Quantum-Limited Distance Estimation in Three-Dimensional Optical Superresolution

• URL: http://arxiv.org/abs/2608.04876v1
• Date: Wed, 05 Aug 2026 14:05:29 GMT
• Title: Quantum-Limited Distance Estimation in Three-Dimensional Optical Superresolution
• Abstract summary: We derive the quantum-limited precision for estimating the full distance between two incoherent point sources.<n>We show that the distance information remains finite in the sub-Rayleigh regime.
• Score: 6.3190120766541575
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum superresolution reveals that the vanishing of separation sensitivity in conventional imaging below the Rayleigh limit does not necessarily indicate a fundamental loss of information in the optical field. However, the quantum limit for estimating the physical distance between two incoherent point sources in three-dimensional imaging systems and its dependence on the spatial structure of the point-spread function remains largely unknown. In this work, we derive the quantum-limited precision for estimating the full distance between two incoherent point sources with arbitrary intensity imbalance in a three-dimensional spatially invariant imaging system. We show that the distance information remains finite in the sub-Rayleigh regime and is governed by the second-order displacement-response tensor of the point-spread function. The eigensystem of this tensor determines the optimal relative orientation between the two sources, and reflection symmetries of the point-spread function can further provide a simplified means of identifying the optimal orientation. This geometric structure is coordinate invariant and provides a direct strategy for improving resolution by physically rotating an anisotropic imaging system to align its optimal principal response direction with the source displacement. For a general three-dimensional Gaussian point-spread function, the response tensor is proportional to the inverse spatial covariance, establishing a direct connection between quantum-limited distance precision and the geometry of Gaussian distribution.

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