Deformable mirror model for open-loop adaptive optics using multivariate adaptive regression splines

Open-loop adaptive optics is a technique in which the turbulent wavefront is measured before it hits the deformable mirror for correction. We present a technique to model a deformable mirror working in open-loop based on multivariate adaptive regression splines (MARS), a non-parametric regression technique. The model's input is the wavefront correction to apply to the mirror and its output is the set of voltages to shape the mirror. We performed experiments with an electrostrictive deformable mirror, achieving positioning errors of the order of 1.2% RMS of the peak-to-peak wavefront excursion. The technique does not depend on the physical parameters of the device; therefore it may be included in the control scheme of any type of deformable mirror.