Optimal Scaling of the Inverse Fraunhofer Diffraction Particle Sizing Problem: Analytic Eigenfunction Expansions
Abstract
There are many possible strategies for sampling the near forward scattering pattern produced by a field of large particles and for subsequently solving the inverse problem in order to obtain an estimate of the particle size distribution. In a previous paper an optimally scaled formulation of the problem was derived based on consideration of condition numbers of the linear system obtained through numerical quadrature of the governing Fredholm integral equation. Here we consider scaling of the problem to involve selection of the parameters under control of the instrument designer (e.g. the number, angular positions, and aperture geometries of the detectors and the number, positions, and widths or weighting functions of the discrete size classes). Since many numerical/analytical schemes for solving for the size distribution given a finite number of scattering measurements are fundamentally very similar, optimal scaling of the problem will improve the performance of the instrument regardless of the selected computational inversion algorithm. This paper considers the analytic eigenfunction expansion method of solving the inverse Fraunhofer diffraction problem, and in particular how the scaling strategy affects the inversions. The eigenfunctions and associated eigenvalues for the diffraction problem (assuming infinite support) are derived in terms of two (variable) scaling parameters which describe the detector geometry and the size class configurations.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1989
- Accession Number
- ADA232715
Entities
People
- E. D. Hirleman
Organizations
- Arizona State University