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• By using generalized Lorenz-Mie theory and Debye series decomposition, the influence of a Gaussian beam on the scattering pattern of drops in the secondary rainbow region is studied. • The secondary rainbow pattern is used to estimate the achievable accuracy when extracting refractive index and size of drops. • The influence of incidence position of the Gaussian beam on the drop characterization is investigated. In the present study the structure of the secondary rainbow is examined for the case of a spherical drop illuminated by a Gaussian beam with its waist radius comparable to the drop radius. Computations are performed using the generalized Lorenz-Mie theory (GLMT) and Debye series. The influence of beam waist radius on the secondary rainbow pattern is investigated. The possibility of extracting size and refractive index from the secondary rainbow pattern is then evaluated by examining the achievable accuracy. The influence of incident position of the beam on extracting drop information is also investigated. For a Gaussian beam centered on the impact parameter associated with the Descartes ray, the absolute error of the refractive index is smaller than 6.8 × 10−4 and the value of relative error for drop radius is smaller than 4.0% for water drops with a radius between 50 and 200 μm. [ABSTRACT FROM AUTHOR]