Wiener bounds for complex permittivity in terahertz spectroscopy: case study of two-phase pharmaceutical tablets

The terahertz measurement technique has become popular in the field of pharmaceutical technology for tablet quality inspection. Spectral data obtained from the tablets is based on the utilization of Fresnel's formulas for an ideal slab. However, a tablet is a porous medium. Hence, in the THz gap one has to assume that a tablet constitutes at least an effective medium if the Fresnel theory is applied in quantitative permittivity spectra analysis. Hence, it is suggested that one should consider instead of the permittivity of homogeneous media the concept of effective permittivity in the THz terminology of porous tablets. Usually the fill factor of a component of a tablet is known but not the detailed bulk structure. Nevertheless, it is possible to estimate the complex effective permittivity of a tablet with the aid of so-called Wiener bounds. The idea of this article is to present a modification of Wiener bounds applied to the estimation of the real and imaginary part of the permittivity of the pure component of a tablet. As an example, the effective complex permittivity of a starch acetate tablet is considered.