### 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 language | English (US) |
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Title of host publication | Optics and Photonics for Information Processing XIII |

Editors | Khan M. Iftekharuddin, Abdul A. S. Awwal, Victor H. Diaz-Ramirez, Andres Marquez |

Publisher | SPIE |

ISBN (Electronic) | 9781510629653 |

DOIs | |

State | Published - Jan 1 2019 |

Event | Optics and Photonics for Information Processing XIII 2019 - San Diego, United States Duration: Aug 13 2019 → Aug 14 2019 |

### Publication series

Name | Proceedings of SPIE - The International Society for Optical Engineering |
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Volume | 11136 |

ISSN (Print) | 0277-786X |

ISSN (Electronic) | 1996-756X |

### Conference

Conference | Optics and Photonics for Information Processing XIII 2019 |
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Country | United States |

City | San Diego |

Period | 8/13/19 → 8/14/19 |

### Fingerprint

### 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

*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

**Surpassing Rayleigh limit : Fisher information analysis of partially coherent source(s).** / Lee, Kwan Kit; Ashok, Amit.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Optics and Photonics for Information Processing XIII.*, 111360H, Proceedings of SPIE - The International Society for Optical Engineering, vol. 11136, SPIE, Optics and Photonics for Information Processing XIII 2019, San Diego, United States, 8/13/19. https://doi.org/10.1117/12.2528540

}

TY - GEN

T1 - Surpassing Rayleigh limit

T2 - Fisher information analysis of partially coherent source(s)

AU - Lee, Kwan Kit

AU - Ashok, Amit

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - coherent point sources

KW - fisher information

KW - rayleigh limit

UR - http://www.scopus.com/inward/record.url?scp=85075789912&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85075789912&partnerID=8YFLogxK

U2 - 10.1117/12.2528540

DO - 10.1117/12.2528540

M3 - Conference contribution

AN - SCOPUS:85075789912

T3 - Proceedings of SPIE - The International Society for Optical Engineering

BT - Optics and Photonics for Information Processing XIII

A2 - Iftekharuddin, Khan M.

A2 - Awwal, Abdul A. S.

A2 - Diaz-Ramirez, Victor H.

A2 - Marquez, Andres

PB - SPIE

ER -