# SIST EN ISO 18314-2:2018

(Main)## Analytical colorimetry - Part 2: Saunderson correction, solutions of the Kubelka-Munk equation, tinting strength, hiding power (ISO 18314-2:2015)

## Analytical colorimetry - Part 2: Saunderson correction, solutions of the Kubelka-Munk equation, tinting strength, hiding power (ISO 18314-2:2015)

ISO 18314-2:2015 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 part of ISO 18314. 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, Deckvermögen (ISO 18314-2:2015)

## Analyse colorimétrique - Partie 2: Correction de Saunderson, solutions de l'équation de Kubelka-Munk, force colorante, pouvoir couvrant (ISO 18314-2:2015)

La présente partie de l'ISO 18314 spécifie la correction de Saunderson pour différentes géométries de mesure et les solutions de l'équation de Kubelka-Munk pour les couches couvrantes et transparentes. Elle spécifie également les méthodes de calcul de la force colorante et de l'écart de couleur résiduel sur la base de différents critères, ainsi que du pouvoir couvrant.

Les méthodes de préparation des échantillons destinés à ces mesurages ne sont pas couvertes par la présente partie de l'ISO 18314. Elles sont fixées par accord entre les parties contractantes ou sont décrites dans d'autres normes nationales ou internationales.

## Analizna kolorometrija - 2. del: Saundersonova korekcija, rešitve Kubelka-Munkove enačbe, barvna jakost in kritnost (ISO 18314-2:2015)

ISO 18314-2:2015 določa Saundersonovo korekturo za različne merilne geometrije in rešitve Kubelka-Munkove enačbe za prikrivajoče ter prosojne plasti. Določa tudi metode za izračune barvne jakosti, vključno z razliko ostankov barv na podlagi različnih kriterijev, in kritnostjo.

Postopki za pripravo vzorcev za te meritve niso del tega dela standarda ISO 18314. O njih se dogovorijo pogodbenice ali pa so opisani v drugih nacionalnih ali mednarodnih standardih.

### General Information

### Relations

### Standards Content (Sample)

SLOVENSKI STANDARD

SIST EN ISO 18314-2:2018

01-november-2018

$QDOL]QDNRORURPHWULMDGHO6DXQGHUVRQRYDNRUHNFLMDUHãLWYH.XEHOND

0XQNRYHHQDþEHEDUYQDMDNRVWLQNULWQRVW,62

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

equation, tinting strength, hiding power (ISO 18314-2:2015)

Analytische Farbmessung - Teil 2: Saunderson-Korrektur, Lösungen der Kubelka-Munk-

Gleichung, Farbstärke, Deckvermögen (ISO 18314-2:2015)

Analyse colorimétrique - Partie 2: Correction de Saunderson, solutions de l'équation de

Kubelka-Munk, force colorante, pouvoir couvrant (ISO 18314-2:2015)

Ta slovenski standard je istoveten z: EN ISO 18314-2:2018

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 18314-2:2018 en,fr,de

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

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SIST EN ISO 18314-2:2018

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SIST EN ISO 18314-2:2018

EN ISO 18314-2

EUROPEAN STANDARD

NORME EUROPÉENNE

October 2018

EUROPÄISCHE NORM

ICS 87.060.10

English Version

Analytical colorimetry - Part 2: Saunderson correction,

solutions of the Kubelka-Munk equation, tinting strength,

hiding power (ISO 18314-2:2015)

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,

force colorante, pouvoir couvrant (ISO 18314-2:2015) Farbstärke, Deckvermögen (ISO 18314-2:2015)

This European Standard was approved by CEN on 19 February 2018.

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, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,

Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, 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

© 2018 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 18314-2:2018 E

worldwide for CEN national Members.

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SIST EN ISO 18314-2:2018

EN ISO 18314-2:2018 (E)

Contents Page

European foreword . 3

2

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SIST EN ISO 18314-2:2018

EN ISO 18314-2:2018 (E)

European foreword

The text of ISO 18314-2:2015 has been prepared by Technical Committee 256 "Pigments, dyestuffs and

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

EN ISO 18314-2:2018 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 April 2019, and conflicting national standards shall be

withdrawn at the latest by April 2019.

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, Former Yugoslav Republic of Macedonia,

France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta,

Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,

Turkey and the United Kingdom.

Endorsement notice

The text of ISO 18314-2:2015 has been approved by CEN as EN ISO 18314-2:2018 without any

modification.

3

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SIST EN ISO 18314-2:2018

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SIST EN ISO 18314-2:2018

INTERNATIONAL ISO

STANDARD 18314-2

First edition

2015-06-01

Analytical colorimetry —

Part 2:

Saunderson correction, solutions of

the Kubelka-Munk equation, tinting

strength, hiding power

Analyse colorimétrique —

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

Kubelka-Munk, force colorante, pouvoir couvrant

Reference number

ISO 18314-2:2015(E)

©

ISO 2015

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SIST EN ISO 18314-2:2018

ISO 18314-2:2015(E)

COPYRIGHT PROTECTED DOCUMENT

© ISO 2015, Published in Switzerland

All rights reserved. Unless otherwise specified, 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

Ch. de Blandonnet 8 • CP 401

CH-1214 Vernier, Geneva, Switzerland

Tel. +41 22 749 01 11

Fax +41 22 749 09 47

copyright@iso.org

www.iso.org

ii © ISO 2015 – All rights reserved

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SIST EN ISO 18314-2:2018

ISO 18314-2:2015(E)

Contents Page

Foreword .iv

1 Scope . 1

2 Terms, definitions, symbols, and abbreviated terms . 1

2.1 Terms and definitions . 1

2.2 Symbols and abbreviated terms. 2

3 Saunderson correction . 4

3.1 General . 4

3.2 Incidence diffuse, observation 0° (d/0°) . 4

3.3 Incidence 45°, observation 0° (45°: 0°) . 4

4 Solution of the Kubelka-Munk equations . 5

5 Determination of relative tinting strength and residual colour difference of

coloured pigments . 6

5.1 General . 6

5.2 Principle . 6

5.3 Procedure . 6

5.3.1 General. 6

5.3.2 Evaluation of absorption at the absorption maximum . 7

5.3.3 Evaluation of the weighted K/S sum . 7

5.3.4 Evaluation by equalizing the tristimulus value, Y .8

5.3.5 Evaluation by equalizing the smallest of the tristimulus values X, Y, and Z .8

5.3.6 Evaluation by equalizing the shade depth . 9

6 Determination of hiding power of pigmented media .10

6.1 General .10

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

power criterion .11

7 Repeatability and reproducibility .12

8 Test report .12

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

D65 and 10° standard observer) .13

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

C and 2° standard observer) .15

Bibliography .17

© ISO 2015 – All rights reserved iii

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SIST EN ISO 18314-2:2018

ISO 18314-2:2015(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 on the meaning of ISO specific terms and expressions related to conformity

assessment, as well as information about ISO’s adherence to the WTO principles in the Technical Barriers

to Trade (TBT) see the following URL: Foreword - Supplementary information

The committee responsible for this document is ISO/TC 256, Pigments, dyestuffs and fillers.

ISO 18314 consists of the following parts, under the general title Analytical colorimetry:

— Part 1: Practical colour measurement

— Part 2: Saunderson correction, solutions of the Kubelka-Munk equation, tinting strength, hiding power

— Part 3: Special indices

iv © ISO 2015 – All rights reserved

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SIST EN ISO 18314-2:2018

INTERNATIONAL STANDARD ISO 18314-2:2015(E)

Analytical colorimetry —

Part 2:

Saunderson correction, solutions of the Kubelka-Munk

equation, tinting strength, hiding power

1 Scope

This part of ISO 18314 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 part of ISO 18314. They

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

2 Terms, definitions, symbols, and abbreviated terms

2.1 Terms and definitions

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

2.1.1

tinting strength

measure of the ability of a colorant, based on its absorption, to impart colour to other materials

2.1.2

relative tinting strength

C

rel

percentage ratio of those mass fractions of the coloured pigment reference and test samples (m and m ,

r t

respectively) that cause the particular tinting strength criterion used to have identical values for the

reference and test samples

2.1.3

tinting strength criterion

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

Note 1 to entry: The tinting strength criteria used in this part of ISO 18314 are the following:

— 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.

Examples of other tinting strength parameters not used in this part of ISO 18314 are the following:

— unweighted sum of the Kubelka-Munk function values;

— chromaticity given by the three colour coordinates (L*, a*, b*);

© ISO 2015 – All rights reserved 1

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SIST EN ISO 18314-2:2018

ISO 18314-2:2015(E)

— reflectance factor at the absorption maximum.

2.1.4

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 equalized

EXAMPLE Given by ΔE*.

2.1.5

standard shade depth

shade depth

measure of the intensity of a colour sensation, which increases with increasing chroma and decreases

with increasing lightness

Note 1 to entry: Standard shade depths are values set by convention. For colourimetric purposes, the standard

shade depth is defined by the shade depth parameter B = 0, which is calculated from the tristimulus value, Y, and

the chromaticity coordinates, x and y.

2.1.6

hiding power

ability of a pigmented medium to hide the colour or the colour differences of a substrate

2.2 Symbols and abbreviated terms

a constant

α* 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

2

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

m

be coated with 1 kg

2

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

v

be coated with 1 l

F(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

2 © ISO 2015 – All rights reserved

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SIST EN ISO 18314-2:2018

ISO 18314-2:2015(E)

K(λ) absorption coefficient

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

r

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

t

L* CIELAB lightness

m mass fraction of coloured pigment reference sample

r

m mass fraction of coloured pigment test sample

t

n refractive index

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

0

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

r

0

side

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

2

reflectance spectrum

R()λ

reflectance of infinitely thick layer

R λ

()

∞

reflectance of the sample

∗

R()λ

Saunderson-corrected reflectance of the black substrate

*

R λ

()

ob

Saunderson-corrected reflectance of the white substrate

*

R λ

()

ow

Saunderson-corrected reflectance of the sample on black substrate

∗

R λ

()

b

Saunderson-corrected reflectance of the sample on white substrate

*

R λ

()

w

modified reflectance spectrum including surface effects

R´λ

()

s saturation

scattering coefficient

S λ

()

T weighted sum

x, y chromaticity coordinates

X, Y, Z tristimulus values

residual colour difference

ΔE *

© ISO 2015 – All rights reserved 3

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SIST EN ISO 18314-2:2018

ISO 18314-2:2015(E)

CIELAB colour difference

*

ΔE

ab

φ hue angle

φ closest angle in the table below the hue angle

o

3 Saunderson correction

3.1 General

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

The formulas are known as Saunderson correction, 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°) and 45° incidence, 0° observation (45°/0°). In nearly every colourimeter 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.

0

For n = 1,5 r = 0,040.

0

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

r :

0

outside. For n = 1,5, r = 0,050.

0

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

2

n = 1,5, r = 0,596.

2

3.2 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 *

()() ()

02

Raλ =+r (1)

()

0

1−rR λ *

()

2

Rrλ −

()

*

0

fora =1: R λ = (2)

()

11−−rr −R λ

()

02

R λ

()

*

fora =1: R λ = (3)

()

1 -r −+rr rR+ λ

()

02 20

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

*

1

11 r− r− R λ

()() ()

00

2

n

R λ = (4)

()

*

1− r R λ

()

2

4 © ISO 2015 – All rights reserved

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SIST EN ISO 18314-2:2018

ISO 18314-2:2015(E)

2

nR λ

()

*

R λ = (5)

()

2

1 −−rr ++rr nr R λ

()

00 00 2

4 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 are

∞

found, which allow the determination of the relation between the scattering and the absorption coefficient:

2

1 −R λ

K λ ()

()

()

∞

= ≡ FR λ (6)

()

()

∞

S λ 2R λ

() ()

∞

respectively the inverse:

2

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):

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 .

() ()

0

1 1 *

aλ = + R λ (8)

() ()

* ∞

2

R λ

()

∞

* 1 1 *

baλλ= −R λ = −R λ (9)

() () () ()

∞ *

2

∞

R λ

()

∞

** **

1 −aRλλ[( )(−+RRλλ)] () R()λ

()

1

00

S λ = Arcoth (10)

()

***

bhλ

() bR()λλ[( ) − R()λ ]

0

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 Formulae (12) and (13), either

Formula (14) or (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)( )][R(()λλ−R() ]

wowb ob bob ow w

aλ = (12)

()

** **

2[(RRλλ)( )(−RRλλ)( )]

boww ob

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SIST EN ISO 18314-2:2018

ISO 18314-2:2015(E)

2

baλλ= −1 (13)

() ()

** **

1a−−()λλ[R() R(λλ)]+ R( )R()λ

1

bobb ob

S(λ)= Arcoth (14)

**

b(λ)h

b(λ)[RR(λλ)R− () ]

bob

** **

1a−−()λλ[R() R(λλ)]+ R( )R()λ

1

woww ow

S(λ)= Arcoth (15)

**

b(λ)h

b(λ)[RR(λλ)R− () ]

wow

*

1R−−()λλ[a() b(λλ)coth{b( )S()λ h}]

* o

R(λ) = (16)

*

a(λλ)R−+() b(λ)cotth{b()λλS( )h}

o

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.

5 Determination of relative tinting strength and residual colour difference of

coloured pigments

5.1 General

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

concentration of the colorant 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.

5.2 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.

5.3 Procedure

5.3.1 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.

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ISO 18314-2:2015(E)

5.3.2 Evaluation of absorption at the absorption maximum

The 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 t

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

r t

C is then obtained from:

rel

K

()

S

t

C = ⋅100 (17)

rel

K

()

S

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

K

()

m

S

t r

= (18)

K

m

() t

S

r

Consequently, Formula (17) can be transformed into the defining Formula (19).

m

r

C =⋅100 (19)

rel

m

t

5.3.3 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 following weighted sum:

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 ,

()

y λ , and z λ for a 10° standard observer (see Reference [4]). 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⋅

()

tr

C = ⋅100 (21)

rel

Tm⋅

()

rt

m

r

T

r

= ⋅100

m

t

T

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

r

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

t

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ISO 18314-2:2015(E)

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

T

r

FF'()λλ= ()⋅ (22)

tt

T

t

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

r

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

t

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

t

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

r

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

t

5.3.4 Evaluation by equalizing the tristimulus value, Y

The 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

r

sampl

**...**

SLOVENSKI STANDARD

oSIST prEN ISO 18314-2:2017

01-december-2017

$QDOL]QDNRORURPHWULMDGHO6DXQGHUVRQRYDNRUHNFLMDUHãLWYH.XEHOND

0XQNRYHHQDþEHEDUYQDMDNRVWLQNULWQRVW,62

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

equation, tinting strength, hiding power (ISO 18314-2:2015)

Analytische Farbmessung - Teil 2: Saunderson-Korrektur, Lösungen der Kubelka-Munk-

Gleichung, Farbstärke, Deckvermögen (ISO 18314-2:2015)

Analyse colorimétrique - Partie 2: Correction de Saunderson, solutions de l'équation de

Kubelka-Munk, force colorante, pouvoir couvrant (ISO 18314-2:2015)

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

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 18314-2:2017 en,fr,de

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

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oSIST prEN ISO 18314-2:2017

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oSIST prEN ISO 18314-2:2017

INTERNATIONAL ISO

STANDARD 18314-2

First edition

2015-06-01

Analytical colorimetry —

Part 2:

Saunderson correction, solutions of

the Kubelka-Munk equation, tinting

strength, hiding power

Analyse colorimétrique —

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

Kubelka-Munk, force colorante, pouvoir couvrant

Reference number

ISO 18314-2:2015(E)

©

ISO 2015

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oSIST prEN ISO 18314-2:2017

ISO 18314-2:2015(E)

COPYRIGHT PROTECTED DOCUMENT

© ISO 2015, Published in Switzerland

All rights reserved. Unless otherwise specified, 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

Ch. de Blandonnet 8 • CP 401

CH-1214 Vernier, Geneva, Switzerland

Tel. +41 22 749 01 11

Fax +41 22 749 09 47

copyright@iso.org

www.iso.org

ii © ISO 2015 – All rights reserved

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oSIST prEN ISO 18314-2:2017

ISO 18314-2:2015(E)

Contents Page

Foreword .iv

1 Scope . 1

2 Terms, definitions, symbols, and abbreviated terms . 1

2.1 Terms and definitions . 1

2.2 Symbols and abbreviated terms. 2

3 Saunderson correction . 4

3.1 General . 4

3.2 Incidence diffuse, observation 0° (d/0°) . 4

3.3 Incidence 45°, observation 0° (45°: 0°) . 4

4 Solution of the Kubelka-Munk equations . 5

5 Determination of relative tinting strength and residual colour difference of

coloured pigments . 6

5.1 General . 6

5.2 Principle . 6

5.3 Procedure . 6

5.3.1 General. 6

5.3.2 Evaluation of absorption at the absorption maximum . 7

5.3.3 Evaluation of the weighted K/S sum . 7

5.3.4 Evaluation by equalizing the tristimulus value, Y .8

5.3.5 Evaluation by equalizing the smallest of the tristimulus values X, Y, and Z .8

5.3.6 Evaluation by equalizing the shade depth . 9

6 Determination of hiding power of pigmented media .10

6.1 General .10

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

power criterion .11

7 Repeatability and reproducibility .12

8 Test report .12

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

D65 and 10° standard observer) .13

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

C and 2° standard observer) .15

Bibliography .17

© ISO 2015 – All rights reserved iii

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oSIST prEN ISO 18314-2:2017

ISO 18314-2:2015(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 on the meaning of ISO specific terms and expressions related to conformity

assessment, as well as information about ISO’s adherence to the WTO principles in the Technical Barriers

to Trade (TBT) see the following URL: Foreword - Supplementary information

The committee responsible for this document is ISO/TC 256, Pigments, dyestuffs and fillers.

ISO 18314 consists of the following parts, under the general title Analytical colorimetry:

— Part 1: Practical colour measurement

— Part 2: Saunderson correction, solutions of the Kubelka-Munk equation, tinting strength, hiding power

— Part 3: Special indices

iv © ISO 2015 – All rights reserved

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oSIST prEN ISO 18314-2:2017

INTERNATIONAL STANDARD ISO 18314-2:2015(E)

Analytical colorimetry —

Part 2:

Saunderson correction, solutions of the Kubelka-Munk

equation, tinting strength, hiding power

1 Scope

This part of ISO 18314 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 part of ISO 18314. They

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

2 Terms, definitions, symbols, and abbreviated terms

2.1 Terms and definitions

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

2.1.1

tinting strength

measure of the ability of a colorant, based on its absorption, to impart colour to other materials

2.1.2

relative tinting strength

C

rel

percentage ratio of those mass fractions of the coloured pigment reference and test samples (m and m ,

r t

respectively) that cause the particular tinting strength criterion used to have identical values for the

reference and test samples

2.1.3

tinting strength criterion

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

Note 1 to entry: The tinting strength criteria used in this part of ISO 18314 are the following:

— 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.

Examples of other tinting strength parameters not used in this part of ISO 18314 are the following:

— unweighted sum of the Kubelka-Munk function values;

— chromaticity given by the three colour coordinates (L*, a*, b*);

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oSIST prEN ISO 18314-2:2017

ISO 18314-2:2015(E)

— reflectance factor at the absorption maximum.

2.1.4

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 equalized

EXAMPLE Given by ΔE*.

2.1.5

standard shade depth

shade depth

measure of the intensity of a colour sensation, which increases with increasing chroma and decreases

with increasing lightness

Note 1 to entry: Standard shade depths are values set by convention. For colourimetric purposes, the standard

shade depth is defined by the shade depth parameter B = 0, which is calculated from the tristimulus value, Y, and

the chromaticity coordinates, x and y.

2.1.6

hiding power

ability of a pigmented medium to hide the colour or the colour differences of a substrate

2.2 Symbols and abbreviated terms

a constant

α* 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

2

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

m

be coated with 1 kg

2

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

v

be coated with 1 l

F(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

2 © ISO 2015 – All rights reserved

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ISO 18314-2:2015(E)

K(λ) absorption coefficient

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

r

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

t

L* CIELAB lightness

m mass fraction of coloured pigment reference sample

r

m mass fraction of coloured pigment test sample

t

n refractive index

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

0

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

r

0

side

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

2

reflectance spectrum

R()λ

reflectance of infinitely thick layer

R λ

()

∞

reflectance of the sample

∗

R()λ

Saunderson-corrected reflectance of the black substrate

*

R λ

()

ob

Saunderson-corrected reflectance of the white substrate

*

R λ

()

ow

Saunderson-corrected reflectance of the sample on black substrate

∗

R λ

()

b

Saunderson-corrected reflectance of the sample on white substrate

*

R λ

()

w

modified reflectance spectrum including surface effects

R´λ

()

s saturation

scattering coefficient

S λ

()

T weighted sum

x, y chromaticity coordinates

X, Y, Z tristimulus values

residual colour difference

ΔE *

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ISO 18314-2:2015(E)

CIELAB colour difference

*

ΔE

ab

φ hue angle

φ closest angle in the table below the hue angle

o

3 Saunderson correction

3.1 General

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

The formulas are known as Saunderson correction, 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°) and 45° incidence, 0° observation (45°/0°). In nearly every colourimeter 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.

0

For n = 1,5 r = 0,040.

0

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

r :

0

outside. For n = 1,5, r = 0,050.

0

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

2

n = 1,5, r = 0,596.

2

3.2 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 *

()() ()

02

Raλ =+r (1)

()

0

1−rR λ *

()

2

Rrλ −

()

*

0

fora =1: R λ = (2)

()

11−−rr −R λ

()

02

R λ

()

*

fora =1: R λ = (3)

()

1 -r −+rr rR+ λ

()

02 20

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

*

1

11 r− r− R λ

()() ()

00

2

n

R λ = (4)

()

*

1− r R λ

()

2

4 © ISO 2015 – All rights reserved

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ISO 18314-2:2015(E)

2

nR λ

()

*

R λ = (5)

()

2

1 −−rr ++rr nr R λ

()

00 00 2

4 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 are

∞

found, which allow the determination of the relation between the scattering and the absorption coefficient:

2

1 −R λ

K λ ()

()

()

∞

= ≡ FR λ (6)

()

()

∞

S λ 2R λ

() ()

∞

respectively the inverse:

2

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):

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 .

() ()

0

1 1 *

aλ = + R λ (8)

() ()

* ∞

2

R λ

()

∞

* 1 1 *

baλλ= −R λ = −R λ (9)

() () () ()

∞ *

2

∞

R λ

()

∞

** **

1 −aRλλ[( )(−+RRλλ)] () R()λ

()

1

00

S λ = Arcoth (10)

()

***

bhλ

() bR()λλ[( ) − R()λ ]

0

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 Formulae (12) and (13), either

Formula (14) or (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)( )][R(()λλ−R() ]

wowb ob bob ow w

aλ = (12)

()

** **

2[(RRλλ)( )(−RRλλ)( )]

boww ob

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ISO 18314-2:2015(E)

2

baλλ= −1 (13)

() ()

** **

1a−−()λλ[R() R(λλ)]+ R( )R()λ

1

bobb ob

S(λ)= Arcoth (14)

**

b(λ)h

b(λ)[RR(λλ)R− () ]

bob

** **

1a−−()λλ[R() R(λλ)]+ R( )R()λ

1

woww ow

S(λ)= Arcoth (15)

**

b(λ)h

b(λ)[RR(λλ)R− () ]

wow

*

1R−−()λλ[a() b(λλ)coth{b( )S()λ h}]

* o

R(λ) = (16)

*

a(λλ)R−+() b(λ)cotth{b()λλS( )h}

o

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.

5 Determination of relative tinting strength and residual colour difference of

coloured pigments

5.1 General

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

concentration of the colorant 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.

5.2 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

**...**

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