Analytical transform techniques to retrieve non-spherical particle size distribution

- Analytical schemes for inversion of non-spherical particle size distribution.
- Intuitive inverse formulas and novel ADT transform fairs for non-spherical particles.
- Useful scaling relations in retrievals for non-spherical particles.

The measurement of particle size distribution (PSD) from the extinction spectra is a challenging problem, especially for non-spherical particles. In this work, the analytical transform techniques are developed to retrieve PSD from the measured scattering data for a variety of shapes of non-spherical particle including spheroids, cuboids, triangular prisms, hexagonal prisms and elliptical cylinders. In the retrieve calculation, all particles have aligned orientations and their extinction cross sections can be adequately calculated by using the anomalous diffraction theory (ADT). It is shown that for each type of the considered non-spherical particles, there exists an ADT transform pair between the size distribution and the extinction spectrum. The inverse formula of PSD from the related ADT transform is therefore established. This result provides a new approach to the solution of the inversion problem and has the potential to be used in finding solutions for more complicated particle shapes. It is found that the solution of inverse scattering for absorbing particles can be simplified to a particular solution in which the character of absorption becomes no longer present.For spheroids, triangular prisms, and elliptical cylinders, the retrieved PSD and the corresponding true PSD always belong to one family of function, due to the scaling relation. Therefore an improper choice of inversion parameters does not significantly affect the type of mode of PSD in a retrieval process.