Are you eager to use your mathematical skills to model and design optical systems for sustainable high-tech devices for billions of people? Do you like to develop and analyze numerical methods for partial differential equations?
InformationThe Computational Illumination Optics group is one of the few mathematics groups worldwide working on mathematical models of optical systems. They develop and analyze numerical methods to solve the resulting differential equations. The team has a healthy portfolio of PhD positions and close collaborations with industrial partners. It consists of four full FTEs at Eindhoven University of Technology and one part-time professor.
The group has three research tracks:
freeform design,
imaging optics and
improved direct methods; for more details see
https://martijna.win.tue.nl/Optics/.
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The goal in freeform design is to compute the shapes of optical surfaces (reflector/lens) that convert a given source distribution, typically LED, into a desired target distribution. The surfaces are referred to as freeform since they do not have any symmetries. The governing equation for these problems is a nonlinear second-order partial differential equation (PDE) of Monge-Ampère type. The PDE is elliptic if we choose a positive right-hand side, it is hyperbolic for a negative one. The field of hyperbolic Monge-Ampère is relatively new. The elliptic cousin of the Monge-Ampère equation is well studied but on the hyperbolic case there are less results and hardly any publications on numerical methods to solve these problems. The elliptic PDE leads to convex or concave solutions, the hyperbolic one to saddle-shaped surfaces.
To design smooth periodic lens arrays, we need to combine concave, convex and saddle-shaped solutions. The research project aims to find solutions to the hyperbolic Monge-Ampère equation and to combine solutions into periodic surfaces.