Theoretical model of microparticle-assisted super-resolution microscopy

We present the three-dimensional theoretical model of microparticle-assisted super-resolution imaging that enables simulation of virtual image formation. The model shows that partial spatial coherence of the illumination is a key prerequisite for achieving super-resolution. We demonstrate that a spherical microparticle enhances the resolving power of an optical system with a limited numerical aperture, allowing features near the particle to be resolved up to the Abbe limit. To overcome this limit, high-frequency oscillations in the spatial correlation function of the radiation are required, leading to out-of-phase superposition of image contributions from different object points. We further show that, in this regime, the optical resolution deteriorates as the object size decreases. Overall, the results establish a consistent framework that reproduces experimentally observed subwavelength imaging and clarifies the underlying physical mechanisms.