Physics of our days

Superresolution and singularities in phase images

Moscow State Institute of Radio Engineering, Electronics, and Automatics (Technical University), prosp. Vernadskogo 78, Moscow, 117454, Russian Federation

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.

Fulltext is available at IOP
PACS: 42.30.−d, 42.79.−e, 87.64.Rr (all)
DOI: 10.1070/PU2008v051n11ABEH006682
Citation: Tychinskii V P "Superresolution and singularities in phase images" Phys. Usp. 51 1161–1169 (2008)
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Оригинал: Тычинский В П «Сверхразрешение и сингулярности в фазовых изображениях» УФН 178 1205–1214 (2008); DOI: 10.3367/UFNr.0178.200811c.1205

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  1. N.L. Popov, I.A. Artyukov et alWave packet in the phase problem in optics and ptychography63 766–774 (2020)

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