Retrieving refractive index of single spheres using the phase spectrum of light-scattering pattern

TL;DR

This paper presents a spectral phase-based method for rapidly and accurately determining the refractive index of single spheres, validated against simulations and real measurements, with advantages in speed over traditional regression methods.

Contribution

The authors develop a novel spectral phase analysis technique for refractive index retrieval that is faster and comparably accurate to existing methods, with specific application to small variation ranges.

Findings

Spectral phase at the main peak quadratically depends on refractive index.

The method is 300 times faster than non-linear regression.

It performs well on both synthetic and real data within its operational range.

Abstract

We analyzed the behavior of the complex Fourier spectrum of the angle-resolved light scattering pattern (LSP) of a sphere in the framework of the Wentzel-Kramers-Brillouin (WKB) approximation. Specifically, we showed that the phase value at the main peak of the amplitude spectrum almost quadratically depends on the particle refractive index, which was confirmed by numerical simulations using both the WKB approximation and the rigorous Lorenz-Mie theory. Based on these results, we constructed a method for characterizing polystyrene beads using the main peak position and the phase value at this point. We tested the method both on noisy synthetic LSPs and on the real data measured with the scanning flow cytometer. In both cases, the spectral method was consistent with the reference non-linear regression one. The former method leads to comparable errors in retrieved particle characteristics but is 300 times faster than the latter one. The only drawback of the spectral method is a limited operational range of particle characteristics that need to be set a priori due to phase wrapping. Thus, its main application niche is fast and precise characterization of spheres with small variation range of characteristics.