ASTM E313-20

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
´1
Designation: E313 − 15 E313 − 20
Standard Practice for
Calculating Yellowness and Whiteness Indices from
Instrumentally Measured Color Coordinates
This standard is issued under the fixed designation E313; 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.
ε NOTE—Section 7 was corrected editorially in June 2015.
1. Scope
1.1 This practice provides numbers that correlate with visual ratings of yellowness or whiteness of white and near-white or
colorless object-color specimens, viewed in daylight by an observer with normal color vision. White textiles, paints, and plastics
are a few of the materials that can be described by the indices of yellowness or whiteness calculated by this practice.
1.2 For a complete analysis of object colors, by a specified observer and under a specified illuminant, use of three parameters
is required. For near-white specimens, however, it is often useful to calculate single-number scales of yellowness or whiteness. This
practice provides recommended equations for such scales and discusses their derivations and uses, and limits to their applicability
(see also Ref (1) ).
1.3 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.4 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 safety, health, and healthenvironmental practices and determine the
applicability of regulatory limitations prior to use.
1.5 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.
2. Referenced Documents
2.1 ASTM Standards:
D1535 Practice for Specifying Color by the Munsell System
D1729 Practice for Visual Appraisal of Colors and Color Differences of Diffusely-Illuminated Opaque Materials
4,5
D1925 Test Method for Yellowness Index of Plastics (Withdrawn 1995)
E284 Terminology of Appearance
E308 Practice for Computing the Colors of Objects by Using the CIE System
E805 Practice for Identification of Instrumental Methods of Color or Color-Difference Measurement of Materials
E991 Practice for Color Measurement of Fluorescent Specimens Using the One-Monochromator Method
E1164 Practice for Obtaining Spectrometric Data for Object-Color Evaluation
E1247 Practice for Detecting Fluorescence in Object-Color Specimens by Spectrophotometry
E1331 Test Method for Reflectance Factor and Color by Spectrophotometry Using Hemispherical Geometry
E1345 Practice for Reducing the Effect of Variability of Color Measurement by Use of Multiple Measurements
E1347 Test Method for Color and Color-Difference Measurement by Tristimulus Colorimetry
E1348 Test Method for Transmittance and Color by Spectrophotometry Using Hemispherical Geometry
E1349 Test Method for Reflectance Factor and Color by Spectrophotometry Using Bidirectional (45°:0° or 0°:45°) Geometry
This practice is under the jurisdiction of ASTM Committee E12 on Color and Appearance and is the direct responsibility of Subcommittee E12.04 on Color and
Appearance Analysis.
Current edition approved Jan. 1, 2015May 1, 2020. Published February 2015May 2020. Originally approved in 1967. Last previous edition approved in 20102015 as
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E313 – 10.E313 – 15 . DOI: 10.1520/E0313-15E01.10.1520/E0313-20.
The boldface numbers in parentheses refer to the list of references at the end of this practice.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
The last approved version of this historical standard is referenced on www.astm.org. Replaced by Section 6 of E313.
The last approved versionReplaced by Section 6 of E313this historical standard is referenced on www.astm.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E313 − 20
E1360 Practice for Specifying Color by Using the Optical Society of America Uniform Color Scales System
E1499 Guide for Selection, Evaluation, and Training of Observers
E1541 Practice for Specifying and Matching Color Using the Colorcurve System (Withdrawn 2007)
3. Terminology
3.1 Terms and definitions in Terminology E284 are applicable to this practice.
3.2 Definitions:
3.2.1 perfect reflecting diffuser, n—ideal reflecting surface that neither absorbs nor transmits light, but reflects diffusely, with the
radiance of the reflecting surface being the same for all reflecting angles, regardless of the angular distribution of the incident light.
3.2.2 whiteness, n—the attribute of color perception by which an object color is judged to approach the preferred white.
3.2.3 whiteness index, WI, n—a number, computed by a given procedure from colorimetric data, that indicates the degree of
departure of an object color from that of a preferred white.
3.2.4 yellowness, n—the attribute of color perception by which an object color is judged to depart from colorless or a preferred
white toward yellow.
3.2.5 yellowness index, YI, n—a number, computed by a given procedure from colorimetric or spectrophotometric data, that
indicates the degree of departure of an object color from colorless or from a preferred white, toward yellow.
3.2.5.1 Discussion—
Negative values of YI denote departure toward blue.
3.3 Definitions of Terms Specific to This Standard:
3.3.1 near white, n—a color having a Munsell value greater than 8.3 (luminous reflectance factor Y = 63) and Munsell chroma
no greater than 0.5 for B hues, 0.8 for Y hues, and 0.3 for all other hues.
3.3.2 preferred white, n—color of a white standard used as the basis for calculating indices of whiteness or yellowness as the
departure of the color of the specimen from that of the preferred white; in this practice, the perfect reflecting diffuser.
4. Summary of Practice
4.1 The calculations described in this practice assume that specimens have been measured according to Practices E1164 and
E308 and one of the Test Methods E1331, E1347, E1348, or E1349, depending on the type of specimen and measuring instrument
used (see also Practice E805).
4.2 This practice takes as a starting point for the calculations CIE tristimulus values X, Y, and Z for one of the CIE standard
observers and one of the CIE standard or recommended illuminants of daylight quality. Such tristimulus values are available by
use of modern color measuring instruments.
4.3 Equations for the preferred methods of calculating YI and WI are described in Sections 6 and 7, respectively. Equations for
calculating other quantities used as indices of yellowness or whiteness are given in Appendix X1 and Appendix X2, respectively.
5. Significance and Use
5.1 This practice should be used only to compare specimens of the same material and same general appearance. For example,
a series of specimens to be compared should have generally similar gloss, texture, and (if not opaque) thickness, and translucency.
5.2 For yellowness measurement, this practice is limited to specimens having dominant wavelength in the range 570 to 580 nm,
or Munsell hue approximately 2.5GY to 2.5Y. For whiteness measurement, this practice is limited to specimens having 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 Y hues, and 0.3 for all
other hues (see 3.3.1).
5.3 The combination of measurement and calculation leading to indices of yellowness or whiteness is a psychophysical process,
that is, the procedures specified are designed to provide numbers correlating with visual estimates made under specified typical
observing conditions. Because visual observing conditions can vary widely, users should compare calculated indices with visual
estimates to ensure applicability. Some standards addressing the visual estimation of color and color difference are Practices
D1535, D1729, E1360, and E1541, and Guide E1499.
5.4 This practice does not cover the preparation of specimens, a procedure that may affect significantly the quantities measured.
In general, specimens should be prepared and presented for measurement in the manner that is standard for the test being
performed. Select enough specimens or specimen areas to provide an average result that is representative of each sample to be
tested. See Practice E1345.
E313 − 20
6. Yellowness Index
6.1 This section contains two main parts: the calculation 6.2 Historical background and 6.3 Calculation of the currently
recommended Yellowness Index. If the user wants to calculate the currently recommended Yellowness Index (YI), it is
recommended toThe historical background of this Yellowness Index is given in Appendix X1skip directly to . Alternative
Yellowness Indices are given in 6.3Appendix X2.
6.2 Background—The currently recommended equation for the calculation of yellowness index is derived from an equation due
to Hunter (2) in 1942: YI = (A − B)/G, where A, B, and G are, respectively, amber or red, blue, and green colorimeter readings.
Another version, used in the 1940s to 1960s for transparent plastics (3, 4), was based on transmittances near the ends of the visible
wavelength region: YI = 100(T − T )/T (with a factor of 100 introduced to give values of YI near unity). This equation failed
680 420 560
to account correctly for differences in the spectral transmittance curves of such plastics, especially after the adoption of ultraviolet
light absorbers to improve weathering, and was soon abandoned. When, in 1957, ASTM solicited new equations for calculating
yellowness indices, Hunter’s equation was converted (5) into CIE tristimulus value form by using Hunter’s approximate relations
between colorimeter readings and those tristimulus values; the resulting equation, YI = 100(1.28X − 1.06Z)/Y, was adopted for use
in Test Method D1925 in 1962.
6.2.1 In the original form of Test Method E313, an alternative equation was recommended for a yellowness index. In terms of
colorimeter readings, it was YI = 100(1 − B/G). Its derivation assumed that, because of the limitation of the concept to yellow (or
blue) colors, it was not necessary to take account 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 of Test Method D1925 equation were rounded to the number of digits
shown, commensurate with the precision of then-existing color measurement instrumentation. It was not intended that more
significance should be attributed to values of YI than that implicit in this number of digits. As instrumentation was improved,
however, it was found that some instruments unexpectedly gave nonzero values of YI for clear air or the perfect reflecting diffuser.
One suggested ((1), p. 205) remedy for this presumed failure of the equation was to increase the number of digits in the numerical
coefficients from two to ten after the decimal point, despite the obvious lack of significance of most of these digits. With modern
instrumentation, it is believed that two digits added to the coefficients in the original Test Method D1925 equation suffice to bring
the nonzero value of YI below 0.0005 on average. The new coefficients are given to this precision in 6.2.3.
6.2.3 Derivation of Equations—Several sets of coefficients are involved in the derivation of the final equations recommended
for calculating yellowness indices. With them evaluated, it is possible to derive highly precise equations for both the CIE 1931
standard observer and the 1964 supplementary standard observer, in combination with either CIE standard illuminant C or D .
The results are given in Table 1.
TABLE 1 Quantities Used in the Earlier Forms of Yellowness
Index Equations
CIE Standard Illuminant and Standard Observer
Quantity
C, 1931 D , 1931 C, 1964 D , 1964
65 65
X 98.074 95.047 97.285 94.811
n
Y 100.000 100.000 100.000 100.000
n
Z 118.232 108.883 116.145 107.304
n
F 0.7987 0.8105 0.7987 0.8103
A
F 0.2013 0.1895 0.2013 0.1897
B
C 1.2769 1.2985 1.2871 1.3013
X
C 1.0592 1.1335 1.0781 1.1498
Z
Residual error −0.0006 −0.0004 −0.0004 −0.0006
TABLE 2 Coefficients for Yellowness Index Equation (1)
CIE Standard Illuminant and Standard Observer
Quantity
D , D ,
65 65
C, 1931 C, 1964
1931 1964
C 1.2769 1.2985 1.2871 1.3013
x
C 1.0592 1.1335 1.0781 1.1498
z
TABLE 1 Coefficients for Yellowness Index Equation (1)
CIE Standard Illuminant and Standard Observer
Quantity
D , D ,
65 65
C, 1931 C, 1964
1931 1964
C 1.2769 1.2985 1.2871 1.3013
X
C 1.0592 1.1335 1.0781 1.1498
Z
6.2.3.1 The first set of coefficients required, consists of the tristimulus values X ,Y , and Z of the perfect reflecting diffuser (or
n n n
clear air) for the above observer-illuminant combinations. These are established by the CIE, and for the present derivation were
taken from the tables of tristimulus weighting factors in Practice E308.
E313 − 20
6.2.3.2 From these “white point” values, it is possible to calculate the coefficients in Hunter’s equation relating tristimulus value
X and colorimeter readings A and B: X = X (F A + F B), thus improving on the approximation F = 0.8 and F = 0.2 originally
n A B A B
used.
6.2.3.3 The coefficients in revised Test Method D1925 equations for YI can be calculated, rounded, and adjusted in the last
retained significant digit to minimize the residual error in the white point values. These coefficients are given in Table 1 as C and
X
C . The tabulation of the residual white point error completes the table.
Z
6.2 Calculation of Yellowness Index (YI)—YI can be calculated for either illuminantIlluminant C or D65, and either the CIE
1931 standard colorimetric observer (2°), or the CIE 1964 standard colorimetric observer (10°).
6.2.1 Use Eq 1 to calculate Yellowness Index (YI):
YI 5 100 C X 2 C Z /Y (1)
~ !
X Z
YI 5 100 C X 2 C Z ⁄Y (1)
~ !
X Z
where X,Y,Z are the measured tristimulus values of the specimen calculated for either Illuminant C or DD65, , and either the
CIE 1931 standard colorimetric observer (2°), or the CIE 1964 standard colorimetric observer (10°); and coefficients C and C
xX zZ
are selected from Table 21 for the chosen illuminant and observer.
7. Whiteness Index
7.1 Background—The earliest equation for whiteness index WI appears to be due to MacAdam (6) and related WI to excitation
purity. This and other equations utilizing the purity have largely been abandoned. Judd This section contains the calculations (7)
appears to have been the first to recognize that a whiteness index should incorporate two terms, one based on the lightness of the
specimen relative to that of a preferred white, and the other describing the difference in chromaticity betweenof the currently
recommended Whiteness Index. The historical background of this Whiteness Index in given in Appendix X3the specimen and that
preferred white. Much debate has arisen over the years as to the nature of the preferred white, but. Alternative measures of
Whiteness are given in Appendix X4at the present time the perfect reflecting diffuser is almost always adopted as that reference.
7.1.1 In the original form of Test Method E313, the equation for WI was based on the above premise and the use of colorimeter
readings G and B only. It was found that the chromaticity factor G − B required three to four times the weighting of the lightness
factor G. Hence the equation was written WI = G − 4(G − B) = 4B − 3G. This equation is no longer recommended.
7.2 CIE Equations—The equations for whiteness recommended in this practice were derived and published (82) by the CIE.
Two equations are given, one for the whiteness index WI and another for a tint index T. Their coefficients are given in Table 32.
The CIE gave coefficients for both standard observers and Ill. DD65; ; those for the 1931 observer and Ill. C were taken from
the American Association of Textile Chemists and Colorists (AATCC) method for WI(93); and those for the 1964 observer and Ill.
C and Ill. DD50 were estimated by Subcommittee E12.04. Those for Ill. C and Ill. DD50 and both observers are unofficial and
50 50
should be used for in-house comparisons only.
7.2.1 Equation for Whiteness Index WI:
WI 5 Y1~WI, x! ~x 2 x!1~WI, y! y 2 y (2)
~ !
n n
WI 5 Y1 WI, x x 2 x 1 WI, y y 2 y (2)
~ ! ~ ! ~ !
~ !
n n
where
where:
Y, x, y = the luminance factor and the chromaticity coordinates of the specimen,
x and y = the chromaticity coordinates for the CIE standard illuminant and source used, and
n n
WI, x and WI, y = numerical coefficients.
Y,x,y are the luminance factor and the chromaticity coordinates of the specimen; x and y are the chromaticity coordinates for the
n n
CIE standard illuminant and source used; and WI,x and WI,y are numerical coefficients.
Values for all these except those measured for the specimen are given in Table 32.
7.2.2 Equation for Tint Index T:
TABLE 32 Coefficients for the Equations for CIE Whiteness Index
and Tint
CIE Standard Illuminant and Observer
Value
C, 31 D , 31 D , 31 C, 64 D , 64 D , 64
50 65 50 65
X 0.3101 0.345
...