Development and control of a new class of segmented deformable mirrors for advanced astronomical imaging applications

This dissertation describes the design, development, fabrication and control of a new class of segmented micro-electro-mechanical system (MEMS) deformable mirrors (DMs) with tip, tilt and piston (TTP) degrees of freedom. The TTP DM consists of a close-packed array of hexagonal mirror segments, each controlled by three independent electrostatic actuators. Mirror segment piston motion is achieved through identical actuator deflection, while out-of-plane rotation is achieved via differential deflection. The new DM is an essential wavefront control component for several advanced astronomical imaging applications. These applications place stringent requirements on mirror segment optomechanical behavior and control properties, which are new to MEMS spatial light modulator technology and are the focus of the presented work.;Two astronomical imaging applications in particular are addressed by the new TTP DM design. The first is a space-based nulling coronagraph telescope that aims to image extrasolar terrestrial planets. The coronagraph requires a segmented DM with tip-tilt-piston motion to correct for wavefront phase and amplitude aberrations in detected starlight. The second application involves using the DM as a variable focus Fresnel mirror with dynamic refocusing abilities for laser guide star tracking in giant land-based telescopes. Production of a suitable DM for both applications involved overcoming significant microfabrication and control challenges.;First, mirror segments are required to maintain better than lambda/100 RMS surface flatness, irrespective of segment angle or operation frame rate. This is challenging because thin polysilicon mirror components tend to curl as a result of the residual stress gradients embedded in the deposited materials, and bend during actuation due to their low rigidity. Furthermore, the surface micromachining process used to fabricate DMs is prone to print-through effects, which worsens surface quality. To address these problems a new actuator design and mirror segment fabrication process were developed. The new actuator design uses embedded flexures to reduce bending moments imparted to the mirror segment during tip-tilt motion that cause it to bend. Epitaxial growth of a thick polysilicon mirror segment is used to improve mirror rigidity as well as create a highly polishable surface with little to no print-through. The epitaxial polysilicon layer is also very responsive to high-temperature dopant anneals, which are used to combat residual stress. Using these new designs, mirror segment surface flatness on the order of 5nm RMS was achieved over the full range of mirror segment motion, +/- 3mrad of tip-tilt and 1mum of piston, simultaneously. Mirror segment optical quality also remains acceptable for laser guide star tracking at mirror switching times faster than 60mus.;Second, the TTP DM segments need to be controlled in an open-loop manner, such that control voltages for simultaneous mirror segment tip, tilt and piston motion are predicted in a single control step. This is complicated by the fact that the mirror segment's actuators are mechanically coupled through the mirror surface. Furthermore, the relationship between actuator control voltage and its displacement is nonlinear. Due to the large number of mirror control states, a purely empirical open-loop control relying on extensive calibration is inefficient. To address this problem a new algorithm was developed which combines a linear analytical model for mirror coupling with a sparse empirical calibration of its nonlinear actuators, allowing the prediction of desired mirror segment actuator positions to a precision of 6nm RMS. The same technique has also been applied to continuous facesheet DM technology, which suffers from similar albeit nonlinear actuator coupling. Shapes at the limit of achievable mirror spatial frequencies with up to 1.5 mum amplitudes have been achieved with less than 15nm RMS surface error. Both algorithms are discussed and demonstrated in the presented work.