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CHARISM A I 7
li. Pigment-binder interaction -Kulbelka-Munk correction
The correction methodology employed"? is based on the Kubelka—Munk theory**4”8 and
was developed by Ramos and Lagorio for the correction of fluorescence spectra of
chlorophyll in plant leaves. It assumes that:
(a) the painted surface is an ideal, homogeneous scattering and absorbing material,
characterized by a scattering coefficient s(A) and an absorption coefficient k(A).
Although this is a broad, and in most cases unrealistic, approximation it will be accepted
here because no quantitative information or identification is sought for image correction;
(b) the incoming radiation is a collimated beam illuminating normally the painted surface
and that no radiation is transmitted through the paint layer. In other words, it is
considered to be optically opaque and no radiation is transmitted to any underlying
layers.
Under these hypotheses, the well-known result of the Kubelka—Munk theory can be obtained:
kA) [L- ROP _
s@) > 2RQ) > RemlRO]
where A represents the wavelength, R(A) is the diffuse reflectance factor (i.e., the ratio
between the reflected radiation at the front surface and the incident radiation), and Rem[R(A)]
is the remission function.
When a luminescent material is present in the scattering media, the Kubelka—Munk theory
can be modified by considering that the radiation emitted can be decomposed into two
photon flows traveling in the direction of the incoming (A) and reflected radiation (Ao),
respectively.*’ A correction factor y(A,Ao) is introduced to account for this given by:
1 1
14 | Rem[R(A)] 14 | Rem[R(A)]{Rem[R(A)] + 2}
Rem[R(A)] + 2] I Rem|[R(Ao) |{Rem|R(Ag)] + 23]
ya, ho) =
Dividing the observed luminescence image by this correction factor yields the true
luminescence.
Version No. 1.0 38 Date : 14/10/2013