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# Optical Inverse Problem Solving in 3-D Deflectometry

-- position closed --

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

## Inverse Problem Solving by Promoting Sparse Signal Models:

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 postdoctoral position concerns the application of the sparsity principle for modeling and solving two optical inverse problems:

1. The reconstruction of the undistorted multifocal intraocular lens images (IOL) from the experimental measurements (close to image deconvolution and image stitching problems)
2. The characterization of a Multiangular Optical Deflectometer embedding the principles of Compressed Sensing.

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

## Application 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 postdoc will be in charge of:

• Designing accurate mathematical models for optical deflectometric acquistion (Forward model);
• Developping efficient methods for reconstructing object surfaces from these measurement (Inverse problem); this should be based on convex optimization promoting sparse signal models or greedy algorithms;
• Extending the principles of optical deflectometry to a multiangular system embedding the Compressed Sensing principle;

In parallel, the postdoc will have to demonstrate his ability to:

• develop image processing methods (e.g., denoising, image stitching) for possible subproblems attached to the main objectives described above;
• co-supervise the work of PhD students working on the same topics;
• write semester reports for the project DETROIT.

Development and 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 postdoc will co-supervise a PhD student working on the same topic and funded by the same project.

## Project and Industrial Context

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-TELE, UCL) which is responsible of the IOL image reconstruction and post-processing algorithms.

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

## Candidate's Profile:

• PhD in Applied Mathematics, Electrical Engineering, Physics, or Computer Science;
• Good knowledge of signal/image processing and classical optics are mandatory;
• Knowledge (even partial) in the following topics constitutes assets:
• Compressed Sensing,
• Multispectral Imaging,
• Coded Aperture,
• Spatial Light Modulator,
• Convex Optimization methods,
• Sparsity Models,
• Image DeNoising and Debluring.
• Programming 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 in collaboration with industrial partners.
• A 20 months postdoctoral contract.

## Visa:

Candidates who are non-EU citizens are required to obtain an appropriate long-term Schengen visa (and this procedure can last some weeks) in order to be hired on this position. This is mandatory for any postdoc contract in Belgium. You can get further information from the nearest Belgian embassy in your country (e.g. by phone/email, for a first contact).

## Application:

Applications should include a full CV, including list of publications, and must be sent before June 1st, 2011.

Names and complete addresses of referees are welcome.

Preselected candidates will be interviewed by Skype.

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

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