Are you fascinated by application-oriented research in mathematics and eager to work at the interface of numerical optimization, optical design, and uncertainty quantification? In this PhD project, you will focus on developing mathematical models and numerical algorithms that systematically integrate uncertainties into the design process of optical systems. The goal is to enable novel design strategies that are robust with respect to perturbations and capable of balancing multiple competing performance criteria.
InformationUncertainties are inherent in many engineering design problems and can be translated into the underlying mathematical models. They may, for example, arise from perturbations in boundary conditions, input parameters, or geometrical properties. When neglecting the influence of uncertainties, the performance of a design solution may deteriorate significantly under these perturbations. The aim of robust design strategies is to account for these uncertainties in the design process, yielding solutions that are less sensitive to perturbations and therefore more reliable in practice. Mathematically, this leads to optimization problems with underlying random partial or ordinary differential equations that require careful modeling and analysis.
Imaging optics involves the design and optimization of imaging systems, such as cameras and telescopes, to most accurately capture and reproduce an image. Modern inverse freeform design methods compute surfaces that convert a given source light distribution to a desired target light distribution. These can be used to guide the design process for imaging systems. These methods naturally lead to challenging mathematical models, including nonlinear partial or ordinary differential equations. However, real-world optical systems are subject to manufacturing tolerances, alignment errors, and material variability. To achieve robust designs, existing inverse design methods must be extended to systematically account for these uncertainties.
The design process in imaging optics is inherently multi-objective, involving different competing performance criteria. This could be on a more systematic level the interplay of quality, cost and manufacturability but also image quality itself can be described by competing performance measures.
A further challenge is therefore to account for the effect of uncertainties on different performance criteria.
Standard formulations for single-criteria robust design do not capture these effects. This requires the development of new formulations and strategies building upon modern robust multi-criteria optimization methods based on Pareto losses.
The aim of this PhD project is to extend the existing freeform design strategies to include uncertainties using spectral methods for uncertainty quantification, such as polynomial chaos expansions, and enable the analysis of trade-off solutions under uncertainty. This allows for the integration of uncertainties in the freeform design of optical systems with a specific focus on telescopic systems. The mathematical disciplines involved are mathematical modeling, numerical analysis, and scientific computing.
Your tasks will involve:
- Conducting research on uncertainty quantification in the context of inverse freeform design,
- Developing and implementing design strategies tailored to robust multi-criteria design,
- Applying the developed methods for designing imaging systems,
- Analyzing and interpreting research data, publishing and presenting your research,
- Participating in academic activities, including seminars, workshops and teaching.
You will be part of our
Computational Illumination Optics group at TU/e, an applied mathematics group dedicated to problems in the field of optics with a lot of interesting industry-related applications (e.g., Signify, ASML and TNO). We will work together and support your research. The group belongs to
CASA (Centre for Applied Analysis, Scientific Computing and Applications), that offers a collaborative research atmosphere with a lot of possibilities for exchange and social activities.