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Abstract
In this paper, we study the feasibility of incorporating the cross-polarized scattered wave in active standoff millimeter-wave imaging in order to improve the edge detection and background suppression for metallic objects. By analyzing the scattering from a perfectly conducting (PEC) patch of a simple geometrical shape we show that the edge diffraction is the major source of cross-polarized scattering. A similar scattering behavior is also observed for a PEC patch placed on a dielectric medium. Hence, the cross-polarized scattered field conveys valuable information about the edges of the object. In addition, the cross-polarized scattering can be utilized to resolve the object from an unstructured reflective background. To put these ideas to the test, a standoff imaging system composed of a continuous-wave (CW) semiconductor source, a focal plane array detector (camera), and collimating and objective lenses at 95 GHz is utilized to image the co- and cross-polarized reflection from metallic patches both in the presence and in the absence of a background medium. In agreement with theory, the experiments reveal that the edges of the object can be enhanced and reflections from a smooth background medium can be suppressed by using the cross-polarized scattering. In this regard, the conducted experiments on the metallic patches placed on the human body also yield promising results.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Millimeter-wave (MMW) or sub-terahertz (sub-THz) imaging has been increasingly considered as an attractive research area in recent years due to great demands for imaging applications in security detection, through package detection, pharmaceutical and biomedical fields. Among different frequency ranges, sub-THz range has attracted great attention because of its unique features. Not ionizing human cells, these waves do not cause damage to individuals and can be used in public places and airports for security purposes [1] or in biomedical imaging for diagnosing different diseases [2]. Also, sub-THz waves have a good penetration into nonmetallic materials that makes it possible to detect objects hidden beneath different types of clothing [3] and detecting hidden objects inside different things [4]. As a result, many research groups have been working on improving the accuracy and speed of MMW and sub-THz imaging by employing various theoretical and practical methods. Advances in THz imaging have also been occurred by the development of quantum cascade lasers (QCL) that relying on its relatively high optical power, enables researchers to investigate various methods to improve imaging quality [5].
MMW imaging is being performed using two different techniques, passive imaging and active imaging. In passive imaging, there is no source to illuminate the object and thermal radiation of the object and also reflections from surrounding illuminations like sky are measured to carry out the imaging process. On the contrary, in active imaging a MMW or sub-THz source is used for illumination and the backscattered waves are measured. As the passive imaging technique relies on the self-radiation of the object, the detected power is dependent upon the object’s temperature difference with respect to the background. Hence, the range of passive imaging is limited in practice and active imaging is preferred in standoff scenarios due to its high dynamic range and signal to noise ratio (SNR) at farther distances [6,7]. In this regard, active imaging systems based on frequency modulated continuous wave (FMCW) radar at various sub-THz atmospheric windows such as 340 GHz, 580 GHz, and 675 GHz have been proposed for 3D imaging of concealed objects at ranges up to 25 m. A FMCW radar system has been developed and been used to conduct experiments at different frequencies from 340 GHz to 675 GHz with a coherent single-pixel detector and centimeter-scale spatial resolution [8–11]. With the advent of sub-THz incoherent array detectors, referred to as sub-THz cameras, the quasi-optical intensity imaging has also been proposed as a low-cost alternative approach to MMW active standoff imaging. In the quasi-optical imaging systems, the object is illuminated by a CW source of radiation and the backscattered wave is focused to the array detector, also called the focal plane array (FPA), via an objective lens or mirror. 2D real-time imaging with centimeter-scale spatial resolution at ranges up to 10 m has been reported with this architecture [4,12].
Irrespective of the imaging system architecture, the specular reflection from nearly-smooth surfaces like the human body or metallic objects is one of the most critical limitations in active MMW standoff imaging [13]. It means that the incident power is predominantly reflected in a direction determined by the Fresnel law of reflection. Hence, the received power in the imaging system can be below the detection threshold if the detector-object line of sight does not coincide with the direction of specular reflection. In other words, even a large metallic plate may not be detected by an active MMW standoff imaging system if it is not oriented properly. A relatively high reflection from the human body poses another challenge to active standoff imaging and makes it difficult to resolve a metallic object from the background [14]. Due to these limitations, the images captured by active imaging systems exhibit speckle and do not look natural which makes the object recognition more challenging as compared to passive (thermal) imaging systems [15].
Polarimetric analysis of the backscattered wave from the object can be a solution to overcome these challenges. In [16], the effect of dielectric roughness on co- and cross-polarized backscatter data has been studied. In [17], the backscatter response of a multi-polarized radar on different outdoor surfaces has been examined in order to be applied in remote sensing projects. In [18], different backscatter data acquired from co- and cross-polarized reflections are used for indoor navigation and mapping. In [19], the effect of cross-polarized reflection on the improvement of concealed weapon detection by a standoff FMCW radar imager at 340 GHz has been investigated. Similar studies on close range holographic imagers at microwave frequencies have also been reported in [20,21]. By assessing the captured imagery of various targets, it is observed that the reflection of the human body is dominantly co-polarized while the threat objects scatter a noticeable level of cross-polarization.
In this paper, we take a closer look at the origin of cross-polarized scattering from metallic surfaces. We limit our study to the scattering from metallic patches of a simple geometrical shape to shed light on the underlying physics of cross-polarized scattering. Firstly, we benefit from the physical theory of diffraction (PTD) to approximate the cross-polarization content of the field scattered from edges of a perfectly conducting (PEC) patch. At the next step, we use the quadratic phase transmittance of an ideal objective lens and the Fresnel diffraction integral to simulate the resultant standoff image of the mentioned PEC patches in a cross-polarization scenario. We also use full-wave simulation based on the physical optics (PO) principle to extract the scattered near-field of a rectangular patch in the presence and in the absence of a background medium to study the polarization of the scattered wave. It is revealed that the flat surface of the patches contributes negligibly in the cross-polarized scattering and the cross-polarized backscatter is mainly caused by the edges. As a result, certain sections of the patch border can be enhanced in the reconstructed cross-polarized image by proper selection of orthogonal linear polarizations used for illumination and detection. Finally, we make use of a quasi-optical imaging setup at 95 GHz to verify the theoretical results by experiments. Metallic patches on a low-reflection foam stand are first studied both in co- and cross-polarized imaging scenarios. Then, the patches are placed on a human body and the mentioned imaging scenarios are repeated. The experimental results, in agreement with theory, reveal that the background reflection can be suppressed and the edges of the object can be enhanced in the cross-polarization scenario at the cost of reduced received power.
2. Analysis of the cross-polarized imagery
In the PO-PTD approximation, the electromagnetic (EM) wave scattering from a PEC object is decomposed into the scattering from its surfaces and the diffraction from its edges. The induced electric current density on the smooth surfaces of the object and the equivalent magnetic and electric edge currents are related to the incident EM field and are considered as the sources of the scattered fields. Having the mentioned currents, one can express the scattered fields by the well-known radiation integrals [22]. It can be shown that the scattering of a linear-polarized incident wave from a flat PEC surface can dominantly be expressed by the mirror-like, or specular, co-polarized reflection. In this case, the cross-polarized scattering is mainly caused by the diffraction from the edges of the PEC plate. Therefore, we focus on the edge diffraction to study the outcome of quasi-optical imaging in a cross-polarized scenario.
If the border of a PEC object is represented by a contour C and each point on this contour is expressed by position vector $\vec{r}^{\prime}$, the diffracted electric field at an arbitrary observation point $\vec{r} = r\hat{r}$ is approximated by the PTD as [23,24]
Using (1), we are now able to analyze the imaging of a PEC object in the cross-polarization scenario in which the object is illuminated by a linear polarized plane wave and the orthogonally-polarized component of the scattered wave is recorded in the image plane. As mentioned in the Introduction, we consider a simple PEC object in the shape of a thin rectangular or circular patch and approximate the cross-polarized imagery via multiplying the diffracted wave by the transmittance of an ideal focusing lens and applying the Fresnel diffraction integral to determine the resultant field in the image plane. Assuming both the object and image planes to be parallel to the xy-plane and considering an ideal lens in between, we can approximate the field intensity in the image plane as [25]
The proposed method of analysis can be applied to estimate the cross-polarized imagery formed by a quasi-optical standoff system in various scenarios. Here, we assume a wavelength of λ=3 mm and analyze the cross-polarized imaging of a 5 cm×5 cm rectangular patch at a distance of do=3 m from a lens of focal distance F=40 cm and diameter D=30 cm. As shown in Fig. 1(a), the object is illuminated by a linear-polarized plane wave at an incidence angle θi. If the incident electric field (${\vec{E}_i}$) lies in the plane of incidence, the cross-polarized scattered electric field is perpendicular to that plane, and vice versa. The scattering scenario shown in Fig. 1(a) is analyzed for the mentioned parameters and for θi=30° and the cross-polarized image is extracted. Figure 1(b) shows the result of this analysis. In this figure, the intensity of cross-polarized component of the electric field at the image plane is depicted. The dashed rectangle shows the border of the patch in the image plane. It is evident that the edges of the object which are in the E-plane of the incident field, i.e. the sides parallel to the x-axis in this scenario, are the dominant source of cross-polarized scattering and are highlighted in the formed image. In another scenario, we replaced the rectangular patch with a circular one of diameter 5 cm and repeated the mentioned analysis without changing any other parameters. The formed image, in this case, is illustrated in Fig. 1(c). Again, it is seen that the upper and the lower edges of the disk which are parallel to the E-plane of the incident wave are enhanced in the image. This finding suggests that the edges of a PEC object can be enhanced via cross-polarized imaging.
Fig. 1. Simulation of the cross-polarized imaging of a PEC patch considering the edge diffraction; the scenario of simulation (a) and the extracted cross-polarized field in the image plane for a rectangular and a circular patch (b, c). By estimating the magnification of the imaging setup as di/do the location of the patch in the image plane is approximated and shown by dashed lines.
3. Cross-polarized scattering in presence of the background medium
In the previous section, we show that the cross-polarized scattered field conveys information about the edges of a free-standing PEC patch. In this section, we study the scattering from a PEC patch in the presence of a background dielectric medium. In this regard, we use the Multilevel Fast Multipole Method (MLFM) and PO solver of Altair FEKO to simulate the near-field scattering from a PEC patch placed on a dielectric of relative permittivity εr=5.6 and conductivity σ=39.4 S/m which are in accordance with the reported electrical properties of the human skin at 100 GHz [26]. To keep the required computational resources affordable, a rectangular PEC plate of dimensions ${3 \times 3 \times 0}{.5}$cm3 on a ${17 \times 17}$cm2 dielectric background is simulated at 100 GHz and the scattered field at a plane near to the surface of the PEC plate is recorded. The mentioned structure is illuminated by a plane wave incident from the right side (positive x-axis) at an angle of θi=40° with respect to the normal to the surface of the PEC plate (xy-plane). The geometry of plane wave incidence is the same as Fig. 1(a). The simulated co- and cross-polarized components of the scattered electric field are illustrated in Fig. 2. In this figure, the electric field intensity on a plane parallel to the PEC surface at the distance of z=8 mm is depicted. The simulations are done both in the presence and in the absence of the background dielectric.
Fig. 2. Simulated scattered field intensity in the vicinity of a 3×3×0.5 cm3 PEC rectangular plate at 100 GHz; (a) Co-polarized scattering from the free-standing PEC plate (in the absence of background medium). (b) Co-polarized scattering from the PEC plate in the presence of a background medium with similar electrical properties as the human skin. (c) Cross-polarized scattering from a free-standing PEC plate. (d) Cross-polarized scattering from the PEC plate in the presence of the background medium. The location of the PEC plate is shown be a dashed square.
As Fig. 2(a) shows, the co-polarized scattered field from a free-standing PEC plate has a high intensity in the vicinity of the PEC surface. Hence, a similar bright region is expected to appear in the co-polarized imagery if the camera is placed in a proper direction. However, in the presence of the background medium, it is quite difficult to resolve the co-polarized field scattered from the PEC object from that reflected from the dielectric surface, as Fig. 2(b) shows. Therefore, it can be challenging to resolve the object from the background in the co-polarized imagery when the surface reflection of the background is comparable to that of the object.
The cross-polarized component of the scattered field in the absence and the presence of the background medium is illustrated in Figs. 2(c) and (d), respectively. Since a smooth dielectric surface produces no cross-polarized reflection, the cross-polarized scattering is only attributed to the edges of the PEC object. As a result, the cross-polarized scattered field has a high intensity in the vicinity of certain edges of the PEC object irrespective of the presence of the background medium. Here, in agreement with the PTD analysis results presented in the previous section, the edges of the PEC plate which are parallel to the E-plane of the incident wave produce the cross-polarized scattering dominantly. Therefore, it is expected that cross-polarized imaging helps also mitigating the background reflections and improves the resolution of the object from the background. It should be added that in both our simulations and measurements the cross-polarized field intensity is typically 10 dB lower than the co-polarized field intensity, as can be seen by comparing parts (a) and (c) of Fig. 2. Thus, the mentioned advantages of the cross-polarized imaging are achieved at the cost of reduced scattering power and limited imaging range, as a result.
Regarding the simulation results of Fig. 2, we have calculated the ratio of maximum co-polar scattered field intensity to maximum cross-polar scattered field intensity at several illumination angles which is presented in Table 1. In the near-field, as Fig. 2 also shows, the peak of the scattered field intensity is in the vicinity of the surface of the rectangular PEC patch for the co-polarized component and it resides near the edges of the patch for the cross-polarized component. As it can be seen from this table, the ratio of co-polar to cross-polar components of the scattered wave decreases with increasing the illumination angle from 15° to 60°, showing that the scattered cross-polarized field from the edges increases by increasing the illumination angle. The observation plane in these simulations for all of the incidence angles is placed at z=8 mm from the surface of the PEC patch.
Table 1. Ratio of intensity of scattered co- and cross-polar components for various illumination angles.
4. Experimental results
In the previous sections, application of the cross-polarized scattering to the standoff quasi-optical imaging is investigated by means of theoretical simulations. It is proposed that the edges of the PEC object can be highlighted and the background reflections can be suppressed in a cross-polarized imaging scenario. These claims are studied experimentally in a MMW quasi-optical imaging setup presented in Fig. 3. The imaging setup consists of a 95 GHz IMPATT diode CW source which illuminates the object plane via a horn antenna and a flat-top beam shaper (FBS) lens [27]. The radiated wave is linearly polarized and the radiated power is about 80 mW. The scattered wave is focused by an objective lens of diameter 30 cm and focal distance 40 cm to a 32×32 array of semiconductor based intensity detectors, also called the camera. The camera, the objective lens and the IMPATT diode source are commercial products of Terasense Inc. [12]. The detectors are polarization sensitive and has a linear cross-polarization discrimination of about 15 dB. The combination of the objective lens and camera provides a spatial resolution of about 3 cm and a field-of-view (FoV) of 70 cm×70 cm at the range of 3 m. Hence, each pixel of the acquired image represents approximately a 2 cm×2 cm square in the object plane. The illumination spot size can also be tuned by changing the relative distance of the horn and the FBS lens [27]. The integration time, or the frame-rate, of the camera is set and the detected intensity at each pixel is recorded by a PC software via a USB connection. More detailed information about the parameters of the imaging setup is presented in Table 2.
Fig. 3. The 95 GHz quasi-optical imaging setup used for the experimental studying of the cross-polarized scattering. The geometry of the setup and the pictures of the constituting components are shown. The setup is designed to provide resolution of 3 cm and FoV of 70 cm at the distance of d=3 m. The illuminated area in the FoV can be tuned by changing the distance of the FBS lens and the horn antenna.
Table 2. Parameters of the imaging setup
Since the source and the camera are linearly polarized, we can conduct experiments both in co- and cross-polarized scenarios by a 90° rotation of either the camera or the source about its axis. Keeping the 3 cm resolution of the imaging setup in mind, the dimensions of the objects are chosen so that their edges are resolvable and are expressed with several pixels in the recorded imagery. The illumination angle, depicted in Fig. 3, is determined by the relative location of the source with respect to the imaging axis. In the experiments, we chose a small angle of incidence (∼5°) in order to implement the specular reflection scenario in the co-polarized measurements. By placing the metallic objects on a low-reflection stand of polystyrene foam, the imaging scenarios are studied in the absence of background reflections. At the next step, a more realistic scenario is adopted by placing the object on a human body. In both cases, the co- and cross-polarized intensity images are recorded which are presented in the following. As mentioned in Table 2, the imaging rate is 6 frames per second for all of the tests.
The measured results in the absence of the background medium are shown in Fig. 4. The metallic objects are a 7 cm×12 cm rectangular patch and a circular disk of diameter 12 cm which are placed on the low-reflection stand. The recorded co-polarized image of the mentioned objects are shown in parts (a) and (b) of Fig. 4. The dashed border of the objects is also superimposed in these figures. As we expected, the surface of the objects is mainly observable in the co-polarized images. The cross-polarized images of the mentioned objects are illustrated in parts (c) and (d) of Fig. 4. In these experiments, the polarization of the illuminating electric field is along the y-axis and sections of the object’s border which are parallel to the incident electric field is revealed in the cross-polarized imagery, as expected from the PTD analysis. The overall intensity profiles in the experimental cross-polarized images are in agreement with the theoretical results of Section 2. However, a considerable degree of discrepancy in the details of experimental and theoretical results is also evident which is caused by various limitations in our experimental setup including the limited resolution of the imaging setup, the limited cross polarization discrimination of the detectors and the cross-polar radiation of the source, and the inevitable imperfections in the shape and alignment of the objects.
Fig. 4. The experimental images of free-standing metallic plates measured by the 95 GHz quasi-optical imaging setup introduced in the text; the normalized co-polarized image of a 12 cm×7 cm rectangular plate (a) and a 12 cm-diameter disk (b) and the corresponding normalized cross-polarized images (c, d). The source polarization is along the y-axis in these measurements.
At the next step, a 7 cm×7 cm rectangular plate is placed on a person’s body and the imaging scenarios are repeated. Figure 5(a) shows a photo of the imaging target. In this experiment, horizontal polarization, i.e. parallel to the x-axis, is used for the illumination of the object. The recorded co- and cross-polarized images are illustrated in Figs. 5(b) and (c), respectively. The main surface of the metallic plate along with a considerable amount of background reflection due to the person’s body is observable in the co-polarized image. However, if the dashed border of the plate is removed from this figure, it will be difficult to resolve the shape of the object from background reflection. This challenge is overcome in the cross-polarized image. As Fig. 5(c) shows, the background reflection is negligible and the x-directed edges of the rectangle, which are parallel to the incident electric field and are shown by arrows in Fig. 5(c), are highlighted in the cross-polarized image. Apart from some discrepancies in the details, the overall results of these experiments are in accordance with our theoretical expectations.
Fig. 5. (a) Experimental imaging of a 7 cm×7 cm metallic plate placed on a person’s body; the recorded co-polarized (b) and cross-polarized (c) intensity images. The source polarization is along the x-axis in these measurements. The location of the metallic plate is shown by a dashed border.
As it can be seen in Fig. 5(b), the presence of the object is presumable in the co-polarized image although not clearly detectable due to background reflections. However, in the cross-polarized image, body reflections are mostly eliminated and the received power is exclusively related to the object. It reveals the potential of cross-polarized imaging in distinguishing an object from the background.
For the sake of quantitative assessment of the measured imagery shown in Figs. 4 and 5, two quantities are defined and reported in Table 3. First, regarding the background suppression, the average intensity of pixels coinciding with the rectangular patch and that of the pixels lying outside the borders of the rectangular patch in the color images of Fig. 5 are calculated. The ratio of the mentioned quantities is referred to as the object-to-background ratio and is reported both for co- and cross-polarized imaging scenarios. It can be a measure of the object contrast with respect to the background (the human body). The superiority of the cross-polarized imaging in background suppression is evident based on this quantity.
Table 3. Quantitative assessment of the measured co- and cross-polarized imagery.
As mentioned before, depending on the direction of the incident polarization, some portion of the object’s edge is highlighted in the cross-polarized imagery. For a rectangular patch, the edges parallel to the incident polarization produce higher cross-polarization and are highlighted in the cross-polarized imagery. The average intensity in the pixels coinciding with the highlighted edges divided by the average intensity of the pixels lying on other edges of the object is the other quantity we define. It is called the cross-polarization edge selectivity and is a measure of polarization-sensitive edge enhancement in the cross-polarized imaging scenario. Based on the measurements of free standing rectangular and circular objects of Fig. 4, this quantity is extracted and is reported in Table 3. In the case of the circular object, the circular border of the object is divided into four quadrants; two parallel to the incident polarization and two perpendicular. The average intensity of pixels in the quadrants parallel to the incident polarization divided by the average intensity of pixels in the other quadrants is defined as the polarization-sensitive edge enhancement in this case. The typical value of this quantity is reported in Table 3 for rectangular and circular shapes. As expected, a higher edge selectivity is achieved for straight edges of a rectangular object.
Here, we take a step further and repeat the last experiment (Fig. 5(c)) for the source polarization along the y-axis. The captured cross-polarized image is shown in Fig. 6(a). As expected, the y-directed edges of the object are highlighted in this case. By simply adding the recorded cross-polarized intensities in the case of x- and y-polarized sources, i.e. Figure 5(c) and Fig. 6(a), we come up with an image containing the complete border of the metallic rectangle. The result of this combination is presented in Fig. 6(b). Figure 6(c) is the result of the application of an edge detection method based on the Canny algorithm [28] to the combined cross-polarization image. It shows that by merging the cross-polarization data of imaging scenarios with two orthogonal source polarizations, the overall border of the metallic object can be resolved from a considerable amount of background reflection.
Fig. 6. (a) The cross-polarized image measured by rotating the source polarization along the y-axis in the experiment introduced in Fig. 5, (b) The combined image produced by adding the cross-polarized images of x- and y-directed source polarizations, (c) The reconstructed shape of the object based on the combined image by an edge detection algorithm.
5. Conclusion
The application of cross-polarized scattering to the active standoff MMW imaging is investigated. The physical origin of the cross-polarized scattering is explored by the physical theory of diffraction and the quasi-optical imaging of free-standing PEC objects is analyzed in this case. By means of full-wave numerical simulations, the results of theoretical analysis are verified and the possibility of background suppression for PEC objects placed on a dielectric medium is proposed. It is found that the cross-polarized component of the scattered field which is dominantly produced by the edges of a metallic object can be exploited in order to enhance the edge detection and reduce the undesired background reflections in active standoff imaging. These claims are also proved experimentally by a 95 GHz quasi-optical imaging setup. Co- and cross-polarized images of metallic plates are recorded both in the absence and in the presence of a background medium. The measurements include a realistic case of a metallic object placed on a person’s body. It is shown that the cross-polarized component of the scattered field conveys precious information about the object’s border and can be incorporated in THz and MMW active standoff imaging systems in order to improve the quality of image reconstruction and object recognition.
Acknowledgements
All the reported measurements were conducted in Terahertz and Far-Infrared Lab., Department of Electrical Engineering, Sharif University of Technology.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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