PhD on Robust numerical methods for inverse optical design

Eindhoven University of Technology
April 14, 2024
Offerd Salary:€2,770
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PhD on Robust numerical methods for inverse optical design



Irène Curie Fellowship



Mathematics and Computer Science



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Job description

Does it fascinate you how mathematics can shed new light upon the world, quite literally?!! In this project, we aim to develop numerical tools to design optical surfaces that transform a source of light into a desired target. To tackle the nonlinear differential equations involved, robust discretization and linearization methods will be derived.

We will take a deep dive into how to design optical elements, such as reflectors, that can transform a given source of light into a desired target distribution. Take the examples of a parallel beam of light (source) being focused onto a single point (target) through the action of a parabolic mirror, or rays from a car headlight (source) being distributed by its optical surfaces to produce a predetermined pattern (target). Figure 1 shows an example of a general case. The equations that describe the optical elements in this scenario are equations of the Monge-Ampère type. They are fundamental due to their connection to optimal transport. However, they are notorious for the difficulties in solving them. The challenges stem from nonlinearities and boundary conditions involved, which thwart the development of efficient numerical tools that yield the optical solutions.

Aim: The goal of this project is to establish a rigorous framework which will allow us to

  • discretize the associated nonlinear differential equations in a well-posed manner and estimate the resulting errors,
  • devise a fast linear iterative scheme for solving the discrete system and prove the convergence of the iterations,
  • do points 1-2 in an adaptive way, maximizing computational efficiency, using a posteriori error estimators.
  • Positioning: The project lies in the confluence of rigorous mathematics, and scientific computing. Moreover, it has deep ties with physics and technology with a promise to improve how optical elements are designed in industry, and how optimal transport problems are solved in general.

    By joining the project you become a part of the bigger ensemble of the Computational Illumination Optics group of Eindhoven University of Technology. You will also partake in a consortia interfacing between industry leaders such as ASML, Signify, Canon, TNO, along with many others.

    The detailed project description and planning can be found here.

    Job requirements
  • A master's degree (or an equivalent university degree) in mathematics or physics. Engineering master's degree holders with an inclination towards mathematics & physics are also encouraged to apply.
  • An analytical mindset, familiarity with numerical methods, or expertise in programming is solicited, preferably all three above. This could be substantiated by academic performance, research experience, MSc theses, industrial exposures, internships etc.
  • 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 station. In 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 employment on teaching tasks.
  • 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. €2,770 max. €3,539).
  • 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 children's 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.
  • Information and application

    About us

    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.

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


    Do you recognize yourself in this profile and would you like to know more? Please contact the hiring manager Koondanibha Mitra, Assistant Professor, [email protected].

    Visit our website for more information about the application process or the conditions of employment. You can also contact [email protected].

    Are you inspired and would like to know more about working at TU/e? Please visit our career page.


    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 a list of your publications and the contact information of three references.
  • Full consideration will be given to candidates who apply till 15 th April 2024. They would hear back from us by 1st May. However, the application will remain open until the position is filled.

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