Spheroidal droplet measurements based on generalized rainbow patterns

The character of the rainbow from a droplet is investigated experimentally and theoretically. In the experiment, light scattering from spheroidal droplets in the vicinity of the primary rainbow region has been observed to contain a variety of characteristic interference patterns which are a generalization of the rainbow from a sphere. These patterns start from being a fold rainbow, change to transverse cusp caustics and then to hyperbolic umbilic catastrophe as the aspect ratio of the droplet increases. A comparison of the observed rainbow patterns in the horizontal equatorial plane with those of Airy theory reveals that these patterns can be used for characterizing droplet, in particular for determining the refractive index and the diameter of the droplet in the equatorial plane. The absolute error of the refractive index is smaller than 1.5×10−4. The absolute relative error of the equatorial diameter is less than 5%.