3D phase space ray tracing for the illumination optics industry. 

The department of Mathematics and Computer Science at TU/e is looking for a PhD candidate who is willing to take up the challenge of conducting research in close collaboration with industry. In particular with Signify, world's leader in lighting; see https://www.signify.com.
You will spend part of your time at Signify.

Background
In the lighting industry a revolution took place. Traditional light sources like incandescent, halogen and gas discharge are replaced by light emitting device (LED) technology. This new source technology allows the use of more sophisticated optical solutions. The purpose of this research project is to develop new methodologies to compute optics that will further improve the properties of LED lighting, such as less glare, improved efficiency and new light effects.

Computational Illumination Optics at TU/e
You will be a member of the Computational Illumination Optics group at TU/e. Our research is focused on the development of simulation tools and design methods for advanced optical systems. We work on three different tracks: (i) inverse methods, (ii) improved simulation tools and (iii) optimization methods. This PhD project belongs to the second track. At this moment the group has eight PhD positions.

The Computational Illumination Optics group is part of the Centre for Analysis, Scientific computing and Applications (CASA); see https://www.win.tue.nl/casa/. Its major research objective is to develop new and to improve existing mathematical (both analytical and numerical) methods for a wide range of applications in science and engineering. Extensive collaboration with researchers of the technical departments as well as with industrial partners is vital.

Project description
The standard simulation method for optical systems is ray tracing. In this method, one computes the paths of a large collection of rays, subject to reflections and/or refractions, from source to target. From the distribution of rays in target space one can compute the target distribution. Subsequently, ray tracing has to be included in an iterative procedure to determine the efficient layout of the system given the desired light output. Ray tracing is a rather slow procedure. Employing the phase space representation of the optical system, one can considerably speed up the method. In this representation, each ray intersecting an optical surface is specified by two space and two direction coordinates, thus constituting a four-dimensional phase space. In a previous project we developed phase space ray tracing for two-dimensional (one space and one direction coordinate) model systems, which proved to be much faster than classic ray tracing; see https://www.win.tue.nl/~martijna/Optics/ for an impression.

You have to extend the previously developed phase space ray tracing method to more realistic three-dimensional optical systems, characterized by a four-dimensional phase space, include Fresnel reflections, and parallelize the simulation code on a GPU. Finally, the code developed should be used for design optimization.

The project requires good programming skills and offers the possibility for cutting-edge research at the interface of scientific computing and computational illumination optics. Furthermore, it is anticipated that the knowledge and software generated in this project will have a profound impact on optical design within Signify.

We are looking for a talented, enthusiastic PhD candidate who meets the following requirements:

• A MSc in Mathematics, Computer Science, Physics or closely related field with above average results;
• A research-oriented attitude;
• Ability to work in a team and interested in collaborating with industrial partners;

You perform scientific research in the described domain;

• Present work at international conferences;
• Publish in scientific journals;
• Assist staff in teaching undergraduate and graduate courses;
• Prepare and defend your PhD thesis.

• A meaningful job in a dynamic and ambitious university with the possibility to present your work at international conferences.
• A full-time employment for four years, with an intermediate evaluation (go/no-go) after nine months.
• To develop your teaching skills, you will spend 10% of your employment on teaching tasks.
• To support you during your PhD and to prepare you for the rest of your career, you will make a Training and Supervision plan and you will have free access to a personal development program for PhD students (PROOF program).
• A gross monthly salary and benefits (such as a pension scheme, pregnancy and maternity leave, partially paid parental leave) in accordance with the Collective Labor Agreement for Dutch Universities.
• Additionally, an annual holiday allowance of 8% of the yearly salary, plus a year-end allowance of 8.3% of the annual salary.
• Should you come from abroad and comply with certain conditions, you can make use of the so-called '30% facility', which permits you not to pay tax on 30% of your salary.
• A broad package of fringe benefits, including an excellent technical infrastructure, moving expenses, and savings schemes.
• Family-friendly initiatives are in place, such as an international spouse program, and excellent on-campus children day care and sports facilities.