Characterizing the nonlinear dynamic behavior of membrane optics

The use of true-membrane reflectors holds the promise of increasing the size of space-based apertures by decreasing payload mass and reducing launch volumes, but figure acquisition and maintenance of the thin, deployed structure present significant control challenges. The ability to manage both the static and dynamic aberrations defines the utility of these compliant mirrors for resolving quality images. The scope of the current study consists of characterizing the non-linear dynamic behavior of membrane reflectors to visible-optics quality under realistic support and loading scenarios. The basis for quality in the finite element model (FEM) deformed shape predictions is established both by comparing FEM and analytical solutions for linear static problems and by studying the convergence of eigen solutions. Most of the results are shown, too, to be within a previously determined range of optically-accurate solutions. The topographical difference between linear and non-linear dynamic solutions is characterized and correlated to support and loading regimes for eventual inclusion in closed-loop-control schemes. The objective of this paper is thus to study the non-linear characteristics of the dynamic behavior of membrane optics as the basis for future work in system identification and figure control.