Realistic sub-Rayleigh imaging with phase-sensitive measurements

Abstract

As the separation between two emitters is decreased below the Rayleigh limit, the information that can be gained about their separation using traditional imaging techniques, photon counting in the image plane, reduces to nil. Assuming the sources are of equal intensity, Rayleigh's 'curse' can be alleviated by making phase-sensitive measurements in the image plane. However, with unequal and unknown intensities the curse returns regardless of the measurement, though the ideal scheme would still outperform image plane counting (IPC), i.e. recording intensities on a screen. We analyze the limits of the super-resolved position localization by inversion of coherence along an edge (SPLICE) phase measurement scheme as the intensity imbalance between the emitters grows. We find that SPLICE still outperforms IPC for moderately disparate intensities. For larger intensity imbalances we propose a hybrid of IPC and SPLICE, which we call 'adapted SPLICE', requiring only simple modifications. Using Monte Carlo simulation, we identify regions (emitter brightness, separation, intensity imbalance) where it is advantageous to use SPLICE over IPC, and when to switch to the adapted SPLICE measurement. We find that adapted SPLICE can outperform IPC for large intensity imbalances, e.g. 10 000:1, with the advantage growing with greater disparity between the two intensities. Finally, we also propose additional phase measurements for estimating the statistical moments of more complex source distributions. Our results are promising for implementing phase measurements in sub-Rayleigh imaging tasks such as exoplanet detection.

Resolving starlight: a quantum perspective

“…With hindsight this is perhaps not surprising, as moments up to the third are needed to fully parametrize unequal sources and the SNR for the third moment is fundamentally poorer. The use of SPLICE for this case was also studied by Bonsma-Fisher and co-workers [69].…”

“…[44,47]. The use of SPLICE for moment estimation was recently proposed by Bonsma-Fisher and coworkers [69].…”

A perspective on multiparameter quantum metrology: From theoretical tools to applications in quantum imaging

“…For the more realistic case of unequal intensities, Rayleigh exacts his revenge: the bound on the separation uncertainty diverges as λ 2 → 0, nevertheless an advantage can be maintained with respect to the direct imaging approach. An analytical and numerical investigation, carried out in [158], reports how an adapted version of SPLICE can perform well even in the regime of significantly unequal intensities. This relies on estimating higher order moments of the output probability distribution for a single photon.…”

Resolution limits of spatial mode demultiplexing with noisy detection

“…The consequences and importance of some of these assumptions, and the possibility of relaxing or incorporating them, have been a subject of a number of recent works. [16][17][18][19][20][21][22][23][24][25] In this paper, we address the e®ects of detection noise on the super-resolving power of the SPADE technique. The organization of this paper is as follows.…”