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| Figure 1 (a) Two photonic wave functions on the image plane, each coming from a point source. X1 and X2 are the point-source positions, θ1 is the centroid, θ2 is the separation, and σ is the width of the point-spread function. (b) If photon counting is performed on the image plane, the statistics are Poisson with a mean intensity proportional to Λ(x)=[|ψ1(x)|2+|ψ2(x)|2]/2 . |
Abstract
Rayleigh’s criterion for resolving two incoherent point sources has been the most influential measure of optical imaging resolution for over a century. In the context of statistical image processing, violation of the criterion is especially detrimental to the estimation of the separation between the sources, and modern far-field superresolution techniques rely on suppressing the emission of close sources to enhance the localization precision. Using quantum optics, quantum metrology, and statistical analysis, here we show that, even if two close incoherent sources emit simultaneously, measurements with linear optics and photon counting can estimate their separation from the far field almost as precisely as conventional methods do for isolated sources, rendering Rayleigh’s criterion irrelevant to the problem. Our results demonstrate that superresolution can be achieved not only for fluorophores but also for stars.
APS Physics: Quantum Theory of Superresolution for Two Incoherent Optical Point Sources
Mankei Tsang, Ranjith Nair, and Xiao-Ming Lu
Phys. Rev. X 6, 031033 – Published 29 August 2016
DOI:http://dx.doi.org/10.1103/PhysRevX.6.031033
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