  We analyzed the behavior of the complex Fourier spectrum of the
angle-resolved light scattering pattern (LSP) of a sphere in the framework of
the Wentzel-Kramers-Brillouin (WKB) approximation. Specifically, we showed that
the phase value at the main peak of the amplitude spectrum almost quadratically
depends on the particle refractive index, which was confirmed by numerical
simulations using both the WKB approximation and the rigorous Lorenz-Mie
theory. Based on these results, we constructed a method for characterizing
polystyrene beads using the main peak position and the phase value at this
point. We tested the method both on noisy synthetic LSPs and on the real data
measured with the scanning flow cytometer. In both cases, the spectral method
was consistent with the reference non-linear regression one. The former method
leads to comparable errors in retrieved particle characteristics but is 300
times faster than the latter one. The only drawback of the spectral method is a
limited operational range of particle characteristics that need to be set a
priori due to phase wrapping. Thus, its main application niche is fast and
precise characterization of spheres with small variation range of
characteristics.
