In this paper we present a fast analytical approach based on Lorenz-Mie theory, which allows us to determine the unknown shell and core radii of two-layered microparticles with refractive indices of 1.0 (air) of the core and 1.5 of the shell, e.g., polymer-coated air bubbles. For this to be achieved, a single particle has to be illuminated (sequentially) both with monochromatic laser light and with a white light source, and the scattered light intensity has to be recorded as a function of the scattering angle in the range from 0 to 170°. Using the autocorrelation and the Fourier transformation of these phase functions, one can deduce the unknown inner and outer radii by comparison with theoretically calculated gauge curves.
O. Sbanski, W. Kiefer, J. Popp, M. Lankers, and G. Rößling, "Sizing of Polymer-Coated Spherical Air Bubbles," Appl. Spectrosc. 54, 1075-1083 (2000)