Qualitative microwave imaging in non-destructive testing and evaluation applications

Abstract

Microwave imaging is an inspiring research topic in which the goal is to obtain constitutive properties of inaccessible targets using measurements of the scattered electric field or scattering parameters. The phrase microwave refers to the frequencies of the electromagnetic fields used in this technology, which can range from several hundred MHz to several hundred GHz. The wavelength of the fields allowed us to analyze the materials without causing any damage within this frequency bandwidth. Because of this characteristic, this research area has discovered various non-destructive testing and evaluation applications in applied sciences, such as biomedical imaging, moving target detection, food imaging, subsurface imaging, concealed weapon detection, and through-the-wall imaging. Instead of reconstructing the electrical parameters, one technique for dealing with microwave inverse scattering problems is to compute an indicator function that holds the information of the targets. These techniques are known as qualitative microwave imaging methods (Q-MWM), and they are typically thought to be linear and non-iterative techniques that are computationally less expensive than their quantitative counterparts. The most extensively researched Q-MWM representatives are truncated singular value decomposition (TSVD), linear sampling method (LSM), and factorization method (FM). The singular sources method (SSM) and the nearfield orthogonality sampling method (NOSM) are comparatively new, yet they have a promising future in microwave imaging. In the first part of the thesis, the problem of microwave imaging of an impedance cylinder is investigated using Newton's approach. To achieve this goal, the scattered field from a circular cylinder with homogenous impedance is determined for plane wave illumination. At this stage, the scattering configuration is considered to be in the form of a TMz scenario. In this scenario, the impedance cylinder is supposed to be infinite along the z-axis, and the electric fields are assumed to be parallel to the same axis. The incident plane wave is assumed to be decomposed into a summation of Bessel functions, whereas the scattered field is assumed to be expressed as a sum of Hankel functions, according to these assumptions. After that, the boundary conditions on the surface of the impedance cylinder are utilized in order to acquire the unknown coefficients in the scattered field. After then, during the inverse scattering phase, it is necessary to make estimates concerning the target's impedance as well as its radius. To achieve this aim, the scattered field of the impedance cylinder is collected at a number of frequencies on a single point surrounding the target. Following this, an initial value is given to both of the variables, and the evaluation of the scattered field that corresponds to these initial values occurs. To arrive at an estimate of the updated amount for each parameter, the difference in the scattered fields is first divided into a matrix. This matrix then contains the derivative of the scattered field with respect to the unknown variables. Then, both of the parameters are updated, and this procedure is repeated as many times as necessary until the difference between the measured and estimated fields falls below a certain threshold that has been established. As a result, we are able to derive an estimate of the impedance as well as the radius of the cylinder. According to the findings, the method that is now suggested is capable of reconstructing the unknown parameters using only a limited aperture and several frequency observations. In the second part of the thesis, we examined differential through-the-wall microwave imaging with several formulations of the TSVD method in a non-anechoic experiment. Past studies have used TSVD with a single transmitting/measuring antenna, whereas we show how to use it with a moving linear transmitting/measuring antenna array. Particularly, for repeated measurements, an averaging procedure is adopted. Three TSVD approaches are tested: TSVD on Contrast Source, TSVD on Contrast and multi frequency TSVD on Contrast. The dimension of the inverted matrix in TSVD on Contrast Source method is comparatively small. Following the solution of equations, a normalization scheme is suggested to eliminate the noise. TSVD on Contrast technique produces better reconstructions than TSVD on Contrast Source method because measured data for all excitations are inverted simultaneously. TSVD on Contrast, however, takes a long time than TSVD on Contrast Source because the inverted matrix becomes larger. Finally, in order to avoid further calibration simulations/measurements in multi frequency TSVD on Contrast, we use TSVD on Contrast solutions to obtain the calibration information. The contrasts are then computed for all frequencies and excitations at the same time. Thus, for multi frequency TSVD on Contrast, the inverted matrix is the largest, the accuracy is the best, and also the computational burden is the greatest. A metallic scatterer is placed behind a wall to evaluate the proposed techniques. The results demonstrate a trade-off between accuracy and computational time when selecting an appropriate inversion approach. Furthermore, each method's norm type selection is evaluated. In the third part of the thesis, the imaging of moving objects with Q-MWM is addressed. The necessity of background measurement is a troublesome aspect of Q-MWM. To avoid this, the total electric field collected at distinct time instants (say, Etotn, Etotl are the total electric fields measured at nth and lth time instants) are implemented to Q-MWM. Thus, the outcome of the Q-MWM can be considered to be the sum of the indicators at these time instants (i.e. Etotn-Etotl produces the differential indicator Inl=In+Il, where In, Il are the indicators at nth and lth time instants). An equation system is developed for indicator values at different time instants using this information for all possible time couples. Without performing any background measurements, the indicator of Q-MWM for each time frame is derived by solving this equation system. The proposed algorithm's performance is validated using 3D and 2D (both transverse magnetic (TM) and transverse electric (TE)) experimental measurements, which are done in a non-anechoic environment, for the LSM, which is an example of Q-MWM. In the fourth part of the thesis, SSM, a qualitative imaging method, is investigated for two-dimensional transverse magnetic electromagnetic (2D-TM EM) inverse scattering cases. Qualitative microwave imaging approaches allow for the rapid and accurate reconstruction of target shapes from scattered electric field measurements. This section's contribution can be stated as follows: (i) The SSM was originally introduced for the far-field scenario; here, we extend the SSM in the near field - inhomogeneous background configuration. Each stage of the extension (which involves an integral equation) is discussed using the linearity and reciprocity principles to provide physical insights. (ii) A relationship is established between the electrical properties of the scatterers and the SSM indicator. (iii) The suggested method is examined for monitoring hyperthermia treatment problems with a realistic breast model to evaluate the performance of SSM in real-world scenarios. The obtained results demonstrate that the SSM is capable of handling realistic breast phantoms for monitoring hyperthermia problems. In the fifth and last part of the thesis, a range-migration technique is presented for near-field microwave imaging using monostatic and bistatic measurement configurations. Calibration measurements are critical for enhancing the precision of both qualitative and quantitative microwave imaging. A calibration measurement should ideally be taken at each desired range (or depth) position in three-dimensional (3-D) near-field imaging, which can be time-consuming. The calibration effort can be reduced to a single measurement at a reference range position if the range behavior of the resolvent kernel of scattering can be predicted analytically. Analytical formulations for range-translation (or range-migration) are already commonly utilized in far-zone radar and acoustic imaging; nevertheless, their accuracy suffers dramatically in near-field situations. The magnitude and phase of the system point-spread function (PSF) are accurately estimated at any desired range position based on a single measurement of the PSF. The proposed migration is conducted in real space, but it can also be implemented with Fourier-domain (or k-space) inversion methods. It is used in simulation-based and experimental examples to confirm its performance and demonstrate its limitations with quantitative microwave holography.