Quantum-limited estimation of the axial separation of two incoherent point sources

Abstract

Improving axial resolution is crucial for three-dimensional optical imaging systems. Here we present a scheme of axial superresolution for two incoherent point sources based on spatial mode demultiplexing. A radial mode sorter is used to losslessly decompose the optical fields into a radial mode basis set to extract the phase information associated with the axial positions of the point sources. We show theoretically and experimentally that, in the limit of a zero axial separation, our scheme allows for reaching the quantum Cramér-Rao lower bound and thus can be considered as one of the optimal measurement methods. Unlike other superresolution schemes, this scheme does not require neither activation of fluorophores nor sophisticated stabilization control. Moreover, it is applicable to the localization of a single point source in the axial direction. Our demonstration can be useful to a variety of applications such as far-field fluorescence microscopy. OCIS codes: (100.6640) Superresolution; (030.4070) Modes; (270.5585) Quantum information and processing. http://dx.

Intensity-Based Axial Localization at the Quantum Limit

“…This agrees with the result recently found in Ref. [29], which discusses the ultimate limits for two-point axial resolution. Direct detection.-In general, the qFI would be distributed between the phase and intensity variations of the measured beam.…”

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 .…”

“…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 separation estimation of two point sources [7][8][9][10][11][12][13][14], with experimental realizations of SPADE imaging using interferometers [12] or digital holography techniques [13,14].…”

Collective super-resolving measurements for mixed bosonic states

“…Specifically, in [9] a measurement in the Hermite Gauss modes of an imaging system, analysing light from two equally bright, incoherent point sources was shown to be capable of resolving two point spread functions (PSF) regardless of their separation. The phenomenon, known as super-resolution, has been the subject of increasing interest both theoretically [10][11][12][13][14][15][16][17][18][19][20] and experimentally [21][22][23][24][25]. However, super-resolving measurements require additional information of some nuisance parameter-in the case of [9] knowledge of the mean of the intensity distribution (the PSFs centroid).…”