Laser diffraction particle sizing : sampling and inversion
Citable URI
http://hdl.handle.net/1912/4757DOI
10.1575/1912/4757Keyword
Particles; DiffractionAbstract
The inverse problem of obtaining particle size distributions from observations
of the angular distribution of near forward scattered light is reexamined.
Asymptotic analysis of the forward problem reveals the information
content of the observations, and the sources of nonuniqueness and
instability in inverting them. A sampling criterion, such that the observations
uniquely specify the size distribution is derived, in terms of the
largest particle size, and an angle above which the intensity is indistinguishable
from an asymptote. The instability of inverting unevenly spaced
data is compared to that of superresolving Fourier spectra. Resolution is
shown to be inversely proportional to the angular range of observations.
The problem is rephrased so that the size weighted number density is
sought from the intensity weighted by the scattering angle cubed. Algorithms
which impose positivity and bounds on particle size improve the
stability of inversions. The forward problem can be represented by an
overdetermined matrix equation by choosing a large integration increment
in size dependent on the frequency content of the angular intensity, further
improving stability.
Experimental data obtained using a linear CCD array illustrates the theory, with standard polystyrene spheres as scatterers. The scattering
from single and trimodal distributions is successfully inverted.
Description
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution August 13, 1987
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