Size and Refractive Index Determination of Single Polystyrene Spheres

The intensity of the light scattered from individual dielectric spheres was measured as a function of the scattering angle, for light polarized parallel and perpendicular to the scattering plane. These sets of data were used to determine the radius and refractive index of the spheres by fitting the data to the scattering function obtained from Mie theory. The light was produced by a He-Cd laser (λ=441.6 nm). Measurements were performed on particles of six discrete sizes with radii in the range 117-1175 nm. Several different measures of the quality of fit were examined, and the least-squares fit, unweighted or weighted with a factor sin²(θ/2), was found to be the best. The values obtained for the index of refraction were found to be within 1% of the published bulk value 1.615. The measured radii differed by several percent from those specified by the manufacturer. Several sources of error were analyzed, and their effects were simulated in numerical experiments. The largest source of error in the instrument was a discrepancy between the actual scattering angle and the reading provided by the instrument. Less significant was the noise introduced by the motion of the particle within the laser beam. A calibration eliminated most of the error in the scattering angle. The precision and accuracy of this technique are estimated to be 0.2% and 0.9%, respectively, of the particle size for particles of a nominal radius of 457 nm.