Introduction The first studies on tomographic

Introduction The first studies on tomographic imaging were dedicated to solving a number of medical problems and appeared in the 1960s. At that time the principal source of analyzed information was the data obtained when measuring the level of radiation absorbed by an object in the X-ray wavelength range [2]. The experiments measured the one- or two-dimensional distributions of the absorbed X-ray radiation for various orientations of the studied object with respect to the direction of radiation propagation. The measured distributions for each orientation formed a set of tomographic projections which were then used to calculate the spatial distribution of the absorptance (optical density) of the material by the Radon inverse transform. The obtained distribution was analyzed using computer technology and visualization tools. A patients health status was then determined from the results of the analysis. Later the progress in X-ray and NMR tomographies, as well as a breakthrough in creating powerful computing and visualization systems, kick started the development of tomography using other spectral ranges. The microwave region was of principal interest. At the same time, the main research direction still involved solving applied medical problems [4,5] of determining the spatial distribution of dielectric permittivity in tissues transparent enough for radiation of the selected region of the microwave range. These are, mainly, bone and fat tissues. The goal of this study is to develop a physical method of tomographically imaging dielectric objects in the microwave wavelength range, in particular, in the upper X- and the lower Ku-ranges.
Designing the microwave tomography method The proposed method involves measuring and subsequently calculating the spatial distribution of optical alk inhibitor density. The obtained distribution is then used to find a permittivity distribution. An experimental setup shown in Fig. 1 was assembled to develop the proposed method. The key elements of the experimental setup are six receive antennas 3 and two transmitter arrays 4 including 256 transmitting elements working on 32 frequencies of the 8–18 GHz microwave range. The installation is in the form of a portal with elements arranged in mirror symmetry relative to the plane passing through the center and oriented parallel to the yz plane. The studied dielectric object 1 is located in the space between the sides of the installation, i.e. in the studied zone 2. When performing experiments in the space lines connecting the receiver–transmitter pairs we measured the elongation of the optical path caused by the presence of the dielectric object in the studied zone. The elongation of the optical path was calculated from the shift in the principal maximum of the inverse Fourier transform [1] of the measured field for each transmitter–receiver pair: where l is the elongation of the optical path; ,F(l) is the field amplitude of the inverse Fourier transform for each rth receiver and each tth transmitter; , and 0 are the complex amplitudes of the measured fields on an rth receiver from a tth transmitter at a kth frequency, with and without the object in the studied zone, respectively; 0 is the phase of the measured field on an rth receiver from a tth transmitter on a kth frequency; is the kth frequency of the set; c is the speed of light. The transmitter array and the receive antenna located on different sides of the studied area form a tomographic projection. Geometrically, this projection is a pyramid with the receive antenna in the apex and the transmitter array in the base (the dashed lines in Fig. 1 show two tomographic projections). The elongation of the optical path calculated for the respective receiver–transmitter pair within a single transmitter array is recorded in each tomographic projection. The configuration of the experimental setup involved measuring the complex amplitudes of the electromagnetic field at 6 receive antennas which corresponded to 6 tomographic projections.