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Quantum Theory of Superresolution for Two Incoherent Optical Point Sources
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 farfield 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.Comment: 18 pages, 11 figures. v1: First draft. v2: Improved the presentation
and added a section on the issues of unknown centroid and misalignment. v3:
published in Physical Review
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