The desire to implement optical structures on much larger scales motivated much of our research into thin films. Given the tremendous expense and difficulties in producing and launching high quantities of large reflectors, it is doubtful that refinements of conventional technology will meet future needs, particularly in a cost-effective manner. A principle of our thin film research at large was the development of accurate modeling and simulation tools. We approached this by developing a family of models of progressing complexity that were validated by test.
We examined the possible use of thin film materials as globally adaptable surfaces for optical applications. Typical adaptive optics are an aggregate of discrete mirrors actuated independently. Individual mirrored elements could not easily be deployed with a large scale inflatable structure and would lack an adequate reaction structure for traditional actuation methods. Rather than utilizing discrete optical elements, we proposed changing the global shape of the surface through a distribution of moments imparted by piezoelectric bimorph actuators. This project examined the effectiveness of global shape control with the discrete moment method as it applied to a simple fixed-fixed beam. Results illustrated that such a method shows promise. First order models can be used in simulation tools to examine control architectures for more complex optical shapes.
Our test beam consisted of an aluminum substrate with a thin piezoelectric layer bonded to its surface. Etching away portions of the external electrode created the individual bimorph actuators that imparted the discrete moments. While these bimorph “cells” could be actuated independently, the applied moments would influence the shape of the beam as a whole. Therefore, it was necessary to measure the total shape of the beam under the influence individual cells. A fixed-fixed beam of this type is linear for small displacements and the desired shape could be approximated as a linear composition of these empirically derived “influence functions”.
Utilizing a laser probe to measure the vertical displacement of the test beam, a milling machine was modified into an x-y scanning bed. Surface displacements were plotted as a matrix of the two positional coordinates allowing extraction of the influence shapes as a function of piezo excitation voltages. While the measured shapes differed from the theoretical models by some degree, several reasonable conditions could explain this disparity including non-ideal fixed-fixed boundary conditions as well as variations in the beam thickness, piezoelectric thickness, bond layer thickness or a combination of all three.
Once a survey of these influence functions was complete, the data was used in a least squares algorithm to estimate initial control values for a global command. Target shapes for this experiment were first and second order curvatures common in optics: a top hat or piston, and a parabola. Initial estimates of control voltage did produce the proper shapes but displacements were generally too low. Only after several steps of manual tuning were the optimal shapes achieved.
The long acquisition time of the scanner proved to be the biggest drawback of the experimental setup. This precluded the evaluation of more sophisticated control loops to fine tune the commanded shape. It also barred us from considering dynamic rather than static shape control. These results however, show that net shape control with bimorphs is achievable within the limits of linear beam theory. Given a means to quickly measure the net shape of the surface, it would not be difficult to use more sophisticated control architectures.