PhD position robust multi-criteria optical design under uncertainty

Introduction

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.

Job Description

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.

Job Requirements

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

• A masters 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)

Conditions of Employment

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 addition we offer you:

• Full-time employment for five years with an intermediate evaluation (go/no-go) after nine months. You will spend 25% of your five-year employment on teaching tasks (PhD-TA).
• 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. 3059 - max. 3881).
• A year-end bonus of 8.3% and annual vacation pay of 8%.
• 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 on-campus childrens day care and sports facilities.
• An allowance for commuting working from home and internet costs.
• A Staff Immigration Team and a tax compensation scheme (the 30% facility) for international candidates.

About us

Eindhoven University of Technology is a leading international university within the Brainport region where scientific curiosity meets a hands-on mindset. We work in an open and collaborative way with high-tech industries to tackle complex societal challenges. Our responsible and respectful approach ensures impact today and in the future. TU/e is home to over 13000 students and more than 7000 staff forming a diverse and vibrant academic community.

With over 110 (assistant associate and full) professors almost 300 PhD and EngD students about 1500 Bachelor students and 1000 Master students the Department of Mathematics and Computer Science (M&CS) is the largest department of the TU/e. By performing top-level fundamental and applied research and maintaining strong ties with industry M&CS aims to contribute to science and innovation in and beyond the region.

Information

Do you recognize yourself in this profile and would you like to know more Please contact the hiring manager Dr. Lisa Kusch .

Visit our website for more information about the application process or the conditions of employment. You can also contact HR services .

Curious to hear more about what its like as a PhD candidate at TU/e Please view the video.

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Application

We invite you to submit a complete application by using the apply button. The application should include a:

• Cover letter in which you describe your motivation and qualifications for the position.
• Curriculum vitae including the contact information of three references. Kindly note that we may reach out to references at any stage of the recruitment process. We recommend notifying your references upon submitting your application.
• Grade lists of your bachelor and master programs.

Ensure that you submit all the requested application documents. Please note that incomplete applications may not be considered and could be rejected.

We look forward to receiving your application and will screen it as soon as possible. The vacancy will remain open until the position is filled.

Please note

• You can apply online. We will not process applications sent by email and/or post.
• A pre-employment screening (e.g. knowledge security check) can be part of the selection procedure. For more information on the knowledge security check please consult the National Knowledge Security Guidelines.
• Please do not contact us for unsolicited services.