Study On The Inverse Algorithms Of Particle-sizing Distributions In Laser Optical Self-mixing Interference

Self-mixing interference (SMI) belongs to heterodyne detection of dynamic light scattering (DLS) for measuring the particle-sizing distributions (PSD) of submicron particles and nanometer particles suspended in suspension. And its power spectral density inversion is ill condition problem. In the corresponding fields, the inversion of PSD is an difficult and important factor, and the inversion result is directly related to the accuracy of the measurement results. The research on this aspect meets the needs of the related fields.This work mainly analysed regularization algorithms of power spectrum inversion, and made some modifications on the corresponding inversion algorithms. The main contents are as following:1,Studied the mechanisms of self-beating and heterodyne detection, and analysed SMI theory and character based on rate equation and Fabry-Perot cavity modal.2,Studied the PSD problem by comparing linear kernel matrix with logarithmic form kernel matrix, the latter retrieved more reasonable distribution than the former.To guarantee the non-negative constraint, Chahine iteration method served as the optimization algorithm.In the unimodal PSD, Morrison smoothing method was adopted, which made smoothing process on the initial distribution of Chahine algorithm. The processed result was better than the unprocessed. For the bimodal PSD, Chahine algorithm hardly performed well, the derived solution showed over-smoothing appearance.3,To solve the bimodal PSD problem, we applied truncated singular value decomposition (TSVD) method. The referenced dot formed by Chahine algorithm reduced the calculation and enhance the validity for determining the optimal regularization parameter in the L-curve. In addition, The TSVD retrieved result was obviously optimized after it was made as the Chahine algorithm initial distribution through the iterated process.4,The power spectrum inversion problem was transferred through Tikhonov regularization, then SVD and total least squares (TLS) behaved and were compared. TLS was verified to have more stability than SVD in simulation.In order to choose the optimal regularization parameter, we proposed the minimum variation of solution method, which is proved to be valid and its advantage for determining regularization parameter in experiment. A better regularization parameter could be gotten through increasing the discrimination between the neighboring ancipital parameters by means of the new method.5,Chahine algorithm stopping criterion was modified with SR-curve, the SR-curve horizontal axis shown root mean square deviation, and the vertical axis shown the solution smoothing constraint, then the modest iterative distribution was chosen with SR-curve. The zero and the first derivative operators were employed as the smoothing constraint. The estimated particle size distribution (PSD) corresponding to the first derivative operator had less relative size distribution error.So far, the satisfied result can not be got if deriving complicated PSD, yet the PSD inversion algorithm largely affect the accuracy of the particle size measurement, this work will have a promoted effect on the particle-sizing distributions inversion algorithm.