Measurement of Scattering Cross Section with a Spectrophotometer with an Integrating Sphere Detector

Abstract

A commercial spectrometer with an integrating sphere (IS) detector was used to measure the scattering cross section of microspheres. Analysis of the measurement process showed that two measurements of the absorbance, one with the cuvette placed in the normal spectrometer position, and the second with the cuvette placed inside the IS, provided enough information to separate the contributions from scattering and molecular absorption. Measurements were carried out with microspheres with different diameters. The data was fitted with a model consisting of the difference of two terms. The first term was the Lorenz-Mie (L-M) cross section which modeled the total absorbance due to scattering. The second term was the integral of the L-M differential cross section over the detector acceptance angle. The second term estimated the amount of forward scattered light that entered the detector. A wavelength dependent index of refraction was used in the model. The agreement between the model and the data was good between 300 nm and 800 nm. The fits provided values for the microsphere diameter, the concentration, and the wavelength dependent index of refraction. For wavelengths less than 300 nm, the scattering cross section had significant spectral structure which was inversely related to the molecular absorption. This work addresses the measurement and interpretation of the scattering cross section for wavelengths between 300 nm and 800 nm.