ASTM E2022-01
(Practice)Standard Practice for Calculation of Weighting Factors for Tristimulus Integration
Standard Practice for Calculation of Weighting Factors for Tristimulus Integration
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 funtions.
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 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 use.
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Designation: E 2022 – 01
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. Scope 3.2.2.1 Discussion—A source is an emitter of visible radia-
tion. An illuminant is a table of agreed spectral power
1.1 This practice describes the method to be used for
distribution that may represent a source; thus, IlluminantAis a
calculating tables of weighting factors for tristimulus integra-
standard spectral power distribution and Source A is the
tionusingcustomspectralpowerdistributionsofilluminantsor
physical representation of that distribution. Illuminant D65 is a
sources, or custom color-matching functions.
standard illuminant that represents average north sky daylight
1.2 This practice provides methods for calculating tables of
but has no representative source.
values for use with spectral reflectance or transmittance data,
3.2.3 spectral power distribution, SPD, S(l),
which are corrected for the influences of finite bandpass. In
n—specification of an illuminant by the spectral composition
addition,thispracticeprovidesmethodsforcalculatingweight-
of a radiometric quantity, such as radiance or radiant flux, as a
ing factors from spectral data which has not been bandpass
function of wavelength.
corrected. In the latter case, a correction for the influence of
bandpass on the resulting tristimulus values is built in to the
4. Summary of Practice
tristimulus integration through the weighting factors.
4.1 CIE color-matching functions are standardized at 1-nm
1.3 This standard does not purport to address all of the
wavelength intervals. Tristimulus integration by multiplication
safety concerns, if any, associated with its use. It is the
of abridged spectral data into sets of weighting factors occurs
responsibility of the user of this standard to establish appro-
at larger intervals, typically 10-nm or 20-nm; therefore, inter-
priate safety and health practices and determine the applica-
mediate 1-nm interval spectral data are missing, but needed.
bility of regulatory limitations prior to its use.
4.2 Lagrange interpolating coefficients are calculated for the
2. Referenced Documents missing wavelengths. The Lagrange coefficients, when multi-
plied into the appropriate measured spectral data, interpolate
2.1 ASTM Standards:
2 the abridged spectrum to 1-nm interval. The 1-nm interval
E 284 Terminology of Appearance
spectrum is then multiplied into the CIE 1-nm color-matching
E 308 Practice for Computing the Colors of Objects by
2 data, and into the source spectral power distribution. Each
Using the CIE System
separate term of this multiplication is collected into a value
2.2 CIE Standard:
3 associated with a measured spectral wavelength, thus forming
CIE Standard S 002 Colorimetric Observers
weighting factors for tristimulus integration.
3. Terminology 4.3 A correction may be applied to the resulting table of
weighting factors to incorporate a correction for the spectral
3.1 Definitions—Appearance terms in this practice are in
data’s bandpass dependence.
accordance with Terminology E 284.
3.2 Definitions of Terms Specific to This Standard:
5. Significance and Use
3.2.1 illuminant, n—real or ideal radiant flux, specified by
5.1 This practice is intended to provide a method that will
its spectral distribution over the wavelengths that, in illuminat-
yield uniformity of calculations used in making, matching, or
ing objects, can affect their perceived colors.
controlling colors of objects. This uniformity is accomplished
3.2.2 source, n—an object that produces light or other
by providing a method for calculation of weighting factors for
radiant flux, or the spectral power distribution of that light.
tristimulus integration consistent with the methods utilized to
obtain the weighting factors for common illuminant-observer
1
This practice is under the jurisdiction of ASTM Committee E12 on Color and
combinations contained in Practice E 308.
Appearance and is the direct responsibility of Subcommittee E12.04 on Color and
5.2 This practice should be utilized by persons desiring to
Appearance Analysis.
Current edition approved June 10, 2001. Published August 2001. calculate a set of weighting factors for tristimulus integration
2
Annual Book of ASTM Standards, Vol 06.01.
who have custom source, or illuminant spectral power distri-
3
Available from USNC-CIE Publications Office, TLA Lighting Consultants, 7
butions, or custom observer response functions.
Pond Street, Salem, MA 01970.
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