text: If , , and  are known for the representative layer of a sample, and ,  and  are known for a layer composed of  representative layers, the ART fractions for a layer with thickness of   are
  If ,  and  are known for a layer with thickness , the ART fractions for a layer with thickness of  are 
  and the fractions for a layer with thickness of  are
  If ,  and  are known for layer   and   and  are known for layer , the ART fractions for a sample composed of layer  and layer  are
  :The symbol  refers to the reflectance of layer  when the direction of illumination is antiparallel to that of the incident beam.  The difference in direction is important when dealing with inhomogeneous layers.  This consideration was added by Paul Kubelka in 1954.