### Abstract

This work shows an analytic solution to the central moments of the angle of linear polarization (AoLP) when the linear Stokes parameters are independent and Gaussian distributed with different means but equal variance. Such a result is useful for distinguishing AoLP features from noise in polarimetry. When the DoLP is high relative to the measurement uncertainty of the linear Stokes vector, AoLP statistics have been shown to be well approximated by a Gaussian distribution. When the DoLP is zero, AoLP values are uniformly distributed. In general, the probability density function (PDF) of AoLP does not have a closed-form solution and this is the first report, to our knowledge, on an exact analytic form for the central moments of the AoLP. This analytic form will be useful when the AoLP is of interest even when the DoLP is low and the corresponding PDF on the AoLP is in between the extreme cases of a Gaussian or a uniform distribution. We also show that a simple propagation of error (PE) analysis underestimates the AoLP variance at extremely low DoLP but is verified for cases of DoLP that are high relative to the Stokes measurement uncertainty. An example use of the AoLP variance in imaging polarimetry is presented.

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

Article number | 113108 |

Journal | Optical Engineering |

Volume | 53 |

Issue number | 11 |

DOIs | |

State | Published - Nov 1 2014 |

### Fingerprint

### Keywords

- Angle of linear polarization
- Polarimetric imaging
- Probability theory
- Stochastic processes

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Engineering(all)

### Cite this

**Relating the statistics of the angle of linear polarization to measurement uncertainty of the Stokes vector.** / Kupinski, Meridith Kathryn; Chipman, Russell A; Clarkson, Eric W.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Relating the statistics of the angle of linear polarization to measurement uncertainty of the Stokes vector

AU - Kupinski, Meridith Kathryn

AU - Chipman, Russell A

AU - Clarkson, Eric W

PY - 2014/11/1

Y1 - 2014/11/1

N2 - This work shows an analytic solution to the central moments of the angle of linear polarization (AoLP) when the linear Stokes parameters are independent and Gaussian distributed with different means but equal variance. Such a result is useful for distinguishing AoLP features from noise in polarimetry. When the DoLP is high relative to the measurement uncertainty of the linear Stokes vector, AoLP statistics have been shown to be well approximated by a Gaussian distribution. When the DoLP is zero, AoLP values are uniformly distributed. In general, the probability density function (PDF) of AoLP does not have a closed-form solution and this is the first report, to our knowledge, on an exact analytic form for the central moments of the AoLP. This analytic form will be useful when the AoLP is of interest even when the DoLP is low and the corresponding PDF on the AoLP is in between the extreme cases of a Gaussian or a uniform distribution. We also show that a simple propagation of error (PE) analysis underestimates the AoLP variance at extremely low DoLP but is verified for cases of DoLP that are high relative to the Stokes measurement uncertainty. An example use of the AoLP variance in imaging polarimetry is presented.

AB - This work shows an analytic solution to the central moments of the angle of linear polarization (AoLP) when the linear Stokes parameters are independent and Gaussian distributed with different means but equal variance. Such a result is useful for distinguishing AoLP features from noise in polarimetry. When the DoLP is high relative to the measurement uncertainty of the linear Stokes vector, AoLP statistics have been shown to be well approximated by a Gaussian distribution. When the DoLP is zero, AoLP values are uniformly distributed. In general, the probability density function (PDF) of AoLP does not have a closed-form solution and this is the first report, to our knowledge, on an exact analytic form for the central moments of the AoLP. This analytic form will be useful when the AoLP is of interest even when the DoLP is low and the corresponding PDF on the AoLP is in between the extreme cases of a Gaussian or a uniform distribution. We also show that a simple propagation of error (PE) analysis underestimates the AoLP variance at extremely low DoLP but is verified for cases of DoLP that are high relative to the Stokes measurement uncertainty. An example use of the AoLP variance in imaging polarimetry is presented.

KW - Angle of linear polarization

KW - Polarimetric imaging

KW - Probability theory

KW - Stochastic processes

UR - http://www.scopus.com/inward/record.url?scp=84911938779&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84911938779&partnerID=8YFLogxK

U2 - 10.1117/1.OE.53.11.113108

DO - 10.1117/1.OE.53.11.113108

M3 - Article

AN - SCOPUS:84911938779

VL - 53

JO - Optical Engineering

JF - Optical Engineering

SN - 0091-3286

IS - 11

M1 - 113108

ER -