56
K. D. Dahm and D. J. Dahm
(which is readily measured experimentally). But this usage requires a known value of
κ, which in Sect. 3.1 was termed the “molar absorptivity.” For non-scattering samples,
extinction of the beam is attributed entirely to absorption. It is often reasonable to
model κ as a constant that represents the inherent ability of the material in question to
absorb light (though limitations to such a model were also noted in Sect. 3.1). It would
be convenient if an analogous linear relationship existed for scattering samples.
As introduced in Sect. 3.6, the classical definition of an “absorption coefficient” is
the fraction of incident light absorbed by a layer of material, divided by the thickness
of that layer. This is a number that can be obtained experimentally for a macroscopic
sample of known thickness. However, previous sections have also illustrated that
scatter and absorption influence each other, and scatter is dependent upon factors
like particle size and shape that are not repeatable from sample to sample. As noted
by Burger et al. in a study of pharmaceutical powders, “many parameters, such as
particle size distribution, packing density, or homogeneity of the investigated powder
mixtures, strongly influence the reflectance spectra [11]. A variation in, for example,
the particle size distribution changes the scattering coefficient and leads to different
reflectance values even for chemically identical samples.” Consequently, one can
calculate an “absorption coefficient” from a remission/transmission experiment on a
scattering sample, and one might view it as somewhat analogous to the Beer’s Law
κ, but one cannot generally use it the same way, as one cannot typically assume it is
“constant.”
Is it possible to separate the effects of absorption and scatter in a scattering sample?
Consider a very thin layer such as that as shown in Fig. 3.11. In the example, 99.5%
of the incident light is transmitted through the layer, 0.3% is absorbed, and 0.2% is
remitted. Consider:
• In general, when light is reflected from the front surface of a layer, it has no
opportunity to be absorbed by that layer, and thus the observed absorption has
been influenced by the process of remission. But in this example, the remission and
absorption are both negligible, so essentially all of the light had the opportunity
to be either remitted or absorbed.
• In general, when light is diverted from its original path by scatter, it is now
penetrating the sample along a different (usually longer) length path, which means
it has a different (usually larger) probability of subsequently being absorbed by
the sample. But this consideration does not apply in Fig. 3.11, since the layer is
very thin and the light only interacts with it a single time.
Fig. 3.11 Hypothetical thin layer in which 99.5% of the incident light is transmitted and 0.2% is
remitted, with the other 0.3% being absorbed
K. D. Dahm and D. J. Dahm
(which is readily measured experimentally). But this usage requires a known value of
κ, which in Sect. 3.1 was termed the “molar absorptivity.” For non-scattering samples,
extinction of the beam is attributed entirely to absorption. It is often reasonable to
model κ as a constant that represents the inherent ability of the material in question to
absorb light (though limitations to such a model were also noted in Sect. 3.1). It would
be convenient if an analogous linear relationship existed for scattering samples.
As introduced in Sect. 3.6, the classical definition of an “absorption coefficient” is
the fraction of incident light absorbed by a layer of material, divided by the thickness
of that layer. This is a number that can be obtained experimentally for a macroscopic
sample of known thickness. However, previous sections have also illustrated that
scatter and absorption influence each other, and scatter is dependent upon factors
like particle size and shape that are not repeatable from sample to sample. As noted
by Burger et al. in a study of pharmaceutical powders, “many parameters, such as
particle size distribution, packing density, or homogeneity of the investigated powder
mixtures, strongly influence the reflectance spectra [11]. A variation in, for example,
the particle size distribution changes the scattering coefficient and leads to different
reflectance values even for chemically identical samples.” Consequently, one can
calculate an “absorption coefficient” from a remission/transmission experiment on a
scattering sample, and one might view it as somewhat analogous to the Beer’s Law
κ, but one cannot generally use it the same way, as one cannot typically assume it is
“constant.”
Is it possible to separate the effects of absorption and scatter in a scattering sample?
Consider a very thin layer such as that as shown in Fig. 3.11. In the example, 99.5%
of the incident light is transmitted through the layer, 0.3% is absorbed, and 0.2% is
remitted. Consider:
• In general, when light is reflected from the front surface of a layer, it has no
opportunity to be absorbed by that layer, and thus the observed absorption has
been influenced by the process of remission. But in this example, the remission and
absorption are both negligible, so essentially all of the light had the opportunity
to be either remitted or absorbed.
• In general, when light is diverted from its original path by scatter, it is now
penetrating the sample along a different (usually longer) length path, which means
it has a different (usually larger) probability of subsequently being absorbed by
the sample. But this consideration does not apply in Fig. 3.11, since the layer is
very thin and the light only interacts with it a single time.
Fig. 3.11 Hypothetical thin layer in which 99.5% of the incident light is transmitted and 0.2% is
remitted, with the other 0.3% being absorbed