Interferometric superlocalization of two incoherent optical point sources

Area of Science:

• Optics and Photonics
• Quantum Metrology
• Super-resolution Imaging

Background:

• Estimating the separation of closely spaced incoherent point sources is a fundamental challenge in optical metrology.
• Traditional methods often face limitations due to the diffraction limit, such as the Rayleigh criterion.
• Achieving super-localization, surpassing classical resolution limits, is crucial for advanced imaging applications.

Purpose of the Study:

• To introduce a novel interferometric method, SLIVER (Super Localization by Image inVERsion interferometry), for enhanced point source separation estimation.
• To analyze the theoretical performance limits of SLIVER using the Cramér-Rao bound.
• To demonstrate the super-localization capability and robustness of SLIVER through simulations.

Main Methods:

• Development of an interferometric setup incorporating an image inversion device.
• Theoretical analysis using the Cramér-Rao bound for photon counting statistics with photon number-resolving and on-off detectors.
• Monte Carlo simulations of the maximum likelihood estimator for source separation estimation.

Main Results:

• The proposed SLIVER method enables mean squared error for source separation estimation that does not increase as sources get closer.
• Super-localization is demonstrated for separations significantly below the Rayleigh criterion.
• Simulations confirm the robustness of SLIVER to misalignment between the optical axis and source centroid.

Conclusions:

• SLIVER offers a powerful new approach for high-precision measurement of closely spaced incoherent point sources.
• The method overcomes the limitations imposed by the Rayleigh criterion, achieving super-localization.
• The technique is applicable to any imaging system with a circularly symmetric point-spread function.