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.
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.
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.
In 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.
As a PhD student your tasks are the following:
We are looking for talented, enthusiastic PhD candidates who meet the following requirements:
A meaningful job in a dynamic and ambitious university, in an interdisciplinary setting and within an international network. You will work on a beautiful, green campus within walking distance of the central train stationm. In addition, we offer you:
Eindhoven University of Technology is an internationally top-ranking university in the Netherlands that combines scientific curiosity with a hands-on attitude. Our spirit of collaboration translates into an open culture and a top-five position in collaborating with advanced industries. Fundamental knowledge enables us to design solutions for the highly complex problems of today and tomorrow.
Do you recognize yourself in this profile and would you like to know more? Please contact
dr.ir. Jan ten Thije Boonkkamp, j.h.m.tenthijeboonkkamp[at]tue.nl.
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