Cooperative Effects Among Partial Waves in Mie Scattering

Observations of an illuminated water droplet at a close distance are described mathematically by the Fourier transform of the Mie-scattering amplitude convolved with the aperture function of the observer’s eye. Most of the sharp enhancements found in the Fourier transform correspond to geometrical rays associated with the various terms in the Debye-series expansion of the Mie amplitude. However, there are some enhancements that cannot be ascribed to any individual Debye-series term. Instead, they arise from a constructive interference cooperation of the phase of a scattering resonance in a single partial wave with the region of the stationary phase corresponding to geometrical orbiting in the m-internal-reflection portion of the Fourier transform of the scattering amplitude. This phase cooperation amplifies the contribution that the scattering resonance makes to the Fourier-transform amplitude.