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Fisher information matrix for branching processes with application to electron-multiplying charge-coupled devices

Fisher information matrix for branching processes with application to electron-multiplying charge-coupled devices
Fisher information matrix for branching processes with application to electron-multiplying charge-coupled devices

The high quantum efficiency of the charge-coupled device (CCD) has rendered it the imaging technology of choice in diverse applications.However, under extremely lowlight conditions where few photons are detected from the imaged object, the CCD becomes unsuitable as its readout noise can easily overwhelm the weak signal. An intended solution to this problem is the electron-multiplying charge-coupled device (EMCCD), which stochastically amplifies the acquired signal to drown out the readout noise. Here, we develop the theory for calculating the Fisher information content of the amplified signal, which is modeled as the output of a branching process. Specifically, Fisher information expressions are obtained for a general and a geometric model of amplification, as well as for two approximations of the amplified signal. All expressions pertain to the important scenario of a Poisson-distributed initial signal, which is characteristic of physical processes such as photon detection. To facilitate the investigation of different data models, a "noise coefficient" is introduced which allows the analysis and comparison of Fisher information via a scalar quantity.We apply our results to the problem of estimating the location of a point source from its image, as observed through an optical microscope and detected by an EMCCD.

Branching process, Electron Multiplication, Fisher information, Quantum-limited imaging, Single molecule microscopy
0923-6082
349-379
Chao, Jerry
550e20b0-8365-42e3-a6fc-1048eb8c2e47
Ward, E. Sally
b31c0877-8abe-485f-b800-244a9d3cd6cc
Ober, Raimund J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36
Chao, Jerry
550e20b0-8365-42e3-a6fc-1048eb8c2e47
Ward, E. Sally
b31c0877-8abe-485f-b800-244a9d3cd6cc
Ober, Raimund J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36

Chao, Jerry, Ward, E. Sally and Ober, Raimund J. (2012) Fisher information matrix for branching processes with application to electron-multiplying charge-coupled devices. Multidimensional Systems and Signal Processing, 23 (3), 349-379. (doi:10.1007/s11045-011-0150-7).

Record type: Article

Abstract

The high quantum efficiency of the charge-coupled device (CCD) has rendered it the imaging technology of choice in diverse applications.However, under extremely lowlight conditions where few photons are detected from the imaged object, the CCD becomes unsuitable as its readout noise can easily overwhelm the weak signal. An intended solution to this problem is the electron-multiplying charge-coupled device (EMCCD), which stochastically amplifies the acquired signal to drown out the readout noise. Here, we develop the theory for calculating the Fisher information content of the amplified signal, which is modeled as the output of a branching process. Specifically, Fisher information expressions are obtained for a general and a geometric model of amplification, as well as for two approximations of the amplified signal. All expressions pertain to the important scenario of a Poisson-distributed initial signal, which is characteristic of physical processes such as photon detection. To facilitate the investigation of different data models, a "noise coefficient" is introduced which allows the analysis and comparison of Fisher information via a scalar quantity.We apply our results to the problem of estimating the location of a point source from its image, as observed through an optical microscope and detected by an EMCCD.

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More information

Accepted/In Press date: 22 March 2011
e-pub ahead of print date: 8 April 2011
Published date: September 2012
Keywords: Branching process, Electron Multiplication, Fisher information, Quantum-limited imaging, Single molecule microscopy

Identifiers

Local EPrints ID: 423634
URI: https://eprints.soton.ac.uk/id/eprint/423634
ISSN: 0923-6082
PURE UUID: 814acedd-2cc8-4f7f-b369-979870912af0
ORCID for E. Sally Ward: ORCID iD orcid.org/0000-0003-3232-7238
ORCID for Raimund J. Ober: ORCID iD orcid.org/0000-0002-1290-7430

Catalogue record

Date deposited: 27 Sep 2018 16:30
Last modified: 24 Sep 2019 00:22

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Contributors

Author: Jerry Chao
Author: E. Sally Ward ORCID iD
Author: Raimund J. Ober ORCID iD

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