Characterization of Sub-Resonant Dielectric Spheres by Millimeter-Wave Scattering Measurements

When measuring the size or relative permittivity of a dielectric particle, usually one of the parameters needs to be known for determining the other one. Scattering measurement methods offer an alternative that allows for extracting both the size and the permittivity of the particle under test at the same time. In this paper, bi-static scattering measurements at millimeter-wave frequencies are applied to characterize sub-resonant dielectric spheres of sub-wavelength size. The size and relative permittivity are extracted simultaneously from measurements at Ka-band (26.5-40 GHz). The experimental setup and the data processing procedure are detailed in depth, and the sources of the systematic errors are discussed. Alumina ceramic spheres (with relative permittivity of approximately 10) of diameter as small as 0.8 mm (less than 1/10 of free-space wavelength) were investigated. The extracted diameters and permittivities agree well with the expected values.