  Adaptive optics normally concerns the feedback correction of phase
aberrations. Such correction has been of benefit in various optical systems,
with applications ranging in scale from astronomical telescopes to
super-resolution microscopes. Here we extend this powerful tool into the
vectorial domain, encompassing higher-dimensional feedback correction of both
polarisation and phase. This technique is termed vectorial adaptive optics
(V-AO). We show that V-AO can be implemented using sensor feedback, indirectly
using sensorless AO, or in hybrid form combining aspects of both. We validate
improvements in both vector field state and the focal quality of an optical
system, through correction for commonplace vectorial aberration sources,
ranging from objective lenses to biological samples. This technique pushes the
boundaries of traditional scalar beam shaping by providing feedback control of
extra vectorial degrees of freedom. This paves the way for next generation AO
functionality by manipulating the complex vectorial field.
