# EN ISO 18314-2:2023

(Main)## Analytical colorimetry - Part 2: Saunderson correction, solutions of the Kubelka-Munk equation, tinting strength, depth of shade, hiding power (ISO 18314-2:2023)

## Analytical colorimetry - Part 2: Saunderson correction, solutions of the Kubelka-Munk equation, tinting strength, depth of shade, hiding power (ISO 18314-2:2023)

This document specifies the Saunderson correction for different measurement geometries and the solutions of the Kubelka-Munk equation for hiding and transparent layers. It also specifies methods for the calculations of the tinting strength including the residual colour difference based on different criteria such as the depth of shade. Finally, methods for determining the hiding power are provided.

The procedures for preparing the samples for these measurements are not part of this document. They are agreed between the contracting parties or are described in other national or international standards.

## Analytische Farbmessung - Teil 2: Saunderson‑Korrektur, Lösungen der Kubelka‑Munk‑Gleichung, Farbstärke, Farbtiefe und Deckvermögen (ISO 18314-2:2023)

Dieses Dokument legt die Saunderson Korrektur für unterschiedliche Messgeometrien sowie die Lösungen der Kubelka Munk Gleichung für deckende und durchsichtige Schichten fest. Es legt außerdem Verfahren zur Berechnung der Farbstärke, einschließlich des Restfarbabstandes, mit unterschiedlichen Kriterien, die auf der Farbtiefe beruhen, fest. Schließlich werden Verfahren zur Bestimmung des Deckvermögens zur Verfügung gestellt.

Die Durchführungen der Probenherstellung für diese Messungen sind nicht Bestandteil dieses Dokuments. Diese werden zwischen den Vertragspartnern vereinbart oder sind in anderen nationalen oder internationalen Normen beschrieben.

## Analyse colorimétrique - Partie 2: Correction de Saunderson, solutions de l'équation de Kubelka-Munk, pouvoir colorant, profondeur de teinte, pouvoir masquant (ISO 18314-2:2023)

Le présent document spécifie la correction de Saunderson pour différentes géométries de mesure et les solutions de l’équation de Kubelka-Munk pour les couches masquantes et transparentes. Il spécifie également les méthodes de calcul du pouvoir colorant et de l’écart de couleur résiduel basées sur différents critères, tels que la profondeur de teinte. Enfin, des méthodes sont fournies pour déterminer le pouvoir masquant.

Les méthodes de préparation des échantillons destinés à ces mesurages ne sont pas couvertes par le présent document. Elles sont fixées par accord entre les parties contractantes ou sont décrites dans d’autres normes nationales ou internationales.

## Analizna kolorimetrija - 2. del: Saundersonova korekcija, rešitve Kubelka-Munkove enačbe, barvna jakost, globina barve in kritnost (ISO 18314-2:2023)

### General Information

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### Standards Content (Sample)

SLOVENSKI STANDARD

SIST EN ISO 18314-2:2023

01-marec-2023

Nadomešča:

SIST EN ISO 18314-2:2018

Analizna kolorimetrija - 2. del: Saundersonova korekcija, rešitve Kubelka-Munkove

enačbe, barvna jakost, globina barve in kritnost (ISO 18314-2:2023)Analytical colorimetry - Part 2: Saunderson correction, solutions of the Kubelka-Munk

equation, tinting strength, depth of shade, hiding power (ISO 18314-2:2023)Analytische Farbmessung - Teil 2: Saunderson-Korrektur, Lösungen der Kubelka-Munk-

Gleichung, Farbstärke, Farbtiefe und Deckvermögen (ISO 18314-2:2023)Analyse colorimétrique - Partie 2: Correction de Saunderson, solutions de l'équation de

Kubelka-Munk, pouvoir colorant, profondeur de teinte, pouvoir masquant (ISO 18314-

2:2023)Ta slovenski standard je istoveten z: EN ISO 18314-2:2023

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 18314-2:2023 en,fr,de

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

---------------------- Page: 1 ----------------------SIST EN ISO 18314-2:2023

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SIST EN ISO 18314-2:2023

EN ISO 18314-2

EUROPEAN STANDARD

NORME EUROPÉENNE

January 2023

EUROPÄISCHE NORM

ICS 87.060.10 Supersedes EN ISO 18314-2:2018

English Version

Analytical colorimetry - Part 2: Saunderson correction,

solutions of the Kubelka-Munk equation, tinting strength,

depth of shade, hiding power (ISO 18314-2:2023)

Analyse colorimétrique - Partie 2: Correction de Analytische Farbmessung - Teil 2: Saunderson-

Saunderson, solutions de l'équation de Kubelka-Munk, Korrektur, Lösungen der Kubelka-Munk-Gleichung,

pouvoir colorant, profondeur de teinte, pouvoir Farbstärke, Farbtiefe und Deckvermögen (ISO 18314-

masquant (ISO 18314-2:2023) 2:2023)This European Standard was approved by CEN on 8 January 2023.

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, Türkiye 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

© 2023 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 18314-2:2023 E

worldwide for CEN national Members.---------------------- Page: 3 ----------------------

SIST EN ISO 18314-2:2023

EN ISO 18314-2:2023 (E)

Contents Page

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

---------------------- Page: 4 ----------------------SIST EN ISO 18314-2:2023

EN ISO 18314-2:2023 (E)

European foreword

This document (EN ISO 18314-2:2023) has been prepared by Technical Committee ISO/TC 256

"Pigments, dyestuffs and extenders" in collaboration with 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 July 2023, and conflicting national standards shall be

withdrawn at the latest by July 2023.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 18314-2:2018.Any feedback and questions on this document should be directed to the users’ national standards

body/national committee. A complete listing of these bodies can be found on the CEN website.

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, Türkiye and the

United Kingdom.Endorsement notice

The text of ISO 18314-2:2023 has been approved by CEN as EN ISO 18314-2:2023 without any

modification.---------------------- Page: 5 ----------------------

SIST EN ISO 18314-2:2023

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SIST EN ISO 18314-2:2023

INTERNATIONAL ISO

STANDARD 18314-2

Second edition

2023-01

Analytical colorimetry —

Part 2:

Saunderson correction, solutions of

the Kubelka-Munk equation, tinting

strength, depth of shade and hiding

power

Analyse colorimétrique —

Partie 2: Correction de Saunderson, solutions de l'équation de

Kubelka-Munk, pouvoir colorant, profondeur de teinte et pouvoir

masquant

Reference number

ISO 18314-2:2023(E)

© ISO 2023

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SIST EN ISO 18314-2:2023

ISO 18314-2:2023(E)

COPYRIGHT PROTECTED DOCUMENT

© ISO 2023

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

© ISO 2023 – All rights reserved

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SIST EN ISO 18314-2:2023

ISO 18314-2:2023(E)

Contents Page

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

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

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

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

4 Symbols and abbreviated terms..........................................................................................................................................................3

5 Saunderson correction ..................................................................................................................................................................................4

5.1 General ........................................................................................................................................................................................................... 4

5.2 Incidence diffuse, observation 0° (d:0°) .......................................................................................................................... 5

5.3 Incidence 45°, observation 0° (45°:0°) ............................................................................................................................... 5

6 Solution of the Kubelka-Munk equations .................................................................................................................................. 5

6.1 General ........................................................................................................................................................................................................... 5

6.2 Method 1 ...................................................................................................................................................................................................... 6

6.3 Method 2 ...................................................................................................................................................................................................... 6

7 Determination of relative tinting strength and residual colour difference ofcoloured pigments ............................................................................................................................................................................................. 7

7.1 General ........................................................................................................................................................................................................... 7

7.2 Principle ....................................................................................................................................................................................................... 7

7.3 Procedure .................................................................................................................................................................................................... 7

7.3.1 General ........................................................................................................................................................................................ 7

7.3.2 Evaluation of absorption at the absorption maximum .................................................................... 7

7.3.3 Evaluation of the weighted K/S sum ................................................................................................................. 8

7.3.4 Evaluation by equalizing the tristimulus value, Y ................................................................................ 9

7.3.5 Evaluation by equalizing the smallest of the tristimulus values X, Y, and Z .................. 9

7.3.6 Evaluation by equalizing the depth of shade ......................................................................................... 10

8 Determination of hiding power of pigmented media ................................................................................................12

8.1 General ........................................................................................................................................................................................................12

8.2 Example for white or light-coloured paints with a contrast ratio of 0,98 as hiding

power criterion ...................................................................................................................................................................................12

9 Repeatability and reproducibility .................................................................................................................................................13

Annex A (normative) Tables of coefficients for calculating a(φ) values (standard illuminant

D65 and 10° standard observer) ......................................................................................................................................................14

Annex B (normative) Tables of coefficients for calculating a(φ) values (illuminant C and 2°

standard observer) ........................................................................................................................................................................................16

Bibliography .............................................................................................................................................................................................................................18

iii© ISO 2023 – All rights reserved

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SIST EN ISO 18314-2:2023

ISO 18314-2:2023(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, dyestuffs and extenders, in

collaboration with the European Committee for Standardization (CEN) Technical Committee CEN/TC

298, Pigments and extenders, in accordance with the Agreement on technical cooperation between ISO

and CEN (Vienna Agreement).This second edition cancels and replaces the first edition (ISO 18314-2:2015), which has been technically

revised.The main changes are as follows:

— the title has been amended by “depth of shade”;

— the terms and definitions in Clause 3 have been aligned with ISO 18451-1;

— the document has been editorially revised and the bibliography has been updated.

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.© ISO 2023 – All rights reserved

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SIST EN ISO 18314-2:2023

INTERNATIONAL STANDARD ISO 18314-2:2023(E)

Analytical colorimetry —

Part 2:

Saunderson correction, solutions of the Kubelka-Munk

equation, tinting strength, depth of shade and hiding

power

1 Scope

This document specifies the Saunderson correction for different measurement geometries and the

solutions of the Kubelka-Munk equation for hiding and transparent layers. It also specifies methods

for the calculations of the tinting strength including the residual colour difference based on different

criteria such as the depth of shade. Finally, methods for determining the hiding power are provided.

The procedures for preparing the samples for these measurements are not part of this document.

They are agreed between the contracting parties or are described in other national or international

standards.2 Normative references

There are no normative references in this document.

3 Terms and definitions

For the purposes of this document, the following terms and definitions apply.

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

— ISO Online browsing platform: available at https:// www .iso .org/ obp— IEC Electropedia: available at https:// www .electropedia .org/

3.1

tinting strength

colour strength

measure of the ability of a colourant to colour other materials because of its absorptive power

[SOURCE: ISO 18451-1:2019, 3.122]3.2

relative tinting strength

relative colour strength

percentage ratio of the tinting strength (3.1) of the colourant under test related to the tinting strength

of a reference colourant[SOURCE: ISO 18451-1:2019, 3.105]

3.3

tinting strength criterion

parameter that describes the colouring effect of a colourant, based on its absorption

Note 1 to entry: The tinting strength criteria used in this document are the following:

© ISO 2023 – All rights reserved---------------------- Page: 11 ----------------------

SIST EN ISO 18314-2:2023

ISO 18314-2:2023(E)

— value of the Kubelka-Munk function at the absorption maximum;

— weighted sum of the Kubelka-Munk function values;

— tristimulus value Y;

— the smallest of the tristimulus values X, Y, Z;

— shade depth parameter B.

Note 2 to entry: Examples of other tinting strength parameters not used in this document are the following:

— unweighted sum of the Kubelka-Munk function values;— chromaticity given by the three colour coordinates (L*, a*, b*);

— reflectance factor at the absorption maximum.

3.4

residual colour difference

colour difference that remains between the white reductions of the reference and test samples when

the tinting strength criterion (3.3) values are the same or have been equalizedEXAMPLE Residual colour difference is given by ΔE*.

3.5

depth of shade

shade depth

colour depth

measure for the intensity of a colour perception that increases with increasing chroma and decreases

with increasing lightnessNote 1 to entry: Colourations having the same depth of shade appear to be prepared using the same concentrations

of colourants having the same tinting strength (3.1).[SOURCE: ISO 18451-1:2019, 3.26, modified — admitted terms “shade depth” and “colour depth” have

been added.]3.6

standard depth of shade

standard shade depth

standard colour depth

depth of shade (3.5) level laid down by convention

[SOURCE: ISO 18451-1:2019, 3.113, modified — admitted terms “standard shade depth” and “standard

colour depth” have been added.]3.7

hiding power

ability of coating to obliterate the colour or colour differences of the substrate

Note 1 to entry: The use of the German expressions “Deckkraft” und “Deckfähigkeit” should be avoided.

Note 2 to entry: The term “coverage” is ambiguous because it is used in some instances to refer to hiding power

and in others to mean spreading rate. The more precise terms hiding power and spreading rate should always be

used.[SOURCE: ISO 18451-1:2019, 3.47]

© ISO 2023 – All rights reserved

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SIST EN ISO 18314-2:2023

ISO 18314-2:2023(E)

4 Symbols and abbreviated terms

a constant

a* CIELAB colour coordinate

a(φ) factor

a(λ) auxiliary variable

b* CIELAB colour coordinate

b(λ) auxiliary variable

B shade depth parameter

C relative tinting strength

rel

D hiding power value indicating the area of the contrast substrate concerned, in m , which can

be coated with 1 kgD hiding power value indicating the area of the contrast substrate concerned, in m , which can

be coated with 1 lF(λ) Kubelka-Munk function

F′(λ) modified Kubelka-Munk function

g(λ) weighting function (defined as the sum of the colour matching functions x()λ , y()λ , and

z λ for a 10° standard observer)h thickness

K coefficient

K(λ) absorption coefficient

(K/S) Kubelka-Munk value of reference sample

(K/S) Kubelka-Munk value of test sample

L* CIELAB lightness

m mass fraction of coloured pigment reference sample

m mass fraction of coloured pigment test sample

n refractive index

r reflection coefficient at the surface for directional light incident perpendicular from outside

reflection coefficient at the surface for directional light incident parallel under 45° from outside

r reflection coefficient for light incident diffusely from the inside of the specimen

R()λ reflectance spectrumR λ reflectance of infinitely thick layer

Saunderson-corrected reflectance spectrum

R()λ

© ISO 2023 – All rights reserved

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SIST EN ISO 18314-2:2023

ISO 18314-2:2023(E)

Saunderson-corrected reflectance of the black substrate

R λ

Saunderson-corrected reflectance of the white substrate

R λ

Saunderson-corrected reflectance of the sample on black substrate

R()λ

Saunderson-corrected reflectance of the sample on white substrate

R()λ

R′ λ modified reflectance spectrum including surface effects

s saturation

S()λ scattering coefficient

SD standard depth of shade

T weighted sum

x, y chromaticity coordinates

X, Y, Z tristimulus values

ΔE *

residual colour difference

CIELAB colour difference

φ hue angle

φ closest angle in the table below the hue angle

r as a subscript, r refers to the reference sample

t as a subscript, t refers to the test sample

5 Saunderson correction

5.1 General

For colorimetric calculation it is necessary to account for surface phenomena to obtain viable results.

The formulae are known as Saunderson correction, and their derivation can be found in References [1]

[3]and [2]. The necessary coefficients are solutions of the Fresnel formulae depending on the index of

refraction for the given binder.The formulae are derived assuming an ideal surface, a perfectly hiding layer and a perfectly diffuse

scattering of light inside the interior of the specimen. Any deviation from these assumptions shall lead

to consideration of the usefulness of the following calculations.The formulae given here are for two of the most widespread geometries: diffuse incidence, 0°

observation (d:0°) [Formula (1), Formula (2) and Formula (3)] and 45° incidence, 0° observation (45°:0°)

[Formula (4) and Formula (5)]. In nearly every colorimeter used, the measurement angle is not 0° but

8°. This deviation is not considered problematic.The constants necessary for the calculation are the following:

r reflection coefficient at the surface for directional light incident perpendicular from outside.

For n = 1,5 r = 0,040.© ISO 2023 – All rights reserved

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SIST EN ISO 18314-2:2023

ISO 18314-2:2023(E)

reflection coefficient at the surface for directional light incident parallel under 45° from out-

side. For n = 1,5, r = 0,050.r reflection coefficient for light incident diffusely from the inside of the specimen. For n =

1,5, r = 0,596.5.2 Incidence diffuse, observation 0° (d:0°)

The constant a = 1 if a gloss trap is closed and a = 0 if the gloss trap is open and the specular reflection

is excluded.11−rr− R λ

()() ()

Rrλ =+a (1)

1−rR()λ

Where a = 1:

Rrλ −

R λ = (2)

11−−rr −R()λ

Where a = 0:

R()λ

R λ = (3)

1 −−rr ++rr R()λ

02 20

5.3 Incidence 45°, observation 0° (45°:0°)

11−rr− R()λ

()()

R()λ = (4)

1−rR()λ

nR λ

R λ = (5)

1−−+rr rr +nr R()λ

00 00 2

6 Solution of the Kubelka-Munk equations

6.1 General

The Kubelka-Munk theory describes the reflection of a pigmented layer by two constants: absorption,

K(λ), and scattering, S(λ). It is based on the following assumptions:a) ideally diffuse radiation distribution on the irradiation side;

b) ideally diffuse radiation distribution in the interior of the layer;

c) no consideration of surface phenomena resulting from the discontinuity in refractive index.

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SIST EN ISO 18314-2:2023

ISO 18314-2:2023(E)

For an infinitely thick, respectively hiding layer with a reflectance of R(λ) , the following solutions

shown in Formula (6) and Formula (7) are found, which allow the determination of the relation between

the scattering and the absorption coefficient:1−R()λ

K()λ

= ≡FR ()λ (6)

S λ 2R λ

() ()

respectively the inverse:

K()λ K()λ K()λ

R()λ =+12− + (7)

S λ S λ S λ

() () ()

For the determination of the scattering and absorption coefficient, two different methods can be applied

(the Saunderson correction shall be used).6.2 Method 1

Measurement of the reflectance of an infinite thick (respectively hiding) layer and the reflectance

* *R λ of a coating of the thickness, h, on a substrate of the reflection R λ , then following Formulae (8),

() ()(9), (10), and (11):

1 1

a()λ = +R()λ (8)

R λ

∞

1 1

* *

baλλ= −R λ = −R λ (9)

() () () ()

∞ ∞

R()λ

** * *

1 − aR()λλ() ++ RR()λλ () R(λλ )

0 0

S()λ = arcoth (10)

bhλ

()

bR()λλ() − R()λ

KSλλ= a λ −1 (11)

() ()[]()

6.3 Method 2

This method applies two layers of equal thickness, h, on black and white substances. After the

determination of the auxiliary variables a(λ) and b(λ) according to Formula (12) and Formula (13), the

scattering coefficient, S(λ) can be calculated using Formula (14) or Formula (15). The possibility with

the least experimental uncertainty should be chosen.* * * * * ** * *

11+RR()λλ() RR()λλ− () ++RR()λλ() RR()λλ− ()

w ow b ob b ob ow w

a λ = (12)

* * * *

2 RR()λλ() −RR()λλ()

b ow w ob

ba()λλ= () −1 (13)

** **

1(−a λλ)(RR)(+ λλ)(+RR)(λ)

bobb ob

S()λ = arcoth (14)

bh()λ

b(λ))(RRλλ)(− )

bob

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SIST EN ISO 18314-2:2023

ISO 18314-2:2023(E)

** **

1(−a λλ)(RR)(+ λλ)(+RR)(λ)

woww ow

S()λ = arcoth (15)

bh()λ

b(λ))(RRλλ)(− )

wow

Using S(λ), the reflectance R(λ)* of a coating of the thickness, h, on a substrate of the reflection R λ is

given by Formula (16):1 −− (Raλλ)( {}) (bbλλ) coth[]() (Shλ )

* 0

R()λ = (16)

aRλ − (()λλ +bb() coth(λλ) Sh()

() []

NOTE The formulation of the Kubelka-Munk theory leads to a system of differential equations. The solution

can be stated in different ways either by the use of the trigonometric functions used here or by the use of

logarithmic functions. They are mathematically equivalent.7 Determination of relative tinting strength and residual colour difference of

coloured pigments

7.1 General

All the methods specified here presuppose, at least approximately, a linear relationship between the

concentration of the colourant and the Kubelka-Munk function.It is assumed that the scattering by the draw-downs being measured is dominated by the white pigment

and the absorption by the coloured pigment. All these conditions shall be met to ascertain correct

results of the methods described here. The Kubelka-Munk function for the white paste can be neglected

in most cases.7.2 Principle

The reference and test samples are incorporated into white pastes. The corresponding reflectance

spectra are measured on opaque draw-downs of the resulting coloured pastes. The appropriate tinting

strength criterion is calculated from the measured values.If the tinting strength criterion values for the reference and test samples differ, the mass fraction of the

sample is increased or decreased until the values become equal. This adjustment may be performed

either experimentally or mathematically.If the tinting strength criterion values for the reference and test samples are the same, or after they

have been equalized, the residual colour difference between the white reductions of the reference and

test samples is calculated from the corresponding reflectance spectra.A spectrophotometer with d:8° or 8°:d measuring geometry with or without gloss trap, or instruments

with 45°:0° or 0°:45° measuring geometry are recommended.7.3 Procedure

7.3.1 General

The reflectance of an opaque draw-down of the white reduction of the reference sample and the

corresponding reflectance of the test sample are measured in the visible spectral range.

7.3.2 Evaluation of absorption at the absorption maximumThe tinting strength criterion is the maximum Kubelka-Munk value. Prerequisite for this method are

equal concentrations of reference and test pigments in the white pastes.© ISO 2023 – All rights reserved

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SIST EN ISO 18314-2:2023

ISO 18314-2:2023(E)

Determine the wavelength in the reflectance spectra of the white reductions at which the reflectance is

a minimum. From the minimum Saunderson-corrected reflectance R * and R *, calculate the Kubelka-

r tMunk values (K/S) and (K/S) for this wavelength by means of Formula (6). The relative tinting strength

r tC is then obtain

**...**

SLOVENSKI STANDARD

oSIST prEN ISO 18314-2:2022

01-februar-2022

Analizna kolorometrija - 2. del: Saundersonova korekcija, rešitve Kubelka-

Munkove enačbe, barvna jakost in kritnost (ISO/DIS 18314-2:2022)

Analytical colorimetry - Part 2: Saunderson correction, solutions of the Kubelka-Munk

equation, tinting strength, depth of shade, hiding power (ISO/DIS 18314-2:2022)Analytische Farbmessung - Teil 2: Saunderson-Korrektur, Lösungen der Kubelka-Munk-

Gleichung, Farbstärke, Deckvermögen (ISO/DIS 18314-2:2022)Analyse colorimétrique - Partie 2: Correction de Saunderson, solutions de l'équation de

Kubelka-Munk, pouvoir colorant, profondeur de teinte, pouvoir masquant (ISO/DIS18314-2:2022)

Ta slovenski standard je istoveten z: prEN ISO 18314-2 rev

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 18314-2:2022 en,fr,de

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

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oSIST prEN ISO 18314-2:2022

DRAFT INTERNATIONAL STANDARD

ISO/DIS 18314-2

ISO/TC 256 Secretariat: DIN

Voting begins on: Voting terminates on:

2022-01-04 2022-03-29

Analytical colorimetry —

Part 2:

Saunderson correction, solutions of the Kubelka-Munk

equation, tinting strength, depth of shade, hiding power

ICS: 87.060.10

This document is circulated as received from the committee secretariat.

THIS DOCUMENT IS A DRAFT CIRCULATED

FOR COMMENT AND APPROVAL. IT IS

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WHICH REFERENCE MAY BE MADE IN

Reference number

NATIONAL REGULATIONS.

ISO/DIS 18314-2:2022(E)

RECIPIENTS OF THIS DRAFT ARE INVITED

TO SUBMIT, WITH THEIR COMMENTS,

NOTIFICATION OF ANY RELEVANT PATENT

RIGHTS OF WHICH THEY ARE AWARE AND TO

PROVIDE SUPPORTING DOCUMENTATION. © ISO 2022

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oSIST prEN ISO 18314-2:2022

ISO/DIS 18314-2:2022(E)

COPYRIGHT PROTECTED DOCUMENT

© ISO 2022

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

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© ISO 2022 – All rights reserved

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oSIST prEN ISO 18314-2:2022

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Contents Page

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

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

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

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

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

5 Saunderson correction ..................................................................................................................................................................................4

5.1 General ........................................................................................................................................................................................................... 4

5.2 Incidence diffuse, observation 0° (d:0°) .......................................................................................................................... 5

5.3 Incidence 45°, observation 0° (45°:0°) ............................................................................................................................... 5

6 Solution of the Kubelka-Munk equations .................................................................................................................................. 5

7 Determination of relative tinting strength and residual colour difference ofcoloured pigments ............................................................................................................................................................................................. 6

7.1 General ........................................................................................................................................................................................................... 6

7.2 Principle ....................................................................................................................................................................................................... 7

7.3 Procedure .................................................................................................................................................................................................... 7

7.3.1 General ........................................................................................................................................................................................ 7

7.3.2 Evaluation of absorption at the absorption maximum .................................................................... 7

7.3.3 Evaluation of the weighted K/S sum ................................................................................................................. 8

7.3.4 E valuation by equalizing the tristimulus value, Y ................................................................................ 8

7.3.5 E valuation by equalizing the smallest of the tristimulus values X, Y, and Z .................. 9

7.3.6 E valuation by equalizing the depth of shade ............................................................................................ 9

8 Determination of hiding power of pigmented media ................................................................................................11

8.1 General ........................................................................................................................................................................................................ 11

8.2 Example for white or light coloured paints with a contrast ratio of 0,98 as hiding

power criterion ...................................................................................................................................................................................12

9 Repeatability and reproducibility .................................................................................................................................................13

10 Test report ...............................................................................................................................................................................................................13

Annex A (normative) Tables of coefficients for calculating a(φ) values (standard illuminant

D65 and 10° standard observer) ......................................................................................................................................................14

Annex B (normative) Tables of coefficients for calculating a(φ) values (illuminant C and 2°

standard observer) ........................................................................................................................................................................................16

Bibliography .............................................................................................................................................................................................................................18

iii© ISO 2022 – All rights reserved

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

This second edition cancels and replaces the first edition (ISO 18314-2:2015), which has been technically

revised.The main changes are as follows:

— the title has been amended by “depth of shade”;

— the terms and definitions in Clause 3 have been aligned with ISO 18451-1;

— the document has been editorially revised and the bibliography has been updated.

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.© ISO 2022 – All rights reserved

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oSIST prEN ISO 18314-2:2022

DRAFT INTERNATIONAL STANDARD ISO/DIS 18314-2:2022(E)

Analytical colorimetry —

Part 2:

Saunderson correction, solutions of the Kubelka-Munk

equation, tinting strength, depth of shade, hiding power

1 Scope

This document specifies the Saunderson correction for different measurement geometries and the

solutions of the Kubelka-Munk equation for hiding and transparent layers. It also specifies methods for

the calculations of the tinting strength including the residual colour difference with different criteria

and of the hiding power.The procedures for preparing the samples for these measurements are not part of this document.

They are agreed between the contracting parties or are described in other national or International

Standards.2 Normative references

There are no normative references in this document.

3 Terms and definitions

For the purposes of this document, the following terms and definitions 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 https:// www .electropedia .org/

3.1

tinting strength

colour strength

measure of the ability of a colourant to colour other materials because of its absorptive power

[SOURCE: ISO 18451-1:2019, 3.122]3.2

relative tinting strength

relative colour strength

percentage ratio of the tinting strength (3.1) of the colourant under test related to the tinting strength

of a reference colourant[SOURCE: ISO 18451-1:2019, 3.105]

3.3

tinting strength criterion

parameter that describes the colouring effect of a colourant, based on its absorption

Note 1 to entry: The tinting strength criteria used in this document are the following:

— value of the Kubelka-Munk function at the absorption maximum;© ISO 2022 – All rights reserved

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— weighted sum of the Kubelka-Munk function values;

— tristimulus value Y;

— the smallest of the tristimulus values X, Y, Z;

— shade depth parameter B.

Examples of other tinting strength parameters not used in this document are the following:

— unweighted sum of the Kubelka-Munk function values;— chromaticity given by the three colour coordinates (L*, a*, b*);

— reflectance factor at the absorption maximum.

3.4

residual colour difference

colour difference that remains between the white reductions of the reference and test samples when

the tinting strength criterion values are the same or have been equalizedEXAMPLE Residual colour difference is given by ΔE*.

3.5

depth of shade

shade depth

colour depth

measure for the intensity of a colour perception that increases with increasing chroma and decreases

with increasing lightnessNote 1 to entry: Colourations having the same depth of shade appear to be prepared using the same concentrations

of colourants having the same tinting strength.[SOURCE: ISO 18451-1:2019, 3.26 modified: synonyms “shade depth” and “colour depth” added]

3.6standard depth of shade

standard shade depth

standard colour depth

depth of shade (3.5) level laid down by convention

[SOURCE: ISO 18451-1:2019, 3.113, modified: synonyms “standard shade depth” and “standard colour

depth” added]3.7

hiding power

ability of coating to obliterate the colour or colour differences of the substrate

Note 1 to entry: The use of the German expressions “Deckkraft” und “Deckfähigkeit” should be avoided.

Note 2 to entry: The term “coverage” is ambiguous because it is used in some instances to refer to hiding power

and in others to mean spreading rate. The more precise terms hiding power and spreading rate should always be

used.[SOURCE: ISO 18451-1:2019, 3.47]

4 Symbols and abbreviated terms

a constant

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a* CIELAB colour coordinate

a(φ) factor

a(λ) auxiliary variable

b* CIELAB colour coordinate

b(λ) auxiliary variable

B shade depth parameter

C relative tinting strength

rel

D hiding power value indicating the area of the contrast substrate concerned, in m , which can be

coated with 1 kgD hiding power value indicating the area of the contrast substrate concerned, in m , which can be

coated with 1 lF(λ) Kubelka-Munk function

F′(λ) modified Kubelka-Munk function

g(λ)

weighting function (defined as the sum of the colour matching functions x λ , y λ , and z λ

() () ()for a 10° standard observer)

h thickness

K coefficient

K(λ) absorption coefficient

(K/S) Kubelka-Munk value of reference sample

(K/S) Kubelka-Munk value of test sample

L* CIELAB lightness

m mass fraction of coloured pigment reference sample

m mass fraction of coloured pigment test sample

n refractive index

r reflection coefficient at the surface for directional light incident perpendicular from outside

reflection coefficient at the surface for directional light incident parallel under 45° from outside

r reflection coefficient for light incident diffusely from the inside of the specimen

reflectance spectrumR λ

reflectance of infinitely thick layer

R λ

Saunderson-corrected reflectance spectrum

R()λ

Saunderson-corrected reflectance of the black substrate

R λ

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Saunderson-corrected reflectance of the white substrate

R λ

Saunderson-corrected reflectance of the sample on black substrate

R λ

Saunderson-corrected reflectance of the sample on white substrate

R λ

modified reflectance spectrum including surface effects

R´ λ

s saturation

scattering coefficient

S λ

SD standard depth of shade

T weighted sum

x, y chromaticity coordinates

X, Y, Z tristimulus values

”*E residual colour difference

CIELAB colour difference

φ hue angle

φ closest angle in the table below the hue angle

5 Saunderson correction

5.1 General

For colorimetric calculation it is necessary to account for surface phenomena to obtain viable results.

[1] [2]The formulas are known as Saunderson correction, their derivation can be found in References and

[3]The necessary coefficients are solutions of the Fresnel formulae depending on the index of refraction

for the given binder.The formulae are derived assuming an ideal surface, a perfectly hiding layer and a perfectly diffuse

scattering of light inside the interior of the specimen. Any deviation from these assumptions shall lead

to consideration of the usefulness of the following calculations.The formulae given here are for two of the most widespread geometries: diffuse incidence, 0°

observation (d:0°) (Formula (1), Formula (2) and Formula (3)) and 45° incidence, 0° observation (45°:0°)

(Formula (4) and Formula (5). In nearly every colorimeter used, the measurement angle is not 0° but 8°.

This deviation is not considered problematic.The constants necessary for the calculation are the following:

r : reflection coefficient at the surface for directional light incident perpendicular from outside.

For n = 1,5 r = 0,040.reflection coefficient at the surface for directional light incident parallel under 45° from out-

r :side. For n = 1,5, r = 0,050.

r : reflection coefficient for light incident diffusely from the inside of the specimen. For n = 1,5, r = 0,596.

2 2© ISO 2022 – All rights reserved

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5.2 Incidence diffuse, observation 0° (d:0°)

The constant a = 1 if a gloss trap is closed and a = 0 if the gloss trap is open and the specular reflection

is excluded.11−rr− R λ

()() ()

Rrλ =+a (1)

0 *

1−rR()λ

Rrλ −

fora =1: R λ = (2)

11−−rr −R λ

R λ

* ()

fora =1: R λ = (3)

1−−rr ++rr R λ

02 20

5.3 Incidence 45°, observation 0° (45°:0°)

1 *

11−rr− R λ

()() ()

R λ = (4)

1−rR λ

nR()λ

R λ = (5)

1−−+rr rr +nr R λ

00 00 2

6 Solution of the Kubelka-Munk equations

The Kubelka-Munk theory describes the reflection of a pigmented layer by two constants: absorption

[K(λ)] and scattering [S(λ)]. It is based on the following assumptions:a) ideally diffuse radiation distribution on the irradiation side;

b) ideally diffuse radiation distribution in the interior of the layer;

c) no consideration of surface phenomena resulting from the discontinuity in refractive index.

For an infinitely thick, respectively hiding layer with a reflectance of R(λ) , the following solutions

(Formula (6) and Formula (7)) are found, which allow the determination of the relation between the

scattering and the absorption coefficient:1−R λ

K λ ()

= ≡FR λ (6)

S λ 2R λ

() ()

respectively the inverse:

K λ K λ K λ

() () ()

R λ =+12− + (7)

()

S λ S λ S λ

() () ()

For the determination of the scattering and absorption coefficient, two different methods can be applied

(the Saunderson correction shall be used):© ISO 2022 – All rights reserved

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Method 1 Measurement of the reflectance of an infinite thick (respectively hiding) layer and the

* *reflectance R λ of a coating of the thickness, h, on a substrate of the reflection R λ , then following

() ()Formulae (8), (9), (10), and (11):

1 1 *

a λ = +R λ (8)

() ()

R λ

∞

* 1 1 *

baλλ= −R λ = −R λ (9)

() () () ()

∞ ∞

R λ

∞

** **

1−aRλλ[( ))−RRλλ+ () R()λ

S λ = arcoth (10)

bhλ

() bRλλ[( )))−R λ

KSλλ= a λ −1. (11)

() () ()

Method 2 This method applies two layers of equal thickness (h) on black and white substances.

After the determination of the auxiliary variables a(λ), b(λ) according to Formula (12) and Formula (13),

either Formula (14) or Formula (15) may be used to calculate the scattering coefficient S(λ). The

possibility with the least experimental uncertainty should be chosen.** ** ** **

[(11+RRλλ)) [(RRλλ)(−+)(+RRλλ)) [[(RRλλ))−

( ( (

wowb ob bob ow w

a λ = (12)

** **

2[(RRλλ)( )(−RRλλ))

boww ob

baλλ= −1 (13)

() ()

** **

1 1(−−a λλ)[R() R(λλ)]+R( )R()λ

bobb ob

S(λ)= arcoth (14)

b(λ)h b(λ)[RR(λλ)R− () ]

bob

** **

1 1(−−a λλ)[R() R(λλ)]+R( )R()λ

woww ow

S(λ)= arcoth (15)

b(λ)h b(λ)[RR(λλ)R− () ]

wow

Using S(λ) the reflectance R(λ) of a coating of the thickness, h, on a substrate of the reflection R()λ is

given by Formula (16):1R−−()λλ[(a )b()λλcoth{b()}S(λ)h ]

* o

R(λ) = (16)

a()λλ−+R( )b()λ cooth{b(λλ)S}()h

NOTE The formulation of the Kubelka-Munk theory leads to a system of differential equations. The solution

can be stated in different ways either by the use of the trigonometric functions used here or by the use of

logarithmic functions. They are mathematically equivalent.7 Determination of relative tinting strength and residual colour difference of

coloured pigments

7.1 General

All the methods specified here presuppose, at least approximately, a linear relationship between the

concentration of the colourant and the Kubelka-Munk function.It is assumed that the scattering by the draw-downs being measured is dominated by the white pigment

and the absorption by the coloured pigment. All these conditions shall be met to ascertain correct

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results of the methods described here. The Kubelka-Munk function for the white paste can be neglected

in most cases.7.2 Principle

The reference and test samples are incorporated into white pastes. The corresponding reflectance

spectra are measured on opaque draw-downs of the resulting coloured pastes. The appropriate tinting

strength criterion is calculated from the measured values.If the tinting strength criterion values for the reference and test samples differ, the mass fraction of the

sample is increased or decreased until the values become equal. This adjustment may be performed

either experimentally or mathematically.If the tinting strength criterion values for the reference and test samples are the same, or after they

have been equalized, the residual colour difference between the white reductions of the reference and

test samples is calculated from the corresponding reflectance spectra.A spectrophotometer with d:8° or 8°:d measuring geometry with or without gloss trap, or instruments

with 45°:0° or 0°:45° measuring geometry are recommended.7.3 Procedure

7.3.1 General

The reflectance of an opaque draw-down of the white reduction of the reference sample and the

corresponding reflectance of the test sample are measured in the visible spectral range.

7.3.2 Evaluation of absorption at the absorption maximumThe tinting strength criterion is the maximum Kubelka-Munk value. Prerequisite for this method are

equal concentrations of reference and test pigments in the white pastes.Determine the wavelength in the reflectance spectra of the white reductions at which the reflectance is

a minimum. From the minimum Saunderson-corrected reflectance R * and R *, calculate the Kubelka-

r tMunk values (K/S) and (K/S) for this wavelength by means of Formula (6). The relative tinting strength

r tC is then obtained using the Formula (17):

rel

K

C = ⋅100 (17)

rel

r

NOTE This method does not involve any explicit equalization of the tinting strength criterion. Because of the

assumption of linearity between the Kubelka-Munk function and the concentration, equalization is implicit in the

formalism of

S m

t r

= (18)

m

Consequently, by using Formula (18), the Formula (17) can be transformed into the defining Formula

(19).C =⋅100 (19)

rel

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7.3.3 Evaluation of the weighted K/S sum

The tinting strength criterion is the weighted K/S sum. From the spectra of the Saunderson-corrected

reflectance R(λ)* for the test and reference samples, calculate the corresponding Kubelka-Munk values

F(λ) = (K/S)(λ) and in each case generate the weighted sum according to Formula (20):

T = ∑ g(λ) ⋅ F(λ) (20)(400-700nm)

The function g(λ) is a weighting function, defined as the sum of the colour matching functions x λ ,

[4]y λ , and z λ for a 10° standard observer (see Reference ). This weighting function is an empirical

() ()function, but without any theoretical foundation.

The relative tinting strength is calculated from the weighted sums and the mass fractions of the test

and reference samples: Tm⋅

C = ⋅100

rel

()Tm⋅

r

= ⋅100 (21)

t

NOTE This method does not involve any explicit equalization of the tinting strength criterion. Because of

the assumption of linearity between the Kubelka-Munk function and the concentration, and hence also between

the Kubelka-Munk function and the tinting strength criterion T, equalization is implicit in the formalism of

Formula (21).If the difference between the tinting strength criterion of the reference sample T and that of the test

sample T is greater than 15 %, the mass fraction of the test sample should be varied accordingly.

To obtain the residual colour difference, the Kubelka-Munk function of the test sample is modified as

given in Formula (22):FF' λλ= ⋅ (22)

() ()

Solving Formula (6) for R [as done in Formula (7)], calculate a modified reflectance spectrum R *'(λ)

for the test sample from its modified Kubelka-Munk function F '(λ) and then subject it to an inverse

Saunderson correction (see Clause 3) to obtain a modified R '(λ) that includes surface effects. This

spectrum yields the colour coordinates of the white reduction of the test sample after equalizing the

tinting strength. Calculate the residual colour difference from the reflectance spectrum R (λ) of the

white reduction of the reference sample and the modified reflectance spectrum R '(λ).

7.3.4 Evaluation by equalizing the tristimulus value, YThe tinting strength criterion is the tristimulus value, Y. From the reflectance spectra, R(λ), for the

white reductions of the test and reference samples, calculate the tristimulus value Y for the reference

sample and Y for the test sample (see ISO 11664-3). The contracting parties agree on the standard

illuminant and standard observer used.From Formula (6) and the Saunderson-corrected reflectance R *(λ) for the white reduction of the test

sample, calculate the corresponding Kubelka-Munk function F (λ) for the test sample. Adjust Y to the

t t© ISO 2022 – All rights reserved

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value for the reference sample by varying m and then use the resulting value of m ' to determine a

t tmodified Kubelka-Munk function F '(λ) as given in Formula (23) for the test sample:

m 'FF' λλ= ⋅ (23)

() ()

Solving Formula (6) for R, calculate a modified reflectance spectrum R *'(λ) for the test sample from its

modified Kubelka-Munk function F '(λ) and subject it to an inverse Saunderson correction to obtain a

modified R '(λ) that includes surface effects. From this spectrum determine Y '.t t

Vary the mass fraction of the test sample until the tinting strength criterion has been equalized as

defined by Formula (24):YY= (24)

This variation of m is best carried out by an iterative mathematical procedure, but may also be done

experimentally.Use Formula (25) to calculate the relative tinting strength from the mass fraction m ' of the test sample

that results in equalization of the tinting strength:

C = ⋅100 (25)

rel

m '

t

Calculate the residual colour difference from the reflectance spectr

**...**

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