Quantum imaging is able to increase the resolution of the optical microscopy. It was shown that both classical [1] and quantum [2] correlated radiation together with coincidence measurements can lead to the resolution improvement.
Here we present an informational approach to optimization of the quantum source for imaging, based on high-order correlation function measurements and involving data post-processing. We formulate quantum imaging problem as a multiparametrical nonlinear optimization problem and characterize it by means of the Fisher information matrix. For a given imaged object, we minimize the lower bound on the total estimation error optimizing the quantum source parameters. In particular, using the Cramer-Rao bound, we minimize the trace of the inverse Fisher matrix in dependence of the source correlation width w.
We show that such an optimization indeed leads to higher spatial resolution for the object inference. Our analysis demonstrates existence of an optimal correlation width for two types of quantum sources: pseudo-thermal source (see picture 1 with d/d0 being dimensionless size of the imaged object features or pixels used for object representation) and biphoton source based on an SPDC crystal. Optimal correlation width was found to be of about 1-2 sizes of object features in both cases.
We demonstrate that use of consistent biased estimators with a bias stemming from physical limitations for parameters values, may considerably improve the error bounds and problem conditioning.
[1] Valencia A., Scarcelli G., D'Angelo M., Shih Y., Phys. Rev. Lett. 94, 063601 (2005).
[2] Pittman T. B., Shih Y.H., Strekalov D. V., Sergienko A.V., Phys. Rev. A. 52, R3429 (1995).
Fundamental science for quantum technologies , Quantum optics and non-classical light sources
