An Iterative Algorithm Based on the Dual Integral Inversion for Particle Sizing

Abstract

In this paper, an iterative algorithm is proposed to retrieve the particle-size distributions via Fraunhofer diffraction. A dual integral inversion was proposed in our previous work, the inversion is robust and generates precise particle sizing, if the diffraction pattern can be accurately captured. In real applications, the pattern can only be partially detected, and the inversion fails to reconstruct the size distributions in detail. However, the results of the inversion can be used to produce an initial estimate. Then, a simulated diffraction pattern was generated from the estimated particle sizes. The deviation between the measured pattern and the simulated one was deduced to correct the results of particle sizing. The corrections can be achieved in an iterative approach, and the particle-size distribution was updated subsequently. The iteration stopped once the deviation was below the target value. Both simulation and experiment were conducted to validate the feasibility and effectiveness of the proposed algorithm. The results demonstrate that the size distribution from the proposed algorithm agrees well with the original phantoms for both noise-free and noise-contaminated data.