Semiparametric estimation for incoherent optical imaging
arXiv:1906.04578 · doi:10.1103/PhysRevResearch.1.033006
Abstract
The theory of semiparametric estimation offers an elegant way of computing the Cramér-Rao bound for a parameter of interest in the midst of infinitely many nuisance parameters. Here I apply the theory to the problem of moment estimation for incoherent imaging under the effects of diffraction and photon shot noise. Using a Hilbert-space formalism designed for Poisson processes, I derive exact semiparametric Cramér-Rao bounds and efficient estimators for both direct imaging and a quantum-inspired measurement method called spatial-mode demultiplexing (SPADE). The results establish the superiority of SPADE even when little prior information about the object is available.
15 pages, 3 figures. v2: minor improvements
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- Efficient lineshape estimation by ghost spectroscopy
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