Quantum Limits on Localizing Point Objects against a Uniformly Bright
Disk
- URL: http://arxiv.org/abs/2211.16395v2
- Date: Sun, 19 Mar 2023 20:07:51 GMT
- Title: Quantum Limits on Localizing Point Objects against a Uniformly Bright
Disk
- Authors: Sudhakar Prasad
- Abstract summary: We calculate the quantum Fisher information (QFI) for estimating, using a circular imaging aperture, the two-dimensional location of a point source against a uniformly bright disk of known center and radius in the ideal photon-counting limit.
A related problem of the quantum limit on estimating the location of a small-area brightness hole in an otherwise uniformly bright disk is also treated perturbatively in powers of the ratio of the areas of the hole and the background disk.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We calculate the quantum Fisher information (QFI) for estimating, using a
circular imaging aperture, the two-dimensional location of a point source
against a uniformly bright disk of known center and radius in the ideal
photon-counting limit. We present both a perturbative calculation of the QFI in
powers of the background-to-source brightness ratio and a numerically exact
calculation of the QFI in the eigen-basis of the one-photon density operator. A
related problem of the quantum limit on estimating the location of a small-area
brightness hole in an otherwise uniformly bright disk, a problem of potential
interest to the extrasolar planet detection community, is also treated
perturbatively in powers of the ratio of the areas of the hole and the
background disk. We then numerically evaluate the Cramer-Rao lower bound (CRB)
for wavefront projections in three separate bases, those comprised of Zernike,
Fourier-Bessel and localized point-source modes, for unbiased estimation of the
two position coordinates of the point source and of the brightness hole center,
respectively, for the two problems. By comparing these CRBs with the
corresponding quantum-limited minimum error variances, given by inverting the
QFI matrix, and with the CRBs associated with direct imaging, we assess the
maximum efficiency of these wavefront projections in performing such
estimations.
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