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# "Optical Inverse Problem Solving in 3-D Deflectometry”

• Dr Laurent Jacques
• Prof. Philippe Antoine
• Prof. Benoît Macq

## Ubiquitous Sparsity:

Nowadays, assuming that a signal (e.g., a 1-D signal, an image or a volume of data) has a sparse representation, namely that this signal is linearly described with few elements taken in a suitable basis, is an ubiquitous hypothesis validated in many different scientific domains. Interestingly, this sparsity assumption is the heart of methods solving inverse problems, namely those estimating a signal from some linear distorting observations. Sparsity stabilizes (or regularizes) these signal estimation techniques often based on L1-norm (or Total Variation norm) minimization and greedy methods.

This PhD position concerns the application of the sparsity principle for modeling and solving the optical inverse problem described in the next section, that is, the reconstruction of the undistorted image of the multifocal intraocular lens (IOL) from the experimental measurements. This research will be carried out in collaboration with a postdoctoral researcher hired for one year on the same project.

Connections with the techniques of image restoration, image deconvolution, and Compressed Sensing are expected.

## Optical Framework:

Improved functional performance is a general trend in ocular surgery today. As an example, multifocal intraocular lens (IOL) achieves different optical powers, as such to enable good near and distant vision. There are two types of multifocal lenses. A refractive multifocal lens is made of concentric rings whose refractive powers alternate from centre to periphery. Diffractive multifocal lens uses light diffraction at an interference grid made of micrometric steps. Such complex surfaces are a real challenge both for manufacturing and for characterization.

This position opening takes place in a 3-year regional project (DETROIT), funded by the Belgian Walloon Region. This project aims at characterizing surfaces by optical deflectometry. The principle is to measure the deviation of the light reflected by each point of the surface. This technique is an interesting alternative to interferometry in order to estimate the surface topography. Indeed measuring the deviation angle instead of the height has several advantages. It is insensitive to vibrations as it is not based on interferences. It is more effective in detecting local details and object contours than height measurement. In deflectometry, the shape of an object is numerically reconstructed from the gradient data with a high accuracy. As an example, 10nm flatness deviation over a 50mm window glass can be observed with high accuracy instrument.

Experimentally, the very short radius of curvature of the IOLs requires the use of wide acceptance optics as such to collect light that is reflected in a large range of angles. The drawback is the very narrow field of view. In order to reduce the acquisition time, a device that images the whole lens shall be preferred but inevitable distortion of the image will be numerically corrected based on the knowledge of instrument response. This solution is challenging but very attractive for industrial perspectives.

## Job description:

The student will develop mathematical methods and algorithms for reconstructing the undistorted IOL image from the experimental measurements, taking into account (and modeling) the particularities of the sensing systems. Calibration of the response of the instrument will be carried out by another partner of the project. However, a close collaboration between the two teams is necessary. Moreover, the PhD student will be co-supervised by a postdoctoral researcher hired on the same topic and funded by the same project.

The optical development takes place in the 3-year project DETROIT. It involves two industrial partners, Physiol and Lambda-X and 3 university partners. Physiol is well-known for its development of IOL. Lambda-X has a large experience in optical characterization of optical components by means of deflectometry. The leading academic partner is the Atomic, Molecular and Optical Physics Laboratory (IMCN-PAMO) of University of Louvain (UCL, Louvain-la-Neuve, Belgium), helped by two other Belgian university partners: the Active Structures Laboratory of the University of Brussels (ASL, ULB), in charge of the development of fast adaptive optics, and the Communications and Remote Sensing laboratory (ICTEAM/ELEN, UCL) which is responsible of the IOL image reconstruction and post-processing algorithms.

Research activity will be carried out in the TELE Laboratory (ICTEAM/ELEN), and partly at IMCN-PAMO and at Lambda-X offices in Nivelles, Belgium.

## Candidate's Profile:

• M.Sc. in Applied Mathematics, Physics, Electrical Engineering, or Computer Science;
• Knowledge (even partial) in the following topics constitutes assets:
• Convex Optimization methods,
• Signal/Image Processing,
• Classical Optics,
• Compressed Sensing and inverse problems.
• Experience with Matlab, C and/or C++.
• Good communications skills, both written and oral;
• Speaking fluently in English or French is required. Writing in English is mandatory.

## We offer:

• A research position in a dynamic and advanced high-tech environment, working on leading-edge technologies and having many international contacts.
• Funding for 2-3 years, with the possibility to extend it by applying for a Belgian NSF grant.

## Application:

Applications should include a detailed resume, copy of grade sheets for B.Sc. and M.Sc. Names and complete addresses of referees are welcome.

Please send applications by email to (replace _AT_ and _DOT_):

	laurent.jacques _AT_ uclouvain _DOT_ be
ph.antoine _AT_ _uclouvain _DOT_ be