Long, Craig SLoveday, Philip WForbes, A2012-11-142012-11-142012-04Long, CS, Loveday,PW, Forbes. 2012. Zernike polynomial based Rayleigh-Ritz model of a piezoelectric unimorph deformable mirror. International Journal of Mechanics and Materials in Design, vol 8(3), pp 237-2451569-1713http://link.springer.com/article/10.1007/s10999-012-9188-4/fulltext.html?nullhttp://hdl.handle.net/10204/6319Copyright: 2012 Springer. This is the post-print version of the work. The definitive version is published in the International Journal of Mechanics and Materials in Design, vol.8(3), pp 237-245Piezoelectric bimorph- or unimorph-type deformable mirrors are commonly used in adaptive optics to correct for time-dependent phase aberrations. In the optics community, the surface deformations that deformable mirrors are required to achieve, are routinely and conveniently described using Zernike polynomials. A Rayleigh-Ritz structural model, which uses Zernike polynomials directly to describe the displacements, is proposed in this paper. The proposed formulation produces a numerically inexpensive model that predicts deformations with remarkable accuracy. Since design variables, such as electrode layout, material properties, and mirror dimensions, are represented analytically, the model is well suited to optimization or sensitivity analysis applications. Furthermore, since the numerical implementation is very efficient, it could be employed in closed-loop control applications. Results achieved with the proposed model compare well with results from a traditional finite element analysis as well as experimental results of a representative design.enDeformable mirrorPiezoelectric unimorphRayleigh-RitzZernike polynomialArticleLong, C. S., Loveday, P. W., & Forbes, A. (2012). Zernike polynomial based Rayleigh-Ritz model of a piezoelectric unimorph deformable mirror. http://hdl.handle.net/10204/6319Long, Craig S, Philip W Loveday, and A Forbes "Zernike polynomial based Rayleigh-Ritz model of a piezoelectric unimorph deformable mirror." (2012) http://hdl.handle.net/10204/6319Long CS, Loveday PW, Forbes A. Zernike polynomial based Rayleigh-Ritz model of a piezoelectric unimorph deformable mirror. 2012; http://hdl.handle.net/10204/6319.TY - Article AU - Long, Craig S AU - Loveday, Philip W AU - Forbes, A AB - Piezoelectric bimorph- or unimorph-type deformable mirrors are commonly used in adaptive optics to correct for time-dependent phase aberrations. In the optics community, the surface deformations that deformable mirrors are required to achieve, are routinely and conveniently described using Zernike polynomials. A Rayleigh-Ritz structural model, which uses Zernike polynomials directly to describe the displacements, is proposed in this paper. The proposed formulation produces a numerically inexpensive model that predicts deformations with remarkable accuracy. Since design variables, such as electrode layout, material properties, and mirror dimensions, are represented analytically, the model is well suited to optimization or sensitivity analysis applications. Furthermore, since the numerical implementation is very efficient, it could be employed in closed-loop control applications. Results achieved with the proposed model compare well with results from a traditional finite element analysis as well as experimental results of a representative design. DA - 2012-04 DB - ResearchSpace DP - CSIR KW - Deformable mirror KW - Piezoelectric unimorph KW - Rayleigh-Ritz KW - Zernike polynomial LK - https://researchspace.csir.co.za PY - 2012 SM - 1569-1713 T1 - Zernike polynomial based Rayleigh-Ritz model of a piezoelectric unimorph deformable mirror TI - Zernike polynomial based Rayleigh-Ritz model of a piezoelectric unimorph deformable mirror UR - http://hdl.handle.net/10204/6319 ER -