Particle size distributions from spectral turbidity: a singular-system analysis

Bertero, M.; Mol, Christine De; Pike, E. R.

doi:10.1088/0266-5611/2/3/003

Cited by 25 publications

(3 citation statements)

References 16 publications

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“…In more recent years, McWhirter and Pike 23 introduced a new approach, known as the analytic eigenfunction theory, which is based on the Mellin transform of the kernel function. This technique, which is particularly suited to problems in which the kernel is a relatively simple analytical function, was applied by Viera and Box 24 and by Bertero and co-workers 25,26 to the inversion of spectral extinction data in the anomalous diffraction approximation. Recently Box et al 27 applied the eigenfunction theory, using the exact Mie extinction kernel, and obtained satisfactory computer simulations, although with a tendency to overestimate the content in small particles.…”

Section: Introductionmentioning

confidence: 99%

Modified version of the Chahine algorithm to invert spectral extinction data for particle sizing

1995

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A modified version of the nonlinear iterative Chahine algorithm is presented and applied to the inversion of spectral extinction data for particle sizing. Simulated data were generated in a λ range of 0.2-2 µm,and particle-size distributions were recovered with radii in the range of 0.14-1.4 µm. Our results show that distributions and sample concentrations can be recovered to a high degree of accuracy when the indices of refraction of the sample and of the solvent are known. The inversion method needs no a priori assumptions and no constraints on the particle distributions. Compared with the algorithm originally proposed by Chahine, our method is much more stable with respect to random noise, permits a better quality of the retrieved distributions, and improves the overall reliability of the fitting. The accuracy and resolution of the method as functions of noise were investigated and showed that the retrieved distributions are quite reliable up to noise levels of several rms percent in the data. The sensitivity to errors in the real and imaginary parts of the refraction index of the particles was also examined.

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Section: Introductionmentioning

confidence: 99%

Modified version of the Chahine algorithm to invert spectral extinction data for particle sizing

1995

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“…A simple way to restore the stability of the solution to obtain regularized, i.e. stable approximate solutions, consists in replacing the expansion (7) by a filtered expansion (7) M-1…”

Section: Generalized and Regularized Solutionsmentioning

confidence: 99%

Inversion Of Light Scattering Data By Singular System Analysis

1987

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We consider the problem of inverting experimental data obtained in light scattering experiments described by linear theories. We discuss applications to particle sizing and we describe fast and easy -to-implement algorithms which permit the extraction, from noisy measurements, of reliable information about the particle size distribution. General setting of the data inversion problemMany light scattering experiments can be described by linear equations, at least to a good approximation. The interpretation of the data to obtain information about e.g. the size or velocity of the scattering particles requires then the solution of a linear inverse problem.

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“…In the case of dilute scatterers and in the anomalous diffraction approximation,' the extinction coefficient and the distribution of the sizes of spherical particles are related by the following Fredholm intégral équa tion of the first kind: g(k) = J K(kr) f(r) dr (1) o The data function g(k) is given by g(k) = T(k)/k (2) and f(r) is the volume distribution f(r) = (4/3) iT r^ N(r) (3) where N(r) is the density of particles of radius r. Using p for the product kr, the intégral kernel in équation (1) is given by 2 3 K(p) = 3(2P + 4 4PsinP 4cosp)/4p = 3(h/2)^/^ P"^''^ "3/2'"^…”

Section: Introductionmentioning

confidence: 99%