SIST ISO 9416:2011

INTERNATIONAL ISO
STANDARD 9416
Second edition
2009-05-01
Paper — Determination of light scattering
and absorption coefficients (using
Kubelka-Munk theory)
Papier — Détermination des coefficients de diffusion et d'absorption de
la lumière (utilisation de la théorie de Kubelka-Munk)

Reference number
©
ISO 2009
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ii © ISO 2009 – All rights reserved

Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions. 2
4 Principle. 3
5 Apparatus . 3
6 Sampling and conditioning. 4
7 Preparation of test pieces. 4
8 Procedure . 4
9 Calculation of results . 5
10 Precision. 5
11 Test report . 6
Annex A (informative) Spectral characteristics of reflectometers for measuring luminance factor. 7
Bibliography . 9

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.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
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.
ISO 9416 was prepared by Technical Committee ISO/TC 6, Paper, board and pulps.
This second edition cancels and replaces the first edition (ISO 9416:1998), of which it constitutes a technical
revision.
iv © ISO 2009 – All rights reserved

Introduction
The opacity of a paper is dependent on its grammage, but it is also intrinsically dependent on the light-
absorption and light-scattering coefficients of the material. These coefficients are calculated from the values of
the reflectance factor over a black backing, the intrinsic reflectance factor and the grammage of the sheet.
The calculation of these coefficients requires luminance factor data obtained by measurement under specified
conditions. Apart from the optical properties of the sample, the luminance factor depends on the conditions of
measurement and particularly on the spectral and geometric characteristics of the instrument used for its
determination. This International Standard should therefore be read in conjunction with ISO 2469 and
ISO 2471.
NOTE This method is based on a theory developed by Kubelka and Munk. This theory describes scattering and
absorption processes with certain approximations and simplifications and can therefore yield questionable results in
extreme cases. However, the Kubelka-Munk theory offers a simple method for determining these coefficients with the
instrument used for the determination of optical properties of paper and pulps. Moreover, the method based on this theory
has been successfully used in practical applications.

INTERNATIONAL STANDARD ISO 9416:2009(E)

Paper — Determination of light scattering and absorption
coefficients (using Kubelka-Munk theory)
1 Scope
This International Standard specifies a method for the calculation of light-scattering and light-absorption
coefficients based upon diffuse reflectance measurements made under the conditions specified in ISO 2469
using the colour matching function y(λ) and CIE illuminant C.
It is emphasized that the strict evaluation of the light-scattering and light-absorption coefficients requires
conditions which cannot be achieved with the instrumentation specified here. The values obtained by
application of this International Standard are dependent on the application of the Kubelka-Munk equations, not
to full reflectance data but to reflectance factor data obtained using the specified d/0° geometry and a gloss
trap.
The use of the method is restricted to white and near-white uncoated papers with an opacity less than about
95 %. Paper that has been treated with a fluorescent dyestuff or that exhibits significant fluorescence can only
be dealt with if a filter with a cut-off wavelength of 420 nm is used to eliminate all the fluorescence effect in the
UVex(420) mode.
NOTE 1 The residual UV-level in the instrument may depend on whether the instrument is adjusted to UV(C) or
UV(D65) conditions prior to switching to the UVex(420) mode, but it is considered that this uncertainty in the residual level
can be ignored in the application of this International Standard.
NOTE 2 Although this method is restricted to paper, it can be applied to pulp sheets, although this is not in accordance
with this International Standard. In general, when pulps are tested, the light-absorption coefficient at 457 nm
corresponding to the ISO brightness value or the spectral absorption coefficients are of greater interest than the weighted
value standardized in this International Standard.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 186, Paper and board — Sampling to determine average quality
ISO 187, Paper, board and pulps — Standard atmosphere for conditioning and testing and procedure for
monitoring the atmosphere and conditioning of samples
ISO 536, Paper and board — Determination of grammage
ISO 2469, Paper, board and pulps — Measurement of diffuse radiance factor
ISO 2471, Paper and board — Determination of opacity (paper backing) — Diffuse reflectance method
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
reflectance factor
R
ratio of the radiation reflected by a surface element of a body, in the direction delimited by a given cone with
its apex at the surface element, to that reflected by the perfect reflecting diffuser under the same conditions of
irradiation
NOTE The ratio is often expressed as a percentage.
3.2
luminance factor (C)
R
y
reflectance factor defined with reference to the visual efficiency function V()λ and the CIE illuminant C
NOTE 1 The visual efficiency function describes the sensitivity of the eye to light, so that the luminance factor
corresponds to the attribute of visual perception of the reflecting surface.
NOTE 2 For computational purposes, the V()λ function is identical to the CIE 1931 colour matching function y()λ.
NOTE 3 The luminance factor (C) is also known as the Y(C/2°)-value. In the previous edition of this International
Standard, it was referred to as the luminous reflectance factor.
3.3
single-sheet luminance factor (C)
R
luminance factor (C) of a single sheet of paper with a black cavity as backing
3.4
intrinsic luminance factor (C)
R
∞
luminance factor (C) of a layer or pad of material thick enough to be opaque, i.e. such that increasing the
thickness of the pad by doubling the number of sheets results in no change in the measured reflectance factor
3.5
opacity (paper backing)
ratio of the single-sheet luminance factor (C), R , to the intrinsic luminance factor (C), R , of the same sample
0 ∞
NOTE The opacity is expressed as a percentage.
3.6
light-absorption coefficient
k
fraction of the spectral radiant flux diffusely incident on a differential layer within a material that is absorbed
when the flux passes through the layer, divided by the thickness of the layer
NOTE The flux referred to is a radiant flux across the differential layer.
2 © ISO 2009 – All rights reserved

3.7
light-scattering coefficient
s
fraction of the spectral radiant flux diffusely incident on a differential layer within a material that is reflected
when the flux passes through the layer, divided by the thickness of the layer
NOTE 1 The flux referred to is a radiant flux across the differential layer.
NOTE 2 It is assumed that no reflection occurs at the boundaries of the material.
NOTE 3 In a two-flux system, the scattering coefficient is equal to the net transfer of flux from the stronger flux to the
weaker flux in a differential layer within a material divided by the product of the thickness of the layer and the difference
between the fluxes (Reference [1] in the Bibliography).
3.8
light-scattering coefficient by reflectance factor measurements (Kubelka-Munk method)
s
r
coefficient calculated by application of the Kubelka-Munk equations to luminance factor data weighted with
respect to the CIE illuminant C, obtained in an instrument having a specified geometry and calibrated in a
specified manner, on the basis of grammage
NOTE s is expressed in square metres per kilogram (m /kg).
r
3.9
light-absorption coefficient by reflectance factor measurements (Kubelka-Munk method)
k
r
coefficient calculated by application of the Kubelka-Munk equations to luminance factor data weighted with
respect to the CIE illuminant C, obtained in an instrument having a specified geometry and calibrated in a
specified manner, on the basis of grammage
NOTE 1 k is expressed in square metres per kilogram (m /kg).
r
NOTE 2 Definitions 3.6 and 3.7 are strictly applicable to monochromatic light but, for the purpose of this International
Standard, they apply to broad-band radiation. In research work, s and k can and should be determined at the relevant
wavelength for the study concerned. As general descriptions of a given paper, they are defined here in relation to the V(l)
function and the CIE illuminant C.
4 Principle
The luminance factor of a single sheet of the paper over a black cavity and the intrinsic luminance factor of the
paper are determined. The grammage is determined in accordance with ISO 536.
The light-absorption and light-scattering coefficients are then calculated from these data using the Kubelka-
Munk theory.
5 Apparatus
5.1 Reflectometer, having the geometric, spectral and photometric characteristics described in ISO 2469,
equipped for the measurement of luminance factor, and calibrated in accordance with the provisions of
ISO 2469.
5.2 Filter-function. In the case of a filter reflectometer, a filter that, in conjunction with the optical
characteristics of the basic instrument, gives an overall response equivalent to the CIE tristimulus value Y of
t
...