Analysis of a compliant static deformable mirror for wavefront error cancellation

The Navy Prototype Optical Interferometer (NPOI) array, located near Flagstaff, Arizona, transports 12.5 cm diameter stellar radiation simultaneously from six primary collectors through a 9,000 cubic foot vacuum relay system prior to entering a specialized laboratory where further manipulations of each beam occur. The relay system redirects each 12.5 cm beam 10 times. Ground-based optical interferometry requires very high quality, ideally flat, relay mirrors. The mirrors used in the relay system have flatness deviation tolerance 32 nm peak-to-valley over the 18.3 cm clear aperture. Once mounted in the 10-element optical train, errors from each mirror tend to stack up and increase the resultant wavefront distortion for that path. This leads to reduced fringe contrast, fringe tracking, and number of observables. In a previous paper, it was shown that it is possible to mitigate the resultant wavefront distortion by using a phase-shifting interferometer combined with a single compliant static deformable mirror and control system. In that work, the mirrors tested showed a fairly uniform, concentric concavity deformation, which a single, centrally located actuator may significantly improve. In this paper, we extend the previous analysis to consider an off-center actuator acting on a mirror to counteract an asymmetric wavefront distortion resulting from the superposition of several relay mirrors. The shape applied to a single corrector mirror was determined from the resultant wavefront distortion of a 7-reflection optical relay system using phase-shifting interferometer data. Finite element analysis results indicating how resultant wavefront error from a collection of slightly deformed mirrors can be cancelled are presented and discussed.