## 1. Introduction

Microwave imaging (MWI) is an imaging technique that can be used to produce a quantitative image of the dielectric profile of the object of interest (OI) by solving the corresponding electromagnetic inverse problem. In MWI, the OI is illuminated by incident electromagnetic fields at the microwave frequency range, and the resulting scattered fields are processed (inverted) to create (reconstruct) the OI’s dielectric profile image. This processing often involves calibrating the measured data and applying an appropriate inversion algorithm to this calibrated measured data. This imaging tool has the potential to be utilized for different applications such as breast cancer detection, stroke diagnosis, through wall imaging, security screening, and industrial non-destructive evaluation [

1,

2,

3,

4,

5,

6,

7,

8,

9,

10]. MWI can also be used in conjunction with other imaging tools, e.g., with magnetic resonance imaging or ultrasound tomography [

11,

12,

13]. In addition, MWI can be performed in the time domain or frequency domain, with the latter being the focus of this paper. Moreover, in some applications, reconstructing the magnetic properties is also of interest (e.g., in [

14]); herein, we only consider non-magnetic objects.

MWI can be performed in at least three fashions: (i) 1D (line reconstruction; e.g., [

15]); (ii) 2D (cross section reconstruction; e.g., [

16]), and (iii) 3D (volumetric reconstruction; e.g., [

17]). This is often determined based on several factors such as the application area, data collection process, and the amount of measured data. For some applications including biomedical imaging, it is desirable to enhance the achievable reconstruction accuracy from MWI. To this end, in addition to the development of appropriate inversion algorithms and regularization techniques, e.g., [

18,

19,

20,

21], several other techniques have been suggested to further improve the achievable image accuracy from MWI. For example, these include (i) using prior spatial information about the OI [

22,

23,

24], (ii) using prior information about the permittivity values or the expected ratio between the real and imaginary parts of the OI’s complex permittivity [

25,

26]; (iii) increasing the number of transceivers and frequencies of operation [

27]; (iv) improving the signal to noise ratio (SNR) of the system [

28]; (v) appropriate data calibration techniques [

7,

29]; (vi) enhanced modeling of the imaging system in the inversion algorithm [

30]. All of the above techniques may be classified under the following two categories. The first category aims to increase the

overall SNR with noise being either the actual noise or the modeling error. (Modeling error is defined as any discrepancies between the actual imaging setup and the numerical model used in the inversion algorithm.) On the other hand, the second category aims to enrich the information content of the data to be used for inversion; this is done by increasing the number of measurements and incorporating prior information (virtual data) about the OI.

The work presented in this paper aims to suppress the effect of undesired scatterers in the inversion process. To this end, we begin by defining undesired scatterers as any scatterers within the imaging chamber in which we are not interested in finding their unknown dielectric properties. Considering the scattered fields due to these undesired scatterers as unwanted signals, or noise, the topic of this paper, therefore, falls under the first category above: i.e., enhancing the overall SNR. Note that the undesired scatterer and the OI might be two distinct objects, or they can be attached to each other. For example, in 2D (cross-sectional) imaging of a 3D object, e.g., breast, the irradiating antenna not only illuminates the cross-section of interest but also illuminates other cross-sections. These other cross sections are then undesired scatterers with respect to the cross section to be imaged. Herein, we investigate how tailoring the incident field can be helpful toward suppressing such undesired scattering effects. Since the focus of this paper is on the incident field (and not the total field), the scope of this work is limited to imaging scenarios in which the induced fields in the dielectric objects are similar to the incident fields. (This is mainly associated with low-contrast and electrically small objects.) In addition, for simplicity, we have also limited the scope of this work to homogeneous lossless OIs and undesired scatterers.

A key aspect which is considered in this paper is that the OI is often placed electrically close to the antenna system, i.e., in its near-field (NF) zone, so as to make the imaging system more compact and also to enrich the information content of the measured data. (NF data collection increases the chance of capturing evanescent waves that contain high spatial resolution information about the OI.) Several NF MWI systems have been developed; however, to the best of our knowledge, all of them utilize standard “far-field (FF) antennas”. Herein, the term “FF antennas” has been used to indicate standard antennas such as dipoles, monopoles, Vivaldi, open ended waveguides which have not been specifically designed to achieve a certain NF distribution. (Some of these FF antennas have been modified, e.g., with a dielectric inclusion, to enhance their NF focusing [

31,

32].) All of these FF antennas have important advantages, e.g., their compactness, ease of modelling in the inversion algorithm, bandwidth, and the ability to easily operate in matching fluids. However, it is beneficial for near-field MWI to investigate antennas which are specifically designed to achieve desired NF distributions: in NF MWI, it is the incident NF of the antenna,

not its FF pattern, that interrogates the OI. As a follow-up to our previous work where we have discussed that the choice of the incident field distribution can affect the achievable reconstruction [

27,

33], we now discuss and demonstrate that a focused incident NF can be used advantageously in NF MWI to suppress undesired scattering events. The idea behind this paper is therefore simple: making sure that the

spotlight of the antenna is on the OI, and not on the undesired scatterers. To this end, we will utilize a NF plate and a Bessel beam launcher to demonstrate the potential advantages of using a focused incident NF beam in MWI. (We have recently presented a concise form of this idea in [

34].) We also note that there exist other techniques for focusing the fields into a hotspot, e.g., using an antenna array configuration [

35,

36,

37]. The focus of this paper is not to compare these focusing techniques; we just note that the radiators used in this paper do not require array feeding networks or array signal processing.

Finally, in this paper, we use the terms focused instead of directive, and distribution instead of pattern since the terms directivity and pattern describe FF properties of antennas, and are more appropriate for the FF zone. We also utilize NF distributions and NF beams interchangeably. In addition, hereafter, we refer to NF MWI simply as MWI for brevity. It should also be noted that the time-dependency of $exp(j\omega t)$ is implicitly assumed throughout this paper.

## 4. Discussion and Conclusions

Broadly speaking, this paper proposes that tailoring the contrast sources induced in the objects can be used advantageously in MWI. This approach has the potential to suppress (or enhance) the sensitivity of the measured data with respect to specific regions of the imaging domain, e.g., a region which requires more accurate assessment. It was noted that we do not have full control over tailoring contrast sources since the induced total fields within the objects are dependent on the objects’ unknown dielectric properties. Due to this difficulty, we have limited the scope of this paper to scenarios in which the induced total field distributions inside homogeneous objects are similar to the illuminating incident field distributions. For the cases where this (Born) assumption does not hold, one option is to utilize an estimate of the dielectric profile of the objects (which might be obtained via a different imaging modality), and then use this prior knowledge to create an incident field distribution that results in a desired total field distribution in the objects.

We also noted the importance of tailoring the incident NF beam of the irradiating antenna, as opposed to its FF pattern, for NF MWI. In this paper, we have investigated two NF beams for imaging which satisfy our desired property: a focused NF distribution. We envision that the area of electromagnetic metasurfaces will offer a systematic tool to synthesize appropriate incident NF distributions to be utilized for imaging (e.g., see [

52]). This is due to the fact that metasurfaces can transform a given excitation electromagnetic field to a desired one by imposing appropriate surface boundary conditions [

53]. In addition, in this work, we did not consider tailoring the polarization of the incident field for the benefit of imaging, which can also be pursued in future.

In this paper, we have only considered focused NF beams with the purpose of minimizing the sensitivity of the collected scattering data to undesired scatterers. However, depending on the application area and purpose, one can employ incident NF beams of different distributions to optimize the retrieval of various features of interest. In addition, within the scope of our assumptions, we have intuitively discussed that this focused NF beam approach can limit the geometrical support of the induced contrast sources, and can therefore result in less required measured data points as compared to scenarios in which wider NF beams are utilized. In addition, one of the other potential advantages of focused NF beams, which has not been investigated here, is the ability to enhance the SNR of the measured data. In some applications, such as those which operate in lossy medium, enhancement of the SNR is critical to enhance the achievable reconstruction accuracy and resolution.

In summary, this paper demonstrated that the use of focused NF beams can suppress some undesired scattering effects. From a broader point of view, the main message of this paper is the suggestion that the incident NF beam, as an MWI system design component, can be advantageously utilized to optimize some imaging aspects, and not just to irradiate the objects.