Estimation of Twist in Uniaxial Cylinders With Inverse Electromagnetic Scattering

Abstract

For the purpose of determining the twist of a homogeneous, locally reacting, uniaxial cylinder, an inverse microwave scattering theory is presented. Remote measurements of the spiral grain of trees and logs are the prime application. Based on practical considerations, it is assumed that the transmitting and receiving antennas are collocated, requiring a three-dimensional modelling. A general theory is first developed, followed by an asymptotic analysis assuming that the distance from the antennas to the cylinder is many wavelengths and many cylinder radii. In this way, a substantial reduction of the numerical complexity, to the level of the two-dimensional case, is achieved. The error of the determined twist angle as function of inherent parameters of the problem using a Cramér-Rao analysis is given. The results from numerical simulations show that this error is low enough for determining the grain angle. Presented parameter studies of the error can be used for minimizing the errors in a measurement set up, of particular interest for non-sophisticated instruments and non-ideal laboratory conditions, by selecting optimum parameters such as frequency and antenna gain. Finally, it is stated that the model has a great potential for developing efficient algorithms for measuring the twist angle.