Clear aperture design criterion for deformable membrane mirror control

• Published in: 2006 IEEE Aerospace Conference p. 15 pp.
• Main Authors: Shepherd, M.J., Cobb, R.G., Baker, W.P.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 2006
• Subjects: Apertures; Atmospheric waves; Biomembranes; Mirrors; Nonlinear distortion; Polynomials; Resists; Shape control; Surface waves; Vibration control
• ISBN: 9780780395459; 078039545X
• ISSN: 1095-323X; 2996-2358
• DOI: 10.1109/AERO.2006.1655889

Active lightweight continuous mirrors, such as deformable membrane mirrors, provide the capability to form conjugate surfaces effective for removing atmospheric distortions of an incoming wavefront. For a circular aperture, the two-dimensional surface corrections are most often described by a truncated set of the Zernike polynomial basis functions. Simultaneously, there exists a requirement in active lightweight membrane mirrors to resist the effects of vibration disturbances which could build at resonance and adversely distort the membrane surface. The spatial content of this motion is typically described by a finite set of Bessel-function based vibration modes below a frequency of interest. To control the vibration modes, it is advantageous to actuate these same shapes for the purpose of attenuation. Perfect surface control would therefore have authority to command both Zernike and vibration mode shapes. This paper provides design criteria for establishing achievable surface deflection performance inside of a "clear aperture" region for a preselected number of desired Zernike polynomials, and a number of retained quasi-statically-actuated vibration mode shapes. The methodology, coined the "modal transformation method" by the authors, is contrasted with a direct projection method in an applied example performed on a MSC.Nastran nonlinear finite element model of a piezoelectric-actuated deformable membrane mirror