Optical Diffraction Method Of Particle Swarm Particle Size Distribution Of The Median Particle Size Probability Density Function Of The Mathematical Model

In this paper, a new mathematical model based on integral median-value theorem is developed to inverse the distribution of particle group, which is used for measuring particle size with Fraunhofer diffiaction theory. In this model, the measured diffraction signal can be described with finite kinds of distributions of diffraction light resulted from single-size particle group. Correspondingly, the distribution of actual particle group can be denoted approximately with a combination of the finite kinds of these particles.Numerical simulations have been proceeded on three kinds of particle groups: single-peak, double-peak and three-peak. The results show that: (1). the error of peak-particle size between experimental value and theoretical value is less than 1 ^m; (2). the measured span value of distribution of particle size is consistent with theoretical value; (3). the error between measured distribution of particle group and the theoretical distribution is about 0.03; (4). the precision as stated above can be still obtained, even if the random noise in the measurement diffraction signal is added up to 20%.This inversion method is a non-mode & non-interation method, and conquers the disadvantage of poor astringency of integral transform methods and the oversensitivity to noise of non-linearity interation.