Mathematical tools are provided for the computation of the scattered field produced by non-spherical particles moving through the measurement volume of a phase Doppler anemometer. The phase distribution of a spheroid with random orientation is computed by using the rigorous extended boundary condition method and the ray theory. In a phase Doppler experiment the spheroid parameters are obtained by fitting the measured phase distribution with the simulated phase distribution. The numerical simulations are supported by experimental results on monodisperse spheroids.