Estimation of particle size distributions from focused beam reflectance measurements based on an optical model

A popular in situ particle characterization technique, which can be applied without dilution, is the focused beam reflectance measurement (FBRM^®). The FBRM probe measures a chord length distribution (CLD) which is different from a particle size distribution (PSD). In order to compare results obtained by an FBRM probe with other measurement technologies such as laser diffraction, it is necessary to reconstruct the PSD from a measured CLD. For this reconstruction a measurement model and an inversion procedure are required. Most FBRM models presented in the literature assume that an FBRM records a geometric chord which can be deduced from a two-dimensional projection of the particle silhouette. In previous work [Kail, N., Briesen, H., Marquardt, W., 2008. Analysis of FBRM measurements by means of a 3D optical model. Powder Technology 185 (3), 211-222] it has been demonstrated that FBRM data show significant deviations from this geometric model. Consequently, an estimation of a PSD using such a geometric FBRM model will fail. A novel FBRM model is developed in this work. This model imitates the chord discrimination algorithm used in a Lasentec D600L FBRM system and takes the intensity profile of the laser beam and the optical aperture of the probe into account. The model is ideally suited for the estimation of a PSD from a measured CLD using a sequential, linear inversion routine, as proposed in this work. The novel FBRM model and the inversion procedure are evaluated using small, mono-disperse polystyrene beads, large ion-exchanger beads, and α-lactose-monohydrate particles. The applicability of the FBRM for PSD measurements is discussed on the basis of these results.