Optical Solutions for Spectral Imaging Inverse Problems with a Shift-Variant System

Inverse problems in spectral imaging have been addressed in the state-of-the-art by encoding scenes to alleviate the ill-posedness, leveraging the knowledge of the forward model of the system. Recent studies have demonstrated that optimizing these coding elements improves the performance of solving the inverse problem. Specifically, to include a coding element without sacrificing the light throughput of the optical system, Diffractive Optical Elements (DOEs) have been employed. Recent works have highlighted the significance of shift-variant systems, which allows an optimized coding for each spatial portion of the scene and for each wavelength. With this in mind, this work proposes a shift-variant optical system using double-phase coding elements by implementing a double DOE architecture. The results show that using this proposed double-DOE architecture leads to better results in terms of high-level tasks, such as spectral image reconstruction and spatialspectral super-resolution. Additionally, this work proves the shift-variant nature of the double-DOE architecture.