Light by Design
LED is the new standard in lighting. However, lighting devices based on LED require an optical system to create a desired light output. In the program ’Light by Design’ we investigate advanced physical models describing the interaction of light with optical systems and develop efficient numerical simulation methods for the design of these systems. The ultimate goal is to develop advanced simulation tools that can be used for virtual prototyping.
The ILI researchers who are participating at the Light by Design program are mainly part of the Computational Illumination Optics group of the department of M&Cs. It is one of the few mathematics groups worldwide working on optical design problems from illumination optics. It has 3 research tracks: freeform design, improved direct methods and imaging optics.
For more information, please visit the website of the research group Computational Illumination Optics at TU/e
TRACK 1: FREEFORM DESIGN
The goal in freeform design is to compute the shapes of optical surfaces (reflector/lens) that convert a given source distribution, typically LED, into a desired target distribution. The surfaces are referred to as freeform since they do not have any symmetries. The governing equation for these problems is a fully nonlinear PDE of Monge-Ampère type.
TRACK 2: IMPROVED DIRECT METHODS
Direct methods, such as ray tracing, compute the target distribution given the source distribution and the layout of the optical system. These methods must be embedded in an iterative procedure to compute the final design and are based on Monte-Carlo simulation. They are known to have slow convergence. Using the Hamiltonian structure of the system and advanced numerical schemes for PDEs, we are working on more efficient and accurate methods.
TRACK 3: IMAGING OPTICS
The third research track is imaging, where the goal is to form a very precise image of an object, minimizing aberrations. Light propagation is described in terms of Lie transformations.
Meet some of our researchers
An ADER discontinuous Galerkin method on moving meshes for Liouville's equation of geometrical opticsJournal of Computational Physics (2023)
Modelling surface light scattering for inverse two-dimensional reflector designJournal of the European Optical Society: Rapid Publications (2023)
Alternative computation of the Seidel aberration coefficients using the Lie algebraic methodJournal of the Optical Society of America A, Optics, Image Science and Vision (2022)
Fresnel reflections in inverse freeform lens designJournal of the Optical Society of America A, Optics, Image Science and Vision (2022)
Design of a freeform two-reflector system to collimate and shape a point source distributionOptics Express (2021)
A Monge-Ampère Least-Squares Solver for the Design of a Freeform LensEuropean Conference on Numerical Mathematics and Advanced Applications (2021)
Numerical Methods for the Hyperbolic Monge-Ampere Equation Based on the Method of CharacteristicsarXiv (2021)