Numerical reconstruction of two-dimensional particle size distributions from laser diffraction data

Ustinov, V.; Tsybrov, E.

Авторы: Ustinov Vladislav, Tsybrov Evgeniy
Журнал: Inverse Problems in Science and Engineering
Том: 28
Номер: 11
Год издания: 2020
Издательство: Taylor & Francis
Местоположение издательства: United Kingdom
Первая страница: 1633
Последняя страница: 1647
DOI: 10.1080/17415977.2020.1761801
Аннотация: In this paper, we consider the two-dimensional Fredholm integral equation of the first kind. The kernel of this equation models the scattering of a laser beam by spheroids having the same fixed orientation. The unknown function under the integral describes the distribution of spheroids along two semi-axes. The input data are the diffraction pattern corresponding to the scattering of the laser beam by the particles. We show that the Tikhonov regularization method allows one to reconstruct two-dimensional distributions in the case when the diffraction pattern is modulated by white noise with relative amplitude up to 1%. In applications, this means novel possibility of obtaining two-dimensional particle size distributions, rather than one-dimensional ones, as in the classical version of the method. This significantly expands the capabilities of particle sizing via static laser diffraction technique. We show that the solution of the corresponding equation is unique in L2 space and exists when the right-hand-side function is in a set dense in L2. We provide test experimental results in the framework of laser ektacytometry of red blood cells, which serves as the main application of the proposed approach presently.KEYWORDS: Particle sizing, Fredholm equation, inverse problem, Tikhonov regularization, laser ektacytometry2010 MATHEMATICS SUBJECT CLASSIFICATION: 45B05
Добавил в систему: Устинов Владислав Дмитриевич

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Numerical reconstruction of two-dimensional particle size distributions from laser diffraction dataстатья