Colorimetry - Part 1: CIE standard colorimetric observers (ISO/CIE 11664-1:2019)

This document specifies colour-matching functions for use in colorimetry. Two sets of colour-matching functions are specified.
—         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.
—         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.

Farbmetrik - Teil 1: CIE farbmetrische Normalbeobachter (ISO/CIE 11664-1:2019)

Dieses Dokument legt Spektralwertfunktionen zur Anwendung in der Farbmetrik fest. Es werden zwei Sätze von Spektralwertfunktionen festgelegt.
a) Spektralwertfunktionen für den CIE 1931 farbmetrischen Normalbeobachter.
Dieser Satz von Spektralwertfunktionen ist repräsentativ für die vergleichende Farbbewertung von Beobachtern mit normalem Farbsehvermögen für Gesichtsfeldgrößen von etwa 1° bis etwa 4°, bei Adaption des Auges an photopisches Sehen (Tagessehen).
b) Spektralwertfunktionen für den CIE 1964 farbmetrischen Normalbeobachter.
Dieser Satz von Spektralwertfunktionen ist repräsentativ für die vergleichende Farbbewertung von Beobachtern mit normalem Farbsehvermögen für Gesichtsfeldgrößen über etwa 4°, bei Adaption des Auges an photopisches Sehen (Tagessehen) mit ausreichend hohem Strahlungsniveau und mit einer solchen spektralen Strahlungsverteilung, das keine Beteiligung von Stäbchenrezeptoren der Netzhaut zu erwarten ist.

Colorimétrie - Partie 1: Observateurs CIE de référence pour la colorimétrie (ISO/CIE 11664-1:2019)

Le présent document définit des fonctions colorimétriques pour leur emploi en colorimétrie. Deux ensembles de fonctions colorimétriques sont définis.
—         Fonctions colorimétriques de l'observateur CIE 1931 de référence pour la colorimétrie.
Cet ensemble de fonctions colorimétriques est représentatif des caractéristiques d'égalisation colorée d'observateurs ayant une vision normale des couleurs, pour un champ visuel d'amplitude angulaire d'environ 1° à environ 4° et pour une vision adaptée au niveau photopique.
—         Fonctions colorimétriques de l'observateur CIE 1964 de référence pour la colorimétrie.
Cet ensemble de fonctions colorimétriques est représentatif des caractéristiques d'égalisation colorée d'observateurs ayant une vision normale des couleurs, pour un champ visuel d'amplitude angulaire supérieure à environ 4° et pour une vision à un niveau photopique suffisamment élevé et avec une répartition spectrale d'énergie telle qu'il n'y ait pas lieu de supposer une intervention des bâtonnets rétiniens.

Kolorimetrija - 1. del: Standardizirani barvnometrični opazovalec CIE (ISO/CIE 11664-1:2019)

Ta dokument določa funkcije ujemanja barv za uporabo v kolometriji. Določena sta sklopa
funkcij ujemanja barv.
a) Funkcije ujemanja barv za standardizirani barvnometrični opazovalec CIE 1931.
Ta sklop funkcij ujemanja barv je reprezentativen za lastnosti ujemanja barv opazovalcev z običajnim razlikovanjem barv za velikosti vidnega polja z zornim kotom od pribl. 1° do pribl. 4° za razlikovanje pri prilagoditvi fotopičnih ravni.
a) Funkcije ujemanja barv za standardizirani barvnometrični opazovalec CIE 1964.
Ta sklop funkcij ujemanja barv je reprezentativen za lastnosti ujemanja barv opazovalcev z običajnim razlikovanjem barv za velikosti vidnega polja z zornim kotom, večjim od 4°, za razlikovanje pri dovolj visokih fotopičnih ravneh in s porazdelitvami spektralne moči, tako da se ne pričakuje prisotnosti paličnic v mrežnici.

General Information

Status
Published
Publication Date
16-Jul-2019
Current Stage
6060 - Definitive text made available (DAV) - Publishing
Due Date
17-Jul-2019
Completion Date
17-Jul-2019

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SLOVENSKI STANDARD
SIST EN ISO/CIE 11664-1:2019
01-september-2019
Nadomešča:
SIST EN ISO 11664-1:2011
Kolorimetrija - 1. del: Standardizirani barvnometrični opazovalec CIE (ISO/CIE
11664-1:2019)
Colorimetry - Part 1: CIE standard colorimetric observers (ISO/CIE 11664-1:2019)
Farbmetrik - Teil 1: CIE farbmetrische Normalbeobachter (ISO/CIE 11664-1:2019)

Colorimétrie - Partie 1: Observateurs CIE de référence pour la colorimétrie (ISO/CIE

11664-1:2019)
Ta slovenski standard je istoveten z: EN ISO/CIE 11664-1:2019
ICS:
17.180.20 Barve in merjenje svetlobe Colours and measurement of
light
SIST EN ISO/CIE 11664-1:2019 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN ISO/CIE 11664-1:2019
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SIST EN ISO/CIE 11664-1:2019
EN ISO/CIE 11664-1
EUROPEAN STANDARD
NORME EUROPÉENNE
July 2019
EUROPÄISCHE NORM
ICS 17.180.20 Supersedes EN ISO 11664-1:2011
English Version
Colorimetry - Part 1: CIE standard colorimetric observers
(ISO/CIE 11664-1:2019)

Colorimétrie - Partie 1: Observateurs CIE de référence Farbmetrik - Teil 1: CIE farbmetrische

pour la colorimétrie (ISO/CIE 11664-1:2019) Normalbeobachter (ISO/CIE 11664-1:2019)

This European Standard was approved by CEN on 24 May 2019.

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, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and

United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels

© 2019 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO/CIE 11664-1:2019 E

worldwide for CEN national Members.
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SIST EN ISO/CIE 11664-1:2019
EN ISO/CIE 11664-1:2019 (E)
Contents Page

European foreword ....................................................................................................................................................... 3

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SIST EN ISO/CIE 11664-1:2019
EN ISO/CIE 11664-1:2019 (E)
European foreword

This document (EN ISO/CIE 11664-1:2019) has been prepared by Technical Committee CEI

"International Commission on Illumination" in collaboration with Technical Committee CEN/TC 139

“Paints and varnishes” the secretariat of which is 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 January 2020, and conflicting national standards shall

be withdrawn at the latest by January 2020.

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. CEN shall not be held responsible for identifying any or all such patent rights.

This document supersedes EN ISO 11664-1:2011.

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, Republic of

North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the

United Kingdom.
Endorsement notice

The text of ISO/CIE 11664-1:2019 has been approved by CEN as EN ISO/CIE 11664-1:2019 without any

modification.
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SIST EN ISO/CIE 11664-1:2019
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SIST EN ISO/CIE 11664-1:2019
INTERNATIONAL ISO/CIE
STANDARD 11664-1
First edition
2019-06
Colorimetry —
Part 1:
CIE standard colorimetric observers
Colorimétrie —
Partie 1: Observateurs CIE de référence pour la colorimétrie
Reference number
ISO/CIE 11664-1:2019(E)
ISO/CIE 2019
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SIST EN ISO/CIE 11664-1:2019
ISO/CIE 11664-1:2019(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO/CIE 2019

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting

on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address

below or ISO’s member body in the country of the requester.
ISO copyright office CIE Central Bureau
CP 401 • Ch. de Blandonnet 8 Babenbergerstraße 9/9A
CH-1214 Vernier, Geneva A-1010 Vienna, Austria
Phone: +41 22 749 01 11 Phone: +43 1 714 3187
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Email: copyright@iso.org Email: ciecb@cie.co.at
Website: www.iso.org Website: www.cie.co.at
Published in Switzerland
ii © ISO/CIE 2019 – All rights reserved
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Contents Page

Foreword ........................................................................................................................................................................................................................................iv

Introduction ..................................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 1

3 Terms and definitions ..................................................................................................................................................................................... 1

4 Specifications ........................................................................................................................................................................................................... 5

4.1 Colour-matching functions ........................................................................................................................................................... 5

4.2 Spectral chromaticity coordinates ......................................................................................................................................... 5

5 Derivation of the colour-matching functions for the CIE 1931 standard colorimetric

observer ......................................................................................................................................................................................................................... 5

5.1 Experimental basis .............................................................................................................................................................................. 5

5.2 Transformation procedures ......................................................................................................................................................... 6

5.3 Transformation properties ........................................................................................................................................................... 6

5.4 Comparison with earlier data .................................................................................................................................................... 7

6 Derivation of the colour-matching functions for the CIE 1964 standard colorimetric

observer ......................................................................................................................................................................................................................... 7

6.1 Experimental basis .............................................................................................................................................................................. 7

6.2 Transformation procedures ......................................................................................................................................................... 7

6.3 Transformation properties ........................................................................................................................................................... 8

6.4 Comparison with earlier data .................................................................................................................................................... 8

7 Practical application of colour-matching functions for CIE standard colorimetric

observers ...................................................................................................................................................................................................................... 8

7.1 Obtaining tristimulus values ....................................................................................................................................................... 8

7.2 The basis for integration ................................................................................................................................................................ 9

7.3 Rod activity................................................................................................................................................................................................. 9

7.4 The use of restricted data .............................................................................................................................................................. 9

7.5 Standard of reflectance .................................................................................................................................................................... 9

Bibliography .............................................................................................................................................................................................................................34

© ISO/CIE 2019 – All rights reserved iii
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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.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www .iso .org/patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to the

World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see www .iso

.org/iso/foreword .html.

This document was prepared by the International Commission on Illumination (CIE) in cooperation

with Technical Committee ISO/TC 274, Light and lighting.

This first edition of ISO/CIE 11664-1 cancels and replaces ISO 11664-1:2007 | CIE S 014-1:2006, of which

it constitutes a minor revision, incorporating minor editorial updates.

A list of all parts in the ISO 11664 and ISO/CIE 11664 series can be found on the ISO website.

Any feedback or questions on this document should be directed to the user’s national standards body. A

complete listing of these bodies can be found at www .iso .org/members .html.
iv © ISO/CIE 2019 – All rights reserved
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Introduction

Colours with different spectral compositions can look alike. An important function of colorimetry is to

determine whether a pair of such metameric colour stimuli will look alike. The use of visual colorimeters

for this purpose is handicapped by variations in the colour matches made among 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.

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INTERNATIONAL STANDARD ISO/CIE 11664-1:2019(E)
Colorimetry —
Part 1:
CIE standard colorimetric observers
1 Scope

This document 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 documents are referred to in the text in such a way that some or all of their content

constitutes requirements 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.

CIE S 017:—, ILV: International Lighting Vocabulary
3 Terms and definitions

For the purposes of this document, the terms and definitions given in CIE S 017 and the following apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at https: //www .iso .org/obp
— IEC Electropedia: available at http: //www .electropedia .org/
3.1
colour stimulus function
φ (λ)
function describing the spectral distribution of the colour stimulus

Note 1 to entry: The colour stimulus function is generated by the spectral distribution of a radiometric quantity,

such as radiance or radiant flux.

Note 2 to entry: For object colours the colour stimulus function, φ (λ), is equal to the product of the relative

spectral distribution, S(λ), and either the spectral reflectance, ρ(λ), or the spectral radiance factor, β(λ), or the

spectral transmittance, τ(λ), depending on the application.
1) Under preparation. Stage at the time of publication: CIE DIS 017:2016.
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[SOURCE: CIE S 017:—, entry 17-23-003, modified — The definition has been completely revised and

the notes to entry have been added.]
3.2
metameric colour stimuli, pl
metamers, pl

spectrally different colour stimuli that have the same tristimulus values in a specified colorimetric system

Note 1 to entry: The corresponding property is called “metamerism”.
[SOURCE: CIE S 017:—, entry 17-23-008]
3.3
monochromatic stimulus
spectral stimulus
stimulus consisting of monochromatic radiation
[SOURCE: CIE S 017:—, entry 17-23-011]
3.4
equi-energy spectrum
equal energy spectrum

spectrum of radiation whose spectral distribution of a radiometric quantity as a function of wavelength

is constant throughout the visible region

Note 1 to entry: The radiation of the equi-energy spectrum is sometimes regarded as an illuminant, in which case

it is denoted by the symbol E.

[SOURCE: CIE S 017:—, entry 17-23-023, modified — “(φ (λ) = constant)” at the end of the definition

omitted.]
3.5
additive mixture

stimulation that combines on the retina the actions of various colour stimuli in such a

manner that they cannot be perceived individually
[SOURCE: CIE S 017:—, entry 17-23-030]
3.6
colour matching

action of making a colour stimulus appear the same in colour as a given colour stimulus

[SOURCE: CIE S 017:—, entry 17-23-031]
3.7
trichromatic system

system for specifying colour stimuli in terms of tristimulus values, based on matching colours by

additive mixture of three suitably chosen reference colour stimuli
[SOURCE: CIE S 017:—, entry 17-23-036]
3.8
reference colour stimuli, pl
three colour stimuli on which a trichromatic system is based

Note 1 to entry: These stimuli are either real colour stimuli or theoretical stimuli which are defined by linear

combinations of real colour stimuli.

Note 2 to entry: In the CIE standard colorimetric systems, the reference colour stimuli are represented by the

symbols [R], [G], [B]; [X], [Y], [Z]; [R ], [G ], [B ] or [X ], [Y ], [Z ].
10 10 10 10 10 10

[SOURCE: CIE S 017:—, entry 17-23-037, modified — “set of three" has been changed to “three" and the

"and" has been changed to "or" in Note 2 to entry.]
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3.9
tristimulus values, pl

amounts of the reference colour stimuli, in a given trichromatic system, required

to match the colour of the stimulus considered

Note 1 to entry: In the CIE standard colorimetric systems, the tristimulus values are represented, for example, by

the symbols R, G, B; X, Y, Z; R , G , B or X , Y , Z .
10 10 10 10 10 10

[SOURCE: CIE S 017:—, entry 17-23-038, modified — “amount of the three reference" has been changed

to "amounts of the reference".]
3.10
colour-matching functions, pl

tristimulus values of monochromatic stimuli of equal radiant flux

[SOURCE: CIE S 017:—, entry 17-23-039, modified — Notes to entry omitted.]
3.11
CIE 1931 standard colorimetric system
X, Y, Z

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 xy()λλ,,() z()λ

adopted by the CIE in 1931

Note 1 to entry: y()λ is identical to V(λ) and hence the tristimulus values Y are proportional to values of

luminance.

Note 2 to entry: The CIE 1931 standard colorimetric system is applicable to centrally viewed fields of angular

subtense between about 1° and about 4° (0,017 rad and 0,07 rad).

Note 3 to entry: The CIE 1931 standard colorimetric system can be derived from the CIE 1931 RGB colorimetric

system using a transformation based on a set of three linear equations. The CIE 1931 RGB system is based on

three real monochromatic reference stimuli.
Note 4 to entry: See also CIE 15, Colorimetry.
[SOURCE: CIE S 017:—, entry 17-23-045]
3.12
CIE 1964 standard colorimetric system
X , Y , Z
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
xyλλ,,z λ adopted by the CIE in 1964
() () ()
10 10 10

Note 1 to entry: The CIE 1964 standard colorimetric system is applicable to centrally viewed fields of angular

subtense greater than about 4° (0,07 rad).

Note 2 to entry: When the CIE 1964 standard colorimetric system is used, all symbols that represent colorimetric

measures are distinguished by use of the subscript 10.
Note 3 to entry: See also CIE 15, Colorimetry.
[SOURCE: CIE S 017:—, entry 17-23-046]
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3.13
CIE colour-matching functions, pl
functions xyλλ,,z λ in the CIE 1931 standard colorimetric system or xyλλ,,z λ
() () () () () ()
10 10 10
in the CIE 1964 standard colorimetric system
[SOURCE: CIE S 017:—, entry 17-23-047]
3.14
CIE 1931 standard colorimetric observer

ideal observer whose colour-matching properties correspond to the CIE colour-matching functions

xyλλ,,z λ adopted by the CIE in 1931
() () ()
[SOURCE: CIE S 017:—, entry 17-23-049]
3.15
CIE 1964 standard colorimetric observer

ideal observer whose colour-matching properties correspond to the CIE colour-matching functions

xyλλ,,z λ adopted by the CIE in 1964
() () ()
10 10 10
[SOURCE: CIE S 017:—, entry 17-23-050, modified — Note 1 to entry omitted.]
3.16
chromaticity coordinates, pl

coordinates expressing the quotients of each of a set of three tristimulus values to their sum

Note 1 to entry: As the sum of the three chromaticity coordinates is equal to 1, two of them are sufficient to

define a chromaticity.

Note 2 to entry: In the CIE standard colorimetric systems, the chromaticity coordinates are represented by the

symbols x, y, z or x , y , z .
10 10 10
Note 3 to entry: The chromaticity coordinates are a quantity of unit one.

[SOURCE: CIE S 017:—, entry 17-23-053, modified — “ratios” has been changed to “quotients”.]

3.17
spectral chromaticity coordinates, pl
r(λ), g(λ), b(λ); x(λ), y(λ), z(λ); r (λ), g (λ), b (λ); x (λ), y (λ), z (λ)
10 10 10 10 10 10
chromaticity coordinates of monochromatic stimuli
[SOURCE: CIE S 017:—, entry 17-23-055]
3.18
spectral luminous efficiency

V(λ), ; V′(λ), ; V (λ), ; V (λ), mes;m 10

the CIE 10° photopic photometric observer>; V (λ), efficiency function for photopic vision>

quotient of the radiant flux at wavelength λ and that at

wavelength λ, such that both produce equally intense luminous sensations for a specified photometric

condition and λ is chosen so that the maximum value of this quotient is equal to 1

[SOURCE: CIE S 017:—, entry 17-21-035, modified — Notes to entry omitted.]
3.19
perfect reflecting diffuser
ideal isotropic diffuser with a reflectance equal to unity
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4 Specifications
4.1 Colour-matching functions

The colour-matching functions xyλλ,,z λ of the CIE 1931 standard colorimetric observer are

() () ()

defined by the values given in Table 1, and those xyλλ,,z λ of the CIE 1964 standard

() () ()
10 10 10

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),

10 10

z (λ); these have been derived from the appropriate colour-matching functions by forming the ratios

according to Formulae (1) to (6):
x λ
x λ = (1)
xyλλ+ +z λ
() () ()
y λ
y λ = (2)
xyλλ+ +z λ
() () ()
z λ
z λ = (3)
xyλλ+ +z λ
() () ()
and
x λ
x λ = (4)
xyλλ+ +z λ
() () ()
10 10 10
y λ
y λ = (5)
xyλλ+ +z λ
() () ()
10 10 10
z λ
z ()λ = (6)
xyλλ+ +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, xyλλ,,z λ , were derived from experimental work

() () ()
[1][2] [3]

carried out by Wright and Guild 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.
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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 rgλλ,,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

Formulae (7) to (9):
 
xrλλ= 0,490+ ,,31gbλλ+ 020 n (7)
() () () ()
 
 
yrλλ= 0,176 97 + 0,,812 40gbλλ+ 0 01063 n (8)
() () () ()
 
 
zrλλ= 0,000+ ,,01gbλλ+ 099 n (9)
() () () ()
 
where
n is a normalizing constant given by Formula (10).
V λ
n= (10)
0,176 97rgλλ+ 0,,812 40 + 0 01063b 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 Formula (11).
1,000 0 ++ 4,590 7 0,060 1
= 55,650 8 (11)
0,176 97 ++ 0,812 40 0,010 63

The values of xyλλ,,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 Formulae (7) to (9) was chosen to achieve the following objectives:

1) The y λ function is identical to the V(λ) function.

2) The values of xyλλ,,z λ are all positive for all wavelengths of the spectrum (unlike

() () ()

rgλλ,,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).
3) The values of z λ are zero for wavelengths longer than 650 nm.
6 © ISO/CIE 2019 – All rights reserved
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SIST EN ISO/CIE 11664-1:2019
ISO/CIE 11664-1:2019(E)
4) The values of x λ are nearly zero at wavelengths around 505 nm.

5) The values of x λ and y λ are small at the short-wavelength end of the spectrum.

() ()
6) 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 xyλλ,,z λ given in Table 1 for the spectral range of 380 nm to 780
...

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