27 October 2003 Response of paraboloidal surfaces to linear thermal gradients
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This paper presents a theoretical (closed-form) solution for the z-axis surface deformations of a linear, homogeneous, unconstrained and isotropic paraboloidal surface subjected to a 3-dimensional linear thermal temperature gradient and soak temperature change. Previously, an equation for the component of the nodal surface displacement in the z direction has been published. Attaching the z-axis component of the nodal surface displacement to the original surface does not accurately describe the final surface. This work extends the previous analysis and presents a polynomial equation for the corrected surface deformation along the z-axis, as well as, the coefficients for the standard Zernike polynomial describing the corrected surface deformation. Also included is a discussion about z-axis temperature gradients across the paraboloidal surface and how to calculate an equivalent soak temperature change.
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Rex M. Kremer, "Response of paraboloidal surfaces to linear thermal gradients", Proc. SPIE 5176, Optomechanics 2003, (27 October 2003); doi: 10.1117/12.510370; https://doi.org/10.1117/12.510370

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