Criterion for determining resolving power in the optical near field

Abstract

The resolution limit, i.e., the lower limit to the size of a luminous object that can be determined accurately by ordinary optical microscopy, was determined over a century ago on the basis of the imprecision that is imparted to the details of an image by diffraction. Such criteria assume one is making observations at distances greater than the wavelength of the light emitted or scattered by the luminous object, i.e., in the so-called far field. Although near-field microscopy is an established imaging technique, the analogous resolution criterion pertinent to the near field, in which the distance between the observer or the observing instrument and the light emitter is smaller than the wavelength, has not yet been quantitatively enunciated. Here I propose two ansatze pertinent to optical resolution in the near field. The first, based on classical physics, concludes that the minimal lateral near-field resolution limit is equal to the (perpendicular) distance between the near-field probe and the object. The second is a quantum limitation based on the uncertainty principle, which shows that the momentum uncertainty arising from atomic vibrations results in a minimal resolvable size, which in most instances is of the order of 10 pm.