Backscattering from a slightly spheroidal air bubble in water: a novel unfolding of the optical glory

Abstract

The optical glory, which is related to a weak focusing of backscattered light, is known to exist for spherical bubbles.1 This caustic, however, is affected by small deviations from sphericity. Hydrodynamics causes freely rising air bubbles in pure water to become slightly spheroidal if the bubble diameter ≳ 250 μm. We modeled and photographed the near backward scattering from slightly spheroidal horizontally illuminated bubbles. Spherical bubbles produce backward-directed glory wavefronts having the local shape of a circular torus. Our model introduces the leading perturbation of those wavefronts resulting from a small deviation from sphericity. The cross-polarized scattering from a sphere1 has a fourfold symmetric sin22φ azimuthal dependence where φ denotes the azimuthal angle. For the spheroids, both the model and the observation give a twofold symmetric pattern. Detailed features of the modeled patterns are confirmed by the observations. This gives a specific example of broken symmetry resulting in an unfolding of a caustic which would otherwise have an infinite codimension.2