Many new types of sensing or imaging surfaces are based on periodic thin films. It is explained how the response of those surfaces to partially coherent fields can be fully characterized by a set of functions in the wavenumber spectrum domain. 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. Sum and difference coordinates in both spatial and spectral domains are conveniently used to represent the characteristic functions, which are specialized here to the case of periodic structures. Those functions can be either computed or obtained experimentally. Simulations rely on solvers based on periodic-boundary conditions, while experiments correspond to Energy Absorption Interferometry (EAI), already described in the literature. We derive rules for the convergence of the representation versus the number of characteristic functions used, as well as for the sampling to be considered in EAI experiments. Numerical examples are given for the case of absorbing strips printed on a semi-infinite substrate.
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