# Method of Multi-Angle Transmission Radiowave Tomography of Dielectric Objects
## 1 Introduction  
Radiowave tomography [1; 2; 3; 4; 5; 6] or microwave tomography [7; 8; 9; 10; 11; 12; 13] is used for remote non-destructive testing, diagnostics for the internal structures of heterogeneous media and the restoration of the forms of opaque objects on the basis of multi-sensory sounding. Radiowave tomography differs from X-ray tomography due to the significant impact of wave effects. Since the wavelength of radio waves is comparable with the size of the heterogeneities, wave effects appear, which do not allow the use of the known algorithms of X-ray tomography [14; 15; 16; 17; 18; 19; 20; 21], working in the ray approximation. The back-projection algorithm is most commonly used for 3D tomography image reconstruction. Wave effects are possible even for X-ray radiation when applied at the nanoscale, but this problem is solved by switching to higher-energy radiation or charged particles [22]. However, there are approaches to extract phase information to take into account wave effects in the projection approximation [23; 24; 25; 26; 27]. Radiowave tomography began development with the availability of digital technologies for the measuring and processing of radio wave signals [1]. In study [1], a tomographic method was proposed for visualizing the reflection and transmission coefficients of the objects under study. To obtain information on the dielectric permittivity, more complex processing algorithms and multi-angle measurements are required. Transmission radiowave tomography involves irradiating the object under study on one side and measuring the spatial amplitude-phase distribution behind the object. The source and the receiver arelocated on opposite sides of the probing object. In this method, the recorded field is blurred and has no sharp boundaries, as in the case of X-ray tomography [14; 15], because of the diffraction effect. The effects of refraction and multiple reflection remain even if the ray approximation is appropriate. When developing methods of tomography using radio waves, it is necessary to take into account the wave nature of such radiation and the phase delays of the signal in the medium. Taking into account the wave effects requires the development of approaches for solving the direct and inverse problems. There are different approaches to solving the problems of transmission radiowave tomography. Cross borehole radar methods used to study the medium between the boreholes are widely used [28; 29; 30; 31; 32]. In fact, cross borehole radar methods implement transmission radiowave tomography. Approaches are used based on the analysis of the time delay of the signal transmission. The travel time tomography method allows the visualization of dielectric inhomogeneities [28]. However, methods of this kind do not take into account the wave nature of radiation, but ray approximation is applied. Similar approaches are used in seismic tomography [33; 34], where the seismic wave velocity distribution in the medium is reconstructed by time delays. The use of such methods is widespread in the method of ultrasonic nondestructive testing [35], in which, similarly to electromagnetic waves, in the scalar approximation, ultrasonic waves are described by the wave equation. However, if the effects of diffraction and refraction are significant in a medium, travel time tomography methods are not effective [36]. Another problem is the resolution of the resulting images in radiowave tomography. To increase the resolution of tomographic images, it is necessary to localize the region of the interaction of radiation with matter. There is already a method of double focusing--the focusing of emitted and received waves with the help of dielectric lenses [37]. As a result, it is possible to form a relatively localized working region, within which the radiation has the form of a collimated wave beam. At the same time, multiple interactions sharply decrease, but the diffraction effects remain significant. Similar principles are used in optical tomography [38; 39], when lenses are used to focus optical waves.