Resolving starlight: a quantum perspective

Abstract

The wave-particle duality of light introduces two fundamental problems to imaging, namely, the diffraction limit and the photon shot noise. Quantum information theory can tackle them both in one holistic formalism: model the light as a quantum object, consider any quantum measurement, and pick the one that gives the best statistics. While Helstrom pioneered the theory half a century ago and first applied it to incoherent imaging, it was not until recently that the approach offered a genuine surprise on the age-old topic by predicting a new class of superior imaging methods. For the resolution of two sub-Rayleigh sources, the new methods have been shown theoretically and experimentally to outperform direct imaging and approach the true quantum limits. Recent efforts to generalize the theory for an arbitrary number of sources suggest that, despite the existence of harsh quantum limits, the quantum-inspired methods can still offer significant improvements over direct imaging for subdiffraction objects, potentially benefiting many applications in astronomy as well as fluorescence microscopy.

Semiparametric estimation for incoherent optical imaging

“…On the practical side, the theory may be accused of assuming ideal conditions for both measurements, such as infinitesimal pixels for direct imaging, the availability of infinitely many modes for SPADE, perfect specification and knowledge of the optical systems, and the absence of excess noise. Reality is necessarily uglier, but the results here remain relevant by serving as fundamental limits (via the data-processing inequality [51,68]) and offering insights into the essential physics. The theoretical and experimental progress on SPADE and related methods so far [69][70][71] has provided encouragement that the theory has realistic potential, and the general results here should motivate further research into the wider applications of quantuminspired imaging methods.…”

“…An intuitive explanation of the enhancement, as well as a discussion of the limitations of SPADE, can be found in Ref. [51]. The constrained CRB with θ 0 = 1 becomes [O(∆ k ) − θ 2 k ]/N = O(∆ k )/N , which is on the same order of magnitude as the fundamental quantum limit [26].…”

“…The advantage of SPADE over direct imaging occurs in the subdiffraction regime, where the width ∆ of the object distribution F with respect to the origin is much smaller than the width of the point-spread function ψ [24][25][26]51]. As the width of ψ is normalized as 1, the regime is defined as For direct imaging in the subdiffraction regime, the image becomes close to the point-spread function, viz., 4) where N , the expected photon number received in total, is given by Eq.…”

“…where the image-plane coordinate z is normalized with respect to the magnification factor, both y and z are normalized with respect to the width of the point-spread function such that they are dimensionless, and ψ is normalized as |ψ(x)| 2 dx = 1. This semiclassical Poisson model can be derived from standard quantum optics [23,51,62].…”

“…Appendix C shows a way of reconstructing F from θ via an orthogonal-series expansion, following Ref. [51]. The score function for each θ j is…”