Discrimination and estimation of incoherent sources under misalignment
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Discrimination and estimation of incoherent sources under misalignment. / De Almeida, J. O.; Kołodyński, J.; Hirche, C.; Lewenstein, M.; Skotiniotis, M.
I: Physical Review A, Bind 103, Nr. 2, 022406, 2021.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Discrimination and estimation of incoherent sources under misalignment
AU - De Almeida, J. O.
AU - Kołodyński, J.
AU - Hirche, C.
AU - Lewenstein, M.
AU - Skotiniotis, M.
PY - 2021
Y1 - 2021
N2 - Spatially resolving two incoherent point sources whose separation is well below the diffraction limit dictated by classical optics has recently been shown possible using techniques that decompose the incoming radiation into orthogonal transverse modes. Such a demultiplexing procedure, however, must be perfectly calibrated to the transverse profile of the incoming light as any misalignment of the modes effectively restores the diffraction limit for small source separations. We study by how much can one mitigate such an effect at the level of measurement which, after being imperfectly demultiplexed due to inevitable misalignment, may still be partially corrected by linearly transforming the relevant dominating transverse modes. We consider two complementary tasks: the estimation of the separation between the two sources and the discrimination between one and two incoherent point sources. We show that, although one cannot fully restore super-resolving powers even when the value of the misalignment is perfectly known, its negative impact on the ultimate sensitivity can be significantly reduced. In the case of estimation we analytically determine the exact relation between the minimal resolvable separation as a function of misalignment whereas for discrimination we analytically determine the relation between misalignment and the probability of error, as well as numerically determine how the latter scales in the limit of long interrogation times.
AB - Spatially resolving two incoherent point sources whose separation is well below the diffraction limit dictated by classical optics has recently been shown possible using techniques that decompose the incoming radiation into orthogonal transverse modes. Such a demultiplexing procedure, however, must be perfectly calibrated to the transverse profile of the incoming light as any misalignment of the modes effectively restores the diffraction limit for small source separations. We study by how much can one mitigate such an effect at the level of measurement which, after being imperfectly demultiplexed due to inevitable misalignment, may still be partially corrected by linearly transforming the relevant dominating transverse modes. We consider two complementary tasks: the estimation of the separation between the two sources and the discrimination between one and two incoherent point sources. We show that, although one cannot fully restore super-resolving powers even when the value of the misalignment is perfectly known, its negative impact on the ultimate sensitivity can be significantly reduced. In the case of estimation we analytically determine the exact relation between the minimal resolvable separation as a function of misalignment whereas for discrimination we analytically determine the relation between misalignment and the probability of error, as well as numerically determine how the latter scales in the limit of long interrogation times.
UR - http://www.scopus.com/inward/record.url?scp=85100649396&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.103.022406
DO - 10.1103/PhysRevA.103.022406
M3 - Journal article
AN - SCOPUS:85100649396
VL - 103
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
SN - 1050-2947
IS - 2
M1 - 022406
ER -
ID: 257365253