The definition and use of optical invariants for thin island films

In the context of a description of the optical properties of thin films in terms of the excess polarization it is shown that four complex constitutive coefficients are needed to describe both the coverage and the location of the film material relative to the surface of the substrate. Expressions are given relating these coefficients for different choices of the position of the dividing surface (with respect to which the excess polarizations are calculated). This makes it possible to construct seven real invariant combinations which are independent of this choice. Formulae for the reflectances and transmittances for s- and p-polarized light in terms of these invariants are given for the case that both the substrate and the ambient are non-absorbing. For the special case of spherical islands, explicit formulae are given for the constitutive coefficients. Finally the theory is applied to interpret experimental results for a thin latex film.