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By analyzing the Poisson equation describing the static behavior of membrane and bimorph deformable mirrors and biharmonic equation describing the continuous facesheet mirror with push-pull actuators, we found that to achieve a high quality correction of low-order aberrations these mirrors should have sufficient number of actuators positioned outside the correction aperture. In particular, any deformable mirror described by the Poisson equation requires at least two actuators to be placed outside the working aperture per period of the azimuthal aberration of the highest expected order. Any deformable mirror described by the biharmonic equation, such as a continuous facesheet mirror with push-pull actuators, requires at least four actuators to be placed outside the working aperture per period of the azimuthal aberration of the highest expected order, and these actuators should not be positioned on a single circle.

Abstract: The paper is devoted to designing an automated algorithm for modeling the function domain of spline curves that is needed for developing tools for R-functional and voxel-functional construction of geometric models of complex shape. Mathematical approaches to solving this problem are discussed. The parametric dependence of a spline on the function domain is investigated. An automated algorithm for constructing the function domain of a spline curve based on a linear combination of the basis Bernstein polynomials is described. [ABSTRACT FROM AUTHOR]