Modified Landweber algorithm for robust particle sizing by using Fraunhofer diffraction

In this paper, a robust modified Landweber algorithm was proposed to retrieve the particle size distributions from Fraunhofer diffraction. Three typical particle size distributions, i.e., Rosin-Rammler, lognormal, and bimodal normal distributions for particles ranging from 4.8 to 96 μm, were employed to verify the performance of the algorithm. To show its merits, the proposed algorithm was compared with the Tikhonov regularization algorithm and the ℓ₁-norm-based algorithm. Simulation results showed that, for noise-free data, both the modified Landweber algorithm and the ℓ₁-norm-based algorithm were better than the Tikhonov regularization algorithm in terms of accuracy. When the data was noise-contaminated, the modified Landweber algorithm was superior to the other two algorithms in both accuracy and speed. An experimental setup was also established and the results validated the feasibility and effectiveness of the proposed method.