A wide-angle light scattering method based on ellipsoidal mirror for particle size distribution measurement

An unconstrained particle size distribution (PSD) inversion method based on the wide-angle light scattering (WALS) method is proposed. The feasibility of the method was validated through simulation, and the optimal number of scattering angles was determined by balancing inversion accuracy and stability. Results show that the relative inversion error decreases with increasing mean particle size. Under uniformly sampled angular configurations, further increasing the number of angles beyond 38 yields only marginal improvements in accuracy, where the average relative error is 2.69%. Moreover, measurement stability does not exhibit a strict positive correlation with the number of angles; 30 and 76 angles demonstrate better stability than 38 and 51. Considering both accuracy and stability, 76 scattering angles are recommended as the optimal configuration, achieving an average relative error of 2.51%. The method performs well for large particles (350–3050 nm), with an average relative error of 0.46%, while the error increases significantly in the small particle range (50–350 nm), reaching 21.03%. The inversion error is approximately proportional to the random measurement error, with a proportionality coefficient of 0.036. When 5% random noise is introduced, the average relative error remains at 21.50%, indicating acceptable stability. This study provides a reference for determining the appropriate number of scattering angles in WALS-based PSD inversion, which is crucial for improving measurement accuracy and efficiency. An experimental setup was designed to validate the method. Results demonstrate that the proposed WALS-based approach can effectively reconstruct PSDs. Compared with reference PSDs, the relative errors for SiO 2 and fly ash particles are 19.54% and 20.95%, respectively, confirming the practical applicability of the method.