text: Also from this process came results for several special cases of two stream solutions for plane parallel layers.
  For the case of zero absorption,      .
  For the case of infinitesimal layers, , and the ART function gives results approaching equivalence to the remission function.
  As the void fraction  of a layer becomes large, .
  The ART is related to the Kortüm–Schuster equation for isotopic scatter by .
  The Dahms argued that the conventional absorption and scattering coefficients, as well as the differential equations which employ them, implicitly assume that a sample is homogenous at the molecular level.  While this is a good approximation for absorption, as the domain of absorption is molecular, the domain of scattering is the particle as a whole. Any approach using continuous mathematics will therefore tend to fail as particles become large.
  Successful application of theory to a real world sample using the mathematics of plane parallel layers requires assigning properties to the layers that are representative of the sample as a whole (which does not require extensively reworking the mathematics).  Such a layer was termed a representative layer, and the theory was termed the representative layer theory.
  Furthermore, they argued that it was irrelevant whether the light moving from one layer to another was reflected specularly or diffusely.  The reflection and back scatter is lumped together as remission.  All light leaving the sample on the same side as the incident beam is termed remission, whether it arises from reflection or back scatter.  All light leaving the sample on the opposite side from the incident beam is termed transmission.  (In a three-flux or higher treatment, such as Giovanellis, the forward scatter is not indistinguishable from the directly transmitted light.  Additionally, Giovanellis treatment makes the implied assumption of infinitesimal particles.)
  They developed a scheme, subject to the limitations of a two-flux model, to calculate the "scatter corrected absorbance" for a sample.  The decadic absorbance of a scattering sample is defined as  or .  For a non scattering sample, , and the expression becomes  or , which is more familiar.  In a non-scattering sample, the absorbance has the property that the numerical value is proportional to sample thickness.  Consequently, a scatter-corrected absorbance might reasonably be defined as one that has that property.
  If one has measured the remission and transmission fractions for a sample,  and , then the scatter-corrected absorbance should have half the value for half the sample thickness. By calculating the values for  and  for successively thinner samples () using the Benford's equations for half thickness, a place will be reached where, for successive values of  (0,1,2,3,...), the expression  becomes constant to within a some specified limit, typically 0.01 absorbance units.  This value is the scatter-corrected absorbance.