Dependence of the forward light scattering on the refractive index of particles

•Forward scattered light depends on the refractive index of transparent particles.•Abnormal intervals makes the inverse problem more difficult.•Abnormal intervals are smoothened in widely-distributed particle systems.•Tikhonov regularization with B-spline functions is proposed for inverse problem.•More information is required for measuring narrow particle systems. In particle sizing technique based on forward light scattering, the scattered light signal (SLS) is closely related to the relative refractive index (RRI) of the particles to the surrounding, especially when the particles are transparent (or weakly absorbent) and the particles are small in size. The interference between the diffraction (Diff) and the multiple internal reflections (MIR) of scattered light can lead to the oscillation of the SLS on RRI and the abnormal intervals, especially for narrowly-distributed small particle systems. This makes the inverse problem more difficult. In order to improve the inverse results, Tikhonov regularization algorithm with B-spline functions is proposed, in which the matrix element is calculated for a range of particle sizes instead using the mean particle diameter of size fractions. In this way, the influence of abnormal intervals on the inverse results can be eliminated. In addition, for measurements on narrowly distributed small particles, it is suggested to detect the SLS in a wider scattering angle to include more information.