One of the most significant developments in life sciences—the discovery of bacteria and protists—was accomplished by Antoni van Leeuwenhoek in the 17th century using a single ball lens microscope. It is shown that the full potential of single lens designs can be realized in a contact mode of imaging by ball lenses with a refractive index of n ≈ 2, suitable for developing compact cellphone-based microscopes. The quality of imaging is comparable to basic compound microscopes, but with a narrower field-of-view, and is demonstrated for various biomedical samples. The maximal magnification (M > 50) with the highest resolution (≈0.66 µm at λ = 589 nm) is achieved for imaging of nanoplasmonic structures by ball lenses made from LASFN35 glass, the index of which is tuned near n = 2 using chromatic dispersion. Due to limitations of geometrical optics, the imaging theory is developed based on an exact numerical solution of the Maxwell equations, including spherical aberration and the nearfield coupling of a point source. The modeling is performed using multiscale analysis: from the field propagation inside ball lenses with diameters to the formation of the diffracted field at distances of ≈105 λ. It is shown that such imaging enables the transition from pixel- to diffraction-limited resolution in cellphone microscopy.