A technique for determining the spectral refractive indices, size, and number density of soot particles from light scattering and spectral extinction measurements in flames

A technique is presented that allows the spectral refractive indices, size, and number density of soot particles in flames to be inferred from a combination of single-wavelength light scattering and multiwavelength extinction measurements. In contrast to previous schemes for inferring optical properties, the present approach does not require the introduction of a model for the spectral dispersion of the refractive index; it employs Kramers-Kronig theory instead. When applied to spherical particles, the only approximations involved are the usual ones associated with using Kramers-Kronig theory to analyze actual data, that is, for those spectral regions where experimental data are not obtainable, extrapolations and interpolations must be made. The particles, however, may be of any size, including Rayleigh-size (for which it is particularly difficult to simultaneously infer particle size, concentration, and complex refractive index). The approach requires a combination of static (elastic) and dynamic (quasielastic) laser light scattering measurements plus measurements of the spectral transmittance. Closure is achieved in data analysis by the introduction of an exact (model-independent) Kramers-Kronig dispersion theory for scattering amplitude functions. The influence of various spectral extrapolation schemes (required because of the finite spectral width of the transmittance data) is thoroughly investigated.