Koo J H, Hirleman E D
Appl Opt. 1992 Apr 20;31(12):2130-40. doi: 10.1364/AO.31.002130.
Five integral transform solutions to the Fredholm integral equation that describes the forward-scattering properties of the distributions of spherical particles in the Fraunhofer diffraction regime have been studied. We have systematically reformulated the family of solutions, including four derivations by three other research groups and one developed as part of this work, using a standardized notation. This synthesis elucidates the mathematical interrelationships and fosters an understanding of the inversion performance of the five solutions. Finally a series of numerical experiments was carried out to demonstrate the relative performance of the techniques when applied to identical sets of simulated forward-scattering signatures.
研究了弗雷德霍姆积分方程的五种积分变换解，该方程描述了夫琅禾费衍射区域中球形粒子分布的前向散射特性。我们使用标准化符号系统地重新表述了这组解，其中包括其他三个研究小组的四种推导以及作为本工作一部分得出的一种推导。这种综合阐明了数学上的相互关系，并有助于理解这五种解的反演性能。最后进行了一系列数值实验，以证明这些技术应用于相同的模拟前向散射特征集时的相对性能。
