  Modelling the scattering of focused, coherent light by nano-scale structures
is oftentimes used to reconstruct or infer geometrical or material properties
of structures under investigation in optical scatterometry. This comprises both
periodic and aperiodic nano-structures. Coherent Fourier scatterometry with
focused light exploits the diffraction pattern formed by the nano-structures in
Fourier plane. While the scattering of a focused beam by a spatially isolated
scatterer is a standard modelling task for state-of-the art electromagnetic
solvers based, e.g., on the finite element method, the case of periodically
structured samples is more involved. In particular when the focused light
covers several grating periods of as it is commonly the case. We will present a
coherent illumination model for scattering of focused beams such as Gaussian --
and Bessel -- beams by periodic structures such as line gratings. The model
allows to take into account optical wavefront aberrations in optical systems
used for both, the illumination and detection of the scattered fields. We
compare the model with strategies implemented on large-scale super-cells and
inverse Floquet-transform strategies to superimpose both near- and far- fields
coherently.
