Dielectric Spectroscopy Using Dual Reflection Analysis of TDR Signals

Time-domain reflectometry (TDR) has been a powerful tool for measuring soil dielectric properties. Initiating from apparent dielectric constant ( K a ) measurement up until apparent and complex dielectric spectroscopies, the embedded information in the TDR signal can be extracted to inspire our understanding of the underlying dielectric behaviors. Multiple full waveform inversion techniques have been developed to extract complex dielectric permittivity (CDP) spectrum, but most of them involved prior knowledge of input function and tedious calibration. This rendered the field dielectric spectroscopy challenging and expensive to conduct. Dual reflection analysis (DRA) is proposed in this study to measure CDP spectrum from 10 MHz to 1 GHz. DRA is a simple, robust, model-free, and source-function free algorithm which requires minimal calibration effort. The theoretical framework of DRA is established and the necessary signal processing procedures are elaborated in this study. Eight materials with different dielectric characteristics are selected to evaluate DRA's performance, by using both simulated and experimental signals. DRA is capable of measuring non-dispersive materials very well, whereas dispersive materials require the assistance of a long-time-window (LTW) extraction method to further extend the effective bandwidth. The DRA approach is suitable for field applications that can only record a limited amount of data points and in-situ dielectric spectroscopy.