SIST EN ISO 11664-1:2011

SLOVENSKI STANDARD
01-november-2011
Kolorimetrija - 1. del: Normalno opazovanje kolorimetrije po CIE (ISO 11664-
1:2007)
Colorimetry - Part 1: CIE standard colorimetric observers (ISO 11664-1:2007)
Farbmetrik - Teil 1: CIE farbmetrische Normalbeobachte (ISO 11664-1:2007)
Colorimétrie - Partie 1: Observateurs CIE de référence pour la colorimétrie (ISO 11664-
1:2007)
Ta slovenski standard je istoveten z: EN ISO 11664-1:2011
ICS:
17.180.20 Barve in merjenje svetlobe Colours and measurement of
light
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EUROPEAN STANDARD
EN ISO 11664-1
NORME EUROPÉENNE
EUROPÄISCHE NORM
April 2011
ICS 17.180.20
English Version
Colorimetry - Part 1: CIE standard colorimetric observers (ISO
11664-1:2007)
Colorimétrie - Partie 1: Observateurs CIE de référence pour Farbmetrik - Teil 1: CIE farbmetrische Normalbeobachte
la colorimétrie (ISO 11664-1:2007) (ISO 11664-1:2007)
This European Standard was approved by CEN on 17 March 2011.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN member.

This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management Centre has the same
status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland,
Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.

EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2011 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 11664-1:2011: E
worldwide for CEN national Members.

Contents Page
Foreword .3

Foreword
The text of ISO 11664-1:2007 has been prepared by Technical Committee CIE “International Commission on
Illumination” of the International Organization for Standardization (ISO) and has been taken over as
held by DIN.
This European Standard shall be given the status of a national standard, either by publication of an identical
text or by endorsement, at the latest by October 2011, and conflicting national standards shall be withdrawn at
the latest by October 2011.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights.
According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following
countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech
Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia,
Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain,
Sweden, Switzerland and the United Kingdom.
Endorsement notice
The text of ISO 11664-1:2007 has been approved by CEN as a EN ISO 11664-1:2011 without any
modification.
INTERNATIONAL ISO
STANDARD 11664-1
CIE S 014-1/E
First edition
2007-10-15
Corrected version
2008-11-01
Colorimetry —
Part 1:
CIE standard colorimetric observers
Colorimétrie —
Partie 1: Observateurs CIE de référence pour la colorimétrie

Reference number
ISO 11664-1:2007(E)
CIE S 014-1/E:2006
©
ISO 2007
ISO 11664-1:2007(E)
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.

©  ISO 2007
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2007 — All rights reserved

ISO 11664-1:2007(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
ISO 11664-1 was prepared as Standard CIE S 014-1/E by the International Commission on Illumination, which
has been recognized by the ISO Council as an international standardizing body. It was adopted by ISO under
a special procedure which requires approval by at least 75 % of the member bodes casting a vote, and is
published as a joint ISO/CIE edition.
The International Commission on Illumination (abbreviated as CIE from its French title) is an organization
devoted to international cooperation and exchange of information among its member countries on all matters
relating to the science and art of lighting.
ISO 11664-1 was prepared by CIE Division 2 Physical measurement of light and radiation.
ISO 11664-1 was initially published by ISO as ISO 10527:2007, and has subsequently been renumbered to be
part 1 of the ISO 11664 series.
ISO 11664 consists of the following parts, under the general title Colorimetry:
⎯ Part 1: CIE standard colorimetric observers [published previously as ISO 10527:2007, which has been
cancelled]
⎯ Part 2: CIE standard illuminants [published previously as ISO 10526:2007, which has been cancelled]
⎯ Part 4: CIE 1976 L*a*b* Colour space
ISO 11664-1:2007(E)
CIE S 014-1/E:2006
CIE S 014-1/E:2006
Standard
Colorimetry -
Part 1: CIE Standard Colorimetric
Observers
Colorimétrie - Partie 1: Observateurs de référence colorimétriques CIE
Farbmessung - Teil 1: CIE farbmetrische Normalbeobachter

CIE Standards are copyrighted and shall not be reproduced in any form, entirely or partly, without
the explicit agreement of the CIE.

CIE Central Bureau, Vienna CIE S 014-1/E:2006
Kegelgasse 27, A-1030 Vienna, Austria
UDC: 535.6.08 Descriptor: Colorimetry, reference data

© CIE 2006 — All rights reserved
ISO 11664-1:2007(E)
CIE S 014-1/E:2006
© CIE, 2006
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced
or utilized in any form or by any means, electronic or mechanical, including photocopying and
microfilm, without permission in writing from CIE Central Bureau at the address below.

CIE Central Bureau
Kegelgasse 27
A-1030 Vienna
Austria
Tel.: +43 1 714 3187 0
Fax: +43 1 714 3187 18
e-mail: ciecb@ping.at
Web: www.cie.co.at/
© CIE 2006 — All rights reserved
vi © ISO 2007 — All rights reserved

ISO 11664-1:2007(E)
CIE S 014-1/E:2006
FOREWORD
Standards produced by the Commission Internationale de l’Eclairage (CIE) are a concise
documentation of data defining aspects of light and lighting, for which international harmony
requires such unique definition. CIE Standards are therefore a primary source of
internationally accepted and agreed data, which can be taken, essentially unaltered, into
universal standard systems.
This CIE Standard replaces ISO/CIE 10527:1991 and was approved by the CIE
Board of Administration and the National Committees of the CIE. This CIE Standard
has been prepared by CIE Division 2 "Physical measurement of light and radiation".
This standard contains only minor changes from the previous standard, in particular the
values in the tables of the colour matching functions and chromaticity coordinates of the CIE
1931 and 1964 standard colorimetric observers are identical with the previous standard, but it
has now been clarified that they apply for standard air.

TABLE OF CONTENTS
FOREWORD vii
INTRODUCTION 1
1. SCOPE 1
2. NORMATIVE REFERENCES 1
3. DEFINITIONS 1
4. SPECIFICATIONS 3
4.1 Colour-matching functions 3
4.2 Spectral chromaticity coordinates 3
5. DERIVATION OF THE COLOUR-MATCHING FUNCTIONS FOR THE CIE 1931
STANDARD COLORIMETRIC OBSERVER 3
5.1 Experimental basis 3
5.2 Transformation procedures 4
5.3 Transformation properties 4
5.4 Comparison with earlier data 4
6. DERIVATION OF THE COLOUR-MATCHING FUNCTIONS FOR THE CIE 1964
STANDARD COLORIMETRIC OBSERVER 5
6.1 Experimental basis 5
6.2 Transformation procedures 5
6.3 Transformation properties 5
6.4 Comparison with earlier data 5
7. PRACTICAL APPLICATION OF COLOUR-MATCHING FUNCTIONS FOR CIE
STANDARD COLORIMETRIC OBSERVERS 5
7.1 Obtaining tristimulus values 5
7.2 The basis for integration 6
7.3 Rod activity 6
7.4 The use of restricted data 6
7.5 Standard of reflectance 6
TABLE 1. COLOUR-MATCHING FUNCTIONS A ND CHROMATICITY COORDINATES
OF CIE 1931 STANDARD COLORIMETRIC OBSERVER 7
TABLE 2. COLOUR-MATCHING FUNCTIONS A ND CHROMATICITY COORDINATES
OF CIE 1964 STANDARD COLORIMETRIC OBSERVER 18
ANNEX: BIBLIOGRAPHY (INFORMATIVE) 29

© CIE, 2006
© CIE 2006 — All rights reserved
ISO 11664-1:2007(E)
CIE S 014-1/E:2006
COLORIMETRY - PART 1: CIE STANDARD COLORIMETRIC OBSERVERS

INTRODUCTION
Colours with different spectral compositions can look alike. An important function of
colorimetry is to determine whether a pair of such metameric colours will look alike. The use
of visual colorimeters for this purpose is handicapped by variations in the colour matches
made amongst observers classified as having normal colour vision. Visual colorimetry also
tends to be time-consuming. For these reasons, it has long been the practice in colorimetry to
make use of sets of colour-matching functions to calculate tristimulus values for colours:
equality of tristimulus values for a pair of colours indicates that the colour appearances of the
two colours match, when they are viewed in the same conditions by an observer for whom the
colour-matching functions apply. The use of standard sets of colour-matching functions
makes the comparison of tristimulus values obtained at different times and locations possible.

1. SCOPE
This International Standard specifies colour-matching functions for use in colorimetry. Two
sets of colour-matching functions are specified.
a) Colour-matching functions for the CIE 1931 standard colorimetric observer
This set of colour-matching functions is representative of the colour-matching properties of
observers with normal colour vision for visual field sizes of angular subtense from about 1° to
about 4°, for vision at photopic levels of adaptation.
b) Colour-matching functions for the CIE 1964 standard colorimetric observer
This set of colour-matching functions is representative of the colour-matching properties of
observers with normal colour vision for visual field sizes of angular subtense greater than
about 4°, for vision at sufficiently high photopic levels and with spectral power distributions
such that no participation of the rod receptors of the retina is to be expected.

2. NORMATIVE REFERENCES
The following referenced documents are indispensable for the application of this document.
For dated references, only the edition cited applies. For undated references, the latest edition
of the referenced document (including any amendments) applies.
rd
CIE 15:2004. Colorimetry, 3 edition.
CIE 17.4-1987. International lighting vocabulary (ILV) - Joint publication IEC/CIE.

3. DEFINITIONS
For the purposes of this International Standard, the following definitions apply. These
definitions are taken from CIE 17.4-1987, where other relevant terms will also be found.
3.1 colour stimulus function, ϕ (λ) (see ILV 845-03-03)
λ
description of a colour stimulus by the spectral concentration of a radiometric quantity (such
as radiance or radiant power) as a function of wavelength
3.2 relative colour stimulus function, ϕ(λ) (see ILV 845-03-04)
relative spectral power distribution of the colour stimulus function
© CIE 2006 — All rights reserved
ISO 11664-1:2007(E)
CIE S 014-1/E:2006
3.3 metameric colour stimuli; metamers (see ILV 845-03-05)
spectrally different colour stimuli that have the same tristimulus values
3.4 monochromatic stimulus: spectral stimulus (see ILV 845-03-08)
stimulus consisting of a monochromatic radiation
3.5 equi-energy spectrum (see ILV 845-03-14)
spectrum of a radiation whose spectral concentration of a radiometric quantity as a function of
wavelength is constant throughout the visible region
3.6 additive mixture of colour stimuli (see ILV 845-03-15)
method of stimulation that combines on the retina the actions of various stimuli in such a
manner that they cannot be perceived individually
3.7 colour matching (see ILV 845-03-16)
action of making a colour stimulus appear the same in colour as a given colour stimulus
3.8 trichromatic system (see ILV 845-03-20)
system for specifying colour stimuli in terms of tristimulus values based on matching colours
by additive mixture of three suitably chosen reference colour stimuli
3.9 reference colour stimuli, [R], [G], [B]; [X], [Y], [Z]; [X ], [Y ], [Z ]; etc. (see ILV 845-03-
10 10 10
21)
set of three colour stimuli on which a trichromatic system is based
3.10 tristimulus values, R, G, B; X, Y, Z; X , Y , Z ; etc. (see ILV 845-03-22)
10 10 10
amounts of three reference colour stimuli, in a given trichromatic system, required to match
the colour of the stimulus considered
3.11 colour-matching functions, r(λ), g(λ), b(λ); x(λ), y(λ), z(λ) ; x (λ), y ()λ , z ()λ ; etc.
10 10 10
(see ILV 845-03-23)
tristimulus values of monochromatic stimuli of equal radiant power
3.12 CIE 1931 standard colorimetric system (X, Y, Z) (see ILV 845-03-28)
system for determining the tristimulus values of any spectral power distribution using the set
of reference colour stimuli [X], [Y], [Z], and the three CIE colour-matching functions
() () ()
xλ , yλ , zλ adopted by the CIE in 1931 and defined in this standard
3.13 CIE 1964 standard colorimetric system (X , Y , Z ) (see ILV 845-03-29)
10 10 10
system for determining the tristimulus values of any spectral power distribution using the set
of reference colour stimuli [X ], [Y ], [Z ], and the three CIE colour-matching functions
10 10 10
x ()λ , y ()λ , z ()λ adopted by the CIE in 1964 and defined in this standard
10 10 10
3.14 CIE colour-matching functions (see ILV 845-03-30)
functions x()λ , y()λ , z()λ in the CIE 1931 standard colorimetric system and
x ()λ , y ()λ , z ()λ in the CIE 1964 standard colorimetric system
10 10 10
3.15 CIE 1931 standard colorimetric observer (see ILV 845-03-31)
ideal observer whose colour-matching properties correspond to the CIE colour-matching
() () ()
functions xλ , yλ , zλ
3.16 CIE 1964 standard colorimetric observer (see ILV 845-03-32)
ideal observer whose colour-matching properties correspond to the CIE colour-matching
functions x ()λ , y (λ), z ()λ
10 10 10
© CIE 2006 — All rights reserved
2 © ISO 2007 — All rights reserved

ISO 11664-1:2007(E)
CIE S 014-1/E:2006
3.17 chromaticity coordinates, r, g, b; x, y, z; x , y , z ; etc. (see ILV 845-03-33)
10 10 10
ratio of each of a set of three tristimulus values to their sum
3.18 spectral chromaticity coordinates, r(λ), g(λ), b(λ); x(λ), y(λ), z(λ); x (λ), y (λ), z (λ); etc.
10 10 10
(see ILV 845-03-36)
chromaticity coordinates of monochromatic stimuli
3.19 spectral luminous efficiency, V(λ) (see ILV 845-01-22)
ratio of the radiant flux at wavelength λ to that at wavelength λ, such that both radiations
m
produce an equal visual response under specified photometric conditions and λ is chosen so
m
that the maximum value of this ratio is equal to 1
3.20 perfect reflecting diffuser (see ILV 845-04-54)
ideal isotropic diffuser with a reflectance equal to unity

4. SPECIFICATIONS
4.1 Colour-matching functions
The colour-matching functions x()λ , y(λ), z(λ) of the CIE 1931 standard colorimetric observer
are defined by the values given in Table 1, and those x (λ), y (λ), z (λ) of the CIE 1964
10 10 10
standard colorimetric observer are defined by the values given in Table 2. The values are
given at 1 nm wavelength intervals from 360 nm to 830 nm. If values are required at closer
wavelength intervals than 1 nm, they should be derived by linear interpolation.
4.2 Spectral chromaticity coordinates
Tables 1 and 2 also give values for the spectral chromaticity coordinates, x(λ), y(λ), z(λ);
x (λ), y (λ), z (λ); these have been derived from the appropriate colour-matching functions
10 10 10
by forming the ratios:
x()λ y(λ) z()λ
x()λ = , y()λ =  and z()λ =
x()λ + y()λ + z()λ x()λ + y()λ + z()λ x()λ + y()λ + z()λ
x ()λ y (λ)
10 10
x ()λ = , y ()λ =  and
10 10
x ()λ + y ()λ + z ()λ x ()λ + y ()λ + z ()λ
10 10 10 10 10 10
z ()λ
z ()λ =
x ()λ + y ()λ + z ()λ
10 10 10
Note: All wavelengths are for standard air.

5. DERIVATION OF THE COLOUR-MATCHING FUNCTIONS FOR THE CIE 1931
STANDARD COLORIMETRIC OBSERVER
5.1 Experimental basis
The CIE 1931 colour-matching functions, x(λ), y(λ), z(λ) were derived from experimental
work carried out by Wright (1928-1930) and by Guild (1931) in which a total of 17 observers
matched the monochromatic stimuli of the spectrum, over the range of about 400 nm to
700 nm, with additive mixtures of red, green and blue lights, using observing fields of 2°
angular subtense.
© CIE 2006 — All rights reserved
ISO 11664-1:2007(E)
CIE S 014-1/E:2006
5.2 Transformation procedures
The experimental results were converted into those that would have been obtained if the
matching had been carried out using, as reference colour stimuli, monochromatic radiations
of wavelengths 700 nm for the red [R], 546,1 nm for the green [G] and 435,8 nm for the blue
[B], measured in units such that equal quantities of [R], [G] and [B] were required to match the
equi-energy spectrum.
The results for the 17 observers were averaged and then slightly adjusted so that by
adding together suitable proportions of the [R], [G], [B] colour-matching functions
r()λ , g()λ , b()λ it was possible to obtain a function identical to that of the CIE spectral
luminous efficiency, V(λ); the proportions used were in the ratios of 1,000 0 to 4,590 7 to
0,060 1, and these were then the relative luminances of unit quantities of [R], [G] and [B]. The
CIE 1931 colour-matching functions were then determined by the following equations:
x()λ = [0,49r()λ + 0,31g()λ + 0,20b(λ)]n
y()λ = [0,176 97r(λ)+ 0,812 40g()λ + 0,010 63b(λ)]n
z()λ = [0,00r()λ + 0,01g()λ + 0,99b(λ)]n
where n is a normalising constant given by
V()λ
n=
0,176 97r()λ + 0,812 40g()λ + 0,010 63b()λ
n is a constant, not a function of wavelength, because the coefficients 0,176 97, 0,812 40,
and 0,010 63 are in the same ratios to one another as the ratio of 1,000 0 to 4,590 7 to
0,060 1; n is equal to
1,000 0 + 4,590 7 + 0,060 1
= 5,650 8
0, 176 97 + 0,812 40 + 0,010 63
The values of x()λ , y()λ , z()λ given in Table 1 from 360 nm to 400 nm and from
700 nm to 830 nm are extrapolations.
5.3 Transformation properties
The transformation given in the above equations was chosen to achieve the following
objectives. First, the y()λ function is identical to the V(λ) function. Second, the values of
x()λ , y()λ , z()λ are all positive for all wavelengths of the spectrum (unlike r()λ , g()λ , b()λ one
of which is negative at most wavelengths because of the need to desaturate spectral stimuli
when matching them with red, green, and blue reference stimuli). Third, the values of z()λ
are zero for wavelengths longer than 650 nm. Fourth, the values of x(λ) are nearly zero at
( ) ( )
wavelengths around 505 nm. Fifth, the values of xλ and yλ are small at the short-
wavelength end of the spectrum. Sixth, the equi-energy spectrum is specified by equal
amounts of X, Y and Z.
Because the y()λ function is identical to the V(λ) function, the Y tristimulus value is
proportional to luminance.
5.4 Comparison with earlier data
The values of x()λ , y()λ , z()λ given in Table 1 for the spectral range of 380 nm to 780 nm at
5 nm intervals, when rounded to four decimal places, agree closely with those originally
published in 1931. There are only three minor differences: at λ = 775 nm the new value of
x()λ is 0,000 1 instead of 0,000 0; at λ = 555 nm, y(λ) = 1,000 0 instead of 1,000 2 and at
λ = 740 nm, y()λ = 0,000 2 instead of 0,000 3. These changes are considered insignificant in
most colorimetric computations.
When the relative luminances of unit quantities of [R], [G] and [B] are deduced from the
data of Tabie 1, the values obtained are 1,000 0 to 4,588 8 to 0,060 3 instead of 1,000 0 to
© CIE 2006 — All rights reserved
4 © ISO 2007 — All rights reserved

ISO 11664-1:2007(E)
CIE S 014-1/E:2006
4,590 7 to 0,060 1, the relative radiances being 71,893 8 to 1,374 7 to 1,000 0 instead of
72,096 2 to 1,379 1 to 1,000 0. These changes are also considered insignificant in practice.
The values given in CIE 15:2004 at 5 nm intervals agree exactly with those given in
Table 1.
6. DERIVATION OF THE COLOUR-MATCHING FUNCTIONS FOR THE CIE 1964
STANDARD COLORIMETRIC OBSERVER
6.1 Experimental basis
The CIE 1964 colour-matching functions x (λ), y (λ), z (λ) were derived from experimental
10 10 10
work carried out by Stiles and Burch (1959) and by Speranskaya (1959) in which a total of 67
observers matched monochromatic stimuli of the spectrum from approximately 390 nm to
830 nm with additive mixtures of red, green, and blue lights, using observing fields of 10°
angular subtense (but ignoring the central 4° or so).
6.2 Transformation procedures
The experimental results were converted into those that would have been obtained if the
matching had been carried out using, as reference colour stimuli, monochromatic radiations
-1 -1
of wavenumbers 15 500 cm for the red [R ], 19 000 cm for the green [G ], and
10 10
-1
22 500 cm for the blue [B ], corresponding approximately to wavelengths 645,2 nm,
526,3 nm and 444,4 nm, respectively. The units used for the quantities of [R ], [G ] and [B ]
10 10 10
were such that equal amounts were required to match the equi-energy spectrum. A weighted
average of the results for the 67 observers was used to provide a set of colour-matching
functions r ()ν , g (ν), b ()ν . The CIE 1964 colour-matching functions were then derived by
10 10 10
the following equations:
() () ( ) ( )
x ν = 0,341080r ν + 0,189 145g ν + 0,387 529b ν
10 10 10 10
y ()ν = 0,139 058r ()ν + 0,837 460g (ν)+ 0,073 316b (ν)
10 10 10 10
z ()ν = 0,000 000r ()ν + 0,039 553g (ν)+ 2,026 200b (ν)
10 10 10 10
In Table 2, the CIE 1964 colour-matching functions x (λ), y (λ), z ()λ are given on a
10 10 10
wavelength basis and were obtained by interpolation from the frequency-based functions
given above. The values in the range of 360 nm to 390 nm are extrapolations.
6.3 Transformation properties
The transformation given in the equations in 6.2 was chosen to achieve a colorimetric system
(X , Y , Z ) having a coordinate system broadly similar to that of the CIE 1931 (X, Y, Z)
10 10 10
system. However, in the 1964 system, the data were not constrained to fit the CIE V(λ)
spectral luminous efficiency function, and the Y tristimulus value is not proportional to
luminance calculated using the V(λ) function.
6.4 Comparison with earlier data
The values given in CIE 15:2004 at 5 nm intervals agree exactly with those given in Table 2.

7. PRACTICAL APPLICATION OF COLOUR-MATCHING FUNCTIONS FOR CIE
STANDARD COLORIMETRIC OBSERVERS
7.1 Obtaining tristimulus values
The data given in Tables 1 and 2 provide the tristimulus values and chromaticity coordinates
of all monochromatic stimuli directly or by interpolation. For stimuli consisting of radiation of
© CIE 2006 — All rights reserved
ISO 11664-1:2007(E)
CIE S 014-1/E:2006
various wavelengths, the tristimulus values X, Y, Z and X , Y , Z are calculated by
10 10 10
integration over the spectral range 360 nm to 830 nm using the following equations:
Xk= ϕλλx dλ Xk= ϕλλx dλ
()() ( ) ( )
λ 10 10 λ 10
∫ ∫
λ λ
Yk= ϕλyλ dλ Yk= ϕλλy dλ
() ( ) ( ) ( )
λ 10 10 λ 10
∫ ∫
λ λ
Zk= ϕλλz dλ Zk= ϕλλz dλ
() ( ) ( ) ( )
λ 10 10 λ 10
∫ ∫
λ λ
where
ϕ()λ is the colour stimulus function of the stimulus considered;
λ
x()λ , y()λ , z()λ , x (λ), y ()λ , z ()λ are the appropriate CIE colour-matching functions;
10 10 10
k and k are constants.
Tristimulus values are usually evaluated on a relative basis, and the constants, k and
k are then chosen according to agreed conventions; however, it is essential that, for stimuli
that will be considered together, the same value for k (or for k ) be adopted, so that all the
tristimulus values involved are assessed on the same basis. For reflecting object-colours, k
and k shall be chosen so that Y and Y are equal to 100 for the perfect reflecting diffuser,
10 10
and, for transmitting object-colours, so that Y and Y are equal to 100 for the perfect
transmitter. In the case of primary light sources, if it is required that Y be equal to the absolute
value of the photometric quantity, k shall be equal to K , the maximum spectral luminous
m
efficacy (which is equal to 683 Im/W) and ϕ (λ) shall then be the spectral concentration of
λ
the radiometric quantity corresponding to the photometric quantity required.
7.2 The basis for integration
The integration step in the equations in 7.1 implies additivity of colour matches: that is, if two
colour stimuli [C1] and [C2] have tristimulus values X Y , Z , and X , Y , Z , respectively, then
1 1 1 2 2 2
the additive mixture of [C1] and [C2] will have tristimulus values X + X , Y + Y , Z + Z .
1 2 1 2 1 2
Experimental investigations have shown that, although additivity of this type sometimes fails
to occur, the principle of additivity is sufficiently valid for predicting colour matches in most
cases of importance in practical colorimetry.
7.3 Rod activity
The tristimulus values in the CIE 1964 standard colorimetric system are relevant only to those
observing conditions where the luminances are sufficiently high and the spectral power
distributions are such that no significant participation of the rod receptors of the retina is to be
expected.
7.4 The use of restricted data
For most practical applications of colorimetry, it is sufficient to use values of colour-matching
functions at less frequent intervals of wavelength than every 1 nm, covering a more restricted
range of wavelengths than from 360 nm to 830 nm, and using fewer decimal places than are
given in Tables 1 and 2. Data and guidelines that facilitate such practice are given in
CIE 15:2004, together with various other recommended procedures for practical colorimetry.
7.5 Standard of reflectance
The perfect reflecting diffuser is the CIE reference standard for the colorimetry of reflecting
samples.
© CIE 2006 — All rights reserved
6 © ISO 2007 — All rights reserved

ISO 11664-1:2007(E)
CIE S 014-1/E:2006
TABLE 1. COLOUR-MATCHING FUNCTIONS AND CHROMATICITY COORDINATES OF
CIE 1931 STANDARD COLORIMETRIC OBSERVER
(The table below is available in electronic form as a supplement to CIE 15:2004.)

Wave-
CIE colour-matching functions Chromaticity coordinates
length
λ nm x()λ y(λ) z(λ)
x(λ) y(λ) z(λ)
360 0,000 129 900 0 0,000 003 917 000 0,000 606 100 0 0,175 56 0,005 29 0,819 15
61 0,000 145 847 0 0,000 004 393 581 0,000 680 879 2 0,175 48 0,005 29 0,819 23
62 0,000 163 802 1 0,000 004 929 604 0,000 765 145 6 0,175 40 0,005 28 0,819 32
63 0,000 184 003 7 0,000 005 532 136 0,000 860 012 4 0,175 32 0,005 27 0,819 41
64 0,000 206 690 2 0,000 006 208 245 0,000 966 592 8 0,175 24 0,005 26 0,819 50

365 0,000 232 100 0 0,000 006 965 000 0,001 086 000 0,175 16 0,005 26 0,819 58
66 0,000 260 728 0 0,000 007 813 219 0,001 220 586 0,175 09 0,005 25 0,819 66
67 0,000 293 075 0 0,000 008 767 336 0,001 372 729 0,175 01 0,005 24 0,819 75
68 0,000 329 388 0 0,000 009 839 844 0,001 543 579 0,174 94 0,005 23 0,819 83
69 0,000 369 914 0 0,000 011 043 23 0,001 734 286 0,174 88 0,005 22 0,819 90

370 0,000 414 900 0 0,000 012 390 00 0,001 946 000 0,174 82 0,005 22 0,819 96
71 0,000 464 158 7 0,000 013 886 41 0,002 177 777 0,174 77 0,005 23 0,820 00
72 0,000 518 986 0 0,000 015 557 28 0,002 435 809 0,174 72 0,005 24 0,820 04
73 0,000 581 854 0 0,000 017 442 96 0,002 731 953 0,174 66 0,005 24 0,820 10
74 0,000 655 234 7 0,000 019 583 75 0,003 078 064 0,174 59 0,005 22 0,820 19

375 0,000 741 600 0 0,000 022 020 00 0,003 486 000 0,174 51 0,005 18 0,820 31
76 0,000 845 029 6 0,000 024 839 65 0,003 975 227 0,174 41 0,005 13 0,820 46
77 0,000 964 526 8 0,000 028 041 26 0,004 540 880 0,174 31 0,005 07 0,820 62
78 0,001 094 949 0,000 031 531 04 0,005 158 320 0,174 22 0,005 02 0,820 76
79 0,001 231 154 0,000 035 215 21 0,005 802 907 0,174 16 0,004 98 0,820 86

380 0,001 368 000 0,000 039 000 00 0,006 450 001 0,174 11 0,004 96 0,820 93
81 0,001 502 050 0,000 042 826 40 0,007 083 216 0,174 09 0,004 96 0,820 95
82 0,001 642 328 0,000 046 914 60 0,007 745 488 0,174 07 0,004 97 0,820 96
83 0,001 802 382 0,000 051 589 60 0,008 501 152 0,174 06 0,004 98 0,820 96
84 0,001 995 757 0,000 057 176 40 0,009 414 544 0,174 04 0,004 98 0,820 98

385 0,002 236 000 0,000 064 000 00 0,010 549 99 0,174 01 0,004 98 0,821 01
86 0,002 535 385 0,000 072 344 21 0,011 965 80 0,173 97 0,004 97 0,821 06
87 0,002 892 603 0,000 082 212 24 0,013 655 87 0,173 93 0,004 94 0,821 13
88 0,003 300 829 0,000 093 508 16 0,015 588 05 0,173 89 0,004 93 0,821 18
89 0,003 753 236 0,000 106 136 1 0,017 730 15 0,173 84 0,004 92 0,821 24

390 0,004 243 000 0,000 120 000 0 0,020 050 01 0,173 80 0,004 92 0,821 28
91 0,004 762 389 0,000 134 984 0 0,022 511 36 0,173 76 0,004 92 0,821 32
92 0,005 330 048 0,000 151 492 0 0,025 202 88 0,173 70 0,004 94 0,821 36
93 0,005 978 712 0,000 170 208 0 0,028 279 72 0,173 66 0,004 94 0,821 40
94 0,006 741 117 0,000 191 816 0 0,031 897 04 0,173 61 0,004 94 0,821 45

395 0,007 650 000 0,000 217 000 0 0,036 210 00 0,173 56 0,004 92 0,821 52
96 0,008 751 373 0,000 246 906 7 0,041 437 71 0,173 51 0,004 90 0,821 59
97 0,010 028 88 0,000 281 240 0 0,047 503 72 0,173 47 0,004 86 0,821 67
98 0,011 421 70 0,000 318 520 0 0,054 119 88 0,173 42 0,004 84 0,821 74
99 0,012 869 01 0,000 357 266 7 0,060 998 03 0,173 38 0,004 81 0,821 81

400 0,014 310 00 0,000 396 000 0 0,067 850 01 0,173 34 0,004 80 0,821 86
01 0,015 704 43 0,000 433 714 7 0,074 486 32 0,173 29 0,004 79 0,821 92
02 0,017 147 44 0,000 473 024 0 0,081 361 56 0,173 24 0,004 78 0,821 98
03 0,018 781 22 0,000 517 876 0 0,089 153 64 0,173 17 0,004 78 0,822 05
04 0,020 748 01 0,000 572 218 7 0,098 540 48 0,173 10 0,004 77 0,822 13

© CIE 2006 — All rights reserved
ISO 11664-1:2007(E)
CIE S 014-1/E:2006
TABLE 1 (continued)
Wave-
CIE colour-matching functions Chromaticity coordinates
length
λ nm x()λ y(λ) z(λ)
x(λ) y(λ) z(λ)
405 0,023 190 00 0,000 640 000 0 0,110 200 0 0,173 02 0,004 78 0,822 20
06 0,026 207 36 0,000 724 560 0 0,124 613 3 0,172 93 0,004 78 0,822 29
07 0,029 782 48 0,000 825 500 0 0,141 701 7 0,172 84 0,004 79 0,822 37
08 0,033 880 92 0,000 941 160 0 0,161 303 5 0,172 75 0,004 80 0,822 45
09 0,038 468 24 0,001 069 880 0,183 256 8 0,172 66 0,004 80 0,822 54

410 0,043 510 00 0,001 210 000 0,207 400 0 0,172 58 0,004 80 0,822 62
11 0,048 995 60 0,001 362 091 0,233 692 1 0,172 49 0,004 80 0,822 71
12 0,055 022 60 0,001 530 752 0,262 611 4 0,172 39 0,004 80 0,822 81
13 0,061 718 80 0,001 720 368 0,294 774 6 0,172 30 0,004 80 0,822 90
14 0,069 212 00 0,001 935 323 0,330 798 5 0,172 19 0,004 82 0,822 99

415 0,077 630 00 0,002 180 000 0,371 300 0 0,172 09 0,004 83 0,823 08
16 0,086 958 11 0,002 454 800 0,416 209 1 0,171 98 0,004 86 0,823 16
17 0,097 176 72 0,002 764 000 0,465 464 2 0,171 87 0,004 89 0,823 24
18 0,108 406 3 0,003 117 800 0,519 694 8 0,171 74 0,004 94 0,823 32
19 0,120 767 2 0,003 526 400 0,579 530 3 0,171 59 0,005 01 0,823 40

420 0,134 380 0 0,004 000 000 0,645 600 0 0,171 41 0,005 10 0,823 49
21 0,149 358 2 0,004 546 240 0,718 483 8 0,171 21 0,005 21 0,823 58
22 0,165 395 7 0,005 159 320 0,796 713 3 0,170 99 0,005 33 0,823 68
23 0,181 983 1 0,005 829 280 0,877 845 9 0,170 77 0,005 47 0,823 76
24 0,198 611 0 0,006 546 160 0,959 439 0 0,170 54 0,005 62 0,823 84

425 0,214 770 0 0,007 300 000 1,039 050 1 0,170 30 0,005 79 0,823 91
26 0,230 186 8 0,008 086 507 1,115 367 3 0,170 05 0,005 97 0,823 98
27 0,244 879 7 0,008 908 720 1,188 497 1 0,169 78 0,006 18 0,824 04
28 0,258 777 3 0,009 767 680 1,258 123 3 0,169 50 0,006 40 0,824 10
29 0,271 807 9 0,010 664 43 1,323 929 6 0,169 20 0,006 64 0,824 16

430 0,283 900 0 0,011 600 00 1,385 600 0 0,168 88 0,006 90 0,824 22
31 0,294 943 8 0,012 573 17 1,442 635 2 0,168 53 0,007 18 0,824 29
32 0,304 896 5 0,013 582 72 1,494 803 5 0,168 15 0,007 49 0,824 36
33 0,313 787 3 0,014 629 68 1,542 190 3 0,167 75 0,007 82 0,824 43
34 0,321 645 4 0,015 715 09 1,584 880 7 0,167 33 0,008 17 0,824 50

435 0,328 500 0 0,016 840 00 1,622 960 0 0,166 90 0,008 55 0,824 55
36 0,334 351 3 0,018 007 36 1,656 404 8 0,166 45 0,008 96 0,824 59
37 0,339 210 1 0,019 214 48 1,685 295 9 0,165 98 0,009 40 0,824 62
38 0,343 121 3 0,020 453 92 1,709 874 5 0,165 48 0,009 87 0,824 65
39 0,346 129 6 0,021 718 24 1,730 382 1 0,164 96 0,010 35 0,824 69

440 0,348 280 0 0,023 000 00 1,747 060 0 0,164 41 0,010 86 0,824 73
41 0,349 599 9 0,024 294 61 1,760 044 6 0,163 83 0,011 38 0,824 79
42 0,350 147 4 0,025 610 24 1,769 623 3 0,163 21 0,011 94 0,824 85
43 0,350 013 0 0,026 958 57 1,776 263 7 0,162 55 0,012 52 0,824 93
44 0,349 287 0 0,028 351 25 1,780 433 4 0,161 85 0,013 14 0,825 01

445 0,348 060 0 0,029 800 00 1,782 600 0 0,161 11 0,013 79 0,825 10
46 0,346 373 3 0,031 310 83 1,782 968 2 0,160 31 0,014 49 0,825 20
47 0,344 262 4 0,032 883 68 1,781 699 8 0,159 47 0,015 23 0,825 30
48 0,341 808 8 0,034 521 12 1,779 198 2 0,158 57 0,016 02 0,825 41
49 0,339 094 1 0,036 225 71 1,775 867 1 0,157 63 0,016 84 0,825 53

© CIE 2006 — All rights reserved
8 © ISO 2007 — All rights reserved

ISO 11664-1:2007(E)
CIE S 014-1/E:2006
TABLE 1 (continued)
Wave-
CIE colour-matching functions Chromaticity coordinates
length
λ nm x()λ y(λ) z(λ)
x(λ) y(λ) z(λ)
450 0,336 200 0 0,038 000 00 1,772 110 0 0,156 64 0,017 71 0,825 65
51 0,333 197 7 0,039 846 67 1,768 258 9 0,155 60 0,018 61 0,825 79
52 0,330 041 1 0,041 768 00 1,764 039 0 0,154 52 0,019 56 0,825 92
53 0,326 635 7 0,043 766 00 1,758 943 8 0,153 40 0,020 55 0,826 05
54 0,322 886 8 0,045 842 67 1,752 466 3 0,152 22 0,021 61 0,826 17

455 0,318 700 0 0,048 000 00 1,744 100 0 0,150 99 0,022 74 0,826 27
56 0,314 025 1 0,050 243 68 1,733 559 5 0,149 69 0,023 95 0,826 36
57 0,308 884 0 0,052 573 04 1,720 858 1 0,148 34 0,025 25 0,826 41
58 0,303 290 4 0,054 980 56 1,705 936 9 0,146 93 0,026 63 0,826 44
59 0,297 257 9 0,057 458 72 1,688 737 2 0,145 47 0,028 12 0,826 41

460 0,290 800 0 0,060 000 00 1,669 200 0 0,143 96 0,029 70 0,826 34
61 0,283 970 1 0,062 601 97 1,647 528 7 0,142 41 0,031 39 0,826 20
62 0,276 721 4 0,065 277 52 1,623 412 7 0,140 80 0,033 21 0,825 99
63 0,268 917 8 0,068 042 08 1,596 022 3 0,139 12 0,035 20 0,825 68
64 0,260 422 7 0,070 911 09 1,564 528 0 0,137 37 0,037 40 0,825 23

465 0,251 100 0 0,073 900 00 1,528 100 0 0,135 50 0,039 88 0,824 62
66 0,240 847 5 0,077 016 00 1,486 111 4 0,133 51 0,042 69 0,823 80
67 0,229 851 2 0,080 266 40 1,439 521 5 0,131 37 0,045 88 0,822 75
68 0,218 407 2 0,083 666 80 1,389 879 9 0,129 09 0,049 45 0,821 46
69 0,206 811 5 0,087 232 80 1,338 736 2 0,126 66 0,053 43 0,819 91

470 0,195 360 0 0,090 980 00 1,287 640 0 0,124 12 0,057 80 0,818 08
71 0,184 213 6 0,094 917 55 1,237 422 3 0,121 47 0,062 59 0,815 94
72 0,173 327 3 0,099 045 84 1,187 824 3 0,118 70 0,067 83 0,813 47
73 0,162 688 1 0,103 367 4 1,138 761 1 0,115 81 0,073 58 0,810 61
74 0,152 283 3 0,107 884 6 1,090 148 0 0,112 78 0,079 89 0,807 33

475 0,142 100 0 0,112 600 0 1,041 900 0 0,109 60 0,086 84 0,803 56
76 0,132 178 6 0,117 53 20 0,994 197 6 0,106 26 0,094 49 0,799 25
77 0,122 569 6 0,122 674 4 0,947 347 3 0,102 78 0,102 86 0,794 36
78 0,113 275 2 0,127 992 8 0,901 453 1 0,099 13 0,112 01 0,788 86
79 0,104 297 9 0,133 452 8 0,856 619 3 0,095 31 0,121 94 0,782 75

480 0,095 640 00 0,139 020 0 0,812 950 1 0,091 29 0,132 70 0,776 01
81 0,087 299 55 0,144 676 4 0,770 517 3 0,087 08 0,144 32 0,768 60
82 0,079 308 04 0,150 469 3 0,729 444 8 0,082 68 0,156 87 0,760 45
83 0,071 717 76 0,156 461 9 0,689 913 6 0,078 12 0,170 42 0,751 46
84 0,064 580 99 0,162 717 7 0,652 104 9 0,073 44 0,185 03 0,741 53

485 0,057 950 01 0,169 300 0 0,616 200 0 0,068 71 0,200 72 0,730 57
86 0,051 862 11 0,176 243 1 0,582 328 6 0,063 99 0,217 47 0,718 54
87 0,046 281 52 0,183 558 1 0,550 416 2 0,059 32 0,235 25 0,705 43
88 0,041 150 88 0,191 273 5 0,520 337 6 0,054 67 0,254 09 0,691 24
89 0,036 412 83 0,199 418 0 0,491 967 3 0,050 03 0,274 00 0,675 97

490 0,032 010 00 0,208 020 0 0,465 180 0 0,045 39 0,294 98 0,659 63
91 0,027 917 20 0,217 119 9 0,439 924 6 0,040 76 0,316 98 0,642 26
92 0,024 144 40 0,226 734 5 0,416 183 6 0,036 20 0,339 90 0,623 90
93 0,020 687 00 0,236 857 1 0,393 882 2 0,031 76 0,363 60 0,604 64
94 0,017 540 40 0,247 481 2 0,372 945 9 0,027 49 0,387 92 0,584 59

© CIE 2006 — All rights reserved
ISO 11664-1:2007(E)
CIE S 014-1/E:2006
TABLE 1 (continued)
Wave-
CIE colour-matching functions Chromaticity coordinates
length
λ nm x()λ y(λ) z(λ)
x(λ) y(λ) z(λ)
495 0,014 700 00 0,258 600 0 0,353 300 0 0,023 46 0,412 70 0,563 84
96 0,012 161 79 0,270 184 9 0,334 857 8 0,019 70 0,437 76 0,542 54
97 0,009 919 960 0,282 293 9 0,317 552 1 0,016 27 0,462 95 0,520 78
98 0,007 967 240 0,295 050 5 0,301 337 5 0,013 18 0,488 21 0,498 61
99 0,006 296 346 0,308 578 0 0,286 168 6 0,010 48 0,513 40 0,476 12

500 0,004 900 000 0,323 000 0 0,272 000 0 0,008 17 0,538 42 0,453 41
01 0,003 777 173 0,338 402 1 0,258 817 1 0,006 28 0,563 07 0,430 65
02 0,002 945 320 0,354 685 8 0,246 483 8 0,004 87 0,587 12 0,408 01
03 0,002 424 880 0,371 698 6 0,234 771 8 0,003 98 0,610 45 0,385 57
04 0,002 236 293 0,389 287 5 0,223 453 3 0,003 64 0,633 01 0,363 35

505 0,002 400 000 0,407 300 0 0,212 300 0 0,003 86 0,654 82 0,341 32
06 0,002 925 520 0,425 629 9 0,201 169 2 0,004 64 0,675 90 0,319 46
07 0,003 836 560 0,444 309 6 0,190 119 6 0,006 01 0,696 12 0,297 87
08 0,005 174 840 0,463 394 4 0,179 225 4 0,007 99 0,715 34 0,276 67
09 0,006 982 080 0,482 939 5 0,168 560 8 0,010 60 0,733 41 0,255 99

510 0,009 300 000 0,503 000 0 0,158 200 0 0,013 87 0,750 19 0,235 94
11 0,012 149 49 0,523 569 3 0,148 138 3 0,017 77 0,765 61 0,216 62
12 0,015 535 88 0,544 512 0 0,138 375 8 0,022 24 0,779 63 0,198 13
13 0,019 477 52 0,565 690 0 0,128 994 2 0,027 27 0,792 11 0,180 62
14 0,023 992 77 0,586 965 3 0,120 075 1 0,032 82 0,802 93 0,164 25

515 0,029 100 00 0,608 200 0 0,111 700 0 0,038 85 0,812 02 0,149 13
16 0,034 814 85 0,629 345 6 0,103 904 8 0,045 33 0,819 39 0,135 28
17 0,041 120 16 0,650 306 8 0,096 667 48 0,052 18 0,825 16 0,122 66
18 0,047 985 04 0,670 875 2 0,089 982 72 0,059 32 0,829 43 0,111 25
19 0,055 378 61 0,690 842 4 0,083 845 31 0,066 72 0,832 27 0,101 01

520 0,063 270 00 0,710 000 0 0,078 249 99 0,074 30 0,833 80 0,091 90
21 0,071 635 01 0,728 185 2 0,073 208 99 0,082 05 0,834 09 0,083 86
22 0,080 462 24 0,745 463 6 0,068 678 16 0,089 94 0,833 29 0,076 77
23 0,089 739 96 0,761 969 4 0,064 567 84 0,097 94 0,831 59 0,070 47
24 0,099 456 45 0,777 836 8 0,060 788 35 0,106 02 0,829 18 0,064 80

525 0,109 600 0 0,793 200 0 0,057 250 01 0,114 16 0,826 21 0,059 63
26 0,120 167 4 0,808 110 4 0,053 904 35 0,122 35 0,822 77 0,054 88
27 0,131 114 5 0,822 496 2 0,050 746 64 0,130 55 0,818 93 0,050 52
28 0,142 367 9 0,836 306 8 0,047 752 76 0,138 70 0,814 78 0,046 52
29 0,153 854 2 0,849 491 6 0,044 898 59 0,146 77 0,810 40 0,042 83

530 0,165 500 0 0,862 000 0 0,042 160 00 0,154 72 0,805 86 0,039 42
31 0,177 257 1 0,873 810 8 0,039 507 28 0,162 53 0,801 24 0,036 23
32 0,
...