Surpassing Rayleigh limit: Fisher information analysis of partially coherent source(s)

Kwan Kit Lee, Amit Ashok

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Tsang et al. have shown that the Fisher information of the two incoherent point source separation, below the Rayleigh limit, is finite and achievable using optical modes measurements.1 However, recent claims regarding partial coherence of sources, no matter how small, leads to necessarily zero Fisher information as the source separation decreases below the Rayleigh limit approaching zero have proved to be controversial.2, 3 Thus, the impact of partial coherence on the photon counting optical modal measurements merits further exploration. In this work, we derive the mutual coherence function (image plane) of two partially coherent point sources and find the classical Fisher information of the source separation using both direct image plane and photon counting modal measurements. A classical Fisher information analysis of partially coherent source(s) leads to some rather surprising results for two-point source resolution as the source separation approaches zero. We find that the magnitude of the Fisher information strongly depends on the degree of (positive/negative) partial coherence, which can be understood using an intuitive semi-classical analysis of direct image plane and photon counting modal measurements. We also provide an error analysis of the maximum likelihood estimators for both measurements.

Original languageEnglish (US)
Title of host publicationOptics and Photonics for Information Processing XIII
EditorsKhan M. Iftekharuddin, Abdul A. S. Awwal, Victor H. Diaz-Ramirez, Andres Marquez
PublisherSPIE
ISBN (Electronic)9781510629653
DOIs
Publication statusPublished - Jan 1 2019
EventOptics and Photonics for Information Processing XIII 2019 - San Diego, United States
Duration: Aug 13 2019Aug 14 2019

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume11136
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X

Conference

ConferenceOptics and Photonics for Information Processing XIII 2019
CountryUnited States
CitySan Diego
Period8/13/198/14/19

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Keywords

  • coherent point sources
  • fisher information
  • rayleigh limit

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

Cite this

Lee, K. K., & Ashok, A. (2019). Surpassing Rayleigh limit: Fisher information analysis of partially coherent source(s). In K. M. Iftekharuddin, A. A. S. Awwal, V. H. Diaz-Ramirez, & A. Marquez (Eds.), Optics and Photonics for Information Processing XIII [111360H] (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 11136). SPIE. https://doi.org/10.1117/12.2528540