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Journal of the Optical Society of America A

Maximizing the information transfer in a quantum-limited light-scattering system

Lars Lading, Thomas Martini Jørgensen

Published Jul 1, 1990• 11 citations
Publisher

Abstract

A quantum-limited light-scattering system is considered. The spatial configuration that maximizes a given figure of merit is investigated, assuming that the emitted light has Poisson photon statistics. A specific system for measuring the velocity of a small particle is considered as an example. An optimum spatial code is found for the case of dominating intrinsic signal noise. The robustness of this solution is discussed in relation to the case of dominating background noise.

DOI
10.1364/josaa.7.001324

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A quantum-limited light-scattering system is considered. The spatial configuration that maximizes a given figure of merit is investigated, assuming that the emitted light has Poisson photon statistics. A specific system for measuring the velocity of a small particle is considered as an example. An optimum spatial code is found for the case of dominating intrinsic signal noise. The robustness of this solution is discussed in relation to the case of dominating background noise.
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A limitation of free-space optical communications is the ease with which the information can be intercepted. Overcoming this limitation is possible by hiding the information within the background optical noise that is present in all real-world situations. We demonstrate the limitations of our experimental system for transferring images over free-space using a photon-pair source emitting two correlated beams. The system uses spontaneous parametric down-conversion to create photon-pairs, where one photon contains the spatial information and the other the heralding information.
Because of quantum noise fluctuations, the rate of error achievable in decision problems involving several possible configurations of a scattering system is subject to a fundamental limit known as the Helstrom bound. Here, we present a general framework to calculate and minimize this bound using coherent probe fields with tailored spatial distributions. As an example, we experimentally study a target located in between two disordered scattering media. We first show that the optimal field distribution can be directly identified using a general approach based on scattering matrix measurements. We then demonstrate that this optimal light field successfully probes the presence of the target with a number of photons that is reduced by more than 2 orders of magnitude as compared to unoptimized fields.
Because of quantum noise fluctuations, the rate of error achievable in decision problems involving several possible configurations of a scattering system is subject to a fundamental limit known as the Helstrom bound. Here, we present a general framework to calculate and minimize this bound using coherent probe fields with tailored spatial distributions. As an example, we experimentally study a target located in between two disordered scattering media. We first show that the optimal field distribution can be directly identified using a general approach based on scattering matrix measurements. We then demonstrate that this optimal light field successfully probes the presence of the target with a number of photons that is reduced by more than 2 orders of magnitude as compared to unoptimized fields.
The accuracy of optical measurements at low light levels is limited by the quantum noise of the source and by the random nature of the interaction with the measured object. The source noise may be reduced by use of nonclassical photon-number squeezed light. This paper considers the use of two photon-correlated beams (generated, for example, by spontaneous parametric downconversion) to measure the optical transmittance of an object. The photons of each beam obey a random Poisson process, but are synchronized in time. One beam is used to probe the object while the other is used as a reference providing information on the realization of the random arrival of photons at the object. The additional information available by such measurement may be exploited to improve the accuracy of the measurement. Various estimators, including the maximum likelihood estimator, are considered and their performance is evaluated and compared with the measurement based on single-beam conventional (Poisson) source and maximally squeezed (fixed photon number) source. The performance advantage established in this paper depends on parameters such as the intensity of the source, the transmittance of the object, the quantum efficiency of the detectors, the background noise, and the degree of correlation of the photon numbers in the two beams.
In metrology, Fisher information is an important metric that quantifies the precision that can be achieved in a measurement. For optical measurements using coherent light it has been shown that Fisher information can be expressed simply using the scattering matrix of the system. Fisher information can be maximized over the input modes to achieve maximum information states, which produce optimally precise estimates for a parameter when the system is limited by photon noise. Here, we extend this approach to multiparameter estimation, in which case Fisher information takes the form of a matrix. We consider several scalar functions of the Fisher matrix to optimize the precision in multiple parameters at the same time. We also consider strategies for dealing with nuisance parameters, which can degrade the achievable precision of other parameters but are not of interest to measure. We corroborate our findings numerically using a scattering system of 2D coupled dipoles.