Quantum limits to optical pointsource localization
Abstract
Motivated by the importance of optical microscopes to science and engineering, scientists have pondered for centuries how to improve their resolution and the existence of fundamental resolution limits. In recent years, a new class of microscopes that overcome a longheld belief about the resolution have revolutionized biological imaging. Termed "superresolution" microscopy, these techniques work by accurately locating optical point sources from far field. To investigate the fundamental localization limits, here I derive quantum lower bounds on the error of locating point sources in free space, taking full account of the quantum, nonparaxial, and vectoral nature of photons. These bounds are valid for any measurement technique, as long as it obeys quantum mechanics, and serve as general nogo theorems for the resolution of microscopes. To arrive at analytic results, I focus mainly on the cases of one and two classical monochromatic sources with an initial vacuum optical state. For one source, a lower bound on the rootmeansquare position estimation error is on the order of $\lambda_0/\sqrt{N}$, where $\lambda_0$ is the freespace wavelength and $N$ is the average number of radiated photons. For two sources, owing to the statistical effect of nuisance parameters, the error bound diverges when their radiated fields overlap significantly. The use of squeezed light to enhance further the accuracy of locating one classical point source and the localization limits for partially coherent sources and singlephoton sources are also discussed. The presented theory establishes a rigorous quantum statiscal inference framework for the study of superresolution microscopy and points to the possibility of using quantum techniques for true resolution enhancement.
 Publication:

Optica
 Pub Date:
 July 2015
 DOI:
 10.1364/OPTICA.2.000646
 arXiv:
 arXiv:1411.2954
 Bibcode:
 2015Optic...2..646T
 Keywords:

 Quantum Physics;
 Physics  Optics
 EPrint:
 9 pages, 3 figures, v2: added discussion and references on singlephoton sources, improved presentation, v3: published in Optica