text: To be representative, the layer must meet the following criteria:
  • The volume fraction of each type of particle is the same in the representative layer as in the sample as a whole.
  • The surface area fraction of each type of particle is the same in the representative layer as in the sample as a whole.
  • The void fraction of the representative layer is the same as in the sample.
  • The representative layer is nowhere more than one particle thick. Note this means the “thickness” of the representative layer is not uniform.  This criterion is imposed so that we can assume that a given photon of light has only one interaction with the layer. It might be transmitted, remitted, or absorbed as a result of this interaction, but it is assumed not to interact with a second particle within the same layer.
  In the above discussion, when we talk about a “type” of particle, we must clearly distinguish between particles of different composition. In addition, however, we must distinguish between particles of different sizes. Recall that scattering is envisioned as a surface phenomenon and absorption is envisioned as occurring at the molecular level throughout the particle. Consequently, our expectation is that the contribution of a “type” of particle to absorption will be proportional to the volume fraction of that particle in the sample, and the contribution of a “type” of particle to scattering will be proportional to the surface area fraction of that particle in the sample. This is why our “representative layer” criteria above incorporate both volume fraction and surface area fraction. Since small particles have larger surface area-to-volume ratios than large particles, it is necessary to distinguish between them.