Design of freeform aplanatic systems

B. Narasimhan; P. Benitez; Juan C. Miñano; Julio Chaves; D. Grabovickic; Milena Nikolic; J. Infante

doi:10.1117/12.2190882

23 September 2015 Design of freeform aplanatic systems

B. Narasimhan, P. Benitez, Juan C. Miñano, Julio Chaves, D. Grabovickic, Milena Nikolic, J. Infante

Proceedings Volume 9629, Optical Systems Design 2015: Illumination Optics IV; 96290C (2015) https://doi.org/10.1117/12.2190882
Event: SPIE Optical Systems Design, 2015, Jena, Germany

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.

Citation Download Citation

B. Narasimhan, P. Benitez, Juan C. Miñano, Julio Chaves, D. Grabovickic, Milena Nikolic, and J. Infante "Design of freeform aplanatic systems", Proc. SPIE 9629, Optical Systems Design 2015: Illumination Optics IV, 96290C (23 September 2015); https://doi.org/10.1117/12.2190882

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KEYWORDS

Artificial intelligence

Imaging systems

Monochromatic aberrations

Palladium

Partial differential equations

Freeform optics

Reflection

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