Equivariant Neural Networks for Controlling Dynamic Spatial Light Modulators

Spatial light modulators (SLMs) are devices that are capable of manipulating incident light by passing it through an array of phase/intensity altering pixels. A recent alternative design involves creating a phase mask by directing a thin film of fluid with thermocapillary forces generated by a controlled temperature map. However, it is difficult to determine the input temperature signal necessary to induce a given height profile. The relationship between temperature and height is given by the thin film equation, a fourth-order nonlinear PDE, which is difficult to solve numerically. To address this problem, we train deep neural networks to directly solve the inverse problem, mapping from the desired height profiles to the needed temperature patterns. We design novel equivariant networks incorporating scale and rotation symmetry of the underlying thin film equation. We demonstrate the effectiveness of equivariant models for learning the complex relationship between input temperature signals and the resulting light patterns, showing they are more accurate than non-equivariant baselines and very computationally efficient. This work has implications for a range of applications, including high-power laser systems, and could lead to more efficient and effective ways to deploy the process of modulation of light in SLMs in a variety of applications.