Square arrays of gold (Au) hemispheroids deposited on a UV-transparent glass substrate reveal a rich optical response when investigated by spectroscopic Mueller Matrix Ellipsometry. Two samples were studied; the first consisted of hemispheroids of parallel radius of 58 nm and height 30 nm with lattice constant 210 nm; the corresponding parameters for the second sample were 38 nm, 20 nm and 125 nm, respectively. By a full azimuthal rotation of the samples, we observe all the Rayleigh anomalies corresponding to grazing diffracted waves, with strong resonances for co-polarization scattered light near the high symmetry points and cross-polarization scattered light around the Localized Surface Plasmon Resonance. Polarization-conversion becomes particularly important at grazing incidence, and the cross-polarization follows the Rayleigh lines. The optical response (neglecting polarization conversion) is modelled in the quasi-static approximation using the so-called Bedeaux-Vlieger formalism, and the Finite Element Method using COMSOL. The direct inversion of the effective (substrate dependent) dielectric function is discussed. (C) 2017 Elsevier B.V. All rights reserved.