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Proceedings Paper

Design of freeform aplanatic systems
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Paper Abstract

Axisymmetric aplanatic systems have been used in the past for solar concentrators and condensers (Gordon et. al, 2010). It is well know that such a system must be stigmatic and satisfy the Abbe sine condition. This problem is well known (Schwarzschild, 1905) to be solvable with two aspherics when the system has rotational symmetry. However, some of those axisymmetric solutions have intrinsically shading losses when using mirrors, which can be prevented if freeform optical surfaces are used (Benitez, 2007). In this paper, we explore the design of freeform surfaces to obtain full aplanatic systems. Here we prove that a rigorous solution to the general non-symmetric problem needs at least three free form surfaces, which are solutions of a system of partial differential equations (PDE). We also present the PDEs for a three surface full aplanat. The examples considered have one plane of symmetry, where a consistent 2D solution is used as boundary condition for the 3D problem. We have used the x-y polynomial representations for all the surfaces, and the iterative algorithm formulated for solving the above said PDE has shown very fast convergence.

Paper Details

Date Published: 23 September 2015
PDF: 12 pages
Proc. SPIE 9629, Optical Systems Design 2015: Illumination Optics IV, 96290C (23 September 2015); doi: 10.1117/12.2190882
Show Author Affiliations
B. Narasimhan, Univ. Politécnica de Madrid (Spain)
P. Benitez, Univ. Politécnica de Madrid (Spain)
Light Prescriptions Innovators (United States)
Juan C. Miñano, Univ. Politécnica de Madrid (Spain)
Light Prescriptions Innovators (United States)
Julio Chaves, Light Prescriptions Innovators (United States)
D. Grabovickic, Univ. Politécnica de Madrid (Spain)
Milena Nikolic, Univ. Politécnica de Madrid (Spain)
J. Infante, Univ. Politécnica de Madrid (Spain)


Published in SPIE Proceedings Vol. 9629:
Optical Systems Design 2015: Illumination Optics IV
Tina E. Kidger; Stuart David, Editor(s)

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