Analytical colorimetry - Part 4: Metamerism index for pairs of samples for change of illuminant (ISO 18314-4:2020)

This document specifies a formalism for the calculation of the illuminant metamerism of solid surface colours. It cannot be applied to colours of effect coatings without metrical adaptation.
This document only covers the phenomenon of metamerism for change of illuminant, which has the greatest meaning in practical application. In the case of chromaticity coordinates of a pair of samples under reference conditions that do not exactly match, recommendations are given on which correction measures are to be taken. Regarding the reproduction of colours, the metamerism index is used as a measure of quality in order to specify tolerances for colour differences between a colour sample and a colour match under different illumination conditions.
The quantification of the illuminant metamerism of pairs of samples is formally performed by a colour difference assessment, for which tolerances that are common for the evaluation of residual colour differences can be used.

Analytische Farbmessung - Teil 4: Metamerie-Index von Probenpaaren bei Lichtartwechsel (ISO 18314-4:2020)

Dieses Dokument legt einen Formalismus zur Berechnung der Lichtart-Metamerie von Uni-Farben fest. Dieser kann ohne Anpassungen in der Metrik nicht auf Effektfarben von Überzügen bzw. Beschichtungen angewendet werden.
Dieses Dokument behandelt nur das Phänomen der Metamerie bei Lichtartwechsel, das in der praktischen Anwendung die größte Bedeutung hat. Für den Fall, dass die Farborte eines Probenpaares unter Referenzbedingungen nicht exakt übereinstimmen, werden Empfehlungen gegeben, welche Korrekturmaßnahmen zu ergreifen sind. Bei der Reproduktion von Farben wird der Metamerie-Index als Qualitätsmaß verwendet, um Toleranzen für Farbunterschiede zwischen einer Farbvorlage und einer Farbnachstellung bei unterschiedlichen Beleuchtungsbedingungen festzulegen.
Die Quantifizierung der Lichtart-Metamerie von Probenpaaren wird formal auf eine Farbabstandsbewertung zurückgeführt, bei der Toleranzen herangezogen werden können, die bei der Bewertung reiner Restfarbabstände üblich sind.
ANMERKUNG   In der Farbliteratur und Fachbüchern wird manchmal auch der Begriff der Geometrischen Metamerie für den Fall verwendet, dass zwei Farben unter einer bestimmten Beobachtungsgeometrie und einer gewählten Kombination aus Normalbeobachter und Lichtart gleich erscheinen, aber bei veränderter Beobachtungsgeometrie als zwei verschiedene Farben wahrgenommen werden. Der Begriff Geometrische Metamerie unterscheidet sich von der in diesem Dokument beschriebenen Metamerie.

Analyse colorimétrique - Partie 4: Indice de metamérisme de paires d'échantillon pour changement d'illuminant (ISO 18314-4:2020)

Analizna kolorometrija - 4. del: Metamerični indeks parov vzorcev pri spremembi vrste svetila (ISO 18314-4:2020)

General Information

Status
Published
Public Enquiry End Date
01-Apr-2021
Publication Date
16-Aug-2021
Technical Committee
Current Stage
6060 - National Implementation/Publication (Adopted Project)
Start Date
11-Jul-2021
Due Date
15-Sep-2021
Completion Date
17-Aug-2021

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SLOVENSKI STANDARD
SIST EN ISO 18314-4:2021
01-september-2021
Analizna kolorometrija - 4. del: Metamerični indeks parov vzorcev pri spremembi
vrste svetila (ISO 18314-4:2020)

Analytical colorimetry - Part 4: Metamerism index for pairs of samples for change of

illuminant (ISO 18314-4:2020)
Analytische Farbmessung - Teil 4: Metamerie-Index von Probenpaaren bei
Lichtartwechsel (ISO 18314-4:2020)

Analyse colorimétrique - Partie 4: Indice de metamérisme de paires d'échantillon pour

changement d'illuminant (ISO 18314-4:2020)
Ta slovenski standard je istoveten z: EN ISO 18314-4:2021
ICS:
17.180.20 Barve in merjenje svetlobe Colours and measurement of
light
87.060.10 Pigmenti in polnila Pigments and extenders
SIST EN ISO 18314-4:2021 en,fr,de

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

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SIST EN ISO 18314-4:2021
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SIST EN ISO 18314-4:2021
EN ISO 18314-4
EUROPEAN STANDARD
NORME EUROPÉENNE
June 2021
EUROPÄISCHE NORM
ICS 87.060.10
English Version
Analytical colorimetry - Part 4: Metamerism index for
pairs of samples for change of illuminant (ISO 18314-
4:2020)

Analyse colorimétrique - Partie 4: Indice de Analytische Farbmessung - Teil 4: Metamerie-Index

metamérisme de paires d'échantillon pour changement von Probenpaaren bei Lichtartwechsel (ISO 18314-

d'illuminant (ISO 18314-4:2020) 4:2020)
This European Standard was approved by CEN on 21 June 2021.

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

© 2021 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 18314-4:2021 E

worldwide for CEN national Members.
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SIST EN ISO 18314-4:2021
EN ISO 18314-4:2021 (E)
Contents Page

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

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SIST EN ISO 18314-4:2021
EN ISO 18314-4:2021 (E)
European foreword

The text of ISO 18314-4:2020 has been prepared by Technical Committee ISO/TC 256 "Pigments,

dyestuffs and extenders” of the International Organization for Standardization (ISO) and has been taken

over as EN ISO 18314-4:2021 by Technical Committee CEN/TC 298 “Pigments and extenders” 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 December 2021, and conflicting national standards

shall be withdrawn at the latest by December 2021.

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.

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 18314-4:2020 has been approved by CEN as EN ISO 18314-4:2021 without any

modification.
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SIST EN ISO 18314-4:2021
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SIST EN ISO 18314-4:2021
INTERNATIONAL ISO
STANDARD 18314-4
First edition
2020-08
Analytical colorimetry —
Part 4:
Metamerism index for pairs of
samples for change of illuminant
Analyse colorimétrique —
Partie 4: Indice de metamérisme de paires d'échantillon pour
changement d'illuminant
Reference number
ISO 18314-4:2020(E)
ISO 2020
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SIST EN ISO 18314-4:2021
ISO 18314-4:2020(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2020

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
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2020 – All rights reserved
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SIST EN ISO 18314-4:2021
ISO 18314-4:2020(E)
Contents Page

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

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

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

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

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

4 Symbols and abbreviated terms ........................................................................................................................................................... 2

5 Reference illuminant........................................................................................................................................................................................ 3

6 Test illuminant ........................................................................................................................................................................................................ 3

7 CIELAB coordinates L*, a*, b* ................................................................................................................................................................... 3

8 Metamerism index for change in illuminant ........................................................................................................................... 4

8.1 General calculation methods ...................................................................................................................................................... 4

8.2 Basic calculation of the metamerism index from colour differences ....................................................... 4

8.3 Correction methods ............................................................................................................................................................................ 5

8.3.1 Additive correction ........................................................................................................................................................ 5

8.3.2 Multiplicative correction ........................................................................................................................................... 5

8.3.3 Spectral correction ......................................................................................................................................................... 6

8.4 Test report ................................................................................................................................................................................................... 9

Annex A (informative) Calculation examples ...........................................................................................................................................10

Bibliography .............................................................................................................................................................................................................................23

© ISO 2020 – All rights reserved iii
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SIST EN ISO 18314-4:2021
ISO 18314-4:2020(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.

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 Technical Committee ISO/TC 256, Pigments, dyestuff and extenders.

A list of all parts in the ISO 18314 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 2020 – All rights reserved
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SIST EN ISO 18314-4:2021
ISO 18314-4:2020(E)
Introduction

For the phenomenon of metamerism of pairs of samples, three different kinds are distinguished:

a) Illuminant metamerism occurs if both of the object colours of a pair of samples are perceived as

being the same only under a specific illuminant (e.g. under illuminant D65), while they differ under

a different illuminant (e.g. illuminant A).

b) Observer metamerism occurs if the object colours of a pair of samples are perceived as being the

same by one observer, while a different observer perceives a colour difference under the same

illuminant and the same reference conditions.

NOTE 1 The observer metamerism is caused by differences between the distributions of spectral colour

matching functions of different observers.

c) Field-size metamerism occurs if both of the object colours of a pair of samples are perceived as

being the same on the retina for a size of an observation field (e.g. defined by the 2° standard

observer), while they differ for a different observation field on the retina (e.g. 10°).

NOTE 2 The reason for field-size metamerism is based on the existent colour matching functions of

an observer during an observation situation. The colour matching functions change with the size of the

observation field on the retina. Such change of the observation field can also occur if, for example, the pair of

samples is examined from different distances.
© ISO 2020 – All rights reserved v
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SIST EN ISO 18314-4:2021
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SIST EN ISO 18314-4:2021
INTERNATIONAL STANDARD ISO 18314-4:2020(E)
Analytical colorimetry —
Part 4:
Metamerism index for pairs of samples for change of
illuminant
1 Scope

This document specifies a formalism for the calculation of the illuminant metamerism of solid surface

colours. It cannot be applied to colours of effect coatings without metrical adaptation.

This document only covers the phenomenon of metamerism for change of illuminant, which has the

greatest meaning in practical application. In the case of chromaticity coordinates of a pair of samples

under reference conditions that do not exactly match, recommendations are given on which correction

measures are to be taken. Regarding the reproduction of colours, the metamerism index is used as a

measure of quality in order to specify tolerances for colour differences between a colour sample and a

colour match under different illumination conditions.

The quantification of the illuminant metamerism of pairs of samples is formally performed by a colour

difference assessment, for which tolerances that are common for the evaluation of residual colour

differences can be used.

NOTE In the colorimetric literature and textbooks, the term geometric metamerism is sometimes used for

the case that two colours appear to be the same under a specific geometry for visual assessment and selected

standard observer and standard illuminant pair, but is perceived as two different colours at changed observation

geometry. The term geometric metamerism is different to metamerism described in this document.

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.

ISO/CIE 11664-1, Colorimetry — Part 1: CIE standard colorimetric observers
ISO/CIE 11664-2:— , Colorimetry — Part 2: CIE standard illuminants
ISO/CIE 11664-4, Colorimetry — Part 4: CIE 1976 L*a*b* colour space
CIE 015, Colorimetry
CIE S 017, 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/

1) Under preparation. Stage at the time of preparation: ISO/CIE DIS 11664-2:2020.

© ISO 2020 – All rights reserved 1
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SIST EN ISO 18314-4:2021
ISO 18314-4:2020(E)
3.1
metamerism

property of spectrally different colour stimuli that have the same tristimulus values in a specified

colorimetric system
[SOURCE: CIE 017:2016, 17-23-006]
3.2
paramerism

characteristic of a pair of samples with spectral colour stimulus functions which have different

fundamental colour stimulus functions as well as different residuals or metameric black values within

the visible spectral range

Note 1 to entry: Parameric objects are characterized by the fact that they reflect colour stimuli of different

spectral power distribution functions under a specified standard illuminant, which cause approximately the

same colour perception under the selected observation conditions.
3.3
colour difference

difference between two colour stimuli, defined as a distance between the points representing them in a

specified colour space

[SOURCE: CIE 017:2016, 17-22-041, modified — symbol ΔE was amended, “Euclidean” and Note 1 to

entry have been deleted.]
3.4
reference illuminant
illuminant with which other illuminants are compared
[SOURCE: CIE S 017:2016, 17-22-109 17]
3.5
test illuminant

illuminant, for which the colour difference (3.3) between the two samples to be tested is assessed

3.6
metamerism-index for change in illuminant
* *

colour difference ΔE (3.3) between the two samples under test illuminant (3.5) if Δ=E 0 is observed

under the reference illuminant (3.4)
3.7
correction method

algorithm for theoretically eliminating a colour difference (3.3) of the pair of samples under the reference

illuminant (3.4)
4 Symbols and abbreviated terms
For the application of this document, the symbols given in Table 1 apply.
Table 1 — Symbols
Symbol Identification
X, Y, Z Standard tristimulus values of a measured object colour
Standard tristimulus values of the used illuminant
X , Y , Z
n n n
x , y , z Colour-matching functions
2 © ISO 2020 – All rights reserved
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SIST EN ISO 18314-4:2021
ISO 18314-4:2020(E)
Table 1 (continued)
Symbol Identification
* * * Basic coordinates of the CIELAB system
L , a , b
ΔL*, Δa*, Δb* Differences between basic coordinates of the CIELAB system
Metamerism index for change in illuminant
 

Vector of the radiometric function of a sample with associated fundamental colour stimulus (f)

NN,,N
and metameric black (r)
λ Wavelength
S Relative spectral distribution function of an illuminant
Vector of the standard tristimulus values
w Integration weights for the calculation of the standard tristimulus values

A Matrix of the integration weights w for the calculation of the standard tristimulus values

R Projection matrix
I Identity matrix
Index spl Sample
Index std Standard
Index t Test illuminant
Index corr Corrected value
Index f Fundamental colour stimulus
Index r Metameric black values (residuals)
Index ref Reference illuminant
Index T Transposed matrix
5 Reference illuminant

The standard illuminant D65 is chosen as reference illuminant in accordance with ISO/CIE 11664-2.

Other reference illuminants required in special cases shall be particularly specified.

6 Test illuminant

The selection of the test illuminant depends on the application. If the test illuminants are not particularly

specified, standard illuminant A in accordance with ISO 11664-2 and/or illuminants of the fluorescent

lamp type, such as FL11 in accordance with CIE 015, shall preferably be selected. The test illuminant

used shall be indicated as an index to M, e.g. M or M .
A FL11

When calculating the standard tristimulus values X, Y, Z under the selected test illuminants, the basic

raster of wavelengths given in ISO 11664-2 or CIE 015 for A and D65, and in CIE 015 for FL11 and

FL2 shall be complied with. In cases of missing measuring values of the standard or sample for these

wavelengths, these values shall be interpolated and/or extrapolated.
7 CIELAB coordinates L*, a*, b*
* * *

The metamerism index M is based on the CIELAB coordinates L , a , b of samples 1 and 2 which are

* * *

to be compared. L , a , b is calculated in accordance with ISO/CIE 11664-4 from the standard

tristimulus values X, Y, Z of the sample for the CIE 1964 10° standard observer in accordance with

* * *

ISO/CIE 11664-1 for the reference illuminant and the selected test illuminant. If calculating L , a , b

under the test illuminant, the respective standard tristimulus values X , Y , Z of the entirely matt

n n n

white surface shall be used (see CIE 015). For the standard illuminants A and D65 or for the illuminant

© ISO 2020 – All rights reserved 3
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SIST EN ISO 18314-4:2021
ISO 18314-4:2020(E)

recommendation FL11, the standard tristimulus values X , Y , Z of the entirely matt white surface

n n n
apply in accordance with Table 2.

Table 2 specifies standard tristimulus values for the frequently used standard illuminants D65 and A as

well as illuminant FL11 and both of the standard observers in accordance with CIE 015.

Table 2 — Standard tristimulus values
2° standard observer 10° standard observer
Standard
tristimulus Illuminant
values
D65 A FL11 D65 A FL11
X 95,04 109,85 100,96 94,81 111,14 103,86
Y 100,00 100,00 100,00 100,00 100,00 100,00
Z 108,88 35,58 64,35 107,32 35,20 65,61

For fluorescent samples, the illuminant used for measurement shall be adjusted as close as possible to

that illuminant for which the standard tristimulus values are to be determined.

NOTE In contrast to non-fluorescent samples, the calculation of metamerism indices for fluorescent samples

is erroneous if the samples are measured only under one illuminant.
8 Metamerism index for change in illuminant
8.1 General calculation methods

Three different correction methods for calculating a metamerism index in the case of paramerism have

been proposed in References [6] to [13]. All methods assume that, for practical cases, there might be

already a small difference between the colours of the sample and the standard even under the reference

illuminant from the very beginning, due to problems of fabrication. In the case of two methods, called

the additive and the multiplicative correction, these inherent colour differences often merge with the

difference introduced by the change of the illuminant. The third method, the spectral correction, works

more fundamentally by the separation of inherent colour differences under the reference illuminant

from those introduced by the change of the illuminant.
NOTE Annex A includes calculation examples.
8.2 Basic calculation of the metamerism index from colour differences

The common formula for a metamerism index at change in illuminant, expressed in CIELAB coordinates

for the test illuminant (t), is given by Formula (1):
22 2
** *
ML=Δ +Δab+Δ (1)
() () ()
tt tt
where
t is the test colour;
* * *
ΔL =−LL ;
t splc,,orrt stdt,
* * *
Δa =−aa ;
t splc,,orrt stdt,
* * *
Δb =−bb .
t splc,,orrt stdt,
4 © ISO 2020 – All rights reserved
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SIST EN ISO 18314-4:2021
ISO 18314-4:2020(E)

The formulae given above are meant as an example if using the CIELAB colour space.

Analogous equations apply for other Euclidian colour spaces such as DIN 99o in DIN 6176. In non-

Euclidian colour spaces such as CIE 94 or CIEDE2000, the specific colour differences are provided

with colour-space dependent weight functions and, in regard to the latter case, are expanded by an

additional rotation term. The CIELAB metric used in the present standard is an example and should be

replaced in practical applications by one of the mentioned more recent metrics (e.g. CIE 94, CIEDE2000,

DIN 99o), which are significantly more uniform than the CIELAB model.
8.3 Correction methods
8.3.1 Additive correction

When using the additive correction, the differences of any colorimetric axis between standard (std)

and sample (spl) under reference conditions (ref), are added to the specific differences between

standard and sample under test conditions (t). The resulting equation for the metamerism index M ,

expressed in CIELAB coordinates, is then given by Formula (2):
22 2
** *
ML=Δ +Δab+Δ (2)
() () ()
t corr corr corr
where
* * **
ΔL = LL−−ΔL ;
corr splt, stdt, ref
* * *
ΔL = LL− .
ref splr, ef stdr, ef
* *

Analogous relationships apply for Δa and Δb . It should be noted that slightly different results are to

be expected, if the correction is applied to standard tristimulus values prior to transformation into a

uniform colour space such as CIELAB or DIN 99o.
8.3.2 Multiplicative correction

When using the multiplicative correction, which is specified in CIE 015 as correction method, the

standard tristimulus values of the sample (spl), which are observed under test conditions (t) are

multiplied with the quotient of the standard tristimulus values of standard (std) and sample (spl),

which are obtained under reference conditions (ref). The resulting equation is given in Formula (3):

stdr, ef
YY= (3)
corr splt,
splr, ef

in which case, again, analogous combinations for X and Z apply. Subsequently, a transformation

corr corr

into a uniform colour space (e.g. CIELAB) takes place and results in Formula (4):

22 2
** *
ML=Δ +Δab+Δ (4)
() () ()
t corr corr corr
with
* * *
Δ=LL −L
corr splc,,orrt stdt,
* *

Analogous relationships apply for the two remaining specific differences Δa and Δb .

corr corr
© ISO 2020 – All rights reserved 5
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SIST EN ISO 18314-4:2021
ISO 18314-4:2020(E)
8.3.3 Spectral correction

The spectral method considers that under the reference illuminant, minor differences between the

tristimulus values of the sample and the standard can already exist, which are not relevant for the

metamerism characteristics. In order to first mathematically compensate them and only determine

the effective component for metamerism at change in illuminant of sample pairs with given spectral

reflectance, the possibility is used to mathematically split a spectral reflectance in two additive

components.

One component describes only the function that is effective for the formation of the colour stimulus

under the reference illuminant and the other component describes a function, which does not lead to a

contribution to the colour stimulus when integrating via the stimulus under the reference illuminant.

This function necessarily includes positive and negative components. The colour stimulus function

resulting from the first component of the spectral reflectance under the reference illuminant that is

effective for the formation of the colour stimulus is called fundamental colour stimulus function, the

respective second part of the colour stimulus function leads to a metameric black of the decomposition

(residue), i.e. an invisible contribution with a resulting colour stimulus identical to zero.

The compensation of the deviations of the colour stimuli of a sample from the standard, which are non-

effective for metamerism characteristics, is realized by replacing the fundamental colour stimulus of

the sample by that of the standard. The component that is effective for the metamerism characteristic

is maintained unchanged, i.e. a new colour stimulus function of the sample is generated from the sum

of the replaced fundamental colour stimulus and the unchanged second component. From the sum, the

metamerism at change in illuminant in regard to the standard is determined.

The following mathematical description of the method of spectral correction is not based on a

decomposition of the colour stimulus function into its fundamental colour stimulus function and the

invisible function of the black stimulus. Rather, a decomposition of the spectral reflectance function of

the respective colour into a “fundamental reflectance function” and a “black” component (metameric

black values) of the reflectance function is used. This method is valid under the assumption that these

components only lead to the visually effective fundamental colour stimulus function and the invisible

function of the metameric black values in combination with the distribution function of the reference

illuminant (here D65). Consequently, the distribution function of the reference illuminant is inherently

included in the decomposition of the reflectance functions. In order to highlight this connection, the

components are additionally marked “for the reference illuminant” when decomposing the reflectance

function of a colour.

In the model of the spectral decomposition of a radiometric function developed by Cohen and Kappauf,

the spectral reflectance of an object colour obtained in the visible spectral range is summarized in the

vector in Formula (5):
 ()
 
 ρλ()
 
N= (5)
 
 
 
 

The components of the vector Nare the reflectance values ρλ ()in=…12,, , of the examined colour,

which are discreetly present on n intervals. For the calculation of the respective standard tristimulus

values XY,,Z from the ref
...

SLOVENSKI STANDARD
oSIST prEN ISO 18314-4:2021
01-marec-2021
Analizna kolorometrija - 4. del: Metamerični indeks parov vzorcev pri spremembi
vrste svetila (ISO 18314-4:2020)

Analytical colorimetry - Part 4: Metamerism index for pairs of samples for change of

illuminant (ISO 18314-4:2020)
Analytische Farbmessung - Teil 4: Metamerie-Index von Probenpaaren bei
Lichtartwechsel (ISO 18314-4:2020)

Analyse colorimétrique - Partie 4: Indice de metamérisme de paires d'échantillon pour

changement d'illuminant (ISO 18314-4:2020)
Ta slovenski standard je istoveten z: prEN ISO 18314-4
ICS:
17.180.20 Barve in merjenje svetlobe Colours and measurement of
light
87.060.10 Pigmenti in polnila Pigments and extenders
oSIST prEN ISO 18314-4:2021 en,fr,de

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

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oSIST prEN ISO 18314-4:2021
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oSIST prEN ISO 18314-4:2021
INTERNATIONAL ISO
STANDARD 18314-4
First edition
2020-08
Analytical colorimetry —
Part 4:
Metamerism index for pairs of
samples for change of illuminant
Analyse colorimétrique —
Partie 4: Indice de metamérisme de paires d'échantillon pour
changement d'illuminant
Reference number
ISO 18314-4:2020(E)
ISO 2020
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oSIST prEN ISO 18314-4:2021
ISO 18314-4:2020(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2020

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

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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
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Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2020 – All rights reserved
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oSIST prEN ISO 18314-4:2021
ISO 18314-4:2020(E)
Contents Page

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

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

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

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

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

4 Symbols and abbreviated terms ........................................................................................................................................................... 2

5 Reference illuminant........................................................................................................................................................................................ 3

6 Test illuminant ........................................................................................................................................................................................................ 3

7 CIELAB coordinates L*, a*, b* ................................................................................................................................................................... 3

8 Metamerism index for change in illuminant ........................................................................................................................... 4

8.1 General calculation methods ...................................................................................................................................................... 4

8.2 Basic calculation of the metamerism index from colour differences ....................................................... 4

8.3 Correction methods ............................................................................................................................................................................ 5

8.3.1 Additive correction ........................................................................................................................................................ 5

8.3.2 Multiplicative correction ........................................................................................................................................... 5

8.3.3 Spectral correction ......................................................................................................................................................... 6

8.4 Test report ................................................................................................................................................................................................... 9

Annex A (informative) Calculation examples ...........................................................................................................................................10

Bibliography .............................................................................................................................................................................................................................23

© ISO 2020 – All rights reserved iii
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oSIST prEN ISO 18314-4:2021
ISO 18314-4:2020(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.

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 Technical Committee ISO/TC 256, Pigments, dyestuff and extenders.

A list of all parts in the ISO 18314 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 2020 – All rights reserved
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oSIST prEN ISO 18314-4:2021
ISO 18314-4:2020(E)
Introduction

For the phenomenon of metamerism of pairs of samples, three different kinds are distinguished:

a) Illuminant metamerism occurs if both of the object colours of a pair of samples are perceived as

being the same only under a specific illuminant (e.g. under illuminant D65), while they differ under

a different illuminant (e.g. illuminant A).

b) Observer metamerism occurs if the object colours of a pair of samples are perceived as being the

same by one observer, while a different observer perceives a colour difference under the same

illuminant and the same reference conditions.

NOTE 1 The observer metamerism is caused by differences between the distributions of spectral colour

matching functions of different observers.

c) Field-size metamerism occurs if both of the object colours of a pair of samples are perceived as

being the same on the retina for a size of an observation field (e.g. defined by the 2° standard

observer), while they differ for a different observation field on the retina (e.g. 10°).

NOTE 2 The reason for field-size metamerism is based on the existent colour matching functions of

an observer during an observation situation. The colour matching functions change with the size of the

observation field on the retina. Such change of the observation field can also occur if, for example, the pair of

samples is examined from different distances.
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oSIST prEN ISO 18314-4:2021
INTERNATIONAL STANDARD ISO 18314-4:2020(E)
Analytical colorimetry —
Part 4:
Metamerism index for pairs of samples for change of
illuminant
1 Scope

This document specifies a formalism for the calculation of the illuminant metamerism of solid surface

colours. It cannot be applied to colours of effect coatings without metrical adaptation.

This document only covers the phenomenon of metamerism for change of illuminant, which has the

greatest meaning in practical application. In the case of chromaticity coordinates of a pair of samples

under reference conditions that do not exactly match, recommendations are given on which correction

measures are to be taken. Regarding the reproduction of colours, the metamerism index is used as a

measure of quality in order to specify tolerances for colour differences between a colour sample and a

colour match under different illumination conditions.

The quantification of the illuminant metamerism of pairs of samples is formally performed by a colour

difference assessment, for which tolerances that are common for the evaluation of residual colour

differences can be used.

NOTE In the colorimetric literature and textbooks, the term geometric metamerism is sometimes used for

the case that two colours appear to be the same under a specific geometry for visual assessment and selected

standard observer and standard illuminant pair, but is perceived as two different colours at changed observation

geometry. The term geometric metamerism is different to metamerism described in this document.

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.

ISO/CIE 11664-1, Colorimetry — Part 1: CIE standard colorimetric observers
ISO/CIE 11664-2:— , Colorimetry — Part 2: CIE standard illuminants
ISO/CIE 11664-4, Colorimetry — Part 4: CIE 1976 L*a*b* colour space
CIE 015, Colorimetry
CIE S 017, 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/

1) Under preparation. Stage at the time of preparation: ISO/CIE DIS 11664-2:2020.

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3.1
metamerism

property of spectrally different colour stimuli that have the same tristimulus values in a specified

colorimetric system
[SOURCE: CIE 017:2016, 17-23-006]
3.2
paramerism

characteristic of a pair of samples with spectral colour stimulus functions which have different

fundamental colour stimulus functions as well as different residuals or metameric black values within

the visible spectral range

Note 1 to entry: Parameric objects are characterized by the fact that they reflect colour stimuli of different

spectral power distribution functions under a specified standard illuminant, which cause approximately the

same colour perception under the selected observation conditions.
3.3
colour difference

difference between two colour stimuli, defined as a distance between the points representing them in a

specified colour space

[SOURCE: CIE 017:2016, 17-22-041, modified — symbol ΔE was amended, “Euclidean” and Note 1 to

entry have been deleted.]
3.4
reference illuminant
illuminant with which other illuminants are compared
[SOURCE: CIE S 017:2016, 17-22-109 17]
3.5
test illuminant

illuminant, for which the colour difference (3.3) between the two samples to be tested is assessed

3.6
metamerism-index for change in illuminant
* *

colour difference ΔE (3.3) between the two samples under test illuminant (3.5) if Δ=E 0 is observed

under the reference illuminant (3.4)
3.7
correction method

algorithm for theoretically eliminating a colour difference (3.3) of the pair of samples under the reference

illuminant (3.4)
4 Symbols and abbreviated terms
For the application of this document, the symbols given in Table 1 apply.
Table 1 — Symbols
Symbol Identification
X, Y, Z Standard tristimulus values of a measured object colour
Standard tristimulus values of the used illuminant
X , Y , Z
n n n
x , y , z Colour-matching functions
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oSIST prEN ISO 18314-4:2021
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Table 1 (continued)
Symbol Identification
* * * Basic coordinates of the CIELAB system
L , a , b
ΔL*, Δa*, Δb* Differences between basic coordinates of the CIELAB system
Metamerism index for change in illuminant
 

Vector of the radiometric function of a sample with associated fundamental colour stimulus (f)

NN,,N
and metameric black (r)
λ Wavelength
S Relative spectral distribution function of an illuminant
Vector of the standard tristimulus values
w Integration weights for the calculation of the standard tristimulus values

A Matrix of the integration weights w for the calculation of the standard tristimulus values

R Projection matrix
I Identity matrix
Index spl Sample
Index std Standard
Index t Test illuminant
Index corr Corrected value
Index f Fundamental colour stimulus
Index r Metameric black values (residuals)
Index ref Reference illuminant
Index T Transposed matrix
5 Reference illuminant

The standard illuminant D65 is chosen as reference illuminant in accordance with ISO/CIE 11664-2.

Other reference illuminants required in special cases shall be particularly specified.

6 Test illuminant

The selection of the test illuminant depends on the application. If the test illuminants are not particularly

specified, standard illuminant A in accordance with ISO 11664-2 and/or illuminants of the fluorescent

lamp type, such as FL11 in accordance with CIE 015, shall preferably be selected. The test illuminant

used shall be indicated as an index to M, e.g. M or M .
A FL11

When calculating the standard tristimulus values X, Y, Z under the selected test illuminants, the basic

raster of wavelengths given in ISO 11664-2 or CIE 015 for A and D65, and in CIE 015 for FL11 and

FL2 shall be complied with. In cases of missing measuring values of the standard or sample for these

wavelengths, these values shall be interpolated and/or extrapolated.
7 CIELAB coordinates L*, a*, b*
* * *

The metamerism index M is based on the CIELAB coordinates L , a , b of samples 1 and 2 which are

* * *

to be compared. L , a , b is calculated in accordance with ISO/CIE 11664-4 from the standard

tristimulus values X, Y, Z of the sample for the CIE 1964 10° standard observer in accordance with

* * *

ISO/CIE 11664-1 for the reference illuminant and the selected test illuminant. If calculating L , a , b

under the test illuminant, the respective standard tristimulus values X , Y , Z of the entirely matt

n n n

white surface shall be used (see CIE 015). For the standard illuminants A and D65 or for the illuminant

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oSIST prEN ISO 18314-4:2021
ISO 18314-4:2020(E)

recommendation FL11, the standard tristimulus values X , Y , Z of the entirely matt white surface

n n n
apply in accordance with Table 2.

Table 2 specifies standard tristimulus values for the frequently used standard illuminants D65 and A as

well as illuminant FL11 and both of the standard observers in accordance with CIE 015.

Table 2 — Standard tristimulus values
2° standard observer 10° standard observer
Standard
tristimulus Illuminant
values
D65 A FL11 D65 A FL11
X 95,04 109,85 100,96 94,81 111,14 103,86
Y 100,00 100,00 100,00 100,00 100,00 100,00
Z 108,88 35,58 64,35 107,32 35,20 65,61

For fluorescent samples, the illuminant used for measurement shall be adjusted as close as possible to

that illuminant for which the standard tristimulus values are to be determined.

NOTE In contrast to non-fluorescent samples, the calculation of metamerism indices for fluorescent samples

is erroneous if the samples are measured only under one illuminant.
8 Metamerism index for change in illuminant
8.1 General calculation methods

Three different correction methods for calculating a metamerism index in the case of paramerism have

been proposed in References [6] to [13]. All methods assume that, for practical cases, there might be

already a small difference between the colours of the sample and the standard even under the reference

illuminant from the very beginning, due to problems of fabrication. In the case of two methods, called

the additive and the multiplicative correction, these inherent colour differences often merge with the

difference introduced by the change of the illuminant. The third method, the spectral correction, works

more fundamentally by the separation of inherent colour differences under the reference illuminant

from those introduced by the change of the illuminant.
NOTE Annex A includes calculation examples.
8.2 Basic calculation of the metamerism index from colour differences

The common formula for a metamerism index at change in illuminant, expressed in CIELAB coordinates

for the test illuminant (t), is given by Formula (1):
22 2
** *
ML=Δ +Δab+Δ (1)
() () ()
tt tt
where
t is the test colour;
* * *
ΔL =−LL ;
t splc,,orrt stdt,
* * *
Δa =−aa ;
t splc,,orrt stdt,
* * *
Δb =−bb .
t splc,,orrt stdt,
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The formulae given above are meant as an example if using the CIELAB colour space.

Analogous equations apply for other Euclidian colour spaces such as DIN 99o in DIN 6176. In non-

Euclidian colour spaces such as CIE 94 or CIEDE2000, the specific colour differences are provided

with colour-space dependent weight functions and, in regard to the latter case, are expanded by an

additional rotation term. The CIELAB metric used in the present standard is an example and should be

replaced in practical applications by one of the mentioned more recent metrics (e.g. CIE 94, CIEDE2000,

DIN 99o), which are significantly more uniform than the CIELAB model.
8.3 Correction methods
8.3.1 Additive correction

When using the additive correction, the differences of any colorimetric axis between standard (std)

and sample (spl) under reference conditions (ref), are added to the specific differences between

standard and sample under test conditions (t). The resulting equation for the metamerism index M ,

expressed in CIELAB coordinates, is then given by Formula (2):
22 2
** *
ML=Δ +Δab+Δ (2)
() () ()
t corr corr corr
where
* * **
ΔL = LL−−ΔL ;
corr splt, stdt, ref
* * *
ΔL = LL− .
ref splr, ef stdr, ef
* *

Analogous relationships apply for Δa and Δb . It should be noted that slightly different results are to

be expected, if the correction is applied to standard tristimulus values prior to transformation into a

uniform colour space such as CIELAB or DIN 99o.
8.3.2 Multiplicative correction

When using the multiplicative correction, which is specified in CIE 015 as correction method, the

standard tristimulus values of the sample (spl), which are observed under test conditions (t) are

multiplied with the quotient of the standard tristimulus values of standard (std) and sample (spl),

which are obtained under reference conditions (ref). The resulting equation is given in Formula (3):

stdr, ef
YY= (3)
corr splt,
splr, ef

in which case, again, analogous combinations for X and Z apply. Subsequently, a transformation

corr corr

into a uniform colour space (e.g. CIELAB) takes place and results in Formula (4):

22 2
** *
ML=Δ +Δab+Δ (4)
() () ()
t corr corr corr
with
* * *
Δ=LL −L
corr splc,,orrt stdt,
* *

Analogous relationships apply for the two remaining specific differences Δa and Δb .

corr corr
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ISO 18314-4:2020(E)
8.3.3 Spectral correction

The spectral method considers that under the reference illuminant, minor differences between the

tristimulus values of the sample and the standard can already exist, which are not relevant for the

metamerism characteristics. In order to first mathematically compensate them and only determine

the effective component for metamerism at change in illuminant of sample pairs with given spectral

reflectance, the possibility is used to mathematically split a spectral reflectance in two additive

components.

One component describes only the function that is effective for the formation of the colour stimulus

under the reference illuminant and the other component describes a function, which does not lead to a

contribution to the colour stimulus when integrating via the stimulus under the reference illuminant.

This function necessarily includes positive and negative components. The colour stimulus function

resulting from the first component of the spectral reflectance under the reference illuminant that is

effective for the formation of the colour stimulus is called fundamental colour stimulus function, the

respective second part of the colour stimulus function leads to a metameric black of the decomposition

(residue), i.e. an invisible contribution with a resulting colour stimulus identical to zero.

The compensation of the deviations of the colour stimuli of a sample from the standard, which are non-

effective for metamerism characteristics, is realized by replacing the fundamental colour stimulus of

the sample by that of the standard. The component that is effective for the metamerism characteristic

is maintained unchanged, i.e. a new colour stimulus function of the sample is generated from the sum

of the replaced fundamental colour stimulus and the unchanged second component. From the sum, the

metamerism at change in illuminant in regard to the standard is determined.

The following mathematical description of the method of spectral correction is not based on a

decomposition of the colour stimulus function into its fundamental colour stimulus function and the

invisible function of the black stimulus. Rather, a decomposition of the spectral reflectance function of

the respective colour into a “fundamental reflectance function” and a “black” component (metameric

black values) of the reflectance function is used. This method is valid under the assumption that these

components only lead to the visually effective fundamental colour stimulus function and the invisible

function of the metameric black values in combination with the distribution function of the reference

illuminant (here D65). Consequently, the distribution function of the reference illuminant is inherently

included in the decomposition of the reflectance functions. In order to highlight this connection, the

components are additionally marked “for the reference illuminant” when decomposing the reflectance

function of a colour.

In the model of the spectral decomposition of a radiometric function developed by Cohen and Kappauf,

the spectral reflectance of an object colour obtained in the visible spectral range is summarized in the

vector in Formula (5):
 ()
 
 ρλ()
 
N= (5)
 
 
 
 

The components of the vector Nare the reflectance values ρλ ()in=…12,, , of the examined colour,

which are discreetly present on n intervals. For the calculation of the respective standard tristimulus

values XY,,Z from the reflectance functions, the product based on the supporting points of the

distribution function of the used illuminant S λ , the respective standard colour-matching function

[see Formula (6)]
αλ()={}xy()λλ,,() z()λ (6)
ii ii

the distance of supporting points Δλ and a normalization constant k shall be determined.

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The components ρλ()of the vector N are the reflectances of the examined colour. Considering the

illuminant S λ , the standard tristimulus components X, Y, Z are calculated from the sum of the

products S λρ λα λλΔ /k with the normalization constant k. The term
() () ()
ii i

αλ = xyλλ,,z λ describes the colour matching functions. The constant k is determined

() {}() () ()
ii ii

from the respective sum Syλλ Δλ for the Y-component of the illuminant considered.

() ()
∑ ii
These products mentioned above are introduced as weights in Formula (7):
wkλλ= S α λλΔ (7)
() () ()
α ii i

All weights of all supporting points for the standard colour-matching curves are given in matrix form in

a n × 3 matrix in Formula (8):
w λ
 () 
w λ y 1 w λ
() ()
x 1 z 1
 
 
w λ
w λ ()w λ
() ()
y 2
x 2 z 2
A=  (8)
   
 
w λ w λ
 () ( ))
w λ
xn () zn
 
The transposed vector in Formula (9):
WX={},,YZ (9)
of the tristimulus values, results in accordance with Formula (10):
WA=⋅N (10)

from the matrix multiplication of the transposed weighting matrix A with the radiometric function N .

From the matrix A of the integration weights Cohen and Kappauf constructed an orthogonal n × n matrix

in Formula (11):
RA=⋅AA A (11)
which application in Formula (12):
RN⋅=N (12)

to the radiometric function N of an object colour isolates its fundamental reflectance function for the

reference illuminant N , which actively forms the process of colour perception.
The tristimulus value W of the difference in Formula (13):
 
NN=−N (13)
i.e. see Formula (14):
WA=⋅N (14)
is zero.
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This contribution, identified as metameric black value or residuals, does not bear any colour information

and does not become visible during the colour-perception process under the reference illuminant. N

contributes positively as well as negatively. Also, regarding the obtained fundamental colour stimuli,

negative vector elements can occur. It is essential that Ni≥∀0 applies for the reflectance function,

which is composed of fundamental reflectance function and the metameric black values, in order to be

physically realized. The n × n projection matrix R depends on the standard observer (2°, 10°) and the

used standard illuminant.

Based on the described decomposition of a spectral reflectance function into a fundamental reflectance

function for the reference illuminant and the residuals as metameric black values of the reflectance

function, Fairman proposed a model of residual colour difference of parameric pairs of samples with

minor colour difference.
 

The vectors N and N describe the reflectance functions of a parameric pair of samples, the

std spl

n elements of which represent the measured reflectance values of the respective object colour within

the visible spectral range. They can be decomposed into their fundamental reflectance functions for

the reference illuminant and metameric black functions (r) for the reference illuminant by means of the

Cohen-Kappauf decomposition in Formula (15) and Formula (16):
 
NN=+N (15)
stdf ,,stdr std
 
NN=+N (16)
splf ,,splr spl

By addition of the residuals of the sample (Index r,spl) and the fundamental reflectance function of the

standard for the reference (Index f,std), a virtual sample with corrected refl
...

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