Particle sizing by the Fraunhofer diffraction method based on an approximate non-negatively constrained Chin-Shifrin algorithm

In the Fraunhofer diffraction particle sizing technique there are relative errors between the particle size distribution (PSD) of the sample and the PSD recovered because there is random noise in the collected diffracted light intensity data and this makes data inversion to recover the PSD problematic. To reduce the noise sensitivity of the Chin-Shifrin inversion algorithm, an improved Chin-Shifrin algorithm is proposed that uses an approximate function to fit the integral kernel function together with a constraint to ensure non-negative inversion results. Furthermore, the tuning factor α of the approximate function is determined by analyzing the relationship between average particle size and the maximum value of the derivative of the diffracted light intensity. The PSDs of standard materials recovered by the Chin-Shifrin algorithm and its improved version are compared. Experimental data show that the improved Chin-Shifrin algorithm can effectively suppress random noise. The relative error of the recovered PSD is <5% and the relative standard deviation is no >10%.