Modal noninteracting controls for deformable mirrors

In this paper, the analytical design of a feedback control system for achieving noninteraction between a finite number of modes of deformable mirrors corresponding to an arbitrary orthonormal basis for the solution space is considered. In this system, each mode can be manipulated independently without affecting the remaining modes. Particular attention is focused on circular deformable mirrors whose modal representation is expressed in terms of Zernike polynomials. Thus, various types of aberrations such as coma, defocus, astigmatism, and distortion can be manipulated independently. Specific results are obtained for a micromachined circular mirror with electrostatic actuators based on a membrane model. Only static noninteracting feedback control system is considered. The paper concludes with a discussion of the physical Implementation of the proposed modal noninteracting control system