Mathematical and computational modeling of a ferrofluid deformable mirror for high-contrast imaging

Abstract

Deformable mirrors (DMs) are an enabling and mission-critical technology in any coronagraphic instrument designed to directly image exoplanets. A new ferrofluid deformable mirror technology for high-contrast imaging is currently under development at Princeton, featuring a flexible optical surface manipulated by the local electromagnetic and global hydraulic actuation of a reservoir of ferrofluid. The ferrofluid DM is designed to prioritize high optical surface quality, high-precision/low-stroke actuation, and excellent low-spatial-frequency performance—capabilities that meet the unique demands of high-contrast coronagraphy in a space-based platform.

To this end, the ferrofluid medium continuously supports the DM face sheet, a configuration that eliminates actuator print-through (or, quilting) by decoupling the nominal surface figure from the geometry of the actuator array. The global pressure control allows independent focus actuation. In this paper we describe an analytical model for the quasi-static deformation response of the DM face sheet to both magnetic and pressure actuation. These modeling efforts serve to identify the key design parameters and quantify their contributions to the DM response, model the relationship between actuation commands and DM surface-profile response, and predict performance metrics such as achievable spatial resolution and stroke precision for specific actuator configurations. Our theoretical approach addresses the complexity of the boundary conditions associated with mechanical mounting of the facesheet, and makes use of asymptotic approximations by leveraging the three distinct length scales in the problem—namely, the low-stroke (~nm) actuation, face sheet thickness (~mm), and mirror diameter (cm). In addition to describing the theoretical treatment, we report the progress of computational multi-physics simulations which will be useful in improving the model fidelity and in drawing conclusions to improve the design.