Eur. Phys. J. D 50, 215-227 (2008)
https://doi.org/10.1140/epjd/e2008-00211-3

Optimal precision of parameter estimation in images with local sub-Poissonian quantum fluctuations

¹ Physics and Image Processing Group, Institut Fresnel, Aix-Marseille Université, École Centrale Marseille, CNRS, D.U. Saint Jérôme, 13013 Marseille, France
² Quantum Optics Group, Laboratoire Kastler Brossel, Université Pierre et Marie Curie-Paris 6, École Normale Supérieure, CNRS, CC74, 4 Place Jussieu, 75252 Paris Cedex 05, France

Corresponding authors: ^a julien.fade@fresnel.fr - ^b treps@spectro.jussieu.fr - ^c philippe.refregier@fresnel.fr

Received: 17 July 2008
Revised: 13 October 2008
Published online: 5 November 2008

Abstract

Non-classical quantum effects allow light with local sub-Poissonian fluctuations below shot noise to be produced. We show that using such light can improve the estimation precision of a parameter in an image beyond the standard Poissonian limit. This benefit is theoretically investigated by means of a phenomenological model of local sub-Poissonian noise which assumes the independence of the fluctuations in each pixel. In particular, a bound on the best precision expectable independently of the exact unbiased estimation protocol used, which is given by the Cramer-Rao bound, is determined from this model. The numerical simulations presented in the special case of the estimation of a displacement of an image perturbed with local sub-Poissonian noise show that a standard estimator can overcome the classical Poissonian limit by reaching this limit precision only beyond a certain value of the photon flux which we characterize. We eventually present some numerical results that demonstrate the generality of the model proposed, of the optimality bounds and of the estimator performance.