Quantum-inspired Optical Super-resolution Imaging with Modal Measurements

Abstract

One of the goals of a traditional imaging system is to acquire image of the scenewith the highest-resolution possible to infer relevant details or features. However, the traditional imaging approach employs a digital focal plane to capture the optical image at or near the diffraction limit followed by electronic-domain post-processing, which is known to be sub-optimal for many tasks (e.g., classification). Using tools from quantum information theory, recent analysis has shown that the traditional imaging approach is sub-optimal for resolving sub-Rayleigh features in the information-theoretic sense. In this work, we employ the framework of classical/quantum information theory to understand the problem of optical resolution from a different perspective. We briefly outline of the concepts of classical and quantum information theory and how they are related to imaging and sensing, in particular resolution problem. Traditionally, in optics one employs the Rayleigh criterion to determine whether two incoherent point source, or in a more general sense, the smallest scale feature of the scene can be resolved. However, this criteria gives only a visual bound of resolvability without any quantification. An information-theoretic analysis allows us to not only quantify resolution but also find its fundamental limit. Using an information-theoretic approach we analyze the resolution of partially coherent point- and line- sources. In particular, we apply the Hermite Gaussian (HG) mode sorting measurement, which is proven to be the best measurement to resolve 2- point sources, proposed by Tsang et al. to partially coherent sources and compare its performance using traditional imaging with high-resolution focal plane arrays. The understanding of this new modal measurement under different scenarios (partial coherence, extended sources, broadband, etc.) has important implications in many real-world applications. We also develop an adaptive measurement scheme to resolve point sources with sub-Rayleigh separation in a constellation. By leveraging the quantum information theory, instead utilizing the HG mode for static measurements, we design a modal basis in each adaptive measurement step as the modal projection basis. We compare this technique with traditional imaging followed by different image estimation algorithms such as deconvolution with k-mean and the state-of-art convolution neural network (CNN) for different image fidelity metrics and demonstrate optical super-resolution in the deep sub-Rayleigh regime. Page