Abstract: A new inversion equation is built upon the particles' scattering theory and its shape influence. The probability distribution function of particles' size,the shape factor function and the distribution function of particle shape are further studied.Firstly,a model and an equation are built upon the characteristics of the Gaussian scattering cavity and the location pobability,a result is obtained from it and the nonlinear influence in a wide range is studied.Secondly,the inversion matrix equation of the particle size distribution is obtained from the discrete characteristics of the particle distribution in both mathematical theories and experiments.At last, a numerical experiment is made to test the method.

Key words: particle shape, size distribution function, scattering, measurement