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 manufacturers 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 beams linear polarization properties (e.g. for calibration purposes) can be fully controlled through pupil masking.
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