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

TL;DR

This paper rigorously analyzes the impact of photon losses and coherence on super-resolution imaging, establishing fundamental limits and validating the optimality of SPADE measurements across different coherence levels.

Contribution

It provides a quantum-mechanical proof of the relation between losses and coherence, derives limits on source separation estimation, and clarifies the validity of measurement strategies in super-resolution imaging.

Findings

Photon losses are fundamental and universally relate to coherence properties.

SPADE measurement remains optimal regardless of source coherence.

Incorrect models with zero transmission lead to misleading resolution claims.

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.