Working principle of the grating-vector-Apodizing Phase Plate. The grating-vAPP is a half-wave retarder pupil-plane optic with a spatially varying fast-axis orientation. The varying fast-axis orientation induces the phase through the geometric phase on the circular polarization states. These polarization states receive the opposite phase and therefore have flipped coronagraphic point spread functions (PSFs). The PSFs are spatially separated by adding a phase ramp to the design. Any offsets from half-wave retardance within the optic reduces the efficiency with which the light will be transferred to the coronagraphic PSFs and results in a leakage PSF.