Constrained linear inversion of optical scattering data for particle size spectra: an approach to angular optimization

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Abstract
A methodology for investigating the variation of particle size distributions retrieved from constrained linear inversion of optical scattering data is presented. By plotting the expected inversion error vs angular scanning parameters (for typical size distribution vectors) one can determine sets of optimum angles based on a minimum error criteria at each particle size. An expression for the expected inversion error at each radius knot is derived. In addition a formulation for the Fredholm quadrature matrix in terms of Legendre coefficients and polynomials is introduced. This method of computation is advantageous when a large number of angles are to be investigated. The derived results are applied to the special case of a Junge Continental Aerosol.