By means of a numerical study we show particle-size distributions retrieved with the Chin-Shifrin, Phillips-Twomey, and singular value decomposition methods. Synthesized intensity data are generated using Mie theory, corresponding to unimodal normal, gamma, and lognormal distributions of spherical particles, covering the size parameter range from 1 to 250. Our results show the advantages and disadvantages of each method, as well as the range of applicability for the Fraunhofer approximation as compared to rigorous Mie theory.

An algorithm is presented based on an evolution strategy to retrieve a particle size distribution from angular light-scattering data. The analyzed intensity patterns are generated using the Mie theory, and the algorithm retrieves a series of known normal, gamma, and lognormal distributions by using the Fraunhofer approximation. The distributions scan the interval of modal size parameters 100 < or = alpha < or = 150. The numerical results show that the evolution strategy can be successfully applied to solve this kind of inverse problem, obtaining a more accurate solution than, for example, the Chin-Shifrin inversion method, and avoiding the use of a priori information concerning the domain of the distribution, commonly necessary for reconstructing the particle size distribution when this analytical inversion method is used.

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A stochastic inverse method is presented based on a hybrid evolutionary optimization algorithm (HEOA) to retrieve a monomodal particle-size distribution (PSD) from the angular distribution of scattered light. By solving an optimization problem, the HEOA (with the Fraunhofer approximation) retrieves the PSD from an intensity pattern generated by Mie theory. The analyzed light-scattering pattern can be attributed to unimodal normal, gamma, or lognormal distribution of spherical particles covering the interval of modal size parameters 46≤α≤150. The HEOA ensures convergence to the near-optimal solution during the optimization of a real-valued objective function by combining the advantages of a multimember evolution strategy and locally weighted linear regression. The numerical results show that our HEOA can be satisfactorily applied to solve the inverse light-scattering problem.