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). Within CASA the Computational Illumination Optics group, https://www.win.tue.nl/~martijna/Optics/
, is working on design methodologies for non-imaging optics and on improved simulation tools.Background
Illumination optics plays an important role in modern society. Products like mobile phones, lamps, car headlights, road lighting and even satellites all utilize illumination optics. A good optical design determines, for example, the energy efficiency of illumination devices, the minimization of light pollution or the sensitivity of sensors in satellites.
The design of novel, sophisticated optical systems requires advances in the mathematical description and numerical simulation methods for these systems. The optics applied in illumination is non-imaging, in contrast to for example a camera lens which is imaging. In non-imaging optics we study the transfer of light from a source to a target. The key problem is to design optical systems that convert a given source energy distribution into a desired target distribution.Project description
Freeform optics, a branch of geometrical optics, is concerned with the design of optical surfaces, either reflectors or lenses, that convert a given source light distribution into a desired target distribution. An example is a single reflector that transforms the emittance of an LED source into an intensity distribution in the far field, as used for street lighting.
The governing laws are the principles of geometrical optics (law of reflection/refraction) and conservation of energy. Geometrical optics gives the optical map from source to target, and combined with energy conservation, this gives rise to the so-called Monge-Ampère equation, which is a second order, nonlinear partial differential equation.Figure 1. On the left a reflector that transforms the energy distribution of a frog to a prince. In the second picture we show the source distribution, in the third the optical map and in the last figure the results of a verification based on raytracing: the system gives indeed the prince.nderschriftIn recent years, we have developed tools to solve the Monge-Ampère equation for many optical systems. So, given the source and target energy distributions, we can calculate the optical geometry immediately, see Figure 1 where we have computed the surface of a reflector that transforms a frog into a prince. These inverse tools have some limitations, e.g., the methods assume an infinitesimal source dimension (point source). However, in reality the sources have a finite size. In addition, effects like absorption, scattering and Fresnel reflections are not considered in the inverse design methodology.
To overcome these shortcomings of inverse methods, we would like to apply in this project techniques from machine learning and artificial intelligence. As a first approach we imagine the following: Using and extending the available tool chain, it is possible to generate a large set of optical geometries and calculate the corresponding light distributions, which include effects from finite source, absorption etc. With this set we train a neural network to find new optical geometries for desired light distributions.Tasks
As a PhD student your tasks are the following:
- Perform scientific research in the described domain.
- Present results at international conferences.
- Publish results in scientific journals.
- Participate in activities of the group and the department.
- Assist SC-staff in teaching undergraduate and graduate courses.