Improved technique of retrieving particle size distribution from angular scattering measurements

- A constrained regularization is proposed for retrieving particle size distributions.
- Distributions are retrieved based on angular scattering measurements.
- The method utilizes quadratic programming on top of Tikhonov regularization.
- The proposed method improves accuracy of reconstruction of distributions.
- The improvement results from a priori knowledge conveyed by constraints.

The paper presents results of the simulation study on improved technique of retrieving the particle size distribution (PSD) of dispersed systems from angular scattering measurements. Determining the PSD based on angular scattering measurements is the inverse problem which can be expressed in terms of the Fredholm integral equation of the first kind when single and incoherent scattering modeled by Mie theory is assumed. However, the problem is highly ill-conditioned when discretized. When one incorporates two constraints to be satisfied by the sought PSD: nonnegativity of PSD values and normalization of PSD to unity when integrated over the whole range of particle size into the Regularized Least Squares (RLS) method, one obtains the proposed Constrained Regularized Least Squares (CRLS) method which consists in solving the quadratic programming problem. Accuracy (bias) and uncertainty of the CRLS solutions were assessed in the study. The study refers to the one similar for spectral extinction measurements performed before. Results of the simulation sensitivity study prove that the CRLS method is capable of retrieving PSD functions with accuracy and uncertainty satisfactory for many industrial applications. However, the method does not manage to reconstruct bimodal PSD functions so that both modes are distinguishable. Retrieved PSD satisfies physical constraints inherently.