Abstract
We demonstrate an approach to obtaining near quantum-limited far-field imaging resolution of incoherent sources with arbitrary distributions. Our method assumes no prior knowledge of the source distribution, but rather uses an adaptive approach to imaging via spatial mode demultiplexing that iteratively updates both the form of the spatial imaging modes and the estimate of the source distribution. The optimal imaging modes are determined by minimizing the estimated Cramér-Rao bound over the manifold of all possible sets of orthogonal imaging modes. We have observed through Monte Carlo simulations that the manifold-optimized spatial mode demultiplexing measurement consistently outperforms standard imaging techniques in the accuracy of source reconstructions and comes within a factor of 2 of the absolute quantum limit as set by the quantum Cramér-Rao bound. The adaptive framework presented here allows for a consistent approach to achieving near quantum-limited imaging resolution of arbitrarily distributed sources through spatial mode imaging techniques.
Highlights
We demonstrate an approach to obtaining near quantum-limited far-field imaging resolution of incoherent sources with arbitrary distributions
We demonstrate an adaptive method for achieving near quantum-limited resolution of thermal or incoherent sources based on optimizing the spatial imaging modes over the manifold of orthonormal functions, which we term manifold-optimized spatial mode demultiplexing (MO-spatial mode demultiplexing imaging (SPADE))
These results suggest that for far-field incoherent imaging, collective measurements can provide at most a factor of 2 improvement in the Cramér-Rao bound (CRB) compared to the optimal projective measurements as provided by MOSPADE imaging, even in the deep sub-Rayleigh regime
Summary
We demonstrate an approach to obtaining near quantum-limited far-field imaging resolution of incoherent sources with arbitrary distributions. It was shown that the traditional method of far-field imaging, (i.e., detecting photons in the position basis in the image plane) which we will refer to as direct imaging, falls significantly short of the quantum limit of resolution when estimating the separation of two incoherent point s ources[6].
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