PINN inspired Freeform Design

Abstract

This project aims to recreate intensity patterns using Fraunhofer diffraction as a means of simulation. These intensity patterns are created by phase shifting specific parts of an incoming field of light. These phase shifts are determined by a B-spline surface, which is in turn controlled by so-called control points. Only a handful of control points can describe a whole surface. The position of these control points is then determined using machine learning and specifically a technique inspired by ‘physics-informed neural networks’, which were introduced last year by Raissi et al. [1]. With this method, simple experiments which sought to recreate intensity patterns known to be in the solution space were carried out. These experiments showed some success, but suffered from the fact that they used too sensitive parameters in the input of the machine learning model, reducing the sophisticated method to a Monte Carlo search, or they used no input at all, which degraded the machine learning model to simple parameter optimization. Nevertheless, these experiments showed that this method has the potential to be used in more flexible optical setups, where multiple configurations can yield the same intensity pattern or where changing the parameters defining the setup do not induce enormous changes in the resulting intensity pattern. In addition, the proposed method relies upon Fraunhofer diffraction, which, when discretized for numerical computation, introduces aliasing issues when the incoming field changes too rapidly. This phenomenon was especially apparent when using point sources that create spherical wave fronts. A possible solution for this issue is to consider ray tracing techniques in future research.