True and false symmetries in the classification of optical scatterers

A plane wave is scattered by a potential of bounded support. Translation, rotation and reflection of the potential, q0 induce transformations of the scattered wave. The latter can be represented by means of Born sequences, where q0 appears under the integral sign: non-local formulas are thus derived, the properties of which are discussed. Next, the symmetries induced by the 1 st BORN approximation are addressed. Invariance of the squared modulus of the scattering amplitude holds for translation and reflection. The transformation T e := 1 3 +Σ 3 l=1e l A l, with {e l ;} real and {A l } the generators of rotations in IR 3 , is investigated. Conditions on the {e l } are derived, by which the scattering amplitude coming from the first BORN approximation is invariant to T e . As an application, these “false symmetries” are compared to those induced by limited angular resolution of a detector in light scattering experiments. Namely, scattering patterns are made available by the TAOS (Two-dimensional Angle-resolved Optical Scattering) method, which consists of detecting single airborne aerosol particles and collecting the intensity of the light they scatter from a pulsed, monochromatic laser beam. The optics and the detector properties determine the resolution at which a pattern is saved. The implications on the performance of TAOS pattern analysis are briefly discussed.