Superresolution and singularities in phase images

The Rayleigh criterion and the Airy radius r0 are not adequate for characterizing spatial resolution in phase and some other functional images. An essential feature of phase images is a possible formation of wavefront dislocations which depend on the position in space of the so-called singular lines [I(x, y, z =0], in the neighborhood of which the phase gradient grad ψ ∼I-1/2 increases and the intensity tends to zero. Based on this gradient phase behavior, the minimal length L dependent on the signal-to-noise ratio (S/N) is proposed as the phase resolution criterion, and a formula for the energy-dependent superresolution, Ξ = r0/L ≅ 2(S/N)1/2, is devised. Measurements on a 100-nm-diameter latex sphere using the Airyscan coherent phase microscope confirmed that a marked (Ξ ≅ 5) superresolution can be achieved. (physics of our days)