Quantum Limited Superresolution of Extended Sources in One and Two Dimensions

Abstract

We calculate the quantum Fisher information (QFI) for estimating, using a circular imaging aperture, the length of a uniformly bright incoherent line source with a fixed mid-point and the radius of a uniformly bright incoherent disk shaped source with a fixed center. Prolate spheroidal wavefunctions (PSWFs) on a centered line segment and its generalized version on a centered disk furnish the respective bases for computing the eigenstates and eigenvalues of the one-photon density operator, from which we subsequently calculate QFI with respect to the spatial parameters of the two sources. Zernike polynomials provide a good set into which to project the full source wavefront, and such classical wavefront projection data can realize quantum limited estimation error bound in each case. We subsequently generalize our approach to analyze sources of arbitrary brightness distributions and shapes using a certain class of Bessel Fourier functions that are closely related to the PSWFs. We illustrate the general approach by computing QFI for estimating the lengths of the principal axes of a uniformly bright, centered elliptical disk.

5 figures, 25 pages

References in corpus (5)

• Quantum metrology from a quantum information science perspective
• Subdiffraction incoherent optical imaging via spatial-mode demultiplexing
• On superresolution imaging as a multiparameter estimation problem
• Numerical Algorithms for the Computation of Generalized Prolate Spheroidal Functions
• Quantum Limited Source Localization and Pair Superresolution under Finite Emission Bandwidth

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• Quantum Limits on Localizing Point Objects against a Uniformly Bright Disk
• Quantum resolution limit of long-baseline imaging using distributed entanglement
• Quantum-limited superresolution of two arbitrary incoherent point sources: beating the resurgence of Rayleigh's curse