It is well known that a finite-size scatterer has a set of natural resonances, which are uniquely determined by the physical properties of the scatterer. This is also the case for a breast tumor which can be regarded as a dielectric scatterer. Since the scatterer is naturally "tuned" at the resonances, it is expected that an increased electromagnetic coupling would take place at the resonance frequencies compared to other frequencies. For a breast tumor, this would mean a higher power absorption, indicating a faster temperature increase resulting in more efficient hyperthermia. In this dissertation, an adaptive microwave concept is demonstrated for breast cancer applications. The general approach is to detect and identify the tumor-specific resonance, determine the electrical location of the tumor, and apply the focused microwave hyperthermia using the identified resonance and the electrical location. The natural resonances vary depending on the tumor size, shape, and breast tissue configuration. Therefore, an adaptive tuning of the microwave source to tumor-specific resonance frequencies could improve the overall efficiency of hyperthermia treatment by allowing for a faster and more effective heating to achieve a desired therapeutic temperature level. Applying the singularity expansion method (SEM), both the resonances and the electrical location can be obtained from the poles and residues, respectively. This SEM-based approach is computationally inexpensive and can easily be implemented as a combination processing into emerging UWB microwave systems. Alternatively, a relatively simple microwave system based on this concept can potentially be used in conjunction with existing mammography. / Ph. D.

Ce manuscrit est consacré à l’étude de la méthode du développement en singularités (SEM) appliquée aux antennes. Dans la première partie de ce travail, trois méthodes d’extraction des pôles de résonance sont présentées et comparées : les méthodes de Prony et Matrix Pencil dans le domaine temporel et la méthode de Cauchy dans le domaine fréquentiel. Une procédure est établie pour optimiser l’extraction avec chaque méthode et une étude de robustesse montre que la méthode Matrix Pencil permet d’obtenir plus de pôles et avec une meilleure précision que les deux autres méthodes en présence de bruit. Dans un second temps, la méthode Matrix Pencil est appliquée sur des réponses d’antennes, obtenues en rayonnement et en Surface Equivalente Radar (SER), et les pôles de résonance extraits sont identiques pour les deux approches. Cette étude valide donc la possibilité d’extraire les pôles de résonance d’une antenne directement à partir de sa SER. La variation de la position des pôles de résonance en fonction des dimensions et de la charge de deux antennes est ensuite étudiée et met en évidence le lien entre l’impédance d’entrée de l’antenne et ses pôles de résonance. Enfin, les mesures de la SER de trois antennes valident expérimentalement l’extraction des pôles de résonance à partir de la SER d’une antenne. Ce travail pose donc les bases de la caractérisation d’antennes à l’aide de la SEM appliquée à la SER de l’antenne. / This manuscript deals with the Singularity Expansion Method (SEM) applied to antenna characterization. In the first part of this work, three resonant poles extraction methods are presented and compared: the Prony and Matrix Pencil methods in the transient domain and the Cauchy method in the frequency domain. A procedure is defined to optimize the extraction with each method and a robustness study shows that Matrix Pencil method allows obtaining more physical poles with a better accuracy than the two other methods in presence of noise. In a second part, the Matrix Pencil algorithm is applied on radiated and backscattered antenna responses. Extracted resonant poles from both responses are exactly the same. This study validates the possibility to extract poles directly from its backscattered response. The position of resonant poles is analyzed with respect to antenna’s dimension and its load for two different cases. This emphasizes the link between antenna poles and antenna input impedance. Finally, RCS measurements of three antennas validate antenna poles extraction directly from its RCS. This work lays the foundations of antenna characterization using the SEM applied to RCS measurements.