Dual-Update Data-Driven Control of Deformable Mirrors Using Walsh Basis Functions

TL;DR

This paper introduces a new data-driven control method for deformable mirrors that updates the mirror model and control actions simultaneously, using Walsh basis functions to improve surface shape accuracy, verified on a 140-actuator MEMS DM.

Contribution

The paper presents a novel dual-update data-driven control approach incorporating Walsh basis functions for deformable mirror surface shaping.

Findings

Achieved root-mean-square surface error of 14-40 nm.

Validated the method experimentally on a 140-actuator MEMS DM.

Potential for further improvement through parameter tuning.

Abstract

In this paper, we develop a novel data-driven method for Deformable Mirror (DM) control. The developed method updates both the DM model and DM control actions that produce desired mirror surface shapes. The novel method explicitly takes into account actuator constraints and couples a feedback control algorithm with an algorithm for recursive estimation of DM influence function models. In addition to this, we explore the possibility of using Walsh basis functions for DM control. By expressing the desired and observed mirror surface shapes as sums of Walsh pattern matrices, we formulate the control problem in the 2D Walsh basis domain. We thoroughly experimentally verify the developed approach on a 140-actuator MEMS DM, developed by Boston Micromachines. Our results show that the novel method produces the root-mean-square surface error in the $14-40$ nanometer range. These results can additionally be improved by tuning the control and estimation parameters. The developed approach is also applicable to other DM types, such as for example, segmented DMs.