Rigorous analysis of the spectral sizing of single particles based on light scattering patterns
Romanov A.V. and Yurkin M.A. Rigorous analysis of the spectral sizing of single particles based on light scattering patterns, Opt. Laser Technol. 151, 108047 (2022). (PDF)
The sizing of particles based on the Fourier transform of its light-scattering patterns has been known for a long time. But it has always been an empirical technique, mostly based on observed (simulated) correlations between the positions of the spectral peaks and particle size (both for spherical and non-spherical shapes). Here we give a rigorous theoretical justification of this method, relating the position of the spectral peaks to the discontinuities of derivatives of autocorrelation function. And the latter is related to the largest distance between two points in a homogeneous particle or to internal interfaces of inhomogeneous ones.
While no simple expression can predict the full spectrum of the light-scattering pattern, we performed a complete analysis in the framework of two approximations. And, more importantly, we proved that the above general relation hold in the framework of a rigorous theory based on the volume-integral equation. This can be illustrated by the following example of a coated sphere. Note, that the third derivative of the autocorrelation function (which is trivial to compute) has discontinuities approximately at the positions of the peaks in the spectrum.
