While ball lenses have been used for centuries, it is only in the last decade that microspheres have been recognized as a tool for imaging beyond the diffraction limit.  Features smaller than a half-wavelength can be resolved when an object is placed near a micron-scale transparent sphere.  Exotic materials are not required to achieve this surprising capability - homogeneous spheres of standard dielectric materials are sufficient.  In this paper, Bekirov and coauthors present a rigorous wave-optics framework for modeling image formation with microspheres, and for calculating key metrics such as resolution and magnification.

The work presented in this paper closes a gap in the literature.  Ray optics are routinely used to model imaging through larger spheres, but these traditional ball lenses are subject to the diffraction limit and so do not offer super-resolution capabilities.  Photonic nanojets (the small focal spots formed behind an illuminated sphere) are a closely related phenomenon and are rigorously modeled by Mie theory.  But while Mie theory is accurate for small spheres, the standard presentation doesn't model imaging - it starts with a far-field illumination of a sphere and allows calculation of fields within and near the sphere.  Here the authors tackle the reciprocal imaging problem - they start with a known object in the near field of the sphere and determine what is coupled into propagating far-field waves.  These propagating waves are then traced backward to determine the characteristics of the virtual image formed by the sphere.  By contributing a rigorous wave-optics model the authors help explain earlier experimental results, while also providing an important tool for exploring new applications of super-resolution imaging using microspheres.

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