Analytical algorithm to retrieve size distribution of an ensemble of randomly oriented arbitrarily shaped particles from spectral absorption measurements

摘要

A new parameterized anomalous diffraction theory (PADT) is proposed, in which the effects of reflection and refraction are included to calculate the orientation-averaged absorption efficiency of arbitrarily shaped particles accurately. Using the PADT, integral transform technique, data mapping approach, and Gaver-Stehfest inversion method, the discretely real summation formula for retrieval of the particle size distribution (PSD) based on absorption data is developed. The spectral representations of moments of PSD are also presented. The retrieval experiments show that the truncation number has a significant impact on the accuracy of PSD inversion, and the relative error reaches the its minimum at the critical truncation number. Compared with the double precision algorithm, the extended precision algorithm can produce more accurate and reliable results at the cost of high CPU time. In addition, the relative error increases with the increase of noise level, but it will be significantly reduced when a smoothing technique is applied.