Particle size inversion of flowing aerosol using Bayesian inference in dynamic light scattering

In dynamic light scattering (DLS) measurements of flowing aerosols, an increase in flow velocity can exacerbate the ill-conditioned nature of the inversion equation, which makes it difficult to obtain accurate particle size by classical inversion methods. We established a probability model using Bayesian inference and derived a posterior probability density function (PDF) containing the undetermined particle size distribution (PSD) parameters. After setting the initial values of the parameters, the Markov chain Monte Carlo (MCMC) algorithm was used to sample the parameters in the posterior PDF, and the sample values of the Markov chain were averaged to obtain the needed PSD parameters. The PSD inverted by the Bayesian method shows that it avoids phenomena such as peak position shift, distribution broadening, and disappearance of one peak in bimodal distributions in regularization inversion. The peak position error and distribution error of the PSD inverted by the Bayesian method no longer increase with the increase of flow velocity. In addition, through the Bayesian method, the flow velocity information contained in the intensity autocorrelation function was accurately obtained, thus achieving online retrieval of PSD and flow velocity of flowing aerosols.