Rigorous analysis of the spectral sizing of single particles based on light scattering patterns

Abstract

The sizing of a single particle based on the Fourier spectrum of its angle-resolved light-scattering pattern (LSP) is widely used in practice but has been lacking rigorous theoretical justification. In this paper we fill this gap, starting with systematic analysis based on the Rayleigh-Gans-Debye (RGD) approximation. We related the LSP spectrum with an integrated autocorrelation function (IAF), determined solely by the particle geometry. If the exact forward scattering is not included in the LSP angular range and the Hann window is used for the Fourier transform, the LSP spectrum vanishes everywhere except near the discontinuities of the IAF derivatives. Thus, the main spectral peak corresponds to the particle diameter, i.e. largest distance between two interior points. Next, we showed that the same qualitative conclusions hold in the Wentzel-Kramers-Brillouin (WKB) approximation and in the general case, when no approximations are employed. In the case of the WKB, we proposed a change of the LSP argument to simplify the description of the resulting peak.