Long, Craig SLoveday, Philip WForbes, ALand, K2011-11-302011-11-302010-01Long, CS, Loveday, PW, Forbes, A and Land, K. 2010. Numerical modelling of a thin deformable mirror for laser beam control. Seventh South African Conference on Computational and Applied Mechanics (SACAM10), University of Pretoria, Pretoria, South Africa, 10-13 January 2010http://hdl.handle.net/10204/5345Seventh South African Conference on Computational and Applied Mechanics (SACAM10), University of Pretoria, Pretoria, South Africa, 10-13 January 2010For intra-cavity laser beam control, a small, low-cost deformable mirror is required. This mirror can be used to correct for time- dependent phase aberrations to the laser beam, such as those caused by thermal expansion of materials. A piezoelectric unimorph design is suitable for this application. The proposed unimorph consists of a copper disc with mirror finish, bonded to a piezoelectric disc. The deformations that the mirror is required to perform are routinely (at least in optical applications) described using Zernike polynomials, which are a complete set of orthogonal functions defined on a unit disc. The challenge is to design a device that can represent selected polynomials as accurately as possible with a specified amplitude. To assist in the design process, numerical modelling is required to predict the deformation shapes that can be achieved by a unimorph mirror with a particular electrode pattern. In this paper a previously proposed axisymmetric Rayleigh-Ritz formulation, is extended to account for non-axisymmetric voltage distributions, and therefore non-axisymmetric displacements. The Rayleigh-Ritz model, which uses the Zernike polynomials directly to describe the displacements, produced a small model (stiffness matrix dimension equal to the number of polynomials used) that predicts the deformations of the piezoelectric mirror with remarkable accuracy. The results using this Rayleigh-Ritz formulation are compared to results from a traditional finite element analysis using a commercial finite element package. Both numerical models were applied to model a prototype deformable mirror and produced good agreement with experimental results.enDeformable mirrorLaser beam controlPiezoelectric unimorphApplied mechanicsLaser beamsSACAM 2010Conference PresentationLong, C. S., Loveday, P. W., Forbes, A., & Land, K. (2010). Numerical modelling of a thin deformable mirror for laser beam control. SACAM 2010. http://hdl.handle.net/10204/5345Long, Craig S, Philip W Loveday, A Forbes, and K Land. "Numerical modelling of a thin deformable mirror for laser beam control." (2010): http://hdl.handle.net/10204/5345Long CS, Loveday PW, Forbes A, Land K, Numerical modelling of a thin deformable mirror for laser beam control; SACAM 2010; 2010. http://hdl.handle.net/10204/5345 .TY - Conference Presentation AU - Long, Craig S AU - Loveday, Philip W AU - Forbes, A AU - Land, K AB - For intra-cavity laser beam control, a small, low-cost deformable mirror is required. This mirror can be used to correct for time- dependent phase aberrations to the laser beam, such as those caused by thermal expansion of materials. A piezoelectric unimorph design is suitable for this application. The proposed unimorph consists of a copper disc with mirror finish, bonded to a piezoelectric disc. The deformations that the mirror is required to perform are routinely (at least in optical applications) described using Zernike polynomials, which are a complete set of orthogonal functions defined on a unit disc. The challenge is to design a device that can represent selected polynomials as accurately as possible with a specified amplitude. To assist in the design process, numerical modelling is required to predict the deformation shapes that can be achieved by a unimorph mirror with a particular electrode pattern. In this paper a previously proposed axisymmetric Rayleigh-Ritz formulation, is extended to account for non-axisymmetric voltage distributions, and therefore non-axisymmetric displacements. The Rayleigh-Ritz model, which uses the Zernike polynomials directly to describe the displacements, produced a small model (stiffness matrix dimension equal to the number of polynomials used) that predicts the deformations of the piezoelectric mirror with remarkable accuracy. The results using this Rayleigh-Ritz formulation are compared to results from a traditional finite element analysis using a commercial finite element package. Both numerical models were applied to model a prototype deformable mirror and produced good agreement with experimental results. DA - 2010-01 DB - ResearchSpace DP - CSIR KW - Deformable mirror KW - Laser beam control KW - Piezoelectric unimorph KW - Applied mechanics KW - Laser beams KW - SACAM 2010 LK - https://researchspace.csir.co.za PY - 2010 T1 - Numerical modelling of a thin deformable mirror for laser beam control TI - Numerical modelling of a thin deformable mirror for laser beam control UR - http://hdl.handle.net/10204/5345 ER -