Into the third dimension: stochastic measurements of Stokes parameters within the Poincaré sphere

Abstract

Inspired by recent use of polarimetry to study the Cosmic Microwave Background and extragalatic supernovae, a foray into the statistical properties of Stokes parameters expressed in spherical coordinates is began, allowing circular polarization and linear polarization to be treated in a unified manner. The use of spherical coordinates is quite necessary as it permits a Stokes polarization state to be expressed in terms of the customary polarization angles and degree of polarization usually needed for human interpretation. As shall be demonstrated, circular and linear polarization are not statistically independent quantities but intertwined in a way that is especially important, for instance, at low signal-to-noise. New distributions, classical estimators, and marginalizations are presented for this "three-dimensional" polarization problem including a generalization of the Rice distribution. The paper concludes with discussion regarding the potential pitfalls of a lower dimensional analysis.

arXiv comment8 pages, 3 figures

References in corpus (23)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• BICEP2 I: Detection Of B-mode Polarization at Degree Angular Scales
• Spectropolarimetry of Supernovae
• A Measurement of the Cosmic Microwave Background B-Mode Polarization Power Spectrum at Sub-Degree Scales with POLARBEAR
• BICEP2 II: Experiment and Three-Year Data Set
• Placing Confidence Limits on Polarization Measurements
• Evidence for Two Distinct Populations of Type Ia Supernovae
• Planck 2013 results. XIX. The integrated Sachs-Wolfe effect
• Evidence for Spectropolarimetric Diversity in Type Ia Supernovae
• Polarimetry of the Type Ia Supernova SN 1996X
• Multi-epoch spectropolarimetry of SN 2009ip: direct evidence for aspherical circumstellar material
• Spectropolarimetric diagnostics of thermonuclear supernova explosions
• Effects of Explosion Asymmetry and Viewing Angle on the Type Ia Supernova Color and Luminosity Calibration
• Fingerprints of Galactic Loop I on the Cosmic Microwave Background
• On the Probability Distributions of Ellipticity
• VLT Spectropolarimetry of the Type Ia SN2005ke - A step towards understanding subluminous events
• The Unification of Asymmetry Signatures of Type Ia Supernovae
• Bayesian analysis of polarization measurements
• A spectropolarimetric view on the nature of the peculiar Type I SN 2005hk
• Spectropolarimetry of the Type Ia Supernova 2012fr
• Three-Dimensional Explosion Geometry of Stripped-Envelope Core-Collapse Supernovae. I. Spectropolarimetric Observations
• Spectropolarimetry of the Type Ia SN 2007sr Two Months After Maximum Light