A general theory of far-field optical microscopy image formation and resolution limit using double-sided Feynman diagrams

Optical resolution of far-field optical microscopy is limited by the diffraction of light, while diverse light-matter interactions are used to push the limit. The image resolution limit depends on the type of optical microscopy; however, the current theoretical frameworks provide oversimplified pictures of image formation and resolution that only address individual types of microscopy and light-matter interactions. To compare the fundamental optical resolutions of all types of microscopy and to codify a unified image-formation theory, a new method that describes the influence of light-matter interactions on the resolution limit is required. Here, we develop an intuitive technique using double-sided Feynman diagrams that depict light-matter interactions to provide a bird's-eye view of microscopy classification. This diagrammatic methodology also allows for the optical resolution calculation of all types of microscopy. We show a guidepost for understanding the potential resolution and limitation of all optical microscopy. This principle opens the door to study unexplored theoretical questions and lead to new applications.