Unfolded optical glory of spheroids: backscattering of laser light from freely rising spheroidal air bubbles in water.

Enhancement in backscattering known as glory scattering results from geometric and material properties of spherically symmetric scatterers. The wave-front shape near the spherical scatterer is locally a circular torus. Radiation from a toroidal wave front is axially focused on the backward-directed axis. It is shown that the axial point caustic unfolds to an astroid caustic as the scatterer's shape changes from spherical to slightly spheroidal. The wave front pertinent for slightly spheroidal scatterers was modeled as a toroidal wave front with a superimposed harmonic angular perturbation. Experimental observations are displayed for cross-polarized backscattering by freely vertical rising, slightly oblate spheroidal air bubbles in water illuminated by a horizontally propagating laser beam. These patterns were recorded with a camera for two different incident-beam polarization directions relative to the axis of rotational symmetry of the bubble. Angular scattering patterns were also computed using a perturbation analysis based on use of the harmonically perturbed toroidal wave front and physical optics. Bubble oblateness was estimated from features of the angular scattering pattern and from hydrodynamic relations.