The fundamental equation that is being solved in laser diffraction analysis of suspended particles is:

      E_v=K_vC_v,

where Ev is a vector with the power of the scattered light at a number of solid angles (32 angles for the LISST instruments), Cv is the volume distribution vector of the suspended particles, and Kv is the so-called kernel matrix containing the scattering signature for a unit volume concentration of each size class of particles (32 for the LISSTs).  If Ev is measured, Cv can be obtained by multiplying Ev with the inverse of Kv.

Traditionally, Kv has been computed using so-called Mie theory, based on the work of Gustav Mie in the early 1900’s.  It is relatively straight-forward to compute Kv for spherical particles of any given diameter.  However, no theory exists that enables us to compute Kv for particles of random shape.

This is unfortunate as most particles in nature are non-spherical.  The question then becomes: Is it possible to create a Kv matrix for random shaped particles in an empirical manner? And, if yes, is it vastly different from the Kv matrix computed under the assumption that the particles are spherical? In particular the latter question is of some importance: If a Kv matrix based on random shaped particles is very different from that of spherical particles it could compromise ~30-40 years of use of lasers as particle sizers in industry and scientific research.

In order to answer these questions one must first create a Kv matrix for random shaped particles based on the scattering signatures of single-sized random shaped particles for each of the 32 size classes of the LISST.  In order to achieve this, particles were separated by settling in a stratified settling column in the laboratory.  Attached to the column was a LISST-100.  Using Stokes Law it was possible to compute the arrival time of particles of a certain size at the level of the laser beam.  The scattering signature that corresponded to a particular particle size could then be selected from a time series of scattering signatures measured as the particles were settling.  This formed the basis for the random shaped Kv matrix.

This new matrix was then compared to the matrix based on spherical particles.  The difference for large particles (> 16 µm) was minimal.  However, for particles smaller than 16 µm, random-shaped particles scattered more light at larger angles than spheres of similar size.  This increased scattering at large angles became larger as particle size decreased.

This phenomenon explains an often-observed rising tail in the fine end of the size distributions.  Fine, random-shaped particles scatter more light at large angles than spheres of similar size, so when the scattering pattern is inverted using a Kv matrix based on sphered the result is that fine particles are being ‘invented’.  This artificially causes an increase in particle volume in the fine end of the size distributions.  Using the natural particle matrix to invert the scattering pattern causes the rising tail of fine particles to disappear.