Wave optics of imaging with contact ball lenses

Abstract

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 $$\sim \lambda /7$$ ∼ λ / 7 , 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 $$30<D/\lambda <4000$$ 30 < D / λ < 4000 covering this transition range and for a broad range of refractive indices $$1.3<n<2.1$$ 1.3 < n < 2.1 . 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 $$n\approx 2$$ n ≈ 2 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 $$D/\lambda $$ D / λ , for which a simple analytical formula is derived. It is demonstrated that a subwavelength resolution is achievable at $$D/\lambda \lesssim 1400$$ D / λ ≲ 1400 . 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.