Fig. 4

Method C—sensorless vectorial adaptive optics. a Simplified schematic of the sensorless V-AO mechanism. Taking a fixed point P(r,q) on the pupil as example, when the axis of the aberration corresponding to this point is known, the circle K is determined. Hence, the vectorial correction must be found to set the input SV’(r,q), corresponding to point T, back to the desired SV(r,q) at point A. In practice, aberration modes are applied that change all of the points on the pupil P(x,y) simultaneously to optimise the focal intensity. Details are elaborated in Additional file 1: Note S7. b V-AO off vs. V-AO on status for a calibration target consisting of piece of thin film waveplate. SOP distributions, patterns on DM, focus profiles, overall slow/fast axis performances (before and after the correction), as well as the axis distributions and their comparison on Poincaré sphere are given. The corrected SOP is more uniform, and the focal spot is sharper. It can be also observed that both corrected axes are more uniform. The complex phase pattern here reveals the extra phase errors that introduced via AO correctors, which are a consequence of the complex interplay between phase and polarisation, and includes dynamic and geometric phases. c Comparison of V-AO off and V-AO on status of a biological sample. Focal spots distributions at three steps, axis orientation corrections, are given for comparison. It can be found that the axis distribution and focal spot profiles are enhanced after the correction process