Micromirror Arrays for Adaptive Optics


Deformable mirrors (DM) shape the wavefront of an optical beam in adaptive-optics (AO) systems. The ability to manipulate wavefront phase quickly allows for real-time correction of aberrated wavefronts. We investigate the design of a micromachined, segmented, highstroke deformable-mirror array for AO. 

To achieve large mirror stroke, polysilicon-nickel bimorph flexures are designed to quiescently elevate surface-micromachined mirror platforms roughly 20 µm above underlying electrodes as a result of tuned residual stresses in the bimorph materials. We control stress in the polysilicon thin films by annealing an amorphous-silicon film surrounded by phosphosilicate (PSG) thin films at various temperatures and times. Varying the anneal conditions allows us to tune stress in electrically conductive polysilicon films from -40 to +215 MPa. We tune the residual stress in the nickel thin films by annealing the films and then cooling them rapidly. At the elevated temperature, the stress in the nickel relaxes from a compressive value towards a zero value. Rapidly cooling the wafer locks in the near-zero stress at the elevated temperature, which results in a tensile stress at room temperature because the coefficient-of-thermal-expansion of nickel is much greater than that of silicon. With this technique, we are able to tune residual stress in the nickel from 0.11 to 2.18 GPa. We assemble ultra-flat, single-crystal-silicon mirror segments onto the surface micromachined mirror platforms using a fluidic self-assembly technique. In collaboration with Uthara Srinivasan, the BSAC student that developed the assembly technique, we assembled 464 µm-diameter hexagonal mirror segments onto the mirror platforms. The mirror segments have average surface errors of 5.8 nm rms without an optical coating, and 2.3 nm rms with a gold optical coating that uses chrome as an adhesion layer. We develop analytical and nonlinear models to describe the bimorph-flexure shape after release. For normalized deflections (deflection at the tip/beam length) of 10%, the differences in beam deflection between the analytical and nonlinear models are less than 1%. To determine when to use the nonlinear models, we derive design curves that show analytical-modeling errors for a given normalized deflection of a fixed–free cantilever. The analytical and nonlinear models match experimental data very well, to within less than 1% (best case) to 10% (worst case). 

To calculate mirror-segment resonant frequency, we derive an equation to describe the bimorph-flexure spring constant in the vertical direction. The vertical-spring constant we calculate comes to within 17% of the experimentally measured value kexpt = 2.32 N/m. To optimize DM performance, we derive an “optimal gap” that minimizes the drive voltage required to displace a mirror to the maximum displacement at a specified frequency. The gap should be set to four times the desired maximum displacement. At the maximum displacement, the natural frequency f0 is reduced to f00 = 1/p3 f0, where f00 is the spring-softened resonant frequency of the mirror segments. Our mirrors have a natural frequency of f0=2.1 kHz and displace 5 µm in piston and tip/tilt motions with a 60 V drive. They do not meet the specifications set forth by the vision-science and astronomy applications they are intended for, however. To determine if our mirrors can meet the vision-science and astronomy applications with a redesign, we derive a DM-performance scaling law. 

For some AO applications, deformable mirrors must have hundreds to thousands of mirror segments. The problem of connecting individual pins to each actuator becomes insurmountable and dictates the need for integrated address electronics. As a result of our study, we introduce a path to integration using CMOS address electronics based on the properties of silicon-germanium-alloy films deposited by low-pressure-chemical-vapor deposition (LPCVD). The mirror platforms could be fabricated directly on top of CMOS circuitry with polycrystalline silicon/germanium films substituted for polysilicon films.

Publication date: 
May 31, 2002
Publication type: 
Ph.D. Dissertation
Helmbrecht M.A., Srinivasan U., Rembe C., Howe R.T., Muller R.S. (2001) Micromirrors for Adaptive-Optics Arrays. In: Obermeier E. (eds) Transducers ’01 Eurosensors XV. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59497-7_297

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