Optimized criteria for angular parameter selection for the Chin-Shifrin integral transform inversion

Abstract

The accuracy of the particle size distribution (PSD) recovered from laser diffraction measurements by the Chin-Shifrin integral transform algorithm is reduced unless the proper angular parameters, including the lower and upper angular integration limits (θ and θ) and the angular resolution (Δθ), are used. To determine the selection criteria for these parameters, we use two metrics: the inversion error of the non-negative PSD, ε, and the fitting error of the scattered laser light, ε. By studying the variation of the minimum θ and ε with the particle size at different inversion errors, and by analyzing the inversion error, as θ and Δθ are varied, the optimized selection criteria for the minimum θ, θ and Δθ are obtained respectively. The inversion errors of the Chin-Shifrin algorithm with different selection criteria are compared, the different PSDs are recovered, and the optimal pixel selection range of the linear charge-coupled-device (CCD) array is determined according to the optimized selection criteria. Simulation results show that the optimized selection criteria for the angular parameters make the PSDs retrieved with the Chin-Shifrin algorithm more accurate.