### Abstract

The Fano factor for an integer-valued random variable is defined as the ratio of its variance to its mean. Light from various scintillation crystals have been reported to have Fano factors from sub-Poisson (Fano factor < 1) to super-Poisson (Fano factor >1 ). For a given mean, a smaller Fano factor implies a smaller variance and thus less noise.We investigated if lower noise in the scintillation light will result in better spatial and energy resolutions. The impact of Fano factor on the estimation of position of interaction and energy deposited in simple gamma-camera geometries is estimated by two methods - calculating the Cramér-Rao bound and estimating the variance of a maximum likelihood estimator. The methods are consistent with each other and indicate that when estimating the position of interaction and energy deposited by a gamma-ray photon, the Fano factor of a scintillator does not affect the spatial resolution. A smaller Fano factor results in a better energy resolution.

Original language | English (US) |
---|---|

Article number | 7027241 |

Pages (from-to) | 42-56 |

Number of pages | 15 |

Journal | IEEE Transactions on Nuclear Science |

Volume | 62 |

Issue number | 1 |

DOIs | |

State | Published - Feb 6 2015 |

### Fingerprint

### Keywords

- Cramér-Rao bound
- energy estimation
- energy resolution
- Fano factor
- Fisher information matrix
- maximum-likelihood estimator
- position estimation
- scintillators
- spatial resolution

### ASJC Scopus subject areas

- Nuclear and High Energy Physics
- Nuclear Energy and Engineering
- Electrical and Electronic Engineering

### Cite this

*IEEE Transactions on Nuclear Science*,

*62*(1), 42-56. [7027241]. https://doi.org/10.1109/TNS.2014.2379620

**Impact of the fano factor on position and energy estimation in scintillation detectors.** / Bora, Vaibhav; Barrett, Harrison H; Jha, Abhinav K.; Clarkson, Eric W.

Research output: Contribution to journal › Article

*IEEE Transactions on Nuclear Science*, vol. 62, no. 1, 7027241, pp. 42-56. https://doi.org/10.1109/TNS.2014.2379620

}

TY - JOUR

T1 - Impact of the fano factor on position and energy estimation in scintillation detectors

AU - Bora, Vaibhav

AU - Barrett, Harrison H

AU - Jha, Abhinav K.

AU - Clarkson, Eric W

PY - 2015/2/6

Y1 - 2015/2/6

N2 - The Fano factor for an integer-valued random variable is defined as the ratio of its variance to its mean. Light from various scintillation crystals have been reported to have Fano factors from sub-Poisson (Fano factor < 1) to super-Poisson (Fano factor >1 ). For a given mean, a smaller Fano factor implies a smaller variance and thus less noise.We investigated if lower noise in the scintillation light will result in better spatial and energy resolutions. The impact of Fano factor on the estimation of position of interaction and energy deposited in simple gamma-camera geometries is estimated by two methods - calculating the Cramér-Rao bound and estimating the variance of a maximum likelihood estimator. The methods are consistent with each other and indicate that when estimating the position of interaction and energy deposited by a gamma-ray photon, the Fano factor of a scintillator does not affect the spatial resolution. A smaller Fano factor results in a better energy resolution.

AB - The Fano factor for an integer-valued random variable is defined as the ratio of its variance to its mean. Light from various scintillation crystals have been reported to have Fano factors from sub-Poisson (Fano factor < 1) to super-Poisson (Fano factor >1 ). For a given mean, a smaller Fano factor implies a smaller variance and thus less noise.We investigated if lower noise in the scintillation light will result in better spatial and energy resolutions. The impact of Fano factor on the estimation of position of interaction and energy deposited in simple gamma-camera geometries is estimated by two methods - calculating the Cramér-Rao bound and estimating the variance of a maximum likelihood estimator. The methods are consistent with each other and indicate that when estimating the position of interaction and energy deposited by a gamma-ray photon, the Fano factor of a scintillator does not affect the spatial resolution. A smaller Fano factor results in a better energy resolution.

KW - Cramér-Rao bound

KW - energy estimation

KW - energy resolution

KW - Fano factor

KW - Fisher information matrix

KW - maximum-likelihood estimator

KW - position estimation

KW - scintillators

KW - spatial resolution

UR - http://www.scopus.com/inward/record.url?scp=85027922012&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85027922012&partnerID=8YFLogxK

U2 - 10.1109/TNS.2014.2379620

DO - 10.1109/TNS.2014.2379620

M3 - Article

AN - SCOPUS:85027922012

VL - 62

SP - 42

EP - 56

JO - IEEE Transactions on Nuclear Science

JF - IEEE Transactions on Nuclear Science

SN - 0018-9499

IS - 1

M1 - 7027241

ER -