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PhD Project Inverse methods for aberration compensation

PhD Project Inverse methods for aberration compensation

We are looking for a strong, motivated PhD student for a project in Scientific Computing / Illumination Optics
Faculteit Wiskunde & Informatica
Graduate Program(s)
Computer Science


The Department of Mathematics and Computer Science of Eindhoven University of Technology has a vacancy for a PhD-student in its Centre for Analysis, Scientific computing and Applications (CASA). CASA comprises the chairs Scientific Computing (SC) and Applied Analysis (TA). CASA’s major research objective is to develop new and to improve existing mathematical (both analytical and numerical) methods for a wide range of applications in science and engineering.


Due to the every increasing demand for smaller and smarter electronics, there is also a growing demand for high end machines to manufacture these. The working of these so-called photolithography machines relies on an optical system that can very precisely direct light of small wave length, typically extreme ultraviolet (EUV), to a substrate to create the nanometer-scale structures required for the electronics. However, optical systems are prone to aberrations, i.e., small distortions of the image on the wafer plane, that have to be corrected. The purpose of this research is to design optical systems that minimize these aberrations, and is conducted in collaboration with ASML.

Project description

Inverse methods are a relatively new class of methods to compute freeform surfaces (without any symmetries) in non-imaging optical systems and are based on the so-called generalised Monge-Ampère equation, which is a nonlinear elliptic PDE. This equation is a combination of the optical map, connecting object and image plane, and the conservation law of energy. Several simulation codes are available to compute one freeform surface. For imaging optical systems, typical for use in photolithography, the optical map has to  be combined with an aberration condition such as the Abbe sine condition, to derive a generalised Monge-Ampère equation. Research topics in this project are, first, investigate other possible conditions, especially for nonsymmetric systems, extend the method to compute multiple freeform surfaces, and finally, develop a simulation code to optimize optical systems for aberrations.


As a PhD student your tasks are the following:

  • Perform scientific research in the described domain;
  • Present results at international conferences;
  • Publish results in scientific journals;
  • Participate in activities of the group and the department;
  • Assist SC-staff in teaching undergraduate and graduate courses (at most 20 % of the time).


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

  • An MSc in (applied) mathematics, physics or a related discipline with a strong back- ground in computational physics;
  • Experience with Matlab and preferably C or C++;
  • Creative, pro-active team player with good analytical skills;
  • Good communicative skills in English, both written and oral.


We offer:

  • A full-time appointment for a period of four years, with an intermediate evaluation after nine months;
  • A gross salary of Euro 2395 per month in the first year increasing up to  Euro 3061 per month in the fourth year;
  • Support for your personal development and career planning including courses, summer schools, conference visits, etc.;
  • A research position in an enthusiastic and internationally renowned research group;
  • A broad package of fringe benefits (e.g. excellent technical infrastructure, saving schemes, excellent sport facilities, and child daycare).

Informatie en sollicitatie

For further information concerning the position, please contact Jan ten Thije Boonkkamp (TU/e), e-mail: j.h.m.tenthijeboonkkamp[at], tel. +31402474123 or Wilbert IJzer- man (Signify), e-mail: wilbert.ijzerman[at], tel. +31610183927.

About employment conditions, please contact mrs. Karin Wels-Noordermeer, e-mail: k.h.wels[at]

Please apply by using the 'Apply for this job' button on top of this page. The preliminary deadline for this position is September 25, 2020. All applications received before this date will be considered.

The application should consist of the following parts:

  • A motivation letter;
  • A Curriculum Vitae;
  • Copies of diplomas and a list of grades of your studies;
  • Names and addresses of two referees;
  • Proof of English language skills (if applicable).

You can upload all the required documents in max. five pdf's (max. 10 Mb).