title: Far-Field Superresolution of Thermal Electromagnetic Sources at the Quantum Limit.
abstract: We obtain the ultimate quantum limit for estimating the transverse separation of two thermal point sources using a given imaging system with limited spatial bandwidth. We show via the quantum Cramér-Rao bound that, contrary to the Rayleigh limit in conventional direct imaging, quantum mechanics does not mandate any loss of precision in estimating even deep sub-Rayleigh separations. We propose two coherent measurement techniques, easily implementable using current linear-optics technology, that approach the quantum limit over an arbitrarily large range of separations. Our bound is valid for arbitrary source strengths, all regions of the electromagnetic spectrum, and for any imaging system with an inversion-symmetric point-spread function. The measurement schemes can be applied to microscopy, optical sensing, and astrometry at all wavelengths.
authors.affiliation: Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, 117583 Singapore.
authors.forename: Ranjith
authors.initials: R
authors.lastname: Nair
authors.affiliation: Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, 117583 Singapore.|Department of Physics, National University of Singapore, 2 Science Drive 3, 117551 Singapore.
authors.forename: Mankei
authors.initials: M
authors.lastname: Tsang