ASTM E2022-11
(Practice)Standard Practice for Calculation of Weighting Factors for Tristimulus Integration
Standard Practice for Calculation of Weighting Factors for Tristimulus Integration
SIGNIFICANCE AND USE
This practice is intended to provide a method that will yield uniformity of calculations used in making, matching, or controlling colors of objects. This uniformity is accomplished by providing a method for calculation of weighting factors for tristimulus integration consistent with the methods utilized to obtain the weighting factors for common illuminant-observer combinations contained in Practice E308.
This practice should be utilized by persons desiring to calculate a set of weighting factors for tristimulus integration who have custom source, or illuminant spectral power distributions, or custom observer response functions.
This practice assumes that the measurement interval is equal to the spectral bandwidth integral when applying correction for bandwidth.
SCOPE
1.1 This practice describes the method to be used for calculating tables of weighting factors for tristimulus integration using custom spectral power distributions of illuminants or sources, or custom color-matching functions.
1.2 This practice provides methods for calculating tables of values for use with spectral reflectance or transmittance data, which are corrected for the influences of finite bandpass. In addition, this practice provides methods for calculating weighting factors from spectral data which has not been bandpass corrected. In the latter case, a correction for the influence of bandpass on the resulting tristimulus values is built in to the tristimulus integration through the weighting factors.
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 and health practices and determine the applicability of regulatory limitations prior to its use.
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Designation: E2022 − 11
StandardPractice for
1
Calculation of Weighting Factors for Tristimulus Integration
This standard is issued under the fixed designation E2022; 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.
1. Scope 3. Terminology
1.1 This practice describes the method to be used for 3.1 Definitions—Appearance terms in this practice are in
calculating tables of weighting factors for tristimulus integra- accordance with Terminology E284.
tionusingcustomspectralpowerdistributionsofilluminantsor
3.2 Definitions of Terms Specific to This Standard:
sources, or custom color-matching functions.
3.2.1 illuminant, n—real or ideal radiant flux, specified by
1.2 This practice provides methods for calculating tables of its spectral distribution over the wavelengths that, in illuminat-
values for use with spectral reflectance or transmittance data, ing objects, can affect their perceived colors.
which are corrected for the influences of finite bandpass. In
3.2.2 source, n—an object that produces light or other
addition,thispracticeprovidesmethodsforcalculatingweight-
radiant flux, or the spectral power distribution of that light.
ing factors from spectral data which has not been bandpass
3.2.2.1 Discussion—A source is an emitter of visible radia-
corrected. In the latter case, a correction for the influence of
tion. An illuminant is a table of agreed spectral power
bandpass on the resulting tristimulus values is built in to the
distribution that may represent a source; thus, IlluminantAis a
tristimulus integration through the weighting factors.
standard spectral power distribution and Source A is the
physical representation of that distribution. Illuminant D65 is a
1.3 The values stated in SI units are to be regarded as
standard illuminant that represents average north sky daylight
standard. No other units of measurement are included in this
but has no representative source.
standard.
3.2.3 spectral power distribution, SPD, S(λ),
1.4 This standard does not purport to address all of the
n—specificationofanilluminantbythespectralcompositionof
safety concerns, if any, associated with its use. It is the
a radiometric quantity, such as radiance or radiant flux, as a
responsibility of the user of this standard to establish appro-
function of wavelength.
priate safety and health practices and determine the applica-
bility of regulatory limitations prior to its use.
4. Summary of Practice
2. Referenced Documents
4.1 CIE color-matching functions are standardized at 1-nm
2
2.1 ASTM Standards:
wavelength intervals. Tristimulus integration by multiplication
E284 Terminology of Appearance
of abridged spectral data into sets of weighting factors occurs
E308 PracticeforComputingtheColorsofObjectsbyUsing
at larger intervals, typically 10-nm or 20-nm; therefore, inter-
the CIE System
mediate 1-nm interval spectral data are missing, but needed.
E2729 Practice for Rectification of Spectrophotometric
4.2 Lagrange interpolating coefficients are calculated for the
Bandpass Differences
missing wavelengths. The Lagrange coefficients, when multi-
2.2 CIE Standard:
plied into the appropriate measured spectral data, interpolate
3
CIE Standard S 002 Colorimetric Observers
the abridged spectrum to 1-nm interval. The 1-nm interval
spectrum is then multiplied into the CIE 1-nm color-matching
1
This practice is under the jurisdiction of ASTM Committee E12 on Color and data, and into the source spectral power distribution. Each
Appearance and is the direct responsibility of Subcommittee E12.04 on Color and
separate term of this multiplication is collected into a value
Appearance Analysis.
associated with a measured spectral wavelength, thus forming
Current edition approved June 1, 2011. Published June 2011. Originally
weighting factors for tristimulus integration.
approved in 1999. Last previous edition approved in 2008 as E2022 – 08. DOI:
10.1520/E2022-11.
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
5. Significance and Use
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
5.1 This practice is intended to provide a method that will
the ASTM website.
yield uniformity of calculations used in making, matching, or
3
Available from USNC-CIE Publications Office (International Commission on
controlling colors of objects. This uniformity is accomplished
Illumination), C/oThomas M. Lemons,TLA-Lighting Consultants, Inc., 7 Pond St.,
Salem, MA 01970, http://www.cie-usnc.org. by providing a method for calculation of weighting fac
...
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.
Designation:E2022–08 Designation: E2022 – 11
Standard Practice for
1
Calculation of Weighting Factors for Tristimulus Integration
This standard is issued under the fixed designation E2022; 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.
1. Scope
1.1 This practice describes the method to be used for calculating tables of weighting factors for tristimulus integration using
custom spectral power distributions of illuminants or sources, or custom color-matching functions.
1.2 This practice provides methods for calculating tables of values for use with spectral reflectance or transmittance data, which
arecorrectedfortheinfluencesoffinitebandpass.Inaddition,thispracticeprovidesmethodsforcalculatingweightingfactorsfrom
spectral data which has not been bandpass corrected. In the latter case, a correction for the influence of bandpass on the resulting
tristimulus values is built in to the tristimulus integration through the weighting factors.
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 and health practices and determine the applicability of regulatory
limitations prior to its use.
2. Referenced Documents
2
2.1 ASTM Standards:
E284 Terminology of Appearance
E308 Practice for Computing the Colors of Objects by Using the CIE System Practice for Computing the Colors of Objects by
Using the CIE System
E2729 Practice for Rectification of Spectrophotometric Bandpass Differences
2.2 CIE Standard:
3
CIE Standard S 002 Colorimetric Observers
3. Terminology
3.1 Definitions—Appearance terms in this practice are in accordance with Terminology E284.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 illuminant, n—real or ideal radiant flux, specified by its spectral distribution over the wavelengths that, in illuminating
objects, can affect their perceived colors.
3.2.2 source, n—an object that produces light or other radiant flux, or the spectral power distribution of that light.
3.2.2.1 Discussion—A source is an emitter of visible radiation. An illuminant is a table of agreed spectral power distribution
that may represent a source; thus, IlluminantAis a standard spectral power distribution and SourceAis the physical representation
of that distribution. Illuminant D65 is a standard illuminant that represents average north sky daylight but has no representative
source.
3.2.3 spectral power distribution, SPD, S(l), n—specification of an illuminant by the spectral composition of a radiometric
quantity, such as radiance or radiant flux, as a function of wavelength.
4. Summary of Practice
4.1 CIE color-matching functions are standardized at 1-nm wavelength intervals. Tristimulus integration by multiplication of
abridged spectral data into sets of weighting factors occurs at larger intervals, typically 10-nm or 20-nm; therefore, intermediate
1-nm interval spectral data are missing, but needed.
1
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.
´1
Current edition approved Dec. 1, 2008. Published January 2009. Originally approved in 1999. Last previous edition approved in 2006 as E2022-06 . DOI:
10.1520/E2022-08.
Current edition approved June 1, 2011. Published June 2011. Originally approved in 1999. Last previous edition approved in 2008 as E2022 - 08. DOI: 10.1520/E2022-11.
2
For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM 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.
3
Available from USNC-CIE Publications Office (International Commission on Illumination), C/oThomas M. Lemons,TLA-Lighting Consultants, Inc., 7 Pond St., Salem,
MA 01970, http://www.cie-usnc.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
1
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E2022 – 11
FIG. 1 The Values of i in Eq 1 are Plotted Above the Abscissa and the Value
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