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Critical angle light scattering from bubbles: an asymptotic series approximation.

C E Dean, P L Marston

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    PubMed
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    This study reveals how light reflects off air bubbles in water, showing that geometrical optics breaks down for larger bubbles. A new approximation accurately describes this critical angle scattering, improving optical bubble sizing.

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    Area of Science:

    • Optics
    • Fluid Dynamics
    • Scattering Theory

    Background:

    • Geometrical optics describes light reflection from surfaces.
    • Air bubbles in water exhibit critical angle scattering, marking a transition from partial to total reflection.
    • Previous models of critical angle scattering have limitations.

    Purpose of the Study:

    • To derive an asymptotic series for critical angle scattering from air bubbles in water.
    • To provide a simple approximation for scattered irradiance.
    • To describe the breakdown of geometrical optics at the critical angle for curved surfaces.

    Main Methods:

    • Derivation of an asymptotic series for critical angle scattering.
    • Neglecting weak contributions from internal reflections.
    • Comparison with smoothed Mie computations for validation.

    Main Results:

    • The scattered irradiance is a monotonically increasing function of bubble radius (a) for a >> lambda.
    • A leading correction term O(beta^(-1/4)) to the scattering amplitude is identified, where beta is the size parameter.
    • This correction is significant for large beta (up to 20,000) and depends on light polarization.

    Conclusions:

    • The derived asymptotic series provides a simple approximation for irradiance and clarifies the breakdown of geometrical optics.
    • The findings improve understanding of optical bubble sizing applications.
    • The study refines physical-optics models for critical angle scattering.