Superresolution and singularities in phase images

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/
Web of Science

000264020300003
Scopus

2-s2.0-63249135614
ADS NASA

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

References (36) ↓ Cited by (17) Similar articles (1)

Peng H Bioinformatics 24 1827 (2008)
Born M, Wolf E Principles Of Optics (Oxford: Pergamon Press, 1965)
Lacoste T et al. Proc. Natl. Acad. Sci. USA 97 9461 (2000)
Betzig E et al. Science 313 1642 (2006)
Bates M et al. Science 317 1749 (2007)
Agrawal A et al. Proc. Natl. Acad. Sci. USA 105 3298 (2008)
Wu D et al. Nano Lett. 8 1159 (2008)
Hell S W Phys. Lett. A 326 140 (2004)
Huang B et al. Science 319 810 (2008)
Carl D et al. Appl. Opt. 43 6536 (2004)
Vyshnyakov G et al. Eur. J. Microsc. And Analysis 87 19 (2004)
Langoju R, Patil A, Rastogi P Opt. Expess 13 7160 (2005)
Rappaz B et al. Opt. Express 13 9361 (2005)
Popescu G et al. J. Biomed. Opt. 10 060503 (2005)
Ikeda T et al. Opt. Lett. 30 1165 (2005)
Popescu G et al. Opt. Lett. 31 775 (2006)
Millerd J E et al. Proc. SPIE 5531 304 (2004)
Nye J F, Berry M V Proc. R. Soc. London A 336 165 (1974)
Bazhenov V Yu, Vasnetsov M V, Soskin M S Pis’ma ZhETF 52 1037 (1990); Bazhenov V Yu, Vasnetsov M V, Soskin M S JETP Lett. 52 429 (1990)
Berry M V, Dennis M R Proc. R. Soc. London A 457 2251 (2001)
Leach J et al. New J. Phys. 7 55 (2005)
Soskin M S, Vasnetsov M V "Singular optics" In Progress In Optics Vol. 42 (Ed. E. Wolf) (Amsterdam: North-Holland, 2001) p. 219
Baranova N B i dr. Pis’ma ZhTEF 33 206 (1981); Baranova N B et al. Sov. JETP Lett. 33 195 (1981)
Angelsky O V et al. Phys. Rev. E 65 036602 (2002)
Tychinsky V Opt. Commun. 81 131 (1991)
Tavrov A V, Tychinsky V P Proc. SPIE 2004 332 (1994)
Tychinsky V P Opt. Commun. 74 41 (1989)
Tychinskii V P i dr. Pis’ma ZhTF 17 (22); Tychinskii V P et al. Sov. Tech. Phys. Lett. 17 815 (1991)
Tychinskii V P i dr. Kvantovaya Elektron. 24 754 (1997); Tychinskii V P et al. Quantum Electron. 27 735 (1997)
Tychinsky V P et al. Opt. Commun. 74 37 (1989)
Tychinskii V P Usp. Fiz. Nauk 177 535 (2007); Tychinskii V P Phys. Usp. 50 513 (2007)
Kretushev A V, Tychinskii V P Kvantovaya Elektron. 32 66 (2002); Kretushev A V, Tychinskii V P Quantum Electron. 32 66 (2002)
Tychinsky V P, Velzel C H F In Current Trends In Optics (Ed. J C Dainty) (San Diego: Academic Press, 1994)
Tychinsky V P et al. in Technical Proc. of the 2006 NSTI Nanotechnology Conf. and Trade Show, Boston, May 7 – 11, 2006 Vol. 2 (2006), Ch. 1, CDROM
Ivanov A B i dr. Rossiiskie Nanotekhnologii 2 (5 - 6) 120 (2007)
Tychinsky V P, Kretushev A V, Luskinovich P N physics/0608093