Retrieval of spheroid particle size distribution from spectral extinction data in the independent mode using PCA approach

Abstract

An improved anomalous diffraction approximation (ADA) method is presented for calculating the extinction efficiency of spheroids firstly. In this approach, the extinction efficiency of spheroid particles can be calculated with good accuracy and high efficiency in a wider size range by combining the Latimer method and the ADA theory, and this method can present a more general expression for calculating the extinction efficiency of spheroid particles with various complex refractive indices and aspect ratios. Meanwhile, the visible spectral extinction with varied spheroid particle size distributions and complex refractive indices is surveyed. Furthermore, a selection principle about the spectral extinction data is developed based on PCA (principle component analysis) of first derivative spectral extinction. By calculating the contribution rate of first derivative spectral extinction, the spectral extinction with more significant features can be selected as the input data, and those with less features is removed from the inversion data. In addition, we propose an improved Tikhonov iteration method to retrieve the spheroid particle size distributions in the independent mode. Simulation experiments indicate that the spheroid particle size distributions obtained with the proposed method coincide fairly well with the given distributions, and this inversion method provides a simple, reliable and efficient method to retrieve the spheroid particle size distributions from the spectral extinction data.