ASTM E2022-16

Standard Practice for Calculation of Weighting Factors for Tristimulus Integration

SIGNIFICANCE AND USE
5.1 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.  
5.2 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.
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 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
1.3 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.

General Information

• Status: Historical
• Publication Date: 31-Jul-2016
• ICS: 85.060 - Paper and board
• Technical Committee: E12 - Color and Appearance
• Drafting Committee: E12.04 - Color and Appearance Analysis

Standards Content (Sample)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: E2022 − 16
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 3.2.2 source, n—an object that produces light or other
radiant flux, or the spectral power distribution of that light.
1.1 This practice describes the method to be used for
3.2.2.1 Discussion—A source is an emitter of visible radia-
calculating tables of weighting factors for tristimulus integra-
tion. An illuminant is a table of agreed spectral power
tionusingcustomspectralpowerdistributionsofilluminantsor
distribution that may represent a source; thus, IlluminantAis a
sources, or custom color-matching functions.
standard spectral power distribution and Source A is the
1.2 The values stated in SI units are to be regarded as
physical representation of that distribution. Illuminant D65 is a
standard. No other units of measurement are included in this
standard illuminant that represents average north sky daylight
standard.
but has no representative source.
1.3 This standard does not purport to address all of the
3.2.3 spectral power distribution, SPD, S(λ),
safety concerns, if any, associated with its use. It is the
n—specificationofanilluminantbythespectralcompositionof
responsibility of the user of this standard to establish appro-
a radiometric quantity, such as radiance or radiant flux, as a
priate safety and health practices and determine the applica-
function of wavelength.
bility of regulatory limitations prior to its use.
4. Summary of Practice
2. Referenced Documents
2
4.1 CIE color-matching functions are standardized at 1-nm
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; therefore, intermediate
the CIE System
1-nm interval spectral data are missing, but needed.
E2729 Practice for Rectification of Spectrophotometric
Bandpass Differences
4.2 Lagrange interpolating coefficients are calculated for the
2.2 CIE Standard:
missing wavelengths. The Lagrange coefficients, when multi-
3
CIE Standard S 002 Colorimetric Observers plied into the appropriate measured spectral data, interpolate
the abridged spectrum to 1-nm interval. The 1-nm interval
3. Terminology
spectrum is then multiplied into the CIE 1-nm color-matching
data, and into the source spectral power distribution. Each
3.1 Definitions—Appearance terms in this practice are in
separate term of this multiplication is collected into a value
accordance with Terminology E284.
associated with a measured spectral wavelength, thus forming
3.2 Definitions of Terms Specific to This Standard:
weighting factors for tristimulus integration.
3.2.1 illuminant, n—real or ideal radiant flux, specified by
its spectral distribution over the wavelengths that, in illuminat-
5. Significance and Use
ing objects, can affect their perceived colors.
5.1 This practice is intended to provide a method that will
yield uniformity of calculations used in making, matching, or
1
This practice is under the jurisdiction of ASTM Committee E12 on Color and
controlling colors of objects. This uniformity is accomplished
Appearance and is the direct responsibility of Subcommittee E12.04 on Color and
by providing a method for calculation of weighting factors for
Appearance Analysis.
tristimulus integration consistent with the methods utilized to
Current edition approved Aug. 1, 2016. Published August 2016. Originally
approved in 1999. Last previous edition approved in 2011 as E2022 – 11. DOI:
obtain the weighting factors for common illuminant-observer
10.1520/E2022-16.
combinations contained in Practice E308.
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
5.2 This practice should be utilized by persons desiring to
Standards volume information, refer to the standard’s Document Summary page on
calculate a set of weighting factors for tristimulus integration
the ASTM website.
3
who have custom source, or illuminant spectral power
Available from CIE (International Commission on Illumination), http://
www.cie.co.at or http://www.techstreet.com. distributions, or custom observer response functions.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
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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 − 11 E2022 − 16
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
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.
1.2 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.3 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
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.
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.
Current edition approved June 1, 2011Aug. 1, 2016. Published June 2011August 2016. Originally approved in 1999. Last previous edition approved in 20082011 as
E2022 – 08.E2022 – 11. DOI: 10.1520/E2022-11.10.1520/E2022-16.
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. 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 CIE (International Commission on Illumination), C/o Thomas M. Lemons, TLA-Lighting Consultants, Inc., 7 Pond St.,
Salem, MA 01970, http://www.cie-usnc.org.http://www.cie.co.at or http://www.techstreet.com.
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, Illuminant A is a standard spectral power distribution and Source A is 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(λ), n—specification of an illuminant by the spectral composition of a radiometric
quantity, such as radiance or radiant flux, as a function of wavelength.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
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E2022 − 16
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; 10-nm; therefore,
intermediate 1-nm interval spectral data are missing, but needed.
4.2 Lagrange interpolating coefficients are calculated for the missing wavelengths. The Lagrange coefficients, when multiplied
into the appropriate measured spectral data, interpolat
...