Probability distribution of scattered intensities

The probability distribution of scattered light intensity is derived when both the size and the number of scattering aerosol particles are random variables. When light is scattered from an ensemble of aerosol particles, the scattered intensity is a random variable itself. Analytical derivation is found for the distribution of scattered intensities. It is shown that in a wide range of experimental conditions the scattered intensity follows Gaussian statistics. For a given sort of aerosols the ratio of the mean value to the standard deviation is shown to be dependent only on the mean number of particles present in the measurement volume. Monte-Carlo simulations and experiments were carried out to prove the expectations of the theory.