Apparatuses and methods for microwave tomography

Abstract

An apparatus (400) for non-invasive microwave tomography of an object (111), and a method (900) for obtaining a representation of an object (111) by means of an apparatus for microwave tomography. The apparatus (400) comprises: a container (120) provided with a first medium (121), an antenna array (130) that is arranged inside the container (120) and that is at least partly encompassed by the first medium (121); a first boundary (122) of the container (120) configured to face at least a part of the external surface of the object (111); and a dampening layer (440) arranged at a second boundary (123) of the container (120) and configured to attenuate reflection of electromagnetic energy, scattered by the object (111), at the second boundary (123) back into the first medium (121). The method (900) comprises: radiating (910) electromagnetic energy from a primary antenna element of an antenna array (130) into the container (120) of the apparatus to irradiate the object (111); and in response to the radiation of the electromagnetic energy, obtaining (920) a representation of a first electric field distribution in the apparatus by means of measurements via the antenna array (130); and obtaining (930) the representation of the object (111) by iteratively adapting a model of a dielectric distribution representing the object.

Description

[0001] APPARATUSES AND METHODS FOR MICROWAVE TOMOGRAPHY TECHNICAL FIELD The present disclosure relates to an apparatus for non-invasive microwave tomography of an object, a method of obtaining a representation of an object by means of an apparatus for microwave tomography, a control system comprising a processing circuitry configured to perform the method, a computer program comprising program code means for performing the method, and a computer readable medium carrying a computer program comprising program code means for performing the method. BACKGROUND Microwaves can be used for imaging purposes. Microwaves typically mean the frequency range 300 MHz to 300 GHz but may also include lower and higher frequencies. Microwave imaging is a technique to non-destructively determine the shape and / or the dielectric properties of an object (such as a body part, a test sample, a manufactured product, a food portion) using penetrating waves. Microwave tomography is a microwave imaging method that provides quantitative information about the distribution of dielectric properties inside an object, and that relies on the measurement of the wave scattered by the object in response to the penetrating wave (also called incident wave). In most instances of microwave tomography, a number of antenna elements are placed around the object to be imaged in a planar, cylindrical, or spherical arrangement (for example) to form an antenna array that produces the penetrating wave and simultaneously measures the response of the object. The array and the object are sometimes immersed into a material acting as coupling medium (such as air, oil, or water) to achieve impedance matching. This setup constitutes an apparatus sometimes called “imaging tank”. The antenna array is used to non-invasively (e.g., without piercing or penetration) measure the scattering induced by the object with respect to the empty tank. Based on the measurements, a reconstruction algorithm attempts to determine the spatial distribution of the dielectric properties inside the tank (including, for example, permittivity and / or electric conductivity) representing the object. To date, however, few applications have been reported. Reported applications include mainly anatomical imaging, industrial monitoring, and non-destructive testing. The scarcity of medical and industrial applications of microwave imaging is mainly due to the poor reliability of existing microwave imaging devices and methods. There is a need for improved apparatuses for non-invasive microwave tomography. There is also a need for improved ways of using apparatuses for microwave tomography purposes. SUMMARY An object of the present disclosure is to provide improved apparatuses for non-invasive microwave tomography, and improved ways of using apparatuses for microwave tomography to obtain a representation of an object. This and other objects, which will become apparent in the following, are accomplished by an apparatus, a method, and a control system, as defined in the accompanying independent claims. According to a first aspect of the present disclosure, there is provided an apparatus for non- invasive microwave tomography of an object. The apparatus comprises a container provided with a first medium, the container being provided with a first boundary configured to face at least a part of an external surface of the object. The apparatus further comprises an antenna array arranged inside the container. The antenna array is at least partly encompassed by the first medium. The antenna array is configured to transmit electromagnetic energy for irradiating the object and is configured to receive electromagnetic energy scattered by the object. The apparatus also comprises a dampening layer arranged at a second boundary of the container. The dampening layer is configured to attenuate reflection of electromagnetic energy, scattered by the object, at the second boundary back into the first medium. The dampening layer reduces the magnitude of undesired reflected electromagnetic energy at the second boundary of the container. This facilitates using the apparatus in image reconstruction methods such as microwave tomography. In particular, the reduction of undesired reflection at the second boundary facilitates a more representative reconstruction / simulation of an electric field distribution in the apparatus (i.e. a reconstruction / simulation of an electric field distribution that may accurately be matched to an electric field distribution obtained from measurements of the antenna array of the apparatus), which in turn enables obtaining a more accurate representation of the object. Furthermore, the dampening layer provides the attenuation without significantly increasing the size of the apparatus. Consequently, an improved apparatus for non-invasive microwave tomography that is compact is provided. The second boundary is preferably different from the first boundary. Furthermore, the first and the second boundaries may constitute a part of the total surface area of the container. In that way, at least some undesired reflection of electromagnetic energy is reduced. Preferably, the container is encapsulated by the first boundary and the second boundary. In other words, the first boundary and the second boundary together constitute the total or a substantial amount, such as more than 80%, of the surface area of the container. In yet some other words, the dampening layer is arranged such that the container is delimited by the external surface of the object and the dampening layer. In this way, undesired reflections back into the first medium are reduced further. According to a least one exemplary embodiment, the dampening layer comprises a second medium. Furthermore, the first medium has a first dielectric loss value at a frequency and the second medium has a second dielectric loss value at the frequency, wherein the second dielectric loss value is at least two times larger than the first dielectric loss value. In this way, electromagnetic energy propagating through the dampening layer is attenuated, which in turn reduces the electromagnetic energy being reflected back into the first medium (e.g., from a boundary of the dampening layer facing structural parts of the apparatus). The dielectric loss value may be parameterized in terms of, e.g., the loss angle δ or a corresponding loss tangent tan(δ). According to a least one exemplary embodiment, the first dielectric loss value is parametrized by a first loss angle and the second dielectric loss value is parametrized by a second loss angle, where the second loss angle is at least two times larger, preferably at least ten times larger, and more preferably at least a hundred times larger than the first loss angle. According to a least one exemplary embodiment, the first medium has a first characteristic impedance value at the frequency and the second medium has a second characteristic impedance value at the frequency, wherein the second characteristic impedance value is within 20% of the first characteristic impedance value. In some examples, the second characteristic impedance value is within 50% of the first characteristic impedance value. In this way, electromagnetic energy reflected back into the first medium, due to the transition from the first medium to the second medium, is attenuated. Preferably, the first medium is selected such that the characteristic impedance value of the first medium matches the average characteristic impedance value of the object, e.g., being within 50% of the average characteristic impedance value of the object. According to at least one exemplary embodiment, the first medium comprises air. Air presents a relatively low-cost medium that exhibits a characteristic impedance close to that of many manufacturing materials, such as plastic, wood and concrete, while also being low-loss. According to another exemplary embodiment, the first medium comprises water. Preferably the water is purified water (also called deionized water, demineralized water, or distilled water). Purified water presents a relatively low-cost medium that exhibits a characteristic impedance close to organic matter, while also being low-loss (e.g., having electric conductivity less than 0.1 S / m). The use of a low-loss coupling medium increases the efficiency of electromagnetic energy transfer between the antenna array and the object. According to a second aspect of the present disclosure, there is provided a method of obtaining a representation of an object by means of an apparatus for microwave tomography. The apparatus comprises a container provided with an antenna array comprising a primary antenna element (which may be called a sending or active antenna element) and one or more secondary antenna elements (which may be called receiving or passive antenna elements) positioned relative to the object. The primary (sending) antenna element may simultaneously also serve as secondary (receiving) antenna element. The space inside the container that is not occupied by the antenna elements is preferably filled with a coupling medium (such as the first medium as is discussed in connection to the first aspect of the present disclosure). The method comprises: radiating electromagnetic energy from the primary antenna element into the container to irradiate the object; and in response to the radiation of electromagnetic energy, obtaining a representation of a first electric field distribution in the apparatus by means of measurements via the one or more secondary antenna elements; and obtaining the representation of the object by iteratively adapting a model of a dielectric distribution representing the object. The adapting comprises, iteratively, obtaining a representation of a second electric field distribution in the apparatus and in the object using a model of the apparatus and the model of the dielectric distribution, wherein the representation of the second electric field distribution is obtained based on constructed electromagnetic energy as scattered by the model of the dielectric distribution and constructed electromagnetic energy as scattered by one or more antenna elements of the antenna array of the model of the apparatus; comparing the representation of the second electric field distribution with the representation of the first electric field distribution to obtain a comparison; and adapting the model of the dielectric distribution based on the comparison and thereby obtaining the representation of the object. In this way, scattering of electromagnetic energy by the object and by the antenna elements of the antenna array of the model of the apparatus are accounted for. In particular, the disclosed method provides a representative reconstruction / simulation of an electric field distribution in the apparatus, i.e., a representation of the second electric field distribution that may be accurately matched to the representation of the first electric field distribution, which in turn enables obtaining an accurate a representation of the object. The effect of the scattering of electromagnetic energy by the antenna elements on the first and second electric field distributions increases with the inverse of the loss angle of the coupling medium. Some microwave apparatuses, such as those utilizing air or purified water as the first medium, typically rely on coupling media with small loss angle. Consequently, the disclosed method allows obtaining an accurate representation of the object using an apparatus with a low-loss coupling medium as the first medium. Furthermore, the effect of the scattering of electromagnetic energy by the antenna elements on the first and second electric field distributions increases the more densely the antenna elements of the antenna array are arranged. Apparatuses for microwave imaging may benefit from denser antenna arrays, and closer to the object, as this results in the apparatus being able to receive a stronger signal from more measurement locations, which allows for a more accurate and more detailed reconstruction of the object. The disclosed method realizes a modeling of the scattering of electromagnetic energy by the antenna elements of the apparatus, which makes the reconstruction more accurate. Consequently, the disclosed method allows obtaining an accurate representation of the object using an apparatus with densely arranged antenna elements. According to a least one exemplary embodiment, the method comprises obtaining the representation of the second electric field distribution by obtaining: a constructed incident electric field distribution from the primary antenna element of the model of the apparatus in the absence of the model of the dielectric distribution, or a measured incident electric field distribution from the primary antenna element of the apparatus in the absence of the object, a constructed primary scattered electric field distribution scattered by the model of the dielectric distribution in response to the constructed or the measured incident electric field distribution, and a constructed secondary scattered electric field distribution scattered by one or more antenna elements of the antenna array of the model of the apparatus in response to the constructed primary scattered electric field distribution. Compared to currently available methods where only the scattering of the electromagnetic energy due to the object is accounted for, the method provides a more representative reconstruction / simulation of an electric field distribution when the scattering due to the antenna elements is not negligible. This provides a representation of the second electric field distribution that may accurately be matched to the representation of the first electric field distribution, which in turn enables obtaining a more accurate representation of the object. According to at least one exemplary embodiment, the method comprises obtaining one or more constructed incident electric field distributions from respective antenna elements of the antenna array of the model of the apparatus in the absence of the model of the dielectric distribution, or one or more measured incident electric field distributions from respective antenna elements of the antenna array of the apparatus in the absence of the object. In that case, the method may further comprise obtaining the constructed secondary scattered electric field distribution based on the one or more constructed incident electric field distributions or the one or more measured incident electric field distributions. This represents an accurate and compact way of modeling the response of the antenna array. This enables efficiently obtaining an accurate representation of the second electric field distribution in the apparatus, which may be matched to the representation of the first electric field distribution, which in turn enables obtaining a more accurate representation of the object. According to at least one exemplary embodiment, the apparatus of the disclosed method is the apparatus according to the first aspect of the present disclosure. The dampening layer of such an apparatus reduces the magnitude of reflected electromagnetic energy at the second boundary of the container. This enables obtaining a more representative reconstruction / simulation of an electric field distribution in the apparatus, i.e., a representation of the second electric field distribution that may be accurately matched to the representation of the first electric field distribution, which in turn enables obtaining a more accurate representation of the object. According to a third aspect of the present disclosure, there is provided a control system comprising a processing circuitry configured to perform the method discussed above. The control system is associated with the above-discussed advantages. The system may comprise the apparatus according to the discussions above. According to a fourth aspect of the present disclosure, there is provided a computer program comprising program code means for performing the method discussed above when said program is run on a computer or on processing circuitry. The computer program is associated with the above-discussed advantages. According to a fifth aspect of the present disclosure, there is provided a computer readable medium carrying a computer program comprising program code means for performing the method discussed above when said program product is run on a computer or on processing circuitry. Generally, all terms used in the claims are to be interpreted according to their ordinary meaning in the technical field, unless explicitly defined otherwise herein. All references to "a / an / the element, apparatus, component, means, step, etc." are to be interpreted openly as referring to at least one instance of the element, apparatus, component, means, step, etc., unless explicitly stated otherwise. The steps of any method disclosed herein do not have to be performed in the exact order disclosed, unless explicitly stated. Further features of, and advantages with, the present disclosure will become apparent when studying the appended claims and the following description. The skilled person realizes that different features of the present disclosure may be combined to create embodiments other than those described in the following, without departing from the scope of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS With reference to the appended drawings, below follows a more detailed description of embodiments of the present disclosure cited as examples. In the drawings: Figure 1 illustrates non-invasive microwave tomography of an object; Figure 2 is a flow chart illustrating a method; Figure 3 shows a response to an incident electric field distribution of an active (primary) antenna in an apparatus for microwave tomography; Figure 4 shows an apparatus for microwave tomography; Figure 5 shows an array coupling model; Figure 6 shows an example of domain discretization in an apparatus; Figure 7 shows three different apparatuses for non-invasive microwave tomography; Figure 8 shows three different arrangements for non-invasive microwave tomography; Figure 9 shows an apparatus and a control system; Figure 10 is a flow chart illustrating a method; and Figure 11 schematically illustrates a control unit. DETAILED DESCRIPTION The present disclosure is described more fully below with reference to the accompanying drawings, in which certain aspects of the present disclosure are shown. The present disclosure may, however, be embodied in many different forms and should not be construed as limited to the embodiments and aspects set forth herein; rather, these embodiments are provided by way of example so that this disclosure will be thorough and complete, and will fully convey the scope of the present disclosure to those skilled in the art. Like numbers refer to like elements throughout the description. It is to be understood that the present disclosure is not limited to the embodiments described herein and illustrated in the drawings; rather, the skilled person will recognize that many changes and modifications may be made within the scope of the appended claims. Figure 1 shows an example of microwave tomography of an object 111 (e.g., a body part , a test sample, a manufactured product, a food portion) by an apparatus 100. The apparatus 100 comprises a container 120 (which may also be called a tank, imaging tank, or bolus) filled with a first medium 121 (which may also be called a coupling medium or background medium) and an antenna array 130 (which may also be called an array antenna). The antenna array 130 is arranged inside the container 120 and is encompassed by the first medium 121. The antenna array 130 is configured to radiate (i.e., transmit) electromagnetic energy into the container 120 towards an object 111, wherein said object is at a first boundary 122 of the container 120, and to receive electromagnetic energy scattered by the object 111 and by other elements in the proximity of the antenna array 130, including but not limited to: the antenna array 130 itself, the container 120 and its boundaries, other structural parts of the apparatus (not shown), and / or the environment surrounding the apparatus (not shown). The container 120 is provided with a first boundary 122 configured to face at least a part of an external surface of the object 111. A second boundary 123 of the container 120 comprises all the boundaries of the container 120 that are not part of the first boundary 122. In Figure 1, the first boundary 122 is the same shape as the external surface of the object 111, and the second boundary 123 is represented by the interface between the container and the environment. Using the measurements of scattered electromagnetic energy via the same antenna array 130, a reconstruction algorithm may determine a dielectric distribution representing the object 111 (such as a distribution of permittivity and / or electric conductivity). The dielectric distribution may be used to obtain a digital three-dimensional image of the object 111. In microwave tomography, the reconstruction of the dielectric distribution representing the object is typically performed over narrow or broadband measurements of the electric field distribution at some locations within the apparatus and in response to an incident electric field distribution due to some electromagnetic source, which is also part of the apparatus. Such measurements may be obtained directly by electric field probes (not shown) placed within the apparatus 100. Alternatively, such measurements may be obtained from scattering matrix (S- parameters) measurements of the antenna array 130 of the apparatus 100, because the values in an S-parameter matrix can be directly related to the local values of an electric field (E-field) distribution. In such case, the number of measurements of the electric field distribution, and their location, correspond to the number of antenna elements in the antenna array 130, and their locations. The S-parameters are measured by letting one antenna element in the antenna array 130 be active at a time, and by measuring the response at the same antenna element (reflection) and at the other passive antenna elements (transmission). Thus, in this process, the electromagnetic source corresponds to the active antenna element, and the incident electric field distribution is the electric field distribution associated to the active antenna element in the absence of the object. When an antenna element ^ is active, a distinction can made between an incident and a scattered electric field distribution thanks to superposition, such that: (1) ^^^^^(^) = ^^^^^(^)+ ^^^^^(^) Where ^^^^^(^) is the value of the total electric field distribution at location ^ when antenna element ^ is active in the presence of the object 111, ^^^^^(^) is the value of the incident electric field distribution at location ^ when antenna element ^ is active in the absence of the object 111, and ^^^^^(^) is the value of the scattered electric field distribution at location ^ and represents the response of the system to the object 111 when antenna element ^ is active. A reconstruction algorithm, such as the one described hereafter, attempts to determine a dielectric distribution within a region (also called reconstruction domain) of the apparatus where the object is expected to be located, such that the values of the electric field distribution as predicted by the internal model of the apparatus, together with the model of the dielectric distribution, match the values of the electric field distribution measured from the apparatus (for instance, via the scattering matrix or electric field probes). Microwave tomography is an ill-posed inverse problem that can be solved by an iterative algorithm. In such an algorithm, a direct problem is solved at each iteration, with different values of the domain to be reconstructed, until the predicted response matches the measured one. An example of such an algorithm 200 is illustrated in Figure 2. As step 210, an empty domain of a dielectric distribution is initialized to the value of the first medium. At step 220, a so-called direct problem is solved, wherein a prediction of the total electric field distribution resulting from an incident electric field distribution is calculated within the reconstruction domain, based on the internal model of the apparatus together with the current estimation of the dielectric distribution. At step 230, the corresponding values of the electric field distribution are calculated at the measurement locations (such as at the antenna elements or electric field probes) based on the previously computed prediction of the electric field distribution within the reconstruction domain. At step 240, the predicted values at the measurement locations are compared to the measured values. If a difference of the comparison is above an error threshold, the dielectric distribution is updated at step 250 according to a known search criterion (for example, via the Gauss-Newton scheme), and the algorithm goes back to step 220. When the difference of the comparison is below the error threshold, the algorithm stops at step 260 and returns the last estimation of the dielectric distribution. Typically, a large number of iterations are needed for convergence. At each iteration, a direct problem must be solved, step 220. To solve the direct problem, several simulation techniques are available, such as the Finite Element Method (FEM), the Finite Difference Time Domain (FDTD) method, or the Method of Moments (MOM), which are based on a detailed model of the apparatus and the object. However, these techniques are computationally expensive. Consequently, performing a full simulation is not an affordable strategy to solve the direct problem within an iterative algorithm such as algorithm 200 of Figure 2. Therefore, many research efforts in microwave tomography have been directed towards finding fast approximations of Maxwell’s equations that can predict the total system response in a much shorter time. A first approximation is to assume the container 120 to be infinitely large, or, equivalently, that the second boundary 123 is located infinitely far from the antenna array 130 and the object 111. A second approximation is to model the antenna elements of the antenna array 130 as point sources (i.e., ignoring their metal structure and their non-metallic parts). Together, these assumptions mean that the electromagnetic energy radiated by an antenna element interacts only with the model of the object, and that the system response is only due to the response of the object. This results in a simple integral equation for the scattered electric field distribution ^^^^^(^) in the frequency domain, which consists only in the electric field distribution scattered by the object ^ ^^^ ^ (^): is the angular frequency, ^ is the speed of light in vacuum, ℛ is the reconstruction domain, ^(^, ^) is the dyadic Green’s function, ^(^) is a contrast distribution directly related to the dielectric distribution representing the object (to be reconstructed), ^ is the domain coordinate, ^ is the source coordinate. The integral in Equation (2) is a sum over the response of each infinitesimal dielectric contrast element in the domain (which comprises the object and part of the first medium) when subjected to the total electric field distribution. The above-mentioned approximations do not hold in many instances of design of microwave apparatuses. For example, in apparatuses using air, purified water, or other low-loss media as the first medium 121, or in apparatuses using compact containers or densely packed antenna arrays, the amount of electromagnetic energy scattered by elements other than the object 111 might no longer be negligible and may severely affect the values of the electric field distribution at the measurement locations, introducing a substantial mismatch between predicted and measured values, which in turn results in the failure of the tomographic reconstruction of the dielectric distribution representing the object 111. Such scattering may arise by the antenna array 130 itself and / or by a boundary (such as the second boundary 123) of the container 120 that is not facing the object 111. Thus, the boundaries of the container 120 not facing the object 111 and the antenna array 130 both relate a particular problem, namely, undesired scattering of electromagnetic energy in the apparatus. When developing the embodiments disclosed herein, it has been realized that using a particular apparatus design and / or using a particular reconstruction method enables the use of an apparatus using a low-loss coupling medium as the first medium 121, or an apparatus using a compact container or a densely packed antenna array, to also be used for microwave tomography purposes. As mentioned, Equation (2) assumes that the container 120 is infinitely large (or, equivalently, that the boundaries of the container 120 not facing the object 111 are located infinitely far from the antenna array 130 and the object 111) and that the antenna elements are modelled as point sources. In reality, the container 120 is of finite size and the interface at the boundaries not facing the object 111 may reflect part of the propagating electromagnetic energy back into the first medium 121, and the antenna elements of the array themselves reflect the electromagnetic energy scattered by the object, causing a back-and-forth bouncing of the wave. Figure 3 shows an example apparatus 100 for non-invasive microwave tomography of an object 111. In the figure, antenna element A of the antenna array 130 is actively transmitting electromagnetic energy, whereas the other antenna elements P of the antenna array 130 are passively receiving electromagnetic energy. The electromagnetic energy transmitted by antenna element A will bounce back and forth between the parts of the antenna elements (such as the conductive structure that radiates, the interfaces between the first medium and the non-metallic structural parts of the antenna, and / or cables connecting the radiating structure to an outside of the apparatus), the second boundary 123 of the container 120, and the object 111. Therefore, the assumptions for Equation (2) are only valid (to a sufficient accuracy) when the electromagnetic wave experiences significant attenuation while propagating, to the point where second and higher order propagations (dashed and dotted lines) become negligible with respect to the first interaction (solid line) with the object 111. Herein, first order propagations include the propagation paths from a transmitting antenna element to another antenna element (possibly via the object 111) or the path from the transmitting antenna back to itself after being reflected (possibly by the object 111). Second order propagations include propagation paths which comprise a single reflection or single scattering of electromagnetic energy by other components / interfaces than the object 111 (i.e., reflections or scattering by the apparatus itself or the environment). Second order propagations may arise from scattering by the antenna elements of the antenna array 130 as discussed above. Second order propagations may also arise from the boundaries of the container 120 that are not facing the object 111 (which, for example, may be facing air when the first medium 121 is water). Third order propagations include propagation paths which comprise two reflections, or scattering of electromagnetic energy two times, by other components / interfaces than the object 111. In general, N-order propagations include propagation paths which comprise N-1 reflections, or scattering of electromagnetic energy N-1 times, by other components / interfaces than the object 111, where N is an integer larger than 1. The higher the order of propagation, the more the electromagnetic energy is attenuated (due to the longer path length). The condition of negligible second and higher order propagations can be emulated using a lossy medium (e.g., a mixture of water and alcohol, glycerol, or salt) as the first medium 121. Unfortunately, in many instances of design of microwave apparatuses, such as apparatuses using air or purified water as the first medium 121, this cannot be realized. In other examples, such as in apparatuses meant for high power microwave treatment, a lossy medium may quickly overheat and absorb most of the power radiated by the antenna array, which is detrimental to the efficiency of the apparatus. Such apparatuses may require the use of a low- loss medium as the first medium 121. The use of a low-loss medium in the container 120, however, results in secondary propagations (i.e., multiple scattering by the antenna elements and reflections at the container boundaries) becoming significantly stronger and affecting the values measured by the antenna elements of the antenna array 130 and / or by electric field probes. This deteriorates the correspondence of the predicted electric field distribution as modelled by Equation (1) with the actual electric field distribution as measured by the apparatus, thereby rendering the reconstruction algorithm inaccurate. When developing the embodiments disclosed herein, it has been realized that to model the interaction between the antenna elements and the object 111, a complex coupling factor ^ can be introduced between the incident electric field distribution ^^^^^(^) of an active antenna element ^ of the apparatus in the absence of the object 111, and the electric field distribution scattered by the antenna array 130 in response to a point source representing an infinitesimal element of the dielectric distribution representing the object 111. Figure 5 shows an example of such a coupling model. In particular, Figure 5 shows an electric field distribution (solid arrows) incident from an infinitesimal point source S and a scattered electric field distribution (dashed wave fronts) resulting from the response of the antenna elements of the antenna array 130. The coupling factor allows a modeling of the electric field distribution scattered by the antenna array 130, in terms of an incident electric field distribution due to an infinitesimal element of the dielectric distribution representing the object 111. Thanks to superposition, the infinitesimal contributions can be integrated over the reconstruction domain as in Equation (2), and the overall electric field distribution scattered by the array in response to the presence of the object becomes: where ^ ^^^ ^ (^^^) is the value of the electric field distribution scattered by the object 111 at the location ^^^ of antenna element ^^, ^^^ is the unitary vector denoting the polarization direction of antenna element ^^, and〈∙,∙〉denotes the scalar product. Equation (3) models the response of the antenna array 130 as a linear combination of the incident electric field distributions ^ ^^^ ^^(^) associated with each antenna element ^ of the array (i.e., the electric field distribution due to an active antenna element ^ in the absence of the object 111 when other antenna elements are passively terminated with a matching load). The coefficients of this linear combination are the values of the electric field distribution ^ ^^^ ^ (^^^) scattered by the object 111 at the locations ^^^of the antenna elements and further projected onto the polarization axes ^^^ of the antenna elements, and further multiplied by the coupling factor ^, which is common to all antenna elements. Using Equation (3), the response of the antenna array 130 can be included in the scattered electric field distribution ^^^^^(^) introduced in Equation (2) as: Equation (4) models the object and antenna element responses but neglects the reflections from the boundaries of the container 120 not facing the object 111. These reflections are preferably addressed in the physical design of the apparatus for microwave tomography. If the medium in the container 120 is lossless or a low-loss medium, the electromagnetic energy may be absorbed at the boundaries of the container 120 not facing the object 111 by means of a dampening layer 440. The dampening layer 440 should preferably exhibit a characteristic impedance close to that of the medium 121 in the container 120, but with a relatively large dielectric loss to realize absorption. Figure 4 shows a physical design of an apparatus 400 for non-invasive microwave tomography of an object 111. The apparatus 400 comprises a container 120 provided with a first medium 121. The container 120 is provided with a first boundary 122 configured to face at least a part of an external surface of the object 111. The container has an inside volume containing the first medium 121. The first medium 121 is at least partly encapsulated by an external surface of the container 120. The first boundary 122 is a part of the external surface of the container 120. In an example, the object 111 is a wood log and the first boundary 122 is arranged about the bark of the wood log. In another example, the object 111 is a body part and the first boundary 122 is arranged about 14 the skin of the body part. Preferably, the container 120 is shaped such that there is little or no gap between the external surface of the object 111 and the first boundary 122 when the first boundary 122 faces the external surface of the object 111. In this way, the transition of electromagnetic properties (such as characteristic impedance) when going from the first medium 121 into the object 111 is controllable. For example, in the case where the first medium 121 is water, it is undesired to have variously sized pockets of air between the first boundary 122 and the external surface of the object 111. The second boundary 123 is also part of the external surface of the container 120. The second boundary 123 may comprise all the boundaries of the container 120 that are not part of the first boundary 122 (i.e., not facing the object 111). The apparatus 400 further comprises a dampening layer 440 arranged at the inner face, such as the face in contact with the first medium 121, of the second boundary 123 of the container 120. Figure 8 shows three examples of relative arrangements of the antenna array 130 and the dampening layer 440. In the topmost example depicted in figure 8, the antenna elements of the antenna array 130 are structurally integrated into the side of the container 120 associated with the second boundary 123. The dampening layer 440 may be interrupted to present respective openings with the size and shape of each corresponding antenna element. In the middle example, each antenna element of the antenna array 130 is suspended at a desired position within the container 120 and the first medium 121 by means of a supporting element that is structurally attached to the container 120. In which case, the dampening layer 440 may be pierced by, and remain adherent to, the supporting element (e.g., a rigid coaxial cable). In some examples, at least one antenna element and / or antenna array 130 is surrounded by the first medium 121. In the bottom example of figure 8, each antenna element is arranged at the first boundary 122 of the container 120, in direct contact with the surface of the object 111. In which case, the dampening layer 440 may uninterruptedly cover the entire second boundary 123 of the container 120 not facing the object 111. Each antenna element of the antenna array 130 has connection means, such as cables, to be connected to a control system (e.g. electrical instrumentation apparatuses) outside of the apparatus 400. These connection means may pierce the dampening layer 440 in order to reach the outside of the container 120. The first medium 121 is preferably selected to match the characteristic impedance of the object 111. For example, the characteristic impedance value of the first medium 121 may be within 50% of the average characteristic impedance value of the object 111. In this way, the electromagnetic energy transmitted by the antenna array 130 may be injected into the object 111 relatively unhindered, i.e., with little reflection at the first boundary 122 back into the first medium 121. For example, if the object 111 is organic matter with high water content, the first medium 121 may be water. In another example, if the object 111 is made of plastic, wood or concrete, the first medium 121 may be air. In yet another example, if the object 111 is organic matter with high fat content, the first medium 121 may be oil. The first medium 121 may be a low-loss medium, where “low-loss” means that less than 50% of the electromagnetic energy radiated by the antenna array 130 is dissipated as heat in the first medium 121 as a result of its electric conductivity. In some of these examples, the first medium 121 has less than 80% of the electromagnetic energy radiated dissipated as heat as a result of its electric conductivity. In this way, the electromagnetic energy transmitted by the antenna array 130 may be injected into the object 111 in an efficient way and without severe losses in the first medium 121. In the example where the first medium 121 is water, “low-loss” may mean if the electric conductivity at 20° C and at 300 MHz is less than 1 S / m, preferably less than 0.1 S / m, and more preferably less than 0.01 S / m. The first medium 121 may comprise water. In which case, the water is preferably purified water. Purified water presents a relatively low-cost medium that presents a characteristic impedance close to organic matter, while also being low-loss. Herein, water is considered to be purified water if it has the maximum contaminant levels according to any of: ISO 3696 grade 1-3; ASTM (D1193) type I-IV, NCCLS type I-III, and Pharmacopoeia EP or USP. The container 120 may be made of various materials. For example, the container 120 may be made of a plastic (such as, but not limited to: PMMA, PC, PE, PP, PET, PVC, ABS). In another example, the container 120 may have structural parts in metal (such as, but not limited to: aluminum, steel, copper, and / or alloys). In particular, the use of metal for the sides of the container 120 associated with the second boundary 123 (i.e., the boundary not facing the object 111) may help to prevent leakage of electromagnetic energy from the apparatus 400 towards the environment, and improve the electromagnetic compatibility of the apparatus 400. In some examples, the surface of the object 111 itself, associated with the first boundary 122 of the container 120, can also serve as structural side to the container 120. In that case, if the first medium 121 is a liquid, the points of contact between the surface of the object 111, the first medium 121, and the other sides of the container 120, may be sealed with a material that adapts its shape to conform to the external surface of the object 111, for instance by using rubber (such as, but not limited to: Silicon, Latex, Nitrile, Neoprene), to prevent leakage of the first medium 121 into the environment. In other examples, the side of the container 120 facing the object, and associated with the first boundary 122 of the container, is also structurally closed and contiguous to the other sides of the container 120, so that the first medium 121 is fully contained regardless of the presence of the object 111. In such case, the side of the container 120 in contact with the object 111 may preferably be thin and made of a material that conforms to the object, for instance rubber (as above), to prevent gaps from forming between the first medium 121 and the object 111. In this case, “thin” may indicate a thickness that allows for more than 50% of the electromagnetic energy radiated by the antenna array 130 into the first medium 121 and towards the object 111 to propagate into the object 111. Alternatively, “thin” may indicate a thickness that allows for less than 50% of the electromagnetic energy radiated by the antenna array 130 into the first medium 121 and towards the object 111 to be reflected back into the first medium 121. The apparatus 400 further comprises an antenna array 130 arranged inside the container 120. The antenna array 130 being arranged “inside the container” may indicate that one or more antenna elements of the antenna array 130 are located in the bulk of the first medium 121 contained by the container 120. The antenna array 130 is at least partly encompassed by the first medium 121. The antenna array 130 is configured to transmit electromagnetic energy for irradiating the object 111 and to receive electromagnetic energy scattered by the object 111. Preferably, the antenna array 130 transmits and receives electromagnetic energy when the first boundary 122 is arranged facing at least a part of an external surface of the object 111. An antenna array 130 (may also be called an array antenna) comprises a plurality of antenna elements arranged inside the container 120. For example, in the case where the apparatus 440 is an apparatus intended for the processing of wood logs, the antenna array 130 may comprise a set of antenna elements arranged in a ring pattern around the wood log. For example, an antenna element may be a dipole antenna (such as, but not limited to: dipole antenna, Yagi-Uda antenna, log-periodic antenna, Vivaldi antenna, loop antenna), a monopole antenna (such as, but not limited to: monopole antenna, patch antenna), or a slot antenna (such as, but not limited to: slot antenna, horn antenna). An antenna element may also be an electric field probe. The antenna elements of the antenna array 130 are at least partly encompassed by the first medium 121, which means that each antenna element is at least partly surrounded by the first medium 121. For example, each antenna element may at least partly be held within the first medium 121. Each antenna element may be structurally integrated into the side of the container 120 associated with the second boundary 123. In which case, the dampening layer 440 may be interrupted to present an opening the size and shape of the antenna element. Alternatively, each antenna element may be suspended at a desired position within the container 120 by means of a supporting element that is attached to the container 120. In which case, the individual supporting elements may pierce the dampening layer 440, and the dampening layer 440 may preferentially be designed to be adherent to the outer surface of the supporting element (for instance, a rigid cable). Each antenna element of the antenna array 130 has connection means, such as cables, to be connected to a control system (e.g. electrical instrumentation apparatuses) outside of the apparatus 400. These connection means may pierce the dampening layer 440 in order to reach the outside of the container 120, and the dampening layer 440 may preferentially be designed to be adherent to the outer surface of the connection means (for instance, a flexible cable). One or more antenna elements of the antenna array 130 are configured to irradiate the object 111. In some embodiments, one primary antenna element at a time is activated to radiate electromagnetic energy at a frequency, while the other secondary antenna elements are left passive and terminated by a matching load (such as, but not limited to, a termination or a measuring instrument). In some examples, the antenna array 130 is arranged to irradiate the object 111 with electromagnetic energy at a frequency in the range of 3 MHz to 300 GHz. In some of these examples, transmitting at a frequency in the range of 10 MHz to 100 GHz, 30 MHz to 30 GHz, 30 MHz to 30 GHz, 100 MHz to 10 GHz, 300 MHz to 3 GHz, or 600 MHz to 1 GHz. In some embodiments, two or more antenna elements simultaneously radiate coherent electromagnetic energy. Here, “coherent” means that each antenna element is driven by a sinusoidal voltage or current source at a frequency or a combination of frequencies that is the same for all active antenna elements. To irradiate the object 111 means that electromagnetic energy is transmitted from one or more antenna elements such that it propagates towards and into the object 111. To transmit electromagnetic energy from an antenna element means that one or more electromagnetic waves are transmitted from that antenna element. One or more antenna elements of the antenna array 130 are configured to receive incoming electromagnetic energy. To receive electromagnetic energy means that part of the electromagnetic energy of an electric field distribution impinging on the antenna element is converted by the antenna element into a voltage or current signal that can be conveyed by connection means (such as cables) to external instrumentation for measurement. The electromagnetic energy may be of a single frequency (also called tone, or sinusoidal wave), such as 434 MHz, or any other frequency within the radiofrequency spectrum (20 kHz - 300 GHz). In other embodiments, the electromagnetic energy may comprise a signal with a bandwidth, such as 2:1 bandwidth, transmitted, for example, at a carrier frequency of 434 MHz, or any other frequency within the radiofrequency spectrum. In yet some other embodiments, the antenna array 130 can be operated sequentially over a set of discrete frequencies, such as from 300 MHz to 600 MHz with steps of 10 MHz, or any other combination of frequencies within the radiofrequency spectrum. The apparatus 400 also comprises a dampening layer 440 arranged at the inner face (i.e. the face in contact with the first medium 121) of the second boundary 123 of the container 120. The dampening layer 440 is configured to attenuate reflection of electromagnetic energy, scattered by the object 111, at the second boundary 123 back into the first medium 121. In other words, the electromagnetic energies of the incoming (from the first medium 121) and outgoing (towards the first medium 121) electromagnetic waves at the second boundary 123 of the container 120 are attenuated by the dampening layer 440. The second boundary 123 is a part of the external surface of the container 120. The second boundary 123 is preferably different from the first boundary 122. According to some aspects, the reflected electromagnetic energy is attenuated relative to the reflected electromagnetic energy that would occur if the dampening layer 440 were absent (e.g., if the first medium 121 would face directly the side of the container at the second boundary 123 without the dampening layer 440). Preferably, the dampening layer 440 is arranged on an inside of the container 120, i.e., inside the volume contained by the container 120. According to some aspects, the magnitude of the reflected electromagnetic energy at the second boundary 123, resulting from incident electromagnetic energy, is attenuated by at least 3 dB relative to the magnitude of the incident electromagnetic energy. In some examples, the reflected electromagnetic energy is attenuated by at least 10 dB relative to the magnitude of the incident electromagnetic energy. It is to be understood that the dampening layer attenuating reflection of electromagnetic energy scattered by the object relates to attenuating the additional scattering induced by the presence of the object with respect to the empty imaging tank. Microwave tomography is typically achieved by differential measurements of the array response. The representation of the object is obtained based on the difference between a measurement of the array response when the object is absent, such as when the imaging tank is filled entirely with the first medium, and a measurement of the array response when the object is present inside the imaging tank. When the imaging tank is empty, the electromagnetic energy radiated by an antenna element of the antenna array at a frequency is propagated into the first medium inside the container as a monochromatic electromagnetic wave. This electromagnetic wave interacts with the structural parts of the apparatus, such as the boundaries of the container or the antenna elements themselves, and the environment, being reflected and refracted multiple times (scattering), interfering with itself, and resulting in a complex (periodic) electromagnetic field distribution. The presence of the object for the second measurement induces additional scattering of the same electromagnetic wave, resulting in a different electromagnetic field distribution. This distribution may be seen as a superposition of the distribution relative to the empty imaging tank and the response of the object alone. The response of the object may in turn be seen as a distribution of small infinitesimal radiating sources, each radiating an electromagnetic wave at the same frequency and with intensity proportional to the dielectric value of the object and the incident electric field distribution at its location. The aim of the differential measurement is, typically, to obtain a virtual measurement of the response of the object alone that can be matched to a simulated or calculated model of the response of the object for tomographic reconstruction purposes. The presence of the object induces additional passive radiation of electromagnetic energy in the form of an electromagnetic wave propagating from the object towards the first medium. This additional electromagnetic wave also interacts with the structural parts of the apparatus and may cause additional undesired scattering that cannot be accurately modelled in the tomographic reconstruction. The function of the dampening layer is to absorb and attenuate the energy of the additional electromagnetic wave(s) radiated by the object and impinging on the boundaries of the container holding the first medium, thus preventing reflection back into the first medium and towards the antenna array. In this way, the additional undesired scattering is reduced and the correspondence between measured object response and simulated or calculated model of the response is improved. Preferably, the container 120 is encapsulated by the first boundary 122 and the second boundary 123. In yet some other words, the first boundary 122 and the second boundary 123 together constitute the total or a substantial amount, such as more than 80%, of the surface area of the container 120. Preferably, the dampening layer 440 is arranged such that the first medium 121 is delimited by the first boundary 122 facing the external surface of the object 111, and by the dampening layer 440. The dampening layer 440 may attenuate the reflected electromagnetic energy in different ways. According to some embodiments, the dampening layer 440 comprises a second medium. The first medium 121 may be associated with a first dielectric loss value at a frequency and the second medium may be associated with a second dielectric loss value at the frequency. In that case, the second dielectric loss value is preferably at least two times larger than the first dielectric loss value. Here, the frequency of the first and the second dielectric loss values preferably correspond to the frequency of the transmitted electromagnetic energy. The dielectric loss value is a measure of the medium’s inherent dissipation of electromagnetic energy (such as by heat), and may be associated with the medium’s electric conductivity and impedance. The dielectric loss value may be parameterized in terms of, e.g., the loss angle δ or a corresponding loss tangent tan(δ). According to some aspects, the first dielectric loss value is parametrized by a first loss angle and the second dielectric loss value is parametrized by a second loss angle, where the second loss angle is at least two times larger, preferably at least ten times larger, and more preferably at least a hundred times larger than the first loss angle. The dampening layer 440 being a “layer” means that it is associated with a thickness. The thickness of the dampening layer 440 may be chosen such that the attenuation experienced by an electromagnetic wave traveling through the second medium of the dampening layer 440 from the first medium 121 towards the second boundary 123 of the container 120, being reflected back into the second medium by the second boundary 123 of the container 120 and towards the first medium 121, is at least 50% of the initial energy of the electromagnetic wave. In some examples, the attenuation of said electromagnetic wave is at least 80% of the initial energy of the electromagnetic wave. The second medium may comprise a radio frequency absorbent material, which attenuates transmission and reflection of electromagnetic energy. A radio frequency absorbent material is preferably not a good electrical insulator (as in, e.g., rubber) and not a good electrical conductor (as in, e.g., copper). An example of a radio frequency absorbent material is a foam material loaded with carbon and / or iron particles. Radio frequency absorbent materials can be resonant, i.e. a particular frequency is attenuated (e.g.1 GHz), or broadband, i.e. a span of frequencies is attenuated (e.g.0.1 GHz to 10 GHz). The attenuation of electromagnetic energy in a direction is dependent on the thickness of the radio frequency absorbent material in the same direction. One example of attenuation per length is 1 dB / cm at 1 GHz. Another example is 10 dB / cm at 10 GHz. According to some embodiments, the second medium comprises water provided with additives (such as e.g. a mixture of water and alcohol, glycerol, or salt) such that the water presents a desired dielectric loss value. If the second medium is a liquid, the dampening layer 440 may comprise its own container (different than container 120) holding that liquid. The container of the second medium may be made of plastic or other non-conducting materials. In which case, the side of the container holding the second medium, that is facing the first medium 121, may preferably be thin. Here, “thin” may indicate a thickness that allows for more than 50% of the electromagnetic energy incident from the first medium 121 and towards the second medium to propagate into the second medium. Alternatively, “thin” may indicate a thickness that allows for less than 50% of the electromagnetic energy incident from the first medium 121 and towards the second medium to be reflected back into the first medium 121. According to some aspects, the first medium 121 has a first characteristic impedance value at the frequency and the second medium has a second characteristic impedance value at the frequency, wherein the second characteristic impedance value is within 50% of the first characteristic impedance value. In some of these examples, the second characteristic impedance value is within 20% of the first characteristic impedance value. In this way, the electromagnetic waves incident on the second boundary 123 from the first medium 121 will propagate into the dampening layer 440 with high efficiency and low reflection. With the dielectric loss value according to the discussions above, the electromagnetic energy of the electromagnetic waves propagating inside the dampening layer 440 will be attenuated. Figure 7 shows three different examples of an apparatus 400. Each example apparatus 400 in Figure 7 comprises the same features as shown in Figure 4, namely, an antenna array 130 (not shown in Figure 7), a container 120 with the first 122 and the second 123 boundaries, a first medium 121, and a dampening layer 440. The topmost example apparatus 400 in Figure 7 is shaped to conform to a spherical object 111. In this example, the dampening layer 440 is arranged about the second boundary 123 of the container 120, and the container 120 is encapsulated by the first boundary 122 and the second boundary 123, with the exception for connection means (not shown) of the antenna elements. In particular, the apparatus 400 forms a shape like a helmet, where all boundaries of the container 120 not facing the object are covered by the dampening layer 440 (with the exception for connection means of the antenna elements). The apparatus is provided with an opening such that the apparatus 400 can be easily mounted on the spherical object 111. In some embodiments, said apparatus may be arranged to be placed on the head of a patient. In some embodiments, said apparatus may be arranged to at least partially surround a product to be evaluated. The example apparatus 400 in the middle of Figure 7 is shaped to conform to a cylindrical object 111. In this example, the dampening layer 440 is arranged about the second boundary 123 of the container 120, and the container 120 is encapsulated by the first boundary 122 and the second boundary 123, with the exception for connection means (not shown) of the antenna elements. In particular, the apparatus 400 forms a torus shape, where all boundaries of the container 120 not facing the cylindrical object 111 are covered by the dampening layer 440 (with the exception for connection means of the antenna elements). In some embodiments, said apparatus may be arranged to be placed at the torso of a patient. In some embodiments, said apparatus may be arranged to accept side of a product to be evaluated. The bottommost example apparatus 400 of Figure 7 is shaped to conform to a planar object 111. In this example, the dampening layer 440 is arranged about the second boundary 123 of the container 120, and the container 120 is encapsulated by the first boundary 122 and the second boundary 123, with the exception for connection means (not shown) of the antenna elements. In particular, the apparatus 400 forms a shape similar to a cuboid, where all boundaries of the container 120 not facing the planar object 111 are covered by the dampening layer 440 (with the exception for connection means of the antenna elements). In some embodiments, said apparatus may be arranged to be placed at an extremity of a patient. In some embodiments, said apparatus may be arranged to be pressed against a surface of a product to be evaluated. Figure 9 shows an example apparatus 400 and an example control system 810. This example apparatus 400 comprises the same features as shown in Figure 4, namely, an antenna array 130, a container 120, a first medium 121, a dampening layer 440. In particular, the antenna array 130 comprises six antenna elements communicatively connected to the control system 810 (e.g., via respective cables). The control system 810 may comprise processing circuitry and a memory (which is discussed in more detail below in connection to Figure 11). The processing circuitry may comprise a receiving module and a transmitting module. The receiving module and the transmitting module may comprise radio frequency circuitry capable of transmitting and receiving electromagnetic energy via the antenna array 130. The receiving module and the transmitting module may also form part of a single transceiver. The receiving module and the transmitting module may be part of a vector network analyzer (VNA). The transmitting module may be part of a signal generator. The receiving module may be part of a signal analyzer such as a spectrum analyzer. As mentioned, when developing the embodiments disclosed here, it has been realized that the interaction between the antenna elements can be accounted for when obtaining a representation of an object 111 by means of an apparatus for microwave tomography. Below follows an example of iteratively finding such a representation of the object 111. Assuming that the dielectric property of choice to represent the object 111 with a dielectric distribution is the complex permittivity (as opposed to, for instance, complex permeability). Further assuming an apparatus (which may be the apparatus 100, the apparatus 400, or another apparatus for microwave tomography), as shown for example in Figure 6, where there are ^ antenna elements at fixed locations and immersed in the first medium 121 (which preferably is uniform) with complex relative permittivity ^^everywhere. The first medium 121 encapsulates the antenna elements (forming the antenna array 130) and is delimited by a first boundary 122 facing an object 111 and by a second boundary 123 configured to present absorbing conditions (an interface to a second medium causing little or no reflections back into the first medium 121). A reconstruction domain ℛ, encompassing the object 111 and part of the first medium 121, is associated to a complex relative permittivity distribution ^(^). The complex relative permittivity distribution ^(^) can be a representation of the object 111. The complex relative permittivity distribution ^(^) can be equivalently treated via a contrast distribution with respect to the first medium, ^(^)= ^(^)− ^^. It is desired to reconstruct the distribution ^(^), and thus the complex relative permittivity distribution ^(^) representing the object 111, everywhere in ℛ from measurements of the electric field distribution of the apparatus in the frequency domain. In the case where the electric field distribution is measured via the same antenna elements of the antenna array 130, one antenna element may be activated at a time, where the other antenna elements are passively terminated, and the frequency response of each antenna element is measured. The response of each antenna element is directly related to the value of the electric field distribution at the antenna element. In the case where the electric field distribution is further measured via additional electric field probes, one antenna element may be activated at a time, and the electric field probe response is directly related to the value of the electric field distribution at the tip of the probe. The configuration where a single antenna element is active and radiating may be called an “illumination”. Thus, there are ^ possible illuminations, each one with a single active antenna element. The contrast ^(^) is reconstructed by means of the following iterative algorithm: Step 1. For each illumination ^: a. Measure a first set of values of the scattered electric field distribution ^^^^^(which may be called a measured scattered electric field distribution) by relating two sets of electric field distribution measurements within the apparatus. b. Calculate a second set of values of the scattered electric field distribution ^^^^^(which may be called a predicted scattered electric field distribution) at the same locations within the apparatus where the measurements ^^^^^have been taken, based on a current guess for the distribution ^(^) together with a model of the antenna array 130, by finding a (numerical) solution to Equation (1) when the scattering term is represented by Equation (4). Step 2. Determine the errors as the differences between the first ^^^^^and the second ^^^^^scattered electric field distributions for at least one of (but preferably all) the measurement locations and for at least one of (but preferably all) illuminations. Step 3. Update the distribution ^(^) in the direction that minimizes the squared sum of the errors between the first and the second scattered electric field distributions. This can be done (for instance) with a standard Gaussian method based on the Jacobian. Other metrics of the difference / error between the first and the second scattered electric field distribution, and corresponding update schemes for the distribution ^(^), may also be used. In general, different methods of finding a local or global minimum of the difference between the first and the second electric field distributions as a function of the distribution ^(^) may be used. Step 4. Halt the algorithm and return the last and best guess for the distribution ^(^) if the total error is below some threshold. The dielectric distribution representing the object 111 can be obtained from the contrast distribution ^(^) and known properties of the first medium ^^as ^(^) = ^(^) + ^^. Otherwise, continue by re-iterating from Step 1 using the updated distribution ^(^). Note that the first time Step 1b is performed by the algorithm, an initial set of value for the distribution ^(^) is used (such as a uniform distribution of some value). Below follows more details of Step 1a. The local value of the electric field distribution at measurement locations for each illumination can be determined, for instance, from S-parameter measurements of the antenna array 130. In which case, the measurement locations correspond to the locations of the antenna elements of the antenna array 130. As an example, Haynes and Moghaddam disclose a method for such a conversion in “Vector Green’s function for S-parameter measurements of the electromagnetic volume integral equation.” IEEE transactions on antennas and propagation 60.3 (2011): 1400-1413. Kim et al. disclose an alternative method for such a conversion in “The design of calculable standard dipole antennas in the frequency range of 1~ 3 GHz.” Journal of the Korean Institute of Electromagnetic and Science 12.1 (2012): 63-69. The values of the electric field distribution measured at the antenna locations can be compactly joined into a matrix ^^, where each element ^^^^= ^^(^^^) contains the value measured by antenna ^^at its location ^^^when antenna element ^ is active, for a total of ^ × ^ complex samples. In the case where additional electric field probes are available, the measurement locations include the locations of the electric field probes, and the measured values can be appended to the columns of ^^at corresponding rows for each illumination. For the rest of the discussion, we consider only the case where only antennas are utilized for the measurement of the electric field distribution. The procedure can easily be generalized to the case where more measurement locations are available, such as when additional electric field probes are utilized. In order to determine the values of the scattered electric field distribution ^^^^^of Equation (1) at the measurement locations, two measurements may be performed. In the first measurement, the object 111 is absent, and replaced by a dummy object of the same size and shape, and with a homogeneous dielectric value equal to the dielectric value of the first medium 121. This provides a measurement of the incident electric field distribution ^^^^^of Equation (1) at the measurement locations. In the second measurement, the object 111 is present. This provides a measurement of the total electric field distribution ^^^^^of Equation (1). The scattered electric field distribution ^^^^^at the measurement locations can then be found as:(11) ^^^^^= ^^^^^− ^^^^^This completes Step 1a of the iterative algorithm. Below follows more details of Step 1b. Herein, the following integral equation describes the frequency response of the domain to illumination ^: (12) ^^^^^(^) = ^^^^^(^) + ^^^^^(^) Where: Where: ^ TOT : total field ^ INC : incident field ^ SCA : scattered field ^ OBJ : object response ^ ARR : array response Equation (12) is used to determine the total electric field distribution ^^^^^(^) given a particular contrast distribution ^(^). Note that ^^^^^(^) may be obtained from electromagnetic simulations, for example by feeding a complete model of the apparatus in the absence of the object 111 to a commercial electromagnetic solver configured to emulate the active radiation from antenna element ^ and the passive termination of the other antenna elements. Note also that ^^^^^(^) may alternatively be obtained via measurements of the electric field distribution inside the apparatus when antenna element ^ is radiating in the absence of the object 111. The contrast distribution ^(^) is known from the current guess in the iteration. The parameter ^ is obtained from coupling measurements or simulations, for example as disclosed by Zanoli et al. in "Antenna Arrangement in UWB Helmet Brain Applicators for Deep Microwave Hyperthermia." Cancers 15.5 (2023): 1447. Green’s dyadic function for a first medium 121 with characteristic propagation constant ^^is given by: Where ^^is the identity matrix of size 3, and: To solve Equation (12) for ^^^^^(^), the domain ℛ may be discretized into ^ small hexahedral grid elements ℛ^of side ^ and centered at ^^=[^^ ^^ ^^]^. It is assumed that ^(^) ≈ ^^and ^^^^^(^) ≈ ^^^^^^over each element. Thus, the following equations can be formulated: In compact form, the discretized values of the electric field distributions at the grid points become column vectors of length 3^: In addition to the discretized values at the grid points, the local values of the electric field distributions at the measurement locations may also be expressed as column vectors of length 3^: Using Equations (20) and (22) in Equation (14), the object term becomes: Define the grid-to-grid effect matrix ^ ∈ ℂ^^×^^with elements: The object term at the grid points ^^can be expressed in discretized form: And concatenated into column arrays: ^ ^^^ (29) ^ ^^^ ^^ ^=^⋮ ^ ^ ^^^ ^^ Such that: (30) ^ ^^^ = ^ ^^^ ^ ^^^Where: Define the grid-to-antenna effect matrix ^^∈ ℂ^^×^^with elements: The object term at the measurement locations ^^^can be expressed in discretized form: (33) ^ ^^^ = ^ ^^^ ^^^∑^ ^^^^^^^^^And concatenated into column arrays: ^ ^^^ (34) ^ ^ ^^ ^ ^^ ^=^⋮ ^ ^ ^^^ ^^ Such that: (35) ^^^^^ ^ ^= ^^^^^^^ Using Equation (33) in Equation (15), the array term becomes: The array term at the grid points ^^can be expressed in discretized form: And concatenated into column arrays: Such that: (38) ^^^^^ ^^^= ^^^^^^^^^^= ^^^^^^^^^^^^^^Where: The array term at the measurement locations ^^^can be expressed in discretized form: And concatenated into column arrays: ^^^^ ^^(41) ^^^^^^= ^ ⋮ ^ ^^^^ ^^Such that: (42) ^^^^^^= ^^^^^^^^^^^^^ ^= ^^^^^^^^^^^^^^^It is now possible to match the discretized electric field distributions ^^at the very same grid points ^^to obtain a set of 3^ equations for the illumination ^: (43) ^^^^^^= ^^^^^^+∑^ ^^^^^^^ ^ ^^^^^^^^^^^^^^^^+ ^∑^^^^^^^^^^^^^By further concatenating the electric field distribution column vectors into 3^ × ^ matrices, it is possible to express Equation (43) in compact form for all illuminations as a matrix equation: (44) ^^^^= ^^^^+ ^^^^^^+ ^^^^^^^^^^^^^^The total electric field distribution at the grid points can thus be found from Equation (44) as: (45) ^^^^= (^^− (^ + ^^^^^^^^^)^)^^^^^^The scattered electric field distribution at the measurement locations can be calculated using the value of ^^^^found via Equation (45) together with Equations (35) and (42): (46) ^^^^^= (^^+ ^^^^^^^^)^^^^^^^Equation (46) provides a set of predicted values ^^^^^of the scattered electric field distribution at the measurement locations that can be readily compared to the set of measured values ^^^^^of the scattered electric field distribution at the same measurement locations. This completes Step 1b of the iterative algorithm. Note that Equation (12), together with Equations (13), (14) and (15), models the entirety of the interactions between the electromagnetic energy incident from the primary antenna element of the antenna array 130, the electromagnetic energy scattered by the object 111, and the electromagnetic energy scattered by the antenna array 130. These interactions include wave reflections or scattering up to any propagation order, provided other elements of the apparatus or the environment do not cause further reflections and scattering of the electromagnetic energy back towards the antenna array 130 and / or the object 111. The latter condition may be achieved with the use of the dampening layer 440 covering the internal face of every side of the container 120 forming the second boundary 123, i.e. every boundary that is not facing the object 111, so as to suppress any reflection or scattering within the apparatus that is not due to an antenna element of the antenna array 130 or the object 111. Figure 10 is a flow chart summarizing the methods discussed above. There is illustrated a method 900 of obtaining a representation of an object 111 by means of an apparatus for microwave tomography. The apparatus comprises a container 120 provided with an antenna array 130 comprising a primary antenna element and one or more secondary antenna elements positioned relative to the object 111. In the apparatus of the method 900, the container 120 may be provided with a first medium 121, and the container 120 may be provided with a first boundary 122 configured to face at least a part of an external surface of the object 111. Furthermore, the antenna array 130 may be arranged inside the container 120 and may be at least partly encompassed by the first medium 121, where the antenna array 130 is configured to transmit electromagnetic energy for irradiating the object 111 and to receive electromagnetic energy scattered by the object 111. In the method 900, the apparatus may be the apparatus 100 or the apparatus 400 discussed above. However, other apparatuses for microwave tomography are also possible. For example, the apparatus may be an apparatus for microwave tomography wherein the first medium 121 is a lossy medium with high electric conductivity, as discussed above. In this way, the electromagnetic energy associated to second order propagations after the interaction of the wave with other elements of the apparatus or the environment is attenuated. Preferably, an apparatus for microwave tomography presenting low levels (magnitude) of reflected electromagnetic energy at the container boundary not facing the external surface of the object 111 is used in the method 900. The method 900 combined with such low level of reflected electromagnetic energy enable quantitative microwave imaging with an apparatus using a low- loss medium as the first medium 121 or a having a compact container 120 design or having a densely packed antenna array 130. The method comprises radiating 910 electromagnetic energy from the primary antenna element into the container 120 to irradiate the object 111. This means that electromagnetic energy is transmitted from the primary antenna element towards the object 111. The electromagnetic energy may be transmitted by means of injecting a signal into an antenna port of the primary antenna element by a control system 810 (comprising, e.g., a VNA or a signal generator). In some examples, radiating 910 electromagnetic energy from the primary antenna element into the container 120 to irradiate the object 111 comprises transmitting in the range of 3 MHz to 300 GHz. In some of these examples, transmitting in the range of 10 MHz to 100 GHz, 30 MHz to 30 GHz, 30 MHz to 30 GHz, 100 MHz to 10 GHz, 300 MHz to 3 GHz, or 600 MHz to 1 GHz. The method further comprises, in response to the radiation of electromagnetic energy, obtaining 920 a representation of a first electric field distribution in the apparatus (e.g. in the container 120) by means of measurements via the secondary antenna elements and / or via electric field probes located into the container 120. The representation of the first electric field distribution may comprise the total electric field distribution ^^^^^as obtained in Step 1a discussed above. Alternatively, the representation of the first electric field distribution may comprise the first scattered electric field distribution ^^^^^as obtained in Step 1a discussed above. In general, the representation of the first electric field distribution may comprise data indicative of the first electric field distribution, such as a matrix with elements indicating a complex field strength at respective spatial locations of the apparatus, or a set of S-parameters of the antenna array 130. The measurements via the antenna array 130 may comprise performing measurements via one or more antenna elements of the antenna array 130 (including the primary antenna element). The measurements via the antenna array 130 may comprise sampling electromagnetic energy by the antenna array 130. The samples may be obtained by a control system 810 (comprising, e.g., a VNA or signal receiver). The samples may be transformed into data indicative of an electric field distribution. The samples are therefore considered to be a representation of the first electric field distribution. The representation of the first electric field distribution ^^may comprise a 3^ × ^ matrix (where ^ is the number of antenna elements in the antenna array 130 of the model of the apparatus) where each element ^^^^= ^^(^^^) contains the value measured at location ^^^when antenna element ^ is active. The method also comprises obtaining 930 the representation of the object 111 by iteratively adapting a model of a dielectric distribution (for instance, ^(^) as incorporated in ^(^) above, but also distributions of properties other than the complex relative permittivity) representing the object 111. The number of iterations is at least one. After at least one iteration, the model of the dielectric distribution constitutes a representation of the object 111. The more iterations that are performed, the better the model of the dielectric distribution represents the object 111. In general, the model of the dielectric distribution may comprise data indicative of a dielectric distribution, such as a column vector with elements consisting of the complex relative permittivity at respective spatial locations. In the first step of the iterative algorithm, the model of the dielectric distribution may comprise a predetermined set of values, e.g., indicative of a uniform distribution of some dielectric value. The adapting comprises, iteratively: obtaining 931 a representation of a second electric field distribution in the apparatus using a model of the apparatus and the model of the dielectric distribution; comparing 932 the representation of the second electric field distribution with the representation of the first electric field distribution to obtain a comparison; and adapting 933 the model of the dielectric distribution based on the comparison and thereby obtaining the representation of the object 111. The representation of the second electric field distribution may comprise the second scattered electric field distribution ^^^^^as obtained in Step 1b discussed above. In general, the representation of the second electric field distribution may comprise data indicative of the second electric field distribution, such as a matrix with elements indicating a complex field strength at respective spatial locations of the container 120 of the model of the apparatus, or a set of S-parameters of the antenna array 130. In general, the representation of the second electric field distribution may comprise data indicative of an electric field distribution at the measurement locations within the model of the apparatus that may be compared with the first representation of the electric field distribution. In other words, the representation of the second electric field distribution may comprise data in the same form as the representation of the first electric field distribution to facilitate the comparison. Furthermore, the first and the second electric field distributions may comprise data indicative of respective electric field values at the same spatial locations. The representation of the second electric field distribution ^^may comprise a 3^ × ^ matrix (where ^ is the number of antenna elements in the antenna array of the model of the apparatus) where each element ^^^^= ^^(^^^) contains the value predicted by the model of Equation (12) at measurement location ^^^when antenna element ^ is active. The model of the apparatus corresponds to the apparatus used to transmit the electromagnetic energy. As such, the model comprises information of the distribution of the antenna elements of the antenna array 130. Such information may comprise information of how the antenna elements are positioned relative to each other and relative the container 120, and electromagnetic characteristics of the antenna elements of the antenna array 130 (such as distribution of the incident electric field, radiation pattern, and reflective properties). The model of the apparatus may further comprise dielectric properties of the first medium 121 (if the apparatus comprises the first medium 121), so-called absorbing boundary conditions at the second boundary 123 of the container of the model of the apparatus, dielectric properties of the second medium (if the apparatus comprises the second medium), or other electromagnetic properties and geometries of the container 120. The comparison may comprise determining the difference according to Step 2 discussed above. In general, the comparison is a metric of a difference between the representation of the first electric field distribution and the representation of the second electric field distribution. If the representations of the first and the second electric field distributions comprise respective matrices, the comparison may comprise a matrix where each matrix element comprises a difference of two corresponding matrix elements of the representations of the first and the second electric field distributions. Alternatively, the comparison may comprise a single value indicative of the difference between the representations of the first and the second electric field distributions. The adapting of the model of the dielectric distribution based on the comparison may comprise the updating of the distribution according to Step 3 discussed above. In general, different methods of finding a local or global minimum of the difference between the representations of the first and the second electric field distributions as a function of the dielectric distribution may be used. Similarly, different methods to update the dielectric distribution based on the comparison may be used. The representation of the second electric field distribution in the apparatus is obtained based on constructed electromagnetic energy as scattered by the model of the dielectric distribution and constructed electromagnetic energy as scattered by one or more antenna elements of the antenna array 130 of the model of the apparatus. The constructed electromagnetic energy may be constructed as simulated electromagnetic energy or simulated electromagnetic waves. The constructed electromagnetic energy may be simulated in an electromagnetic simulation tool. Such electromagnetic simulation tool may be based, for example, on the so-called Finite Element Method (FEM), or on the so-called Finite Difference Time Domain (FDTD) method, or on the so-called Method of Moments (MOM), or on other numerical methods for the solution of Maxwell’s equations given a constructed domain and boundary conditions. Preferably, the constructed electromagnetic energy has the same signal content in terms of bandwidth and carrier frequency. The method 900 accounts for scattering of electromagnetic energy by one or more antenna elements of the antenna array of the model of the apparatus. Thus, the method 900 provides a representative reconstruction / simulation of an electric field distribution in the apparatus. i.e., a representation of the second electric field distribution that may accurately be matched to the representation of the first electric field distribution, which in turn enables obtaining an accurate a representation of the object 111. In some examples, the method 900 is a non-therapeutic method for obtaining a representation of objects that are not living humans or animals, such as manufactured products and food. In some examples, the method 900 is, or is part, of a therapeutic method, such as a heat treatment method. The effect of the scattering of electromagnetic energy by the antenna elements of the antenna array 130 on the first and second electric field distributions increases with the inverse of the loss angle of the first medium 121. Some microwave apparatuses, such as those utilizing air or purified water as the first medium, typically rely on coupling media with small loss angle. Consequently, the disclosed method allows obtaining an accurate representation of the object 111 using an apparatus with a low-loss coupling medium as the first medium 121. Furthermore, the effect of the scattering of electromagnetic energy by the antenna elements of the antenna array 130 on the first and second electric field distributions increases the more densely the antenna elements of the antenna array 130 are arranged. Apparatuses for microwave imaging may benefit from denser antenna arrays and closer to the object 111, as this results in the apparatus being able to receive a stronger signal from more measurement locations, which allows for a more accurate and more detailed reconstruction of the object. The method 900 realizes a complete modeling of the scattering of electromagnetic energy by the antenna elements of the apparatus, which makes the reconstruction more accurate. Consequently, the disclosed method allows obtaining an accurate representation of the object 111 using an apparatus with densely arranged antenna elements. The representation of the second electric field distribution relative to illumination ^ may include two sets of values ^^and ^^^, the first set ^^being a representation of the values at the discretization grid points ^^, while the second set ^^^being a representation of the values at the measurement locations ^^^. The method 900 may comprise obtaining the representation of the second electric field distribution by obtaining 934: a constructed incident electric field distribution from the primary antenna element ^ of the model of the apparatus in the absence of the model of the dielectric distribution, or a measured incident electric field distribution from the primary antenna element ^ of the apparatus in the absence of the object 111, a constructed primary scattered electric field distribution scattered by the model of the dielectric distribution in response to the constructed or the measured incident electric field distribution, and a constructed secondary scattered electric field distribution scattered by one or more antenna elements of the antenna array 130 of the model of the apparatus in response to the constructed primary scattered electric field distribution. An electromagnetic simulation tool may be used to obtain the constructed incident electric field distribution ^^^^^(associated with a primary antenna element ^) in the absence of the model of the dielectric distribution. In other words, a simulation of ^^^^^(^) is performed where the antenna element ^ of the model of the apparatus irradiates electromagnetic energy in the model of the apparatus without a model of the dielectric distribution, or, in other words, where the model of the dielectric distribution is replaced by a homogeneous dielectric distribution exhibiting the same value as the first medium. As an example, ^^^^^may be obtained by sampling ^^^^^(^) at the discretization grid points ^^and at the measurement locations ^^^. The measured incident electric field distribution ^^^^^(associated with a primary antenna element ^) may be measured by means of electric field distribution measurements. Such electric field distribution measurements may be realized with a so-called minimally perturbing electric field probe attached to a scanning arm sweeping the volume of interest at corresponding discretization grid points within the container 120 of the apparatus in the absence of the object 111 when antenna element ^ is active. In other words, the incident electric field distribution ^^^^^(^) may be measured inside the apparatus at corresponding locations ^^and ^^^when the object 111 is absent, antenna element ^ is active, and all other antenna elements of the antenna array 130 are passively terminated. In general, the constructed or the measured incident electric field distribution may comprise data indicative of an electric field, e.g., in the form of a matrix with elements indicating a complex field strength at respective spatial locations of the model of apparatus. The constructed or the measured incident electric field distribution (^^^^^) may comprise a 3^ × ^ matrix (where ^ is the number of elements in the discretization grid, and ^ is the number of antenna elements in the antenna array of the model of the apparatus) where each element ^^^^^^= ^^^^^(^^) contains the measured or simulated value at grid point ^^when antenna element ^ is active. Similarly, the representation of the constructed incident electric field distribution (^^^^^^) may comprise a 3^ × ^ matrix (where ^ is the number of antenna elements in the antenna array of the model of the apparatus) where each element = ^^^^^(^^^) contains the measured or simulated value at measurement location ^^^when antenna element ^ is active. The constructed primary scattered electric field distribution , ^^^^^ ^ ) scattered by the model of the object in response to the constructed incident electric field distribution may comprise ^ ^^^ ^ (^) as defined in Equation (14), which is discussed in Step 1b above. In general, the constructed primary scattered electric field distribution (^ ^^^ ^, ^^^^^ ^ ) may comprise data indicative of an electric field, e.g., in the form of a matrix with elements indicating a complex field strength at respective spatial locations of the model apparatus. The constructed primary scattered electric field distribution (^ ^^^ ^ ) may comprise a 3^ × ^ matrix (where ^ is the number of elements in the discretization grid, and ^ is the number of antenna elements in the antenna array of the model of the apparatus) where each element ^ ^^^ ^^= ^ ^^^ ^ (^^) contains the calculated value at grid point ^^when antenna element ^ is active. The constructed primary scattered electric field distribution (^^^^^ ^ ) may comprise a 3^ × ^ matrix (where ^ is the number of antenna elements in the antenna array of the model of the apparatus) where each element ^ ^^^ ^^^= ^ ^^^ ^ (^^^) contains the calculated value at measurement location ^^^when antenna element ^ is active. The constructed secondary scattered electric field distribution (^^^^^, ^^^^^^) scattered by one or more of the antenna elements of the antenna array of the model of the apparatus in response to the constructed primary scattered electric field distribution may comprise ^^^^^(^) as defined in Equation (15), which is discussed in Step 1b above. In general, the constructed secondary scattered electric field distribution (^^^^^, ^^^^^^) may comprise data indicative of an electric field, e.g., in the form of a matrix with elements indicating a complex field strength at respective spatial locations of the model of the apparatus. The constructed secondary scattered electric field distribution (^^^^^) may comprise a 3^ × ^ matrix (where ^ is the number of elements in the discretization grid, and ^ is the number of antenna elements in the antenna array of the model of the apparatus) where each element contains the calculated value at grid point ^^when antenna element ^ is active. The constructed secondary scattered electric field distribution (^^^^^^) may comprise a 3^ × ^ matrix (where ^ is the number of antenna elements in the antenna array of the model of the apparatus) where each element contains the calculated value at measurement location ^^^ when antenna element ^ is active. Optionally, each antenna element in the antenna array 130 acts as the primary antenna element ^ in turn. In other words, electromagnetic energy is transmitted, in turn, by each antenna element. In that case, the method may comprise obtaining a respective corresponding representation of a first electric field distribution in the apparatus by means of measurements via the antenna array 130 by letting each antenna element in turn transmit electromagnetic energy. For each such respective representation of a first electric field distribution in the apparatus, a respective corresponding representation of a second electric field distribution in the apparatus is obtained and compared with the corresponding respective representation of the first electric field distribution in the apparatus. The adapting of the model of the dielectric distribution may, in that case, be based on all comparisons. The representation of the second electric field distribution in the apparatus being obtained based on constructed electromagnetic energy as scattered by at least one of the antenna elements of the antenna array of the model of the apparatus may mean that the second electric field distribution is estimated based on a linear combination of one or more individual simulations estimating the incident electric field distribution ^^^^^(^) associated with antenna element ^ of the apparatus in a model of the apparatus and resulting from the constructed electromagnetic energy transmitted from the antenna element ^ when acting as primary antenna within the model of the apparatus in the absence of the model of the dielectric distribution. Alternatively, the second electric field distribution may be estimated based on a linear combination of one or more individual measurements of the incident electric field distribution ^^^^^(^) associated with antenna element ^ of the apparatus and resulting from the measured electromagnetic energy transmitted from the antenna element ^ when acting as primary antenna within the apparatus in the absence of the object. The coefficients used in the linear combination may comprise a coupling factor in the form of a complex scalar value and determined, for instance, as described in the referenced literature. Each individual coefficient relative to an antenna element ^ of the antenna array of the model of the apparatus, and used in the linear combination, may further comprise a projection of the constructed primary scattered electric field distribution at the location ^^and along the unitary polarization vector ^^of the antenna element ^ of the antenna array of the model of the apparatus. The method may comprise obtaining 935 one or more constructed incident electric field distributions from respective antenna elements of the antenna array 130 of the model of the apparatus in the absence of the model of the dielectric distribution, or one or more measured incident electric field distributions from respective antenna elements of the antenna array 130 of the apparatus in the absence of the object 111. In that case, the method may further comprise obtaining 936 the constructed secondary scattered electric field distribution based on the one or more constructed incident electric field distributions or the one or more measured incident electric field distributions. Figure 11 schematically illustrates, in terms of a number of functional units, the components of a control system 810 according to embodiments of the discussions herein. This control system 810 may be comprised in the apparatus 400 or be a separate from the apparatus 400. Processing circuitry 1010 is provided using any combination of one or more of a suitable central processing unit (CPU), multiprocessor, microcontroller, digital signal processor (DSP), etc., capable of executing software instructions stored in a computer program product, e.g. in the form of a storage medium 1030. The processing circuitry 1010 may further be provided as at least one application specific integrated circuit (ASIC), or field programmable gate array (FPGA). Particularly, the processing circuitry 1010 is configured to cause the control system 810 to perform a set of operations, or steps, such as the method discussed in connection to Figure 10. For example, the storage medium 1030 may store the set of operations, and the processing circuitry 1010 may be configured to retrieve the set of operations from the storage medium 1030 to cause the control system 810 to perform the set of operations. The set of operations may be provided as a set of executable instructions. Thus, the processing circuitry 1010 is thereby arranged to execute methods as herein disclosed. The storage medium 1030 may also comprise persistent storage, which, for example, can be any single one or combination of magnetic memory, optical memory, solid-state memory or even remotely mounted memory. The control system 810 may further comprise an interface 1020 for communications with at least one external device. As such, the interface 1020 may comprise one or more transmitters and receivers, comprising analogue and digital components and a suitable number of ports for wireline or wireless communication. The processing circuitry 1010 controls the general operation of the control system 810, e.g., by sending data and control signals to the interface 1020 and the storage medium 1030, by receiving data and reports from the interface 1020, and by retrieving data and instructions from the storage medium 1030. Other components, as well as the related functionality, of the control system 810 are omitted in order not to obscure the concepts presented herein. There is also disclosed herein a computer readable medium carrying a computer program comprising program code means for performing the method illustrated in Figure 10, when said program product is run on a control system 810. The computer readable medium and the code means may together form a computer program product.

[0002] Herein, the following notation is used. Summary of styles: ^ ^ : a (complex) scalar ^ ^ : a (complex) vector ^ ^ : a (complex) scalar matrix OR the size of a set ^ ^ : a (complex) vector matrix (a matrix with 3 × 1, 1 × 3 or 3 × 3 blocks) Summary of symbols: ^^ =[^ ^ ^]^: coordinates^ : source coordinates ^ ^ : angular frequency ^ ^ : speed of light (in vacuum) ^ ^(^, ^) : dyadic Green’s function ^ ^(^): complex relative permittivity distribution (representing the object) ^ ^^: complex relative permittivity value (of the first medium) ^ ^(^) : contrast distribution (to be reconstructed) ^ ^ : coupling factor (of antenna to field intensity at its location) ^ ℛ : reconstruction domain ^ ^ : number of antenna elements (or measurement locations) ^ ^ : number of grid elements (for domain discretization) ^ ^^: polarization direction of antenna ^ (unitary vector) ^ ^^(^^) : identity matrix of diagonal ^ (3^) ^ ^^(^) : value of the electric field distribution at ^ when antenna ^ is active (continuous) ^ ^^^: value of the electric field distribution at ^^when antenna ^ is active (discrete) ^ ^^: vector of discrete electric field distribution values (illumination ^) ^ ^ : matrix of discrete electric field distribution values (all illuminations) ^ ^ : predicted discrete values at grid points ^ ^^: predicted discrete values at measurement locations ^ ^^: measured discrete values at measurement locations Summary of labels: ^ TOT : total field (in the presence of the object) ^ INC : incident field (in the absence of the object) ^ SCA : scattered field ^ OBJ : object response ^ ARR : array response

Claims

CLAIMS 1. An apparatus (400) for non-invasive microwave tomography of an object (111), the apparatus (400) comprising: a container (120) provided with a first medium (121), the container (120) being provided with a first boundary (122) configured to face at least a part of an external surface of the object (111); an antenna array (130) arranged inside the container (120), the antenna array (130) being at least partly encompassed by the first medium (121), and configured to transmit electromagnetic energy for irradiating the object (111) and to receive electromagnetic energy scattered by the object (111); and a dampening layer (440) arranged at a second boundary (123) of the container (120), wherein the dampening layer (440) is configured to attenuate reflection of electromagnetic energy, scattered by the object (111), at the second boundary (123) back into the first medium (121).

2. The apparatus (400) according to claim 1, wherein the container (120) is encapsulated by the first boundary (122) and the second boundary (123).

3. The apparatus (400) according to any previous claim, wherein the dampening layer (440) comprises a second medium, and wherein the first medium (121) has a first dielectric loss value at a frequency and the second medium has a second dielectric loss value at the frequency, wherein the second dielectric loss value is at least two times the first dielectric loss value.

4. The apparatus (400) according to claim 3, wherein the first medium (121) has a first characteristic impedance value at the frequency and the second medium has a second characteristic impedance value at the frequency, wherein the second characteristic impedance value is within 50% of the first characteristic impedance value.

5. The apparatus (400) according to any previous claim, wherein the first medium (121) comprises air or purified water.

6. A method (900) of obtaining a representation of an object (111) by means of an apparatus for microwave tomography, wherein the apparatus comprises a container (120) provided with an antenna array (130) comprising a primary antenna element and one or more secondary antenna elements positioned relative to the object (111), the method comprising: radiating (910) electromagnetic energy from the primary antenna element into the container (120) to irradiate the object (111); and in response to the radiation of electromagnetic energy,obtaining (920) a representation of a first electric field distribution in the apparatus by means of measurements via the one or more secondary antenna elements ; and obtaining (930) the representation of the object (111) by iteratively adapting a model of a dielectric distribution representing the object (111), wherein the adapting comprises, iteratively, obtaining (931) a representation of a second electric field distribution in the apparatus using a model of the apparatus and the model of the dielectric distribution, wherein the representation of the second electric field distribution is obtained based on constructed electromagnetic energy as scattered by the model of the dielectric distribution and constructed electromagnetic energy as scattered by one or more antenna elements of the antenna array (130) of the model of the apparatus, comparing (932) the representation of the second electric field distribution with the representation of the first electric field distribution to obtain a comparison, and adapting (933) the model of the dielectric distribution based on the comparison and thereby obtaining the representation of the object (111).

7. The method (900) according to claim 6, wherein the method comprises obtaining the representation of the second electric field distribution by obtaining (934): a constructed incident electric field distribution from the primary antenna element of the model of the apparatus in the absence of the model of the dielectric distribution or a measured incident electric field distribution from the primary antenna element of the apparatus in the absence of the object (111), a constructed primary scattered electric field distribution scattered by the model of the dielectric distribution in response to the constructed or the measured incident electric field distribution, and a constructed secondary scattered electric field distribution scattered by one or more antenna elements of the antenna array (130) of the model of the apparatus in response to the constructed primary scattered electric field distribution.

8. The method (900) according to any of claim 7, wherein the method comprises: obtaining (935) one or more constructed incident electric field distributions from respective antenna elements of the antenna array (130) of the model of the apparatus in the absence of the model of the dielectric distribution, or one or more measured incident electric field distributions from respective antenna elements of the antenna array (130) of the apparatus in the absence of the object (111); andobtaining (936) the constructed secondary scattered electric field distribution based on the one or more constructed incident electric field distributions or the one or more measured incident electric field distributions.

9. The method (900) according to any of claims 6-8, wherein the apparatus is the apparatus (400) according to any of claims 1-5.

10. A control system (810) comprising a processing circuitry (1010) configured to perform the method (900) according to any of claims 6-9.

Images