TY - JOUR

T1 - Attaining the quantum limit of superresolution in imaging an object's length via predetection spatial-mode sorting

AU - Dutton, Zachary

AU - Kerviche, Ronan

AU - Ashok, Amit

AU - Guha, Saikat

N1 - Funding Information:
The authors thank Michael Grace for useful comments on the manuscript. This work was supported in part by the Defense Advanced Research Projects Agency (DARPA) REVEAL program under Contract No. HR0011-16-C-0026 and in part by a DARPA EXTREME program seedling under Contract No. HR0011-17-1-0007. The content or the information presented in this paper does not necessarily reflect the position or policy of either DARPA or the U.S. Government, and no such official endorsement should be inferred. This document does not contain technology or technical data controlled under either the U.S. International Traffic in Arms Regulations or the U.S. Export Administration Regulations.
Publisher Copyright:
© 2019 American Physical Society.

PY - 2019/3/25

Y1 - 2019/3/25

N2 - We consider estimating the length of an incoherently radiating quasimonochromatic extended object of length much smaller than the traditional diffraction limit, the Rayleigh length. This is the simplest abstraction of the problems of estimating the diameter of a star in astronomical imaging or the dimensions of a cellular feature in biological imaging. We find, as expected by the Rayleigh criterion, that the Fisher information (FI) of the object's length, per integrated photon, vanishes in the limit of small sub-Rayleigh length for an ideal image-plane direct-detection receiver. With an image-plane Hermite-Gaussian (HG) mode sorter followed by direct detection, we show that this normalized FI does not diminish with decreasing object length. The FI per photon of both detection strategies gradually decreases as the object length greatly exceeds the Rayleigh limit, due to the relative inefficiency of information provided by photons emanating from near the center of the object about its length. We evaluate the quantum Fisher information per unit integrated photon and find that the HG mode sorter exactly achieves this limit at all values of the object length. Further, a simple binary mode sorter maintains the advantage of the full mode sorter at highly sub-Rayleigh lengths. In addition to this FI analysis, we quantify improvement in terms of the actual mean-square error of the length estimate using predetection mode sorting. We consider the effect of imperfect mode sorting and show that the performance improvement over direct detection is robust over a range of sub-Rayleigh lengths.

AB - We consider estimating the length of an incoherently radiating quasimonochromatic extended object of length much smaller than the traditional diffraction limit, the Rayleigh length. This is the simplest abstraction of the problems of estimating the diameter of a star in astronomical imaging or the dimensions of a cellular feature in biological imaging. We find, as expected by the Rayleigh criterion, that the Fisher information (FI) of the object's length, per integrated photon, vanishes in the limit of small sub-Rayleigh length for an ideal image-plane direct-detection receiver. With an image-plane Hermite-Gaussian (HG) mode sorter followed by direct detection, we show that this normalized FI does not diminish with decreasing object length. The FI per photon of both detection strategies gradually decreases as the object length greatly exceeds the Rayleigh limit, due to the relative inefficiency of information provided by photons emanating from near the center of the object about its length. We evaluate the quantum Fisher information per unit integrated photon and find that the HG mode sorter exactly achieves this limit at all values of the object length. Further, a simple binary mode sorter maintains the advantage of the full mode sorter at highly sub-Rayleigh lengths. In addition to this FI analysis, we quantify improvement in terms of the actual mean-square error of the length estimate using predetection mode sorting. We consider the effect of imperfect mode sorting and show that the performance improvement over direct detection is robust over a range of sub-Rayleigh lengths.

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U2 - 10.1103/PhysRevA.99.033847

DO - 10.1103/PhysRevA.99.033847

M3 - Article

AN - SCOPUS:85064045002

VL - 99

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 3

M1 - 033847

ER -