1、BSI Standards PublicationBS ISO 18314-2:2015Analytical colorimetryPart 2: Saunderson correction, solutionsof the Kubelka-Munk equation, tintingstrength, hiding powerBS ISO 18314-2:2015 BRITISH STANDARDNational forewordThis British Standard is the UK implementation of ISO 18314-2:2015.The UK particip
2、ation in its preparation was entrusted to Technical Committee STI/1, Pigments.A list of organizations represented on this committee can be obtained on request to its secretary.This publication does not purport to include all the necessary provisions of a contract. Users are responsible for its corre
3、ct application. The British Standards Institution 2015.Published by BSI Standards Limited 2015ISBN 978 0 580 86040 9ICS 87.060.10Compliance with a British Standard cannot confer immunity from legal obligations.This British Standard was published under the authority of the Standards Policy and Strate
4、gy Committee on 30 June 2015.Amendments/corrigenda issued since publicationDate T e x t a f f e c t e dBS ISO 18314-2:2015 ISO 2015Analytical colorimetry Part 2: Saunderson correction, solutions of the Kubelka-Munk equation, tinting strength, hiding powerAnalyse colorimtrique Partie 2: Correction de
5、 Saunderson, solutions de lquation de Kubelka-Munk, force colorante, pouvoir couvrantINTERNATIONAL STANDARDISO18314-2First edition2015-06-01Reference numberISO 18314-2:2015(E)BS ISO 18314-2:2015ISO 18314-2:2015(E)ii ISO 2015 All rights reservedCOPYRIGHT PROTECTED DOCUMENT ISO 2015, Published in Swit
6、zerlandAll 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 re
7、quested from either ISO at the address below or ISOs member body in the country of the requester.ISO copyright officeCh. de Blandonnet 8 CP 401CH-1214 Vernier, Geneva, SwitzerlandTel. +41 22 749 01 11Fax +41 22 749 09 47copyrightiso.orgwww.iso.orgBS ISO 18314-2:2015ISO 18314-2:2015(E)Foreword iv1 Sc
8、ope . 12 Terms, definitions, symbols, and abbreviated terms . 12.1 Terms and definitions . 12.2 Symbols and abbreviated terms. 23 Saunderson correction . 43.1 General . 43.2 Incidence diffuse, observation 0 (d/0) 43.3 Incidence 45, observation 0 (45: 0) . 44 Solution of the Kubelka-Munk equations .
9、55 Determination of relative tinting strength and residual colour difference of coloured pigments 65.1 General . 65.2 Principle 65.3 Procedure 65.3.1 General 65.3.2 Evaluation of absorption at the absorption maximum . 75.3.3 Evaluation of the weighted K/S sum 75.3.4 Evaluation by equalizing the tris
10、timulus value, Y .85.3.5 Evaluation by equalizing the smallest of the tristimulus values X, Y, and Z .85.3.6 Evaluation by equalizing the shade depth . 96 Determination of hiding power of pigmented media 106.1 General 106.2 Example for white or light coloured paints with a contrast ratio of 0,98 as
11、hiding power criterion 117 Repeatability and reproducibility .128 Test report 12Annex A (normative) Tables of coefficients for calculating a() values (standard illuminant D65 and 10 standard observer) 13Annex B (normative) Tables of coefficients for calculating a() values (standard illuminant C and
12、2 standard observer) 15Bibliography .17 ISO 2015 All rights reserved iiiContents PageBS ISO 18314-2:2015ISO 18314-2:2015(E)ForewordISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International
13、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, al
14、so 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.
15、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 eleme
16、nts 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
17、 (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 ISOs adhere
18、nce to the WTO principles in the Technical Barriers to Trade (TBT) see the following URL: Foreword - Supplementary informationThe 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 color
19、imetry: Part 1: Practical colour measurement Part 2: Saunderson correction, solutions of the Kubelka-Munk equation, tinting strength, hiding power Part 3: Special indicesiv ISO 2015 All rights reservedBS ISO 18314-2:2015Analytical colorimetry Part 2: Saunderson correction, solutions of the Kubelka-M
20、unk equation, tinting strength, hiding power1 ScopeThis 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
21、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 Standar
22、ds.2 Terms, definitions, symbols, and abbreviated terms2.1 Terms and definitionsFor the purposes of this document, the following terms and definitions apply.2.1.1tinting strengthmeasure of the ability of a colorant, based on its absorption, to impart colour to other materials2.1.2relative tinting st
23、rengthCrelpercentage ratio of those mass fractions of the coloured pigment reference and test samples (mrand mt, respectively) that cause the particular tinting strength criterion used to have identical values for the reference and test samples2.1.3tinting strength criterionparameter that describes
24、the colouring effect of a colorant, based on its absorptionNote 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 smalles
25、t 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*);INTERNATIONAL STANDARD
26、ISO 18314-2:2015(E) ISO 2015 All rights reserved 1BS ISO 18314-2:2015ISO 18314-2:2015(E) reflectance factor at the absorption maximum.2.1.4residual colour differencecolour difference that remains between the white reductions of the reference and test samples when the tinting strength criterion value
27、s are the same or have been equalizedEXAMPLE Given by E*.2.1.5standard shade depthshade depthmeasure of the intensity of a colour sensation, which increases with increasing chroma and decreases with increasing lightnessNote 1 to entry: Standard shade depths are values set by convention. For colourim
28、etric 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.2.1.6hiding powerability of a pigmented medium to hide the colour or the colour differences of a substrate2.2 Symbols a
29、nd abbreviated termsa constant* CIELAB colour coordinatea() factora() auxiliary variableb* CIELAB colour coordinateb() auxiliary variableB shade depth parameterCrelrelative tinting strengthDmhiding power value indicating the area of the contrast substrate concerned, in m2, which can be coated with 1
30、 kgDvhiding power value indicating the area of the contrast substrate concerned, in m2, which can be coated with 1 lF() Kubelka-Munk functionF() modified Kubelka-Munk functiong()weighting function (defined as the sum of the colour matching functions x (), y (), and z ()for a 10 standard observer)h t
31、hicknessK coefficient2 ISO 2015 All rights reservedBS ISO 18314-2:2015ISO 18314-2:2015(E)K() absorption coefficient(K/S)rKubelka-Munk value of reference sample(K/S)tKubelka-Munk value of test sampleL* CIELAB lightnessmrmass fraction of coloured pigment reference samplemtmass fraction of coloured pig
32、ment test samplen refractive indexr0reflection coefficient at the surface for directional light incident perpendicular from outsider0reflection coefficient at the surface for directional light incident parallel under 45 from out-sider2reflection coefficient for light incident diffusely from the insi
33、de of the specimenR()reflectance spectrumR ()reflectance of infinitely thick layerR()reflectance of the sampleR*()obSaunderson-corrected reflectance of the black substrateR*()owSaunderson-corrected reflectance of the white substrateR ()bSaunderson-corrected reflectance of the sample on black substra
34、teR*()wSaunderson-corrected reflectance of the sample on white substrateR()modified reflectance spectrum including surface effectss saturationS ()scattering coefficientT weighted sumx, y chromaticity coordinatesX, Y, Z tristimulus valuesE *residual colour difference ISO 2015 All rights reserved 3BS
35、ISO 18314-2:2015ISO 18314-2:2015(E)Eab*CIELAB colour difference hue angleoclosest angle in the table below the hue angle3 Saunderson correction3.1 GeneralFor colourimetric calculation it is necessary to account for surface phenomena to obtain viable results. The formulas are known as Saunderson corr
36、ection, their derivation can be found in References 1 and 2 The necessary coefficients are solutions of the Fresnel formulae3depending 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 li
37、ght 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/
38、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:r0: reflection coefficient at the surface for directional light incident perpendicular from outside. For n = 1,5 r0=
39、 0,040.r0:reflection coefficient at the surface for directional light incident parallel under 45 from outside. For n = 1,5, r0= 0,050.r2: reflection coefficient for light incident diffusely from the inside of the specimen. For n = 1,5, r2= 0,596.3.2 Incidence diffuse, observation 0 (d/0)The constant
40、 a = 1 if a gloss trap is closed and a = 0 if the gloss trap is open and the specular reflection is excluded.RarrrRrR()=+()()()()0022111*(1)fora=()=() ()111002: RRrrr R*(2)fora=()=()+ +()110220: RR-r rrrR*(3)3.3 Incidence 45, observation 0 (45: 0)Rr r nRr R*()=()()()()11110022(4)4 ISO 2015 All right
41、s reservedBS ISO 18314-2:2015ISO 18314-2:2015(E)RnRrrrr nrR*()=()+()20000221(5)4 Solution of the Kubelka-Munk equationsThe Kubelka-Munk theory describes the reflection of a pigmented layer by two constants: absorption K() and scattering S(). It is based on the following assumptions:a) ideally diffus
42、e 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(), the foll
43、owing solutions are found, which allow the determination of the relation between the scattering and the absorption coefficient:KSRRFR()()=()()()()122(6)respectively the inverse:RKSKSKS()=+()()()()+()()122(7)For the determination of the scattering and absorption coefficient two different methods can
44、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 ()* of a coating of the thickness, h, on a substrate of the reflection R ()0*.aRR*()=()+()121(8)baRRR*()=()()=()()121(9)SbhaR RRRbR* * (
45、)=()()+1100Arcoth()() () ()()()*R ()0(10)KSa()=() ()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(), b() according to Formulae (12) and (13), either Formula (14) or (15) may be used to calculat
46、e the scattering coefficient S(). The possibility with the least experimental uncertainty should be chosen.aRR RR RR R* * * ()=+()()()()()()11wowb ob bob() () ()()()() ow wbowwob* *RRR RR2(12) ISO 2015 All rights reserved 5BS ISO 18314-2:2015ISO 18314-2:2015(E)ba()=()21 (13)S( )1b( )hArcoth1a()R() R
47、( ) R( )R()b( )bobbob =+* *RR( )R() bob*(14)S( )1b( )hArcoth1a()R() R( )R( )R()b( )wowwow =+* *RR( )R() wow*(15)R( )1R()a() b( )cothb( )S()ha( )R() b( )cooo *=+ tthb()S( )h(16)NOTE The formulation of the Kubelka-Munk theory leads to a system of differential equations. The solution can be stated in d
48、ifferent 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 pigments5.1 GeneralAll 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
