PhD Project Freeform Light Guides for Homogeneous Illumination

Applicants are invited to apply for a PhD scholarship in computer science at Eindhoven University of Technology. There is no application deadline for this position.

PhD project Scientific Computing / Illuminations Optics Freeform light guides for homogeneous illumination. The Department of Mathematics and Computer Science of Eindhoven University of Technology has a vacancy for a PhD-student in its Centre for Analysis, Scientific computing and Applications (CASA).

The Department of Mathematics and Computer Science of Eindhoven University of Technologyhas a vacancy for a PhD-student in its Centre for Analysis, Scientific computingand Applications (CASA). CASA comprises the chairs Scientific Computing (SC) andApplied Analysis (TA). Its major research objective is to develop new and to improveexisting mathematical (both analytical and numerical) methods for a wide range of applicationsin science and engineering.

Illumination optics plays an important role in modern society. Products like mobilephones, lamps, car headlights, road lighting and even satellites all utilize illuminationoptics. A good optical design determines, for example, the energy efficiency of illuminationdevices, the minimization of light pollution or the sensitivity of sensors in satellites.The design of novel, sophisticated optical systems requires advances in the mathematicaldescription and numerical simulation methods for these systems.

The optics applied in illumination is nonimaging, in contrast to for example a cameralens which is imaging. In nonimaging optics we study the transfer of light from a sourceto a target. The key problem is to design optical systems that convert a given sourceintensity into a desired target intensity.

A modern trend in illumination optics is to use scattering elements in addition to commonlyused refractive (lenses) or reflective (mirrors) optical components. For example,in LED lighting systems scattering surfaces are used to hide too bright light sources andto redistribute the light. The physical description of scattering surfaces, on the one hand,and refractive/reflective surfaces, on the other hand, is quite different.

To bridge the gap between the corresponding subdisciplines scattering and geometricaloptics, an NWO/TTW perspectief project was proposed by UT, TU Delft and TU/e,called Free-Form Scattering Optics. This proposal is supported by leading parties in the illuminationindustry: TNO, ASML, Signify, Lumileds, Demcon and Schott. In this project12 PhD students work on different topics related to a) the fundamentals of scattering, b)the fundamentals of free-form optics, c) homogenization and diffusion and d) control thedirection of light by interference.

This PhD project relates to the work package c) homogenization and diffusion.

An alternative description of the propagation of light in an optical system is based on thephase space representation of the system. In this representation, each ray is defined byone or two space and direction coordinates, thus constituting a two or four dimensionalphase space. The propagation of one ray can be described by the movement of a point inphase space, and the propagation of an entire beam can be interpreted as a 'flow' in phasespace. This flow is governed by Liouville's equation, which is a first order hyperbolicconservation law. Sophisticated solution methods for the two-dimensional equation exist.

The purpose of this research project is to extend the solution methods to the fourdimensionalLiouville equation and to apply these methods to wave guides. More specifically,the Liouville solvers should be combined with methods from optimal control todesign wave guides that create a homogeneous light output.

As a PhD student your tasks are the following:

We are looking for talented, enthusiastic PhD candidates who meet the following requirements:

The application should consist of the following parts:


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