Near-field microscopy with a single-photon point-like emitter: Resolution versus the aperture tip?

We discuss theoretically the concept of spatial resolution in near-field scanning optical microscopy (NSOM) in light of a recent work [Opt. Express 17 (2009) 19969] which reported on the achievement of active tips made of a single ultrasmall fluorescent nanodiamond grafted onto the apex of a substrate tip and on their validation in NSOM imaging. Since fluorescent nanodiamonds tend to decrease steadily in size, we assimilate a nanodiamond-based tip to a point-like single photon source and compare its ultimate resolution with that offered by standard metal-coated aperture NSOM tips. We demonstrate both classically and quantum mechanically that NSOM based on a point-like tip has a resolving power that is only limited by the scan height over the imaged system whereas the aperture-tip resolution depends critically on both the scan height and aperture diameter. This is a consequence of the complex distribution of the electromagnetic field around the aperture that tends to artificially duplicate the imaged objects. We show that the point-like tip does not suffer from this "squint" and that it rapidly approaches its ultimate resolution in the near-field as soon its scan height falls below the distance between the two nano-objects to be resolved.