Adaptive Modal Superposition Mirrors

Abstract

Deformable Mirrors (DMs) are the sophisticated and expensive parts of Adaptive Optics systems to compensate for optical wavefront aberrations. The objective of this work is the design, fabrication, and characterisation of an affordable optical DM working based on the principles of the vibration ‎of circular membranes. Such a Vibrating Membrane Mirror (VMM), contrary to the most current DMs, does not require any microactuators and serves as a lightweight, low-cost, and ‎high-speed mirror. Firstly, one has to address the primary concern whether the surface of vibration mode shapes can compensate for optical wavefront aberrations or not. To do that, I conduct a numerical study and show that there is a great resemblance between the Zernike Polynomials and the Bessel functions, which are the mathematical sets describing the wavefront of atmospheric aberrations and the eigenfunctions of a circular membrane, respectively. Then, a Piezo-Plate-Membrane model is introduced to broaden the current understanding ‎of the dynamics of piezoelectric thin films. This model possesses higher Degrees of Freedom compared to the traditional models and assists researchers to optimise the design of electromechanical devices made of piezoelectric thin films. Piezoelectric Poly-vinylidene fluoride (PVDF) thin films are also introduced as promising ‎candidates for the vibrating membrane in the proposed VMM. A prototype was constructed and its modal parameters were measured to show to what extent the ‎VMM can mitigate optical aberrations. A Finite Element model is developed in ABAQUS and the dynamics of VMM is also analysed under different geometries and exciting signals. There was a good agreement between the experimental and FEA Results. The optical performance of the VMM was also investigated using an imaging Michelson interferometer, wavefront sensors, and Atomic Force Microscope. The theoretical and experimental findings of studying the dynamics of PVDF paved the way for introducing a new vibration sensor. I developed a novel multi-resonance PVDF sensor with applications in monitoring the structural vibration of machinery and civil structures without affecting their responses due to its negligible weight and tuneable resonant frequency. As a result of this study, I have provided the ability to design, analyses and parameterise a piezoelectric PVDF film for adaptive optics as well as vibration sensing. The agreement of analytical, numerical and experimental investigations allow extreme confidence in the future design of such devices.