Cusp diffraction catastrophe from spheroids: generalized rainbows and inverse scattering

The angular location of the recently discovered cusp pattern in the far-field scattering from an oblate spheroid is calculated as a function of the aspect ratio D/H. The calculation assumes the diameter D >> lambda and is limited to illumination perpendicular to the short axis of the spheroid. It agrees with observations for water drops in the range 1.22 < D/H < 1.37 with D ~ 1 mm.