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Please use this identifier to cite or link to this item: http://hdl.handle.net/10204/3941

Title: Modelling and optimization of a deformable mirror for laser beam control
Authors: Loveday, PW
Long, CS
Forbes, A
Land, K
Keywords: Laser beam control
Deformable mirror
Unimorph
Intra-cavity adaptive mirror
Piezoelectric unimorph
Zernike polynomials
Numerical modelling
Rayleigh-Ritz model
Finite element model
SACAM 2008
Issue Date: Mar-2008
Publisher: South African Conference on Computational and Applied Mechanics
Citation: Loveday, PW, Long, CS et al. Modelling and optimization of a deformable mirror for laser beam control. 6th South African Conference on Computational and Applied Mechanics (SACAM 2008), Cape Town, 26-28 March 2008, pp 219-228
Abstract: An intra-cavity adaptive mirror is required to compensate for time-dependent phase aberrations to the laser beam, such as those caused by thermal lensing. A piezoelectric unimorph design can provide a small, low-cost deformable mirror for this application. The unimorph consists of a metallic disc, with a mirror finish, bonded to a piezoelectric disc. In adaptive optics the deformations that the mirror is required to perform are described by the Zernike polynomials, which are a complete set of orthogonal functions. The challenge is to design a device that can represent selected polynomials as accurately as possible with specified amplitude. Numerical modelling is required to predict the deformation shapes that can be achieved by a unimorph mirror with a particular electrode pattern. The results from a Rayleigh-Ritz model and a finite element model employing elements including rotational degrees of freedom were compared to results from a conventional finite element model. The Rayleigh-Ritz model, which used 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. While this method requires some effort to implement and is not very flexible, it does provide insight into the operation of the deformable mirror and can be used to optimize the design in an elegant manner. The finite element model including rotational degrees of freedom is more efficient than the conventional finite element model but retains the flexibility of this model. This method was applied to model a prototype deformable mirror and produced good agreement with experimental results.
Description: 6th South African Conference on Computational and Applied Mechanics (SACAM 2008), Cape Town, 26-28 March 2008
URI: http://hdl.handle.net/10204/3941
Appears in Collections:Laser physics and technology
Sensor science and technology
General science, engineering & technology

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