Improving the resolution of an optical microscope using ring-like illumination and scanning the direction of the diffracted light with a slit

A non-periodic sample, which also contains a periodic structure with a period smaller than the resolution limit of the optical microscope used for imaging it, was illuminated with the cone of white-light produced by a ring-shaped condenser with a numerical aperture larger than the objective lens. By rotating a slit placed at the back focal plane of the objective lens, we obtained several pairs of real plane and Fourier plane images corresponding to different diffraction directions. We simulated, discussed, and demonstrated a numerical algorithm capable of producing a high-resolution image of the sample after processing the experimental images.