TY - JOUR

T1 - Attaining quantum limited precision of localizing an object in passive imaging

AU - Sajjad, Aqil

AU - Grace, Michael R.

AU - Zhuang, Quntao

AU - Guha, Saikat

N1 - Funding Information:
The authors thank Mankei Tsang and Ranjith Nair for valuable discussions. This work was supported by a Defense Advanced Research Projects Agency (DARPA) Defense Sciences Office seedling project awarded under Contract No. W911NF2010039. Q.Z. acknowledges the DARPA Young Faculty Award for support through Grant No. N660012014029.
Publisher Copyright:
© 2021 American Physical Society.

PY - 2021/8

Y1 - 2021/8

N2 - We investigate our ability to determine the mean position, or centroid, of a linear array of equally bright incoherent point sources of light whose continuum limit is the problem of estimating the center of a uniformly radiating object. We consider two receivers, an image-plane ideal direct-detection imager and a receiver that employs Hermite-Gaussian (HG) spatial-mode demultiplexing in the image plane, prior to shot-noise-limited photon detection. We compare the Fisher information (FI) for estimating the centroid achieved by these two receivers, which quantifies the information-accrual rate per photon, and compare those with the quantum Fisher information (QFI): the maximum attainable FI by any choice of measurement on the collected light allowed by physics. We find that focal-plane direct imaging is strictly suboptimal, although not by a large margin. We also find that not only is the HG mode sorter, which is the optimal measurement for estimating the separation between point sources (or the length of a line object), suboptimal, but it performs worse than direct imaging. We study the scaling behavior of the QFI and direct imaging's FI for a continuous uniformly bright object in terms of its length and find that both are inversely proportional to the object's length when it is sufficiently larger than the Rayleigh length. Finally, we propose a two-stage adaptive modal receiver design that attains the QFI for centroid estimation.

AB - We investigate our ability to determine the mean position, or centroid, of a linear array of equally bright incoherent point sources of light whose continuum limit is the problem of estimating the center of a uniformly radiating object. We consider two receivers, an image-plane ideal direct-detection imager and a receiver that employs Hermite-Gaussian (HG) spatial-mode demultiplexing in the image plane, prior to shot-noise-limited photon detection. We compare the Fisher information (FI) for estimating the centroid achieved by these two receivers, which quantifies the information-accrual rate per photon, and compare those with the quantum Fisher information (QFI): the maximum attainable FI by any choice of measurement on the collected light allowed by physics. We find that focal-plane direct imaging is strictly suboptimal, although not by a large margin. We also find that not only is the HG mode sorter, which is the optimal measurement for estimating the separation between point sources (or the length of a line object), suboptimal, but it performs worse than direct imaging. We study the scaling behavior of the QFI and direct imaging's FI for a continuous uniformly bright object in terms of its length and find that both are inversely proportional to the object's length when it is sufficiently larger than the Rayleigh length. Finally, we propose a two-stage adaptive modal receiver design that attains the QFI for centroid estimation.

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U2 - 10.1103/PhysRevA.104.022410

DO - 10.1103/PhysRevA.104.022410

M3 - Article

AN - SCOPUS:85113133749

VL - 104

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 2

M1 - 022410

ER -