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

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.

Refractive index of human red blood cells between 290 nm and 1100 nm determined by optical extinction measurements

“…4 allows to measure the same quantity as the monochromator-based setup previously used by Gienger et al . 42 to validate the method for spectral RI determination of particles. However, the setup in Fig.…”

“…As presented in Ref. 42 , we expand the unknown function α , describing the wavelength-dependent increment of the real RI with concentration, into a finite serieswith real coefficients a j , where the g j are orthonormal basis functions. Here, we use a set of orthonormalized third-order cardinal splines with a uniform grid spacing of Δ λ = 10 nm.…”

“…The method we developed to determine the complex RI of biological cells in cell suspensions is applied to determine RIs of sphered RBCs between 290 nm and 1100 nm. To this end we modified a procedure recently proposed and tested for non-absorbing polystyrene microspheres 42 . The method is based on measurement of collimated transmittance of a dilute cell suspension.…”

Microfluidic lab-on-a-chip characterization of nano- to microparticles suspensions by light extinction spectrometry

“…Increasing substantially the optical path length [47] and integrating a microfluidiccontrolled optical router [48] for multiplexed analyses with a single spectrometer would also be a benefit for practical applications. The consideration of particles with more complex shapes and compositions [30,33,35,36], as well as multiple scattering or polarization effects [41,42], is also part of the perspectives of the present work.…”

“…To address these issues, we report a novel approach to characterize particle size distributions (PSDs) and concentrations of nano-to microparticles in static as well as flowing suspensions. This approach is based on the principle of light extinction spectrometry (LES) [24][25][26][27][28][29][30][31][32][33][34][35][36] and a photonic lab-on-a-chip with three scale-probing channels, see Figure 1. After this brief introduction, section 2 summarizes the background and basic requirement of LES.…”