The Rayleigh criterion and the Airy radius $r_0$ 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 $\varphi \approx I^{-1/2}$ 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 super-resolution, $\Xi = r_0/L \cong 2(S/N)^{1/2}$, is devised. Measurements on a 100-nm-diameter latex sphere using the Airyscan coherent phase microscope confirmed that a marked ($\Xi \cong 5$) superresolution can be achieved.

PACS: 42.30.−d, 42.79.−e, 87.64.Rr (all) DOI: 10.1070/PU2008v051n11ABEH006682 URL: https://ufn.ru/en/articles/2008/11/c/ 000264020300003 2-s2.0-63249135614 2008PhyU...51.1161T Citation: Tychinskii V P "Superresolution and singularities in phase images" Phys. Usp. 51 1161–1169 (2008) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Оригинал: Тычинский В П «Сверхразрешение и сингулярности в фазовых изображениях» УФН 178 1205–1214 (2008); DOI: 10.3367/UFNr.0178.200811c.1205