PhD position robust multi-criteria optical design under uncertainty

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.

Information
Uncertainties 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.

Requirements

We are looking for talented enthusiastic PhD candidates who meet the following requirements:

• A master’s degree in (applied) mathematics
• Experience with mathematical modeling, optimization techniques and scientific computing
• Experience with programming (C, C++, Python, Matlab or alike)
• Creative pro-active team player with good analytical skills
• A research-oriented attitude
• Ability to work in an interdisciplinary team and interested in collaborating with industrial partners
• Motivated to develop your teaching skills and coach students
• Fluent in spoken and written English (C1 level)

Contract terms

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 station.

In addition, we offer you:

• Full-time employment for four years, with an intermediate assessment after nine months. You will spend a minimum of 10% of your four-year employment on teaching tasks, with a maximum of 15% per year of your employment.
• Salary and benefits (such as a pension scheme, paid pregnancy and maternity leave, partially paid parental leave) in accordance with the Collective Labour Agreement for Dutch Universities , scale P (min. € 3,204 - max. € 4,051 gross base salary per month (full-time)).
• In addition to your base salary, you will receive an 8% holiday allowance and an 8.3% year-end bonus, both calculated based on your annual gross base salary.
• Generous leave options: a standard 29 days (based on a 38 hour working week) per year that you can increase to 41 days by working two hours more per week (flexible working hours). This is prorated if you work part-time.
• As a TU/e employee, you participate in the ABP pension scheme, providing retirement pension and pension benefits for surviving dependents and occupational disability. TU/e pays 70% of the pension premium, while employees contribute the remaining 30%.
• High-quality training programs and other support to grow into a self-aware, autonomous scientific researcher. At TU/e we challenge you to take charge of your own learning process .
• An excellent technical infrastructure, and on-campus children's day care.
• Unlimited access to the modern on‑campus TU/e Student Sports Center at an exceptionally affordable rate.
• We support your wellbeing with free 24/7 access to OpenUp, providing you and your family with mental health support, expert guidance, and online training.
• An allowance for commuting, working from home and internet costs.
• A Staff Immigration Team and a tax compensation scheme (the Expat Scheme ) for international candidates.

On our website you can discover even more information about our conditions of employment . Build on your career at TU/e!