Determination of particle size distribution by light extinction method using improved pattern search algorithm with Tikhonov smoothing functional

An inversion technique which combines the pattern search algorithm with the Tikhonov smoothing functional for retrieval of particle size distribution (PSD) by light extinction method is proposed. In the unparameterized shape-independent model, we first transform the PSD inversion problem into an optimization problem, with the Tikhonov smoothing functional employed to model the objective function. The optimization problem is then solved by the pattern search algorithm. To ensure good convergence rate and accuracy of the whole retrieval, a competitive strategy for determining the initial point of the pattern search algorithm is also designed. The accuracy and limitations of the proposed technique are tested by the inversion results of synthetic and real standard polystyrene particles immersed in water. In addition, the issues about the objective function and computation time are further discussed. Both simulation and experimental results show that the technique can be successfully applied to retrieve the PSD with high reliability and stability in the presence of random noise. Compared with the Phillips–Twomey method and genetic algorithm, the proposed technique has certain advantages in terms of reaching a more accurate and steady optimal solution with less computational effort, thus making this technique more suitable for quick and accurate measurement of PSD.