  The apodizing phase plate (APP) is a solid-state pupil optic that clears out
a D-shaped area next to the core of the ensuing PSF. To make the APP more
efficient for high-contrast imaging, its bandwidth should be as large as
possible, and the location of the D-shaped area should be easily swapped to the
other side of the PSF. We present the design of a broadband APP that yields two
PSFs that have the opposite sides cleared out. Both properties are enabled by a
half-wave liquid crystal layer, for which the local fast axis orientation over
the pupil is forced to follow the required phase structure. For each of the two
circular polarization states, the required phase apodization is thus obtained,
and, moreover, the PSFs after a quarter-wave plate and a polarizing
beam-splitter are complementary due to the antisymmetric nature of the phase
apodization. The device can be achromatized in the same way as half-wave plates
of the Pancharatnam type or by layering self-aligning twisted liquid crystals
to form a monolithic film called a multi-twist retarder. As the VAPP introduces
a known phase diversity between the two PSFs, they may be used directly for
wavefront sensing. By applying an additional quarter-wave plate in front, the
device also acts as a regular polarizing beam-splitter, which therefore
furnishes high-contrast polarimetric imaging. If the PSF core is not saturated,
the polarimetric dual-beam correction can also be applied to polarized
circumstellar structure. The prototype results show the viability of the
vector-APP concept.
