Mathematical tools are provided for the computation of the scattered field produced by a non-spherical particle moving through the measurement volume of a phase Doppler anemometer. The Doppler signal is modeled by using the rigorous extended boundary condition method and an approximate ray theory. The region of applicability of ray theory is discussed. In particular, a pure refraction model is considered for large particles. It is shown that under some circumstances the phase Doppler technique may be used for sizing of spheroidal particles.