Prof. Edouard Oudet Profile

Prof. Edouard Oudet

at Lab Jean Kuntzmann

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Proceedings Article | 17 May 2022 Presentation + Paper

Optimal dense and random addressing design of emissive points in a retinal projection device

Fabian Rainouard, Matthias Colard, Olivier Haeberlé, Edouard Oudet, Christophe Martinez

Proceedings Volume 12138, 121380R (2022) https://doi.org/10.1117/12.2620243

KEYWORDS: Waveguides, Point spread functions, Electrodes, Signal to noise ratio, Mathematical modeling, Retina, Eye, Switches, Laser sources, Image segmentation

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One of the big challenges of Augmented Reality (AR) is to create ergonomic smart glasses. Our laboratory proposes an unconventional concept of AR glasses based on self-focusing of multiple beams into the eye. The device comprises a dense electrode network that allows extracting light from a dense waveguide network at the intersections points. Each beam emitted at these points is reflected by a holographic element that directs light towards the eye with a proper angular direction. The image pixels are created on the retina by the interferences of various beam distributions. This paper presents a method to optimize the design of waveguides and electrodes to increase the number of pixels on the final image. Our method considers a first waveguide (resp. electrode) as a curve described by a succession of segments with a unique absolute angle crossing a horizontal (resp. vertical) axe. The other waveguides (resp. electrodes) are created by the translation of the curves so that the minimal distance between two curves is equal to a fixed value. We use the B-Splines mathematical model to approximate the succession of segments. An iterative method adapted to B-Splines allows calculating the intersections between waveguides and electrodes. An Emissive Point Distribution (EPD) is obtained by selecting random groups of waveguides and electrodes. Each EPD forms one pixel onto the retina. The Point Spread Function (PSF) of this EPD characterizes the self-focusing efficiency. We calculate the Signal-to-Noise-Ratio of each EPD to evaluate the quality of the whole self-focusing process and we compare it to the Airy function. Our new mathematical model improves by a factor 3.5 the number of pixels for an equivalent SNR in comparison to the model we previously used.

Proceedings Article | 5 March 2021 Poster + Presentation + Paper

Improved mathematical model for a dense network of waveguide and electrode design

Fabian Rainouard, Christophe Martinez, Basile Meynard, Olivier Haeberle, Edouard Oudet

Proceedings Volume 11689, 116891N (2021) https://doi.org/10.1117/12.2578309

KEYWORDS: Waveguides, Electrodes, Mathematical modeling, Signal to noise ratio, Integrated optics, Glasses, Eye, Waveguide modes, Retina, Projection systems

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Our team works on a new concept of smart glasses for augmented reality applications. Our retinal projector consists of a dense waveguide network to transport light on the surface of a glass and an electrode network to extract light. The laser beams are extracted through holographic elements that direct light into the eye. The images are directly created on the retina without optics. The emissive points (EPs) are defined as the intersections between dense waveguide and electrode networks. Design of the Emissive Point Distribution (EPD) is of primary importance in the imaging process. Previous results showed that EPs must be randomly distributed inside the pupil in order to obtain a good self-focusing effect. To evaluate self-focusing, we calculate the Signal-to-Noise-Ratio (SNR) of the point spread function and compare it to the Airy function. Our first EPD model considers waveguides and electrodes designed as a sum of cosine functions. At the inter- section point between a waveguide’s function and an electrode’s function, the composition of these two functions is canceled. We use Newton’s method to find this point. With this model, we can have a good SNR but the number of available pixels is low. Our second model is based on B-Spline curves to represent the waveguide and electrode networks. With this model we can easily locally modify the curves. We develop tools specially adapted for B-Spline curves to find intersections. We also establish properties on the minimum distance between two curves.

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