Joint optimal measurement for locating two incoherent optical point sources near the Rayleigh distance

• URL: http://arxiv.org/abs/2302.07606v2
• Date: Thu, 27 Apr 2023 11:25:36 GMT
• Title: Joint optimal measurement for locating two incoherent optical point sources near the Rayleigh distance
• Authors: Yingying Shi and Xiao-Ming Lu
• Abstract summary: At the Rayleigh distance the incompatibility coefficient vanishes and thus the tradeoff relation no longer restricts the simultaneous optimization of measurement for a joint estimation. We construct such a joint optimal measurement by an elaborated analysis on the operator algebra of the symmetric logarithmic derivative.
• Score: 1.14219428942199
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The simultaneous optimization of the centroid estimation and the separation estimation of two incoherent optical point sources is restricted by a tradeoff relation through an incompatibility coefficient. At the Rayleigh distance the incompatibility coefficient vanishes and thus the tradeoff relation no longer restricts the simultaneous optimization of measurement for a joint estimation. We construct such a joint optimal measurement by an elaborated analysis on the operator algebra of the symmetric logarithmic derivative. Our work not only confirms the existence of a joint optimal measurement for this specific imaging model, but also gives a promising method to characterize the condition on measurement compatibility for general multiparameter estimation problems.

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