Abstract
A novel interferometric method - SLIVER (Super Localization by Image inVERsion interferometry) - is proposed for estimating the separation of two incoherent point sources with a mean squared error that does not deteriorate as the sources are brought closer. The essential component of the interferometer is an image inversion device that inverts the field in the transverse plane about the optical axis, assumed to pass through the centroid of the sources. The performance of the device is analyzed using the Cramér-Rao bound applied to the statistics of spatially-unresolved photon counting using photon number-resolving and on-off detectors. The analysis is supported by Monte-Carlo simulations of the maximum likelihood estimator for the source separation, demonstrating the superlocalization effect for separations well below that set by the Rayleigh criterion. Simulations indicating the robustness of SLIVER to mismatch between the optical axis and the centroid are also presented. The results are valid for any imaging system with a circularly symmetric point-spread function.
Highlights
Rayleigh’s criterion for resolution of two incoherent point sources, which asserts that a minimum separation between the sources equal to the diffraction-limited spot size is necessary for them to be resolvable, has perhaps been the most influential resolution criterion in the history of optics despite its heuristic character [1,2]
This phenomenon was dubbed Rayleigh’s curse in [7] as it suggests a fundamental limitation in resolving incoherent point sources even when the role of the average detected photon number is taken into account
We propose a new interferometric scheme for estimating source separation that we call SLIVER (Super Localization by Image inVERsion interferometry) and that yields finite resolution for arbitrarily small values of the source separation and for arbitrary source strengths
Summary
Rayleigh’s criterion for resolution of two incoherent point sources, which asserts that a minimum separation between the sources equal to the diffraction-limited spot size is necessary for them to be resolvable, has perhaps been the most influential resolution criterion in the history of optics despite its heuristic character [1,2]. Based on the Cramer-Rao (CR) lower bound of estimation theory [6], it was shown in [3, 4] that any (unbiased) estimate of the separation between the sources based on image-plane photon counting must suffer a divergent mean squared error for a given mean photon number as the separation tends to zero This phenomenon was dubbed Rayleigh’s curse in [7] as it suggests a fundamental limitation in resolving incoherent point sources even when the role of the average detected photon number is taken into account. A linear optics-based measurement – spatial-mode demultiplexing (SPADE) – was proposed and shown in principle to approach the quantum bound for all values of the separation These results are in stark contrast to the performance of image-plane photon counting mentioned above, as the divergent behavior of the minimum MSE with decreasing separation – Rayleigh’s curse – is conspicuously absent. We offer an explanation for the superlocalization effect of SLIVER at small values of separation in the language of estimation theory applied to the photodetection statistics for thermal light
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
