  Many objects on the sky exhibit a centrosymmetric polarization pattern,
particularly in cases involving single scattering around a central source.
Utilizing a novel liquid crystal device (the ``theta cell'') that transforms
the coordinate system of linear polarization in an image plane from Cartesian
to polar, the observation of centrosymmetric polarization patterns can be
improved: instead of measuring Stokes Q and U on the sky, one only needs to
measure Stokes Q' in the new instrument coordinate system. This reduces the
effective exposure time by a factor of two and simplifies the polarization
modulator design. According to the manufacturer's specifications and to
measurements in the lab, the liquid crystal device can be applied in the
visible and NIR wavelength range. Astronomical science cases for a``radial
polarimeter'' include exoplanet detection, imaging of circumstellar disks,
reflection nebulae and light echos, characterization of planetary atmospheres
and diagnostics of the solar K-corona. The first astronomical instrument that
utilizes a theta cell for radial polarimetry is the S5T (Small Synoptic Second
Solar Spectrum Telescope), which accurately measures scattering polarization
signals near the limb of the sun. These observations are crucial for
understanding the nature and origin of weak, turbulent magnetic fields in the
solar photosphere and elsewhere in the universe. A ``radial polarimeter''
observing a slightly defocused point source performs one-shot full linear
polarimetry. With a theta cell in a pupil plane, a beam's linear polarization
properties (e.g. for calibration purposes) can be fully controlled through
pupil masking.
