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• For NNTSVD, accurate particle sizing rely on optimal sampling points selection. • The number of sampling points must be less than the number of ACF channels. • There is weak similarity between the relative error of PSD and the residual of ACF. • Optimal sampling points can be achieved by minimum residual criterion. The number of particle size distribution (PSD) sampling points is an important factor to affect the accuracy of dynamic light scattering (DLS) inversion. If the number of sampling points is not selected properly, the accuracy of inversion results will be reduced or results will deviate seriously from the true value. To solve the problem, combining non-negative truncated singular value decomposition (TSVD), by studying the relationship between number of sampling points, relative error (RE) of PSD and number of autocorrelation function (ACF) channels, it is concluded that the upper limit of optimal sampling points is limited by the number of ACF channels. Under different sampling points, the study of RE of PSD and the residual (RES) of electric field ACF shows that there is a weak similarity between them. Then a criterion for determining the optimal number of sampling point is constructed. Finally, a non-negative constrained TSVD method for PSD adaptive sampling (PSDAS-NNTSVD) is proposed according to the upper limit condition of optimal number of sampling points and its determination criterion. Simulated DLS data for unimodal particles of 160 channels and bimodal particles of 120 channels were inverted under three noise levels of 1 × 10−4, 1 × 10−3, 1 × 10−2, respectively. The results show that, the peak position of PSDs inverted by PSDAS-NNTSVD is closer to the true value and the proposed method has better anti-noise ability. The inversion results of bimodal measured particles from 60 to 203 nm also verified the performance of the method. [ABSTRACT FROM AUTHOR]

Highlights • The influence of the intensity deviation of Fraunhofer diffraction pattern from the Mie scattering pattern on the polydisperse PSD recovered by the C–S algorithm is analyzed for the first time. • The optimal range of angles is determined based on the inversion error of PSD recovered by the C–S algorithm from the Mie scattering light pattern in different angular ranges. • By analyzing the inversion error of recovered PSDs, the influence of different particle sizes and distribution widths on the optimal range of angle is determined. Abstract In laser diffraction particle sizing measurements, only light in the range of forward small scattering angles is used to recover the particle size distribution (PSD). The Chin–Shifrin (C–S) integral transform algorithm is used to recover the particle size distributions (PSDs). However, this algorithm is based on the Fraunhofer diffraction theory, which may be used to approximate the scattered light pattern at small scattering angles. By comparing the inversion results recovered using the C–S algorithm from the two series of simulated light scattering data we determine the optimal range of angular integration for which the Fraunhofer diffraction approximation and the C–S algorithm may be used to reconstruct the PSD. One series is simulated using Mie scattering to calculate the true intensity pattern and for the other series is used to approximate the intensity pattern. For both series the data is calculated over a range of scattering angles. The effect of the deviation of the Fraunhofer diffraction pattern from the Mie scattering pattern is studied and the optimal range of angles is determined based on the inversion error of recovered PSD. The results show that the intensity pattern deviation will lead to variations in the recovered PSD. Also, the larger the angular range, the poorer the results. The optimal range of integration angle of the C–S algorithm for the various PSDs with different distribution widths and particle sizes is analyzed. The results indicate that the smaller the particle size and the wider the PSD, the smaller the optimal angular range. [ABSTRACT FROM AUTHOR]