XiEff Representation for Interpretable Near-Field Imaging

Near-field optics, or near-field electrodynamics, is a field that studies the interaction between materials and light at spatial scales smaller than the wavelength. At these extremely small scales, below the diffraction limit, the interaction between materials and electromagnetic fields can exhibit unique behaviors and properties not observed in conventional optics. This area of research is crucial for understanding the optical characteristics of nanotechnical systems and nanoscale biological objects. One of the primary tools used in near-field optics research is scanning nearfield optical microscopy (SNOM), which allows researchers to measure near-field optical images (NFI). However, these images often lack visual clarity and interpretability. The main goal of this paper is to introduce a novel approach that addresses the challenge of NFI interpretability. Inspired by the progress in physics-informed neural networks (PINNs), we propose an unsupervised method that introduces the XiEff representation - a neural field-based parameterization of the effective susceptibility. By integrating XiEff into the Lippmann-Schwinger integral equation for near-field optics, we develop an optimization strategy to reconstruct the effective susceptibility distribution directly from NFI data. The optimized XiEff representation provides an interpretable and explainable model of the particle's shape. Extensive evaluations on a synthetically generated NFI dataset demonstrate the effectiveness of the method, achieving high intersection-over-union between XiEff and ground truth shapes, even for complex geometries. Furthermore, the approach exhibits desirable robustness to measurement noise, a crucial property for practical applications.