## 1 Introduction  
One of the important applications of electromagnetic imaging problems is the detection and imaging of the localized pathological changes in human organs or tissues [1, 2]. In recent years, many studies have been carried out on various parts of human body such as the head, breast, arm, etc., which are non-homogeneous and have frequency-dependent electromagnetic parameters [3, 4, 5, 6]. When such structures are placed in free space for imaging purposes, due to their constitutive parameters with high dielectric contrast and loss, there will be a problem with the relative poor penetrating of the incident field into the structure and a considerable part of the field will be reflected back. To overcome this difficulty, one of the measures may be taken is the existence of a background space with appropriate parameters. If the contrast difference between the inhomogeneous structure under examination and the medium in which the structure is placed can be reduced enough, as a result of the usage of an appropriate background medium, better transmission and lesser reflection of the incoming field into the structure will be possible, and the field will interact with the structures to be detected and imaged. These types of media are called as \"matching media\" and a relatively limited number of studies exist in the literature [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13] since medical microwave imaging is a new developing technique compared to conventional approaches such as MR, X-ray, etc. Microwave imaging applications have largely concentrated on the head (brain) [4; 7; 10; 11; 12] and female breast [2; 3; 9; 11], but microwave imaging of the arm [1; 5; 7], limb [1] and bone [6; 13] have also drawn interest. The satisfactory imaging quality of the human arm with microwave-based alternative medical technologies requires a background space (matching medium) to directly decrease the reflected field and to transmit the incident field by a sufficient amount at the arm boundary. In recent years, several contributions concerned with microwave imaging of human arm and matching medium have been reported in the literature. For instance, [PERSON] et al. [7] used a microwave tomographic scanner for biomedical applications using deionized water for matching purposes and presented tomographic slices of an in vivo human forearm. In [1], the authors outlined a process for an appropriate matching fluid and generated images of a human forearm using an experimental microwave tomography system designed for limb imaging. [PERSON] et al. [5] presented a pilot study using a microwave tomography system with a matching fluid of deionized water and table salt, and they imaged the forearms of five adult male and female volunteers between the ages of 30 and 48. [PERSON] et al. [6] investigated the application of microwave imaging to monitor the in vivo dielectric properties of human bones and, hence, aid in the monitoring of osteoporosis. [PERSON] et al. [13] conducted a study to evaluate the use of microwave tomography for imaging human bones with varying parameters, where the authors proposed the use of an ultrasound gel instead of the more traditional glycerin/water solution as a matching medium. Different studies related to the human arm may also be mentioned. [PERSON] et al. [14] showed that metamaterial structures can increase the focusation of electromagnetic energy in the human arm to larger deep areas without the undesired radiation of the surrounding area. [PERSON] et al. [15] studied the behavior of an ultra-wideband antenna and tested the antenna in free space, outside and inside of a numerically modeled human arm. In the literature, there are studies on layered cylindrical structures that can be analytically solved and human arm models built with these structures. The aim of all these models is to reveal the interaction of electromagnetic waves with the relevant structures, that is, to solve a scattering problem.