Back to sources – the role of losses and coherence in super-resolution imaging revisited

Stanislaw Kurdzialek

Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warszawa, Poland
Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warszawa, Poland

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Abstract

Photon losses are intrinsic for any translationally invariant optical imaging system with a non-trivial Point Spread Function, and the relation between the transmission factor and the coherence properties of an imaged object is universal – we demonstrate the rigorous proof of this statement, based on the principles of quantum mechanics. The fundamental limit on the precision of estimating separation between two partially coherent sources is then derived. The careful study of the role of photon losses allows to resolve conflicting claims present in previous works. We compute the Quantum Fisher Information for the generic model of optical 4f imaging system, and use prior considerations to validate the result for a general, translationally invariant imaging apparatus. We prove that the spatial-mode demultiplexing (SPADE) measurement, optimal for non-coherent sources, remains optimal for an arbitrary degree of coherence. Moreover, we show that some approximations, omnipresent in theoretical works about optical imaging, inevitably lead to unphysical, zero-transmission models, resulting in misleading claims regarding fundamental resolution limits.

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Cited by

[1] Francesco V. Pepe, Giovanni Scala, Gabriele Chilleri, Danilo Triggiani, Yoon-Ho Kim, and Vincenzo Tamma, "Distance sensitivity of thermal light second-order interference beyond spatial coherence", The European Physical Journal Plus 137 6, 647 (2022).

[2] Giacomo Sorelli, Manuel Gessner, Mattia Walschaers, and Nicolas Treps, "Quantum limits for resolving Gaussian sources", Physical Review Research 4 3, L032022 (2022).

[3] Mankei Tsang, "Poisson Quantum Information", arXiv:2103.08532.

[4] Kevin Liang, S. A. Wadood, and A. N. Vamivakas, "Coherence effects on estimating general sub-Rayleigh object distribution moments", Physical Review A 104 2, 022220 (2021).

[5] Giacomo Sorelli, Manuel Gessner, Mattia Walschaers, and Nicolas Treps, "Gaussian quantum metrology for mode-encoded parameters: general theory and imaging applications", arXiv:2202.10355.

[6] Konstantin Katamadze, Boris Bantysh, Andrey Chernyavskiy, Yurii Bogdanov, and Sergei Kulik, "Breaking Rayleigh's curse for multi-parameter objects using BLESS technique", arXiv:2112.13244.

[7] Ilya Karuseichyk, Giacomo Sorelli, Manuel Gessner, Mattia Walschaers, and Nicolas Treps, "Resolving Mutually Coherent Bright Point-Sources", arXiv:2111.02233.

The above citations are from Crossref's cited-by service (last updated successfully 2022-10-04 09:09:35) and SAO/NASA ADS (last updated successfully 2022-10-04 09:09:36). The list may be incomplete as not all publishers provide suitable and complete citation data.