  In most of the cases the magnetooptic Kerr effect (MOKE) techniques rely
solely on the effects 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 experimental data. Handling and
understanding the underlying origin of QMOKE could be the key to utilize this
effect for investigation of antiferromagnetic materials in the future due to
their vanishing first order MOKE contribution. Also, better understanding of
QMOKE and hence better understanding of magnetooptic (MO) effects in general is
very valuable, as the MO effect is very much employed in research of ferro- and
ferrimagnetic materials. Therefore, we present our QMOKE and longitudinal MOKE
spectroscopy setup with a spectral range of 0.8--5.5\,eV. The setup is based on
light modulation through a photoelastic modulator and detection of
second-harmonic intensity by a lock-in amplifier. To measure the Kerr
ellipticity an achromatic compensator is used within the setup, whereas without
it Kerr rotation is measured. The separation of QMOKE spectra directly from the
measured data is based on measurements with multiple magnetization directions.
So far the QMOKE separation algorithm is developed and tested for but not
limited to cubic (001) oriented samples. The QMOKE spectra yielded by our setup
arise from two quadratic MO parameters $G_s$ and $2G_{44}$, being elements of
quadratic MO tensor $\bm{G}$, which describe perturbation of the permittivity
tensor in the second order in $\bm{M}$.
