Influence functions for a hysteretic deformable mirror with a high-density 2D array of actuators.

Area of Science:

• Optics and optical engineering
• Materials science
• Control systems engineering

Background:

• Deformable mirrors are crucial for adaptive optics systems.
• Piezoelectric materials offer precise actuation but can exhibit hysteresis.
• Distributed actuation with high-density electrode arrays presents control challenges.

Purpose of the Study:

• To develop a semi-analytical model for a hysteretic deformable mirror with distributed piezoelectric actuation.
• To establish a method for calculating actuator influence functions considering electrode arrangement.
• To determine optimal actuator pressures for achieving desired surface deformations.

Main Methods:

• A semi-analytical model was developed to simulate facesheet deformation.
• A method for calculating actuator influence functions was derived.
• Simulations were used to validate the model and analyze deformation.

Main Results:

• The model accurately describes facesheet deformation from a high-density actuator array.
• The interconnection layout of electrodes was optimized.
• Optimal actuator pressures for desired surface control were identified.

Conclusions:

• The presented modeling approach enables precise control of deformable mirrors.
• This work contributes to advancements in adaptive optics and optical system design.
• The method facilitates the optimization of piezoelectric actuator arrays for specific applications.