Periodic thin-film structures are widely used as absorptive structures for electromagnetic radiation. We show that the absorption behavior for partially coherent illumination can be fully characterized by a set of characteristic functions in wavenumber space. We discuss the prediction of these functions using electromagnetic solvers based on periodic boundary conditions, and their measurement experimentally using Energy Absorption Interferometry (EAI). The theory is developed here for the case of 2D absorbers with TE illumination and arbitrary material properties in the plane of the problem, except for the resistivity, which is assumed isotropic. Numerical examples are given for the case of absorbing strips printed on a semi-infinite substrate. We derive rules for the convergence of the representation as a function of the number of characteristic functions used, as well as conditions for sampling in EAI experiments.