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 nonsymmetric 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 xy polynomial representations for all the surfaces, and the iterative algorithm formulated for solving the above said PDE has shown very fast convergence.  
International

Si 
Congress

Illumination Optics IV. Optical Systems Design 2015 

960 
Place


Reviewers

Si 
ISBN/ISSN

9781628418187 


Start Date

07/09/2015 
End Date

08/09/2015 
From page

1 
To page

12 

Optical Systems Design 2015. Proc. SPIE 9629. 96290C 