The magnetooptic Kerr effect (MOKE) is a well known and handy tool to characterize ferro-, ferri- and antiferromagnetic materials. Many of the MOKE techniques employ effects solely linear in magnetization $bm{M}$. Nevertheless, a higher-order term being proportional to $bm{M}^2$ and called quadratic MOKE (QMOKE) can additionally contribute to the experimental data. Here, we present detailed QMOKE spectroscopy measurements in the range of 0.8 -- 5.5,eV based on a modified 8-directional method applied on ferromagnetic bcc Fe thin films grown on MgO substrates. From the measured QMOKE spectra, two further complex spectra of the QMOKE parameters $G_s$ and $2G_{44}$ are yielded. The difference between those two parameters, known as $Delta G$, denotes the strength of the QMOKE anisotropy. Those QMOKE parameters give rise to the QMOKE tensor $bm{G}$, fully describing the perturbation of the permittivity tensor in the second order in $bm{M}$ for cubic crystal structures. We further present experimental measurements of ellipsometry and linear MOKE spectra, wherefrom permittivity in the zeroth and the first order in $bm{M}$ are obtained, respectively. Finally, all those spectra are described by ab-initio calculations.
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