Optimal placement of binary actuators in deformable optical systems

Abstract

Recently, exploration has been conducted into the applicability of binary mechatronics to active figure correction in large optical systems such as space telescopes and ground-based solar-thermal concentrators. This Thesis will continue this exploration. The information-theoretic requirements of the corrective commands required in active optics will be explored to understand the dimensionality of the continuous workspace sampled by binary actuation. In both the minimal expected error and the minimal computation time sense, the optimal discrete workspace is the uniform discrete distribution. A rigorous analogy between binary mechatronics and discrete random variables will be used to show that this optimal workspace is achievable by a linear superposition of actuators with exponentially decreasing influences on the optical surface. It will be proven that elasticity can be exploited to construct mechanisms where constant magnitude actuators exhibit exponentially decaying influences on certain parts of the mechanism, allowing for designs where individual binary actuators correspond to binary bits of the required deformation. A planar truss mechanism designed with this philosophy will be presented and shown to have independent kinematic control of multiple adjacent displacements on its top side. Finally, this design will be shown extend to three dimensions in a manner applicable to optical figure correction. Due to the complexity of mechanisms that meet the optimality criteria, only theoretical analysis will be presented.