Geometric optics applied to drops passing through a focused Gaussian beam

The present study examines the scattered light intensity from a drop passing through a Gaussian beam of a diameter comparable to or smaller than the drop. This is the situation encountered when using the time-shift technique, an optical technique used to characterize drops and aerosols according to the size and the velocity. In simulating the signals received by such an instrument, the computational effort involved when using, for instance, the Generalized Lorenz-Mie Theory or vector ray-tracing, is immense and hardly practical for use in instrument design and/or optimization. In this study theoretical expressions based on geometric optics are derived as an alternative, and they are shown to adequately capture the main features of the time-shift signals. These solutions require little computational effort and can be effectively used to explore the dependencies of the signals on various input factors, thus allowing further instrument development. On the other hand, these relations are also of general interest in the field of light scattering from drops and aerosols.