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Determination of the aerosol size distribution by analytic inversion of the extinction spectrum in the complex anomalous diffraction approximation

机译：复杂异常衍射近似中消光光谱的解析反演确定气溶胶粒径分布

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摘要

A new derivation is presented for the analytical inversion of aerosol spectral extinction data to size distributions. It is based on the complex analytic extension of the anomalous diffraction approximation (ADA). We derive inverse formulas that are applicable to homogeneous nonabsorbing and absorbing spherical particles. Our method simplifies, generalizes, and unifies a number of results obtained previously in the literature. In particular, we clarify the connection between the ADA transform and the Fourier and Laplace transforms. Also, the effect of the particle refractive-index dispersion on the inversion is examined. It is shown that, when Lorentz's model is used for this dispersion, the continuous ADA inverse transform is mathematically well posed, whereas with a constant refractive index it is ill posed. Further, a condition is given, in terms of Lorentz parameters, for which the continuous inverse operator does not amplify the error.
机译：提出了一种新的推导方法，用于将气溶胶光谱消光数据解析为尺寸分布。它基于反常衍射近似（ADA）的复杂分析扩展。我们推导出适用于均质非吸收性和吸收性球形颗粒的逆公式。我们的方法简化，归纳和统一了先前文献中获得的许多结果。特别是，我们阐明了ADA变换与傅立叶变换和拉普拉斯变换之间的联系。此外，检查了粒子折射率分散对反演的影响。结果表明，当洛伦兹模型用于该色散时，连续ADA逆变换在数学上是合适的，而在折射率恒定的情况下是合适的。此外，根据洛伦兹参数给出了连续逆算子不放大误差的条件。

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