Resolution limits of spatial mode demultiplexing with noisy detection

Abstract

We consider the problem of estimating the spatial separation between two mutually incoherent point light sources using the super-resolution imaging technique based on spatial mode demultiplexing (SPADE) with noisy detectors. We show that in the presence of noise, the resolution of the measurement is limited by the signal-to-noise ratio (SNR) and the minimum resolvable spatial separation has a characteristic dependence of [Formula: see text]. Several detection techniques, including direct photon counting, as well as homodyne and heterodyne detection are considered.

Optimal Observables and Estimators for Practical Superresolution Imaging

“…Accordingly, this estimator is remarkably simpler to implement experimentally than standard methods requiring the full counting statistics. Moreover, it takes into account misalignment [18,33,34], cross talk [35], and detector noise [36][37][38], and therefore it is directly relevant for practical applications. Even in the presence of the aforementioned imperfections, for faint sources, this estimator is efficient, i.e., it saturates the Cramér-Rao bound.…”

Imaging arbitrary incoherent source distributions with near quantum-limited resolution

“…Instead, the quantum limit is achieved by projecting the light field onto a set of orthogonal spatial modes before detection, sometimes referred to as spatial mode demultiplexing imaging (SPADE). Subsequent work, both theoretical and experimental, has confirmed this approach for achieving quantum-limited localization of two point sources 7 – 15 , including in the presence of noise and crosstalk 16 – 18 , with experimental realizations of SPADE using interferometers 12 , digital holography 13 , 14 , and nonlinear techniques 15 . In addition, the use of multi-plane light conversion methods has demonstrated the feasability of demultiplexing a large number of imaging modes 19 – 21 .…”

Moment-based superresolution: Formalism and applications

“…Electronic noise at the detection stage introduces additional photon counts, the dark counts, which contain no information on the parameter value d. Consequently, the signal-to-noise ratio in each detection mode is reduced by dark counts (dc). The impact of this noise source on distance estimation via spatial-mode demultiplexing has been investigated in the recent literature [37][38][39]. Despite the different approaches, all these works obtained the same qualitative result: Dark counts cause the Fisher information to drop to zero for small source separations.…”

“…The derivative vector is obtained from the mean intensity per pixel (37), where the dependence on the parameter d is only contained in the functions i j and i j (38),…”