The Lattice Geometry of Walsh-Function-Based Adaptive Optics

We show that there is an intrinsic link between the use of Walsh aberration modes in adaptive optics (AO) and mathematics lattices. The discrete binary nature these means are infinite combinations mode coefficients can optimally correct same aberration. Finding such a correction hence poorly conditioned optimisation problem be difficult to solve. This mitigated by confining AO space defined fundamental Voronoi cell lattice. By restricting this way, one ensure only set corresponds optimum property used enable design efficient estimation algorithms solve inverse finding aberrations from sequence measurements wavefront sensorless system. benefit approach illustrated using neural-network-based estimator.