Best tip-tilt correction residuals on a normalised tip-tilt. Panel a: tip-tilt normalised between minus one and one. Panel b: 2D local piston. Panel c: 2D pyramid. Panel d: 2D axisymmetric Gaussian profile. Panel e: Upper left: 2D axisymmetric ALPAO profile. Lower right: True ALPAO influence functions. Panel f: 2D sinc function. The blue frames represent the simulation domain D. The dots emphasise the actuator positions. – Aperture: disc of diameter 95%D.