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    This study introduces a single depolarization parameter to model polarized bi-directional scattering distribution functions (pBSDFs), simplifying measurements to just two polarimetric data points for improved material characterization.

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    Area of Science:

    • Optics and Photonics
    • Materials Science
    • Polarimetry

    Background:

    • Polarized bi-directional scattering distribution functions (pBSDFs) are complex 4x4 matrix functions describing light scattering.
    • Existing models, like Priest and Meier's, use a weighted sum of Fresnel matrices and ideal depolarizers.
    • Characterizing material polarization properties often requires extensive Mueller matrix measurements.

    Purpose of the Study:

    • To simplify the modeling of pBSDFs by introducing a single depolarization parameter.
    • To reduce the complexity of pBSDF fitting from full Mueller matrix measurements to just two polarimetric measurements.
    • To investigate the mathematical relationship between Fresnel matrices, ideal depolarizers, and depolarization in Mueller matrices.

    Main Methods:

    • Developed a single depolarization parameter to represent the relative weight of an ideal depolarizer and Fresnel matrix in pBSDF models.
    • Proposed a measurement scheme requiring only two polarimetric measurements for pBSDF fitting.
    • Analyzed the degeneracy of weights in the incoherent addition of coherent states for Mueller matrices within the span of Fresnel and depolarizer components.

    Main Results:

    • Successfully related the weighting between Fresnel and depolarizer components to a single, one-dimensional depolarization parameter.
    • Demonstrated a simplified fitting scheme using only two polarimetric measurements instead of a full Mueller matrix.
    • Observed triply degenerate weights in the incoherent addition of coherent states for Mueller matrices, consistent with the proposed model.
    • Validated the findings across diverse materials (five colored plastics) with varying surface textures (nine types) and measurement conditions (geometries and wavebands).

    Conclusions:

    • The single depolarization parameter offers a computationally efficient and experimentally simpler method for pBSDF characterization.
    • The proposed two-measurement scheme significantly reduces the experimental burden for material polarimetric analysis.
    • The observed triple degeneracy provides fundamental insight into the structure of Mueller matrices representable by Fresnel and depolarizer combinations.