Improved mathematical model for a dense network of waveguides and electrodes design

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.