Wave optics of imaging with contact ball lenses

Recent progress in microspherical superlens nanoscopy raises a fundamental question about the transition from super-resolution properties of mesoscale microspheres, which can provide a subwavelength resolution [Formula: see text], to macroscale ball lenses, for which the imaging quality degrades because of aberrations. To address this question, this work develops a theory describing the imaging by contact ball lenses with diameters [Formula: see text] covering this transition range and for a broad range of refractive indices [Formula: see text]. Starting from geometrical optics we subsequently proceed to an exact numerical solution of the Maxwell equations explaining virtual and real image formation as well as magnification M and resolution near the critical index [Formula: see text] which is of interest for applications demanding the highest M such as cellphone microscopy. The wave effects manifest themselves in a strong dependence of the image plane position and magnification on [Formula: see text], for which a simple analytical formula is derived. It is demonstrated that a subwavelength resolution is achievable at [Formula: see text]. The theory explains the results of experimental contact-ball imaging. The understanding of the physical mechanisms of image formation revealed in this study creates a basis for developing applications of contact ball lenses in cellphone-based microscopy.