Investigation of low-angle laser light scattering patterns using the modified Twomey iterative method for particle sizing

Abstract

We first applied the Twomey iteration method to the low-angle laser light scattering (LALLS) method. The Twomey method is known by the simple iteration algorithm for Fredholm integral equation. However, the algorithm is not applied to the LALLS result itself because the kernel function pattern is not stable. We solved the unstable kernel issue by modifying the Twomey algorithm to fit the LALLS data in this study. The performance of inversion was studied by computer simulation and experimental results from detectors containing 24 elements from angle 0.0005 to 2.5 rad. The computer simulation was carried out for particles of mean sizes from 0.1 to 1000 μm with mono-dispersion and log-normal distributions. A conventional algorithm is also carried out to compare the performance of the Twomey method. The noise effect of the inverse problem was tested by computer simulation. Experimental results were measured with standard polystyrene latex from 0.081 to 1007 μm. All the tests were performed under conditions in which the light from a linearly polarized laser at 633 nm was scattered by a diluted aqueous suspension. The modified Twomey (MT) method and conventional method show good reproduction results for particles with log-normal distributions. However, narrow distribution particles indicate that the MT method shows excellent reproduction results when compared with the conventional method.