PHYSICS OF OUR DAYS: 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 phiv ~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 cong 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 cong 5) superresolution can be achieved.