Optimal angular range for the Chin–Shifrin inversion algorithm in particle sizing by laser diffraction

Abstract

In laser diffraction particle sizing measurements, only light in the range of forward small scattering angles is used to recover the particle size distribution (PSD). The Chin–Shifrin (C–S) integral transform algorithm is used to recover the particle size distributions (PSDs). However, this algorithm is based on the Fraunhofer diffraction theory, which may be used to approximate the scattered light pattern at small scattering angles. By comparing the inversion results recovered using the C–S algorithm from the two series of simulated light scattering data we determine the optimal range of angular integration for which the Fraunhofer diffraction approximation and the C–S algorithm may be used to reconstruct the PSD. One series is simulated using Mie scattering to calculate the true intensity pattern and for the other series is used to approximate the intensity pattern. For both series the data is calculated over a range of scattering angles. The effect of the deviation of the Fraunhofer diffraction pattern from the Mie scattering pattern is studied and the optimal range of angles is determined based on the inversion error of recovered PSD. The results show that the intensity pattern deviation will lead to variations in the recovered PSD. Also, the larger the angular range, the poorer the results. The optimal range of integration angle of the C–S algorithm for the various PSDs with different distribution widths and particle sizes is analyzed. The results indicate that the smaller the particle size and the wider the PSD, the smaller the optimal angular range.