Extinction spectra of suspensions of microspheres: Determination of spectral refractive index and particle size distribution with nanometer accuracy

TL;DR

This paper introduces a method to accurately determine the spectral refractive index and size distribution of microspheres from extinction spectra, using Mie theory and numerical optimization, with uncertainty estimation.

Contribution

It presents a novel approach that simultaneously infers size, size distribution, and spectral refractive index of microspheres from extinction measurements.

Findings

Achieved nanometer accuracy in particle size determination.

Successfully estimated wavelength-dependent refractive index.

Provided uncertainty quantification for all parameters.

Abstract

A method is presented to infer simultaneously the wavelength-dependent real refractive index (RI) of the material of microspheres and their size distribution from extinction measurements of particle suspensions. To derive the averaged spectral optical extinction cross section of the microspheres from such ensemble measurements, we determined the particle concentration by flow cytometry to an accuracy of typically 2% and adjusted the particle concentration to ensure that perturbations due to multiple scattering are negligible. For analysis of the extinction spectra we employ Mie theory, a series-expansion representation of the refractive index and nonlinear numerical optimization. In contrast to other approaches, our method offers the advantage to simultaneously determine size, size distribution and spectral refractive index of ensembles of microparticles including uncertainty estimation.