The analysis of influencing factors on Tikhonov and truncated singular value decomposition inversion of flowing aerosol particle in dynamic light scattering

Dynamic light scattering (DLS) has been proved to be a feasible method to measure the flowing aerosol particle size distribution (PSD). However, since the flowing aerosol particle is affected by the Brownian motion diffusion and the uniform translational motion relative to optical scattering volume, its inversion is more complex than traditional DLS. In this paper, Tikhonov and truncated singular value decomposition (TSVD) are used to invert aerosol particles with different noise levels and flow velocities. After the analysis of the influencing factors, the results showed that: For unimodal small aerosol particles, in the case of low flow velocity, the inversion errors of TSVD are smaller than those of Tikhonov. For unimodal particles with high flow velocity, the increase in flow velocity will weaken the PSD information distribution of DLS measurement, which becomes another factor affecting PSD inversion besides noise. In addition, truncation of singular values further results in loss of PSD information distribution. The inversion accuracy of TSVD decreases obviously. Tikhonov adopts the strategy of modifying the small singular value, which will not lose all the PSD information distribution carried by the singular value while reducing the influence of noise. In this case, Tikhonov is more suitable. For bimodal aerosol particles, the resolution of the DLS particle sizing measurement is limited by the noise mixed in the intensity autocorrelation function data and the inherently lower information content of the data. On this basis, the influence of flow velocity will further cause the loss of data information. Tikhonov has better performance indicators and stronger bimodal resolution. The experimental results are in good agreement with the simulation results.