Semiparametric estimation for incoherent optical imaging
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 incoherent imaging under the effects of diffraction and photon shot noise, where...
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| Format: | Article |
| Language: | English |
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American Physical Society
2019-10-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.1.033006 |
| Summary: | 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 incoherent imaging under the effects of diffraction and photon shot noise, where the object may consist of an arbitrary number of point sources and the moments of their distribution are the parameters of interest. 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. |
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| ISSN: | 2643-1564 |