Evaluation of the Accuracy of the Remote Determination of the Brewster Angle when Measuring Physicochemical Parameters of Soil

Abstract

In precision farming technology, the moisture of the soil, its granulometric composition, specific conductivity and a number of other physical and chemical parameters are determined using remote radar sensing. The most important parameters are those measured in the area of the plant root system located well below the “air-surface” boundary. In order to create conditions for the penetration of electromagnetic waves through the “air-surface” interface with a minimum reflection coefficient, the irradiation of the Earth’s surface is carried out obliquely with an angle of incidence close to the Brewster angle. The reflection coefficient, and, consequently, the Brewster angle, depend on the complex dielectric permittivity of the surface soil layer and are not known a priori. To determine the Brewster angle, the usual method is to search for the minimum amplitude of the vertically polarized signal reflected from the surface. Another approach is when the first derivative of the dependence of the modulus of the complex amplitude of a vertically polarized interference wave, taken with respect to the angle of incidence, is set equal to zero. In turn, in real dielectrics such as agricultural soils, the amplitude of the vertically polarized signal reflected from the surface is directly proportional to the reflection coefficient and does not have a pronounced minimum, which reduces the accuracy of the measurements. Based on the solution of the Helmholtz wave equation for a three-layered structure of the propagation medium (air, upper fertile soil layer, soil layer below the groundwater level), a model of the process of forming an interference wave under oblique irradiation of a planar layered dielectric with losses has been developed. Using the developed model, factors influencing the accuracy of determining the Brewster angle have been identified. For the first time, it is proposed to use the phase shift between the oscillations of the interference waves with vertical and horizontal polarization to measure the Brewster angle. A comparative assessment of the accuracy of determining the Brewster angle using known amplitude methods and the proposed phase method has been carried out. The adequacy of the method was experimentally confirmed. Recommendations have been developed for the practical application of the phase method of finding the Brewster angle for assessing the dielectric permittivity of soil and its moisture content.