comparisons only.7.2.1 Equation for Whiteness Index WI:WI 5 Y1~WI, x!~xn2 x!1~WI, y!~yn2 y!(2)TABLE 1 Quantities Used in the Earlier Forms of YellownessIndex EquationsQuantityCIE Standard Illuminant and Standard ObserverC, 1931 D65, 1931 C, 1964 D65, 1964Xn98.074 95.047 97.285 94.811Yn100.000 100.000 100.000 100.000Zn118.232 108.883 116.145 107.304FA0.7987 0.8105 0.7987 0.8103F