Author: Danilo Andrade de Jesus, Wrocław University of Technology

Recently a method that simplifies calculation of geometrical point spread function has been proposed for circularly symmetric systems (Gagnon et al., App. Opt. 2014). The method is based on Chebyshev polynomials and it is realized with the help of Matlab Chebfun toolbox – a new tool for computing with functions developed at Oxford University. An extension of this method to 2D non-circularly symmetric systems was proposed by Danilo A. Jesus and D. Robert Iskander and currently submitted to ARVO 2015 Meeting in Denver, CO. In this method, surfaces, rays, and refractive indices are all represented in functional forms being approximated by Chebyshev polynomials. Although not all properties of 1D Chebyshev polynomials are present in their 2D representations, there are many benefits of using them including the ease of surface representation, manipulation of multiple surface designs, and the ability to represent gradient index (GRIN) type lenses.

Such a representation appears to be an ideal tool for performing ray tracing in anatomically correct eye models such as the one proposed by Liou and Brennan (Figure 1). It was established that computational complexity (assessed as the CPU time) increases with the addition of each surface in a linear form indicating that the method has a great computational potential to be used for more intricate eye models in which, for example, the crystalline lens is described with multiple surfaces. Performing ray tracing with Chebfun toolbox substantially simplifies calculations as it is based on object oriented programming with handle functions. Realization of the ray tracing technique in Matlab is particularly attractive among researchers for whom other ray tracing optical engineering packages such as those employed in Zemax are more cumbersome and sometimes difficult to acquire. 

 Figure 1: An example of chebfun-based ray tracing using the anatomically correct eye model of Liou and Brenner (JOSA A, 1997) where all the distances corresponds to millimeters.