Fig. 1

Vectorial aberrations, vectorial adaptive optics (V-AO), and correction methods ranging from sensor-based to sensorless. a Schematic of a system affected by vectorial aberration and a V-AO compensated system. The V-AO module encompasses a polarisation module and a phase module. Here the V-AO module pre-corrects the vectorial aberration. The state of polarisation (SOP) and phase profiles, as well as focus profile are given as sketches illustrating states ‘before’ and ‘after’ V-AO correction. b Sketches of three different V-AO correction methods. Method A (sensor-based V-AO): A MM sensor is used to measure the aberration then give feedback to V-AO module for pre-correction, hence leading to the desired light field output. PSG polarisation state generator, PSA polarisation state analyser. Method B (quasi-sensorless V-AO): A polariser filters the intensity before the pupil, and the pupil intensity profile detected on a camera after the polariser serves as feedback for V-AO module to correct the aberration (the full setup is detailed in Additional file 1: Note S1). P: Polariser. Method C (modal-sensorless V-AO): Focal intensity is used as proxy for optimising the output phase and SOPs of the beam hence completing the V-AO loop