Sub-diffraction far-field dark-field nanoscopy via low-index microlens and deep learning

Abstract

Far-field imaging methods capable of resolving samples beyond the diffraction limit of light are essential for understanding the intricate details of molecular interactions in physical chemistry and biophysics. Here, we demonstrate the use of low-index microspheres to enhance the performance of a conventional optical microscope for sub-diffraction far-field imaging under dark-field conditions. Our results show that fully immersed SiO2 microsphere lenses, positioned without physical contact with the sample surface, enable the resolution of sub-wavelength features as small as 100 nm. Furthermore, we introduce a generative Schrödinger bridge framework that integrates dark-field measurements acquired at multiple working distances to learn a mapping between low- and high-resolution image manifolds. As a result, low-resolution dark-field inputs can be reconstructed into high-quality, high-resolution outputs with improved structural fidelity. The proposed deep learning-based microsphere-assisted imaging system achieves a maximum working distance of approximately 25.0 μm, offering a promising route for nanoscale imaging of single molecules and biological structures.