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

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 max and θ min ) 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 1 , and the fitting error of the scattered laser light, ε 2 . By studying the variation of the minimum θ max and ε 2 with the particle size at different inversion errors, and by analyzing the inversion error, as θ min and Δθ are varied, the optimized selection criteria for the minimum θ max , θ min 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.