ASTM E2022-06e1

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 E 308.
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.

General Information

• Status: Historical
• Publication Date: 30-Jun-2006
• ICS: 85.060 - Paper and board
• Technical Committee: E12 - Color and Appearance
• Drafting Committee: E12.04 - Color and Appearance Analysis

Relations

• Replaces: ASTM E2022-06 - Standard Practice for Calculation of Weighting Factors for Tristimulus Integration
• Effective Date: 01-Jul-2006
• Replaced By: ASTM E2022-08 - Standard Practice for Calculation of Weighting Factors for Tristimulus Integration
• Effective Date: 01-Dec-2008
• Referred By: ASTM E308-22 - Standard Practice for Computing the Colors of Objects by Using the CIE System
• Effective Date: 01-Jul-2006

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
´1
Designation: E 2022 – 06
Standard Practice for
1
Calculation of Weighting Factors for Tristimulus Integration
This standard is issued under the fixed designation E 2022; 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
´ NOTE—The units statement in subsection 1.3 was added editorially in May 2008.
3
1. Scope CIE Standard S 002 Colorimetric Observers
1.1 This practice describes the method to be used for
3. Terminology
calculating tables of weighting factors for tristimulus integra-
3.1 Definitions—Appearance terms in this practice are in
tionusingcustomspectralpowerdistributionsofilluminantsor
accordance with Terminology E 284.
sources, or custom color-matching functions.
3.2 Definitions of Terms Specific to This Standard:
1.2 This practice provides methods for calculating tables of
3.2.1 illuminant, n—real or ideal radiant flux, specified by
values for use with spectral reflectance or transmittance data,
its spectral distribution over the wavelengths that, in illuminat-
which are corrected for the influences of finite bandpass. In
ing objects, can affect their perceived colors.
addition,thispracticeprovidesmethodsforcalculatingweight-
3.2.2 source, n—an object that produces light or other
ing factors from spectral data which has not been bandpass
radiant flux, or the spectral power distribution of that light.
corrected. In the latter case, a correction for the influence of
3.2.2.1 Discussion—A source is an emitter of visible radia-
bandpass on the resulting tristimulus values is built in to the
tion. An illuminant is a table of agreed spectral power
tristimulus integration through the weighting factors.
distribution that may represent a source; thus, IlluminantAis a
1.3 The values stated in SI units are to be regarded as
standard spectral power distribution and Source A is the
standard. No other units of measurement are included in this
physical representation of that distribution. Illuminant D65 is a
standard.
standard illuminant that represents average north sky daylight
1.4 This standard does not purport to address all of the
but has no representative source.
safety concerns, if any, associated with its use. It is the
3.2.3 spectral power distribution, SPD, S(l),
responsibility of the user of this standard to establish appro-
n—specification of an illuminant by the spectral composition
priate safety and health practices and determine the applica-
of a radiometric quantity, such as radiance or radiant flux, as a
bility of regulatory limitations prior to its use.
function of wavelength.
2. Referenced Documents
4. Summary of Practice
2
2.1 ASTM Standards:
4.1 CIE color-matching functions are standardized at 1-nm
E 284 Terminology of Appearance
wavelength intervals. Tristimulus integration by multiplication
E 308 Practice for Computing the Colors of Objects by
of abridged spectral data into sets of weighting factors occurs
Using the CIE System
at larger intervals, typically 10-nm or 20-nm; therefore, inter-
2.2 CIE Standard:
mediate 1-nm interval spectral data are missing, but needed.
4.2 Lagrangeinterpolatingcoefficientsarecalculatedforthe
missing wavelengths. The Lagrange coefficients, when multi-
plied into the appropriate measured spectral data, interpolate
1
This practice is under the jurisdiction of ASTM Committee E12 on Color and
the abridged spectrum to 1-nm interval. The 1-nm interval
Appearance and is the direct responsibility of Subcommittee E12.04 on Color and
spectrum is then multiplied into the CIE 1-nm color-matching
Appearance Analysis.
data, and into the source spectral power distribution. Each
Current edition approved July 1, 2006. Published July 2006. Originally approved
in 1999. Last previous edition approved in 2001 as E 2022 - 01.
separate term of this multiplication is collected into a value
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
3
Standards volume information, refer to the standard’s Document Summary page on Available from USNC-CIE Publications Office, TLA Lighting Consultants, 7
the ASTM website. Pond Street, Salem, MA 01970.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
1

---------------------- Page: 1 ----------------------
´1
E2022–06
FIG. 1 The Values of i in Eq 1 are Plotted Above the Abscissa and the Values of r are Plotted Below for A) the First Measurement
Interval; B) the Intermediate Measurement Intervals; and, C) the Last Measurement Interval Being Interpolated
associated with a measured sp
...

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.
e1
Designation:E2022–01 Designation: E 2022 – 06
Standard Practice for
1
Calculation of Weighting Factors for Tristimulus Integration
This standard is issued under the fixed designation E 2022; 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 (e) indicates an editorial change since the last revision or reapproval.
1
e NOTE—The units statement in subsection 1.3 was added editorially in May 2008.
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
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:
E 284 Terminology of Appearance
E 308 Practice for Computing the Colors of Objects by Using the CIE System
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 E 284.
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.
Current edition approved June 10, 2001. Published August 2001.
Current edition approved July 1, 2006. Published July 2006. Originally approved in 1999. Last previous edition approved in 2001 as E 2022 - 01.
2
For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
, Vol 06.01.volume information, refer to the standard’s Document Summary page on the ASTM website.
3
Available from USNC-CIE Publications Office, TLA Lighting Consultants, 7 Pond Street, Salem, MA 01970.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
1

---------------------- Page: 1 ----------------------
e1
E2022–06
FIG. 1— The Values of i in Eq 1 are p Plotted a Above the a Abscissa and the v Values of r arepPlottedbBelow forA)thefFirstm
Measurement i Interval; B) the i Intermediate m Measurement i Intervals; and, C) the l Last m Measurement i Interval b Being i
Interpolated.
4.2 Lagrange interpolating coefficients are calculated for the mis
...