Three PhD positions on computational illumination optics design

The 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://www.win.tue.nl/~martijna/Optics/. The following mathematical disciplines are important in our work: geometrical optics, ray tracing, (numerical) PDEs, transport theory, nonlinear optimization, Lie operators and Hamiltonian systems.

As part of the research program Optical coherence; optimal delivery and positioning (OPTIC) we focus on the computational modeling aspects and offer three PhD projects:

OPTIC1 Finite-source Monge-Ampère
For an ideal source — point source or perfect parallel beam — it is known how to directly compute the freeform surfaces that convert a given light distribution at the source into a required target distribution. In applications where a real source does not match these ideals, an iterative procedure is needed to consider the finite extent of the source. In this project we aim to directly compute optical surfaces for finite sources
OPTIC2 Multi-beam freeform
For ideal sources and light rays that follow a single path from light source to target screen, we know how to compute the required freeform surfaces (lenses or reflectors).
In this project we will develop a Monge-Ampère-based algorithm to design 3D optical systems where light beams can be split and rays may follow different paths. This is important for applications as it may lead to more compact designs
OPTIC3 Surface scattering with 3D Monge-Ampère
For ideal sources and ideal optical surfaces (perfect lens or perfect mirror) we can solve the Monge-Ampère equation to find the shapes of the surfaces. Scattering elements send light rays in multiple directions and can be used to reduce glare in optical systems. However, current design methods that include scattering use a slow iterative process.
In this project we will develop fast direct design methods for 3D optical systems with scattering surfaces