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Statistics of normalized Stokes polarization parameters.

Nathan Hagen

    Applied Optics
    |August 18, 2018
    PubMed
    Summary

    Normalized Stokes parameters, crucial in polarization optics, have theoretically undefined statistical properties. Our study demonstrates they are practically well-behaved, providing accurate approximations and experimental validation.

    Area of Science:

    • Optics and Photonics
    • Statistical Optics
    • Polarization Measurement

    Background:

    • Normalized Stokes parameters are derived from ratios of light polarization components to intensity.
    • These parameters theoretically exhibit undefined means and variances, posing challenges in analysis.
    • Despite theoretical issues, normalized Stokes parameters are widely used in polarization research.

    Purpose of the Study:

    • To investigate the practical behavior of normalized Stokes parameters.
    • To reconcile theoretical statistical pathologies with experimental utility.
    • To provide accurate approximations for their probability densities.

    Main Methods:

    • Theoretical analysis of probability density functions for normalized Stokes parameters.

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  • Derivation of approximate density expressions.
  • Experimental validation using laboratory measurements of polarized light.

    • Main Results:

    • Normalized Stokes parameters, despite theoretical undefinedness, show well-behaved practical distributions.
    • Approximate probability density functions were derived.
    • Laboratory measurements confirmed the theoretical predictions and practical behavior.

    Conclusions:

    • The practical utility of normalized Stokes parameters is validated, despite their theoretical statistical limitations.
    • The derived approximate densities offer a robust framework for their analysis.
    • This work bridges the gap between theoretical statistical challenges and experimental application in polarization optics.