Enhancing axial localization with wavefront control.

Enhancing the ability to resolve axial details is crucial in three-dimensional optical imaging. We provide experimental evidence showcasing the ultimate precision achievable in axial localization using vortex beams. For Laguerre-Gauss (LG) beams, this remarkable limit can be attained with just a single intensity scan. This proof-of-principle demonstrates that microscopy techniques based on LG vortex beams can potentially benefit from the introduced quantum-inspired superresolution protocol.

Intensity-Based Axial Localization at the Quantum Limit.

We derive fundamental precision bounds for single-point axial localization. For Gaussian beams, this ultimate limit can be achieved with a single intensity scan, provided the camera is placed at one of two optimal transverse detection planes. Hence, for axial localization there is no need of more complicated detection schemes. The theory is verified with an experimental demonstration of axial resolution 3 orders of magnitude below the classical depth of focus.

Reading out Fisher information from the zeros of the point spread function.

We show that, for optical systems whose point spread functions exhibit isolated zeros, the information one can gain about the separation between two incoherent point light sources does not scale quadratically with the separation (which is the distinctive dependence causing Rayleigh's curse) but only linearly. Moreover, the dominant contribution to the separation information comes from regions in the vicinity of these zeros. We experimentally confirm this idea, demonstrating significant superresolution using natural or artificially created spectral doublets.

Quantum-Limited Time-Frequency Estimation through Mode-Selective Photon Measurement.

By projecting onto complex optical mode profiles, it is possible to estimate arbitrarily small separations between objects with quantum-limited precision, free of uncertainty arising from overlapping intensity profiles. Here we extend these techniques to the time-frequency domain using mode-selective sum-frequency generation with shaped ultrafast pulses. We experimentally resolve temporal and spectral separations between incoherent mixtures of single-photon level signals ten times smaller than their optical bandwidths with a tenfold improvement in precision over the intensity-only Cramér-Rao bound.

Optimal measurements for resolution beyond the Rayleigh limit.

We establish the conditions to attain the ultimate resolution predicted by quantum estimation theory for the case of two incoherent point sources using a linear imaging system. The solution is closely related to the spatial symmetries of the detection scheme. In particular, for real symmetric point spread functions, any complete set of projections with definite parity achieves the goal.