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Abstract
A high-contrast target with complex shape, especially concave surfaces, often exhibits strong high-order scattering during forward propagation, which is often misinterpreted as artifacts or phantom targets during imaging. In this work, a bistatic imaging method for reducing artifacts caused by high-order scattering from concave objects under cylindrical millimeter-wave scanning geometry is proposed. The effects of multiple reflections within concave structures are firstly analyzed by using ray-tracing techniques. It is observed that these troublesome multiple reflection echoes are often confined in limited scattering angles. Under this specific requirement for transceiver setup, a bistatic cylindrical aperture synthesis technique is proposed to obtain accurate images of concave object despite strong high-order scattering. To verify this method, simulated imaging results in bistatic near-field cylindrical imaging geometry are presented. Finally, the effectiveness of artifact reduction is confirmed by experimental results of complex metallic targets with concave outlines.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Due to the increasing demand for short-range imaging capabilities, high resolution microwave and millimeter wave imaging technologies are developing rapidly in various applications, such as nondestructive evaluation of buildings, through-wall imaging, and personnel surveillance at public spaces [1–5]. Several security imaging systems have been deployed in airports, showing good performances and practicability [6,7].
To detect various types of objects, high image resolution and accurate surface reconstruction is needed. Thus, image artifacts caused by complex shape targets are a non-negligible issue in practice. One of the typical problems was reported in [8], where artifacts exist in the reconstructed image at the gaps between arms and legs of the human body during cylindrical portal scanning, which may cause false alarms. It is recognized that such artifacts are caused by high-order scattering, which introduces ambiguity during forward propagation. This means same measured signals could be caused by different objects under different possible number of reflections within the object itself. Such type of artifacts is not recoverable in the current monostatic setup by typical reconstruction techniques [9] without very specific prior information about the object under imaging.
The problem caused by high-order scattering in concave structures are well-known, and has been studied in different fields. The connection between multiple-scattering mechanism and reconstructed image using linear inversion algorithm has been investigated in [10] for microwave imaging. Efforts in the field of radar cross section (RCS) measurement are devoted to improve the accuracy of electromagnetic (EM) calculation [11,12], rather than investigating the mechanism of how multiple reflection influences the measurement signal for imaging. In the field of Synthetic Aperture Radar (SAR) imaging, the distribution of equivalent scattering centers of the dihedral-type objects was investigated [13]. Due to the far-field condition, results from SAR are not directly feasible for near-field imaging. Assuming the power spectrum density function of the target is known, an FBP-type inversion method was proposed for imaging in a multiple scattering environment [14]. By applying ray-tracing approximation to the Green function, interactions between the target and environment were included in the reconstruction without consideration of high-order scattering among different parts of the target. Efforts in the field of electromagnetic inverse scattering have been focused on reconstructing the distribution of physical parameters such as the target’s dielectric properties considering multiple reflections [15–19], which represents an important approach to the high-order scattering problem. Such techniques may suffer from the ill-posed problem and high computation costs for electrically large objects. Therefore, although high-order scattering in concave structures has been studied in many areas, there are still difficult issues to be solved for near-field imaging.
This paper focuses on the analysis of high-order scattering effects using a typical concave structure, dihedral, for discussion, and proposes a bistatic cylindrical near-field imaging approach to achieve more accurate reconstruction of concave objects. Here near-field refers to the condition where the antenna aperture is located within the near-field of the target under imaging. By introducing ray-tracing method, the formation and characteristic of multiple reflections under high-frequency approximation are investigated. It is found that multiple reflections exhibit strong directivity. Therefore, the effects of multiple reflections can be reduced by changing the acquisition scheme from monostatic to bistatic measurements, and by choosing appropriate bistatic angles. To cope with the new acquisition setup, a bistatic aperture synthesis technique based on quasi-monostatic approximation is further introduced to produce high quality reconstructions under large bistatic measurement angles.
In the following, Section II explains the formation of artifacts caused by multiple reflections in concave structures. Section III investigates the characteristic of multiple reflections and presents the bistatic artifact reduction method and aperture synthesis technique. Section IV provides experimental result of a complex shaped target with cavities and a pair of pliers to verify the method. Conclusions are discussed in Section V.
2. Formation of artifacts
Within a classical beamforming or back-projection type reconstruction technique, a target is assumed as an assembly of independent scattering points as hypothesized under Born or Kirchhoff approximation under which high-order scattering among targets is not considered. In this section, reconstructions of dihedral structures are provided to illustrate how artifacts are produced by multiple reflections. Then high-order scattering events are tracked and analyzed by ray-tracing method to reveal the mechanism of artifact formation.
2.1 Imaging with monostatic measurement
Figure 1(a) gives the illustration of the near-field cylindrical imaging geometry under study and the reconstruction of dihedral structures. The dihedral opening angles are 90° and 60°, respectively, and their edge length is 0.2m in this scenario. The measured wideband monostatic signals are simulated by EM full wave computing method of moments (MoM) from 12GHz to 24GHz. Then the image is reconstructed by the conventional monostatic imaging algorithm used in cylindrical aperture synthesis (CAS) [20], which treats all received signals as single scattering events.
Fig. 1 Illustration of cylindrical imaging geometry and reconstruction of dihedral (with 90° and 60° opening angle) using a conventional cylindrical aperture synthesis algorithm.
Reconstructions of 90° and 60° dihedrals are shown in Fig. 1(b). It can be seen that the image of 90° dihedral exhibits a very strong scattering point at the vertex of the dihedral, which is marked as part B. The scattering point is so strong that the two edges of the dihedral is not visible. In the image of 60° dihedral, some parts of the edges are reconstructed at their actual positions, marked as part A, but the parts of the inner edges are missing, and there also exists another symmetric structure at the top of the structure, which is marked as part B. In this scenario, the high-order scattering artifact makes the whole structure appearing as three isolated objects.
2.2 Ray-tracing analysis
The propagation range is the key to understanding the mechanism of artifact formation. Here we utilize ray-tracing method to describe the propagation of EM wave and the process of multiple reflections. In this work, we assume the metallic dihedrals under study are electrical large objects, fulfilling the condition of high frequency approximation [21], thus EM wave can be described directly by rays whose behavior follows the mirror reflection principle, in which consecutive mirrored points with respect to the edges of the dihedral are used to simplify the estimation of the propagation distance.
Figure 2 illustrates the schematic of ray-tracing method. A bunch of rays emit from the transceiver at a monostatic acquisition point A(r0, θ0), where r0 is the distance between the antenna and the rotation center and θ0 is the observation angle. Under the mirror reflection principle, the length of propagation path equals to the distance between point A and the last mirror point, as point B in the presented scenario, and recorded as RangeAB, which formulation could be expressed as follows.
where φAB is the angle corresponding to the line segment AB, which can be expressed by observing angle θ0, and reflection times n. The range equation can be expressed as follow.where .The range equation can help illustrate the formation of artifacts in the reconstructed images. If n is even, the propagation range is constant, and its time domain signal is a straight line and reconstructed into a strong point, such as the 90° dihedral image. Alternatively, if n is odd, the equivalent radiating point, which is the center of measuring point and its mirror point, behaves as the scatter position in the image. For single reflection, the equivalent reflection point is on the edge of dihedral, as shown in Fig. 3(a), so it coincides with the actual position of a part of the target. For multiple reflections, the equivalent reflection point is outside the edge of dihedral, which will be reconstructed as artifacts as shown in Fig. 3(b). According to the range equation, the propagation distance of three-times reflection of the 60° dihedral equals to the propagation distance of one-time reflection of the 180° dihedral. Consequently such ambiguities cause artifacts of the 60° dihedral to appear as a straight line. In summarize, due to the existence of multiple reflections among the two planes of the dihedral, the equivalent reflection point will not coincide with the edge of the object, causing artifacts outside the true surface of the target.
Fig. 3 Schematic illustration of the ray tracing method for understanding the propagation range of dihedrals and the cause of artifacts in scenarios. (a) with and (b) without multiple reflections.
3. Artifact reduction method
In this section, the angular and frequency distribution of single and multiple reflections are first investigated, based on which we formulate the approach to reduce artifact by utilizing appropriate bistatic transceiver angles combined with bistatic aperture synthesis technique.
3.1 Characteristic of multiple reflection echoes
Figure 4 shows the distribution of echoes from both 60° and 90° dihedral structures under different incident and bistatic receive angles. Corresponding illustration of ray tracing process is presented in Fig. 5. With the help of ray-tracing analysis, it is observed that the received signals are divided into different regions according to the number of reflection times. For a 90° dihedral, when incident angle is near the bisector of dihedrals (−30° to 30° incident angle), the received signals near 0° bistatic angles are mostly waves that have been reflected twice before exiting the structure. As the incident angle increases to above ± 40°, signals collected over a wide range of bistatic angles will be only single scattering waves. When the opening angle of the dihedral structure is decreased to 60°, signals from two and three reflection times are concentrated around low incident and receive angles. And the single scattering events are further pushed towards higher incident angles over a wide range of bistatic receive angles.
It is noticeable that single scattering signals always occur at large incident angles, and always exhibit a wide bistatic receive angles. And higher order reflection signals often appear at small incident angles near the bisector of the concave object. Consequently, we could choose larger incident angles to avoid receiving multiple reflection echoes which can help reduce artifacts. In addition, we should choose multiple bistatic transceiver angles to enlarge the effective signal receiving range, to rebuild a more complete image.
Figure 6 and Fig. 7 illustrate the effect of this proposed scheme using imaging results of the 90° and the 60° dihedral at different bistatic angles while avoiding incident angles from −25° to 25°. It can be seen that for the 90° dihedral, with the increase of bistatic angle, artifact at the vertex of the dihedral is weakened, but the edges of the 90° dihedral are slightly shortened. When the bistatic angle increases to 30°, the central part of the dihedral begins to be missing. For the 60° dihedral, the artifact labeled as part B in Fig. 1(b) disappears since most of the multiple reflection signals are avoid. It can be also observed that signals from different bistatic measurement angles corresponds to slightly different parts of the inner surface of the concave structure. Therefore, it would be recommended to use a few bistatic angles in order to achieve a more complete outline of the object. It is necessary to note that the proposed method does require prior knowledge on the opening angle or main scattering direction of the concave structure under imaging.
Fig. 6 Reconstructions of 90° dihedral using 0°, 10°, 20°, 30° bistatic angles while avoiding incident angles from −25° to 25°.
Fig. 7 Reconstructions of 60° dihedral at 0°, 10°, 20°, 30° bistatic angles while avoiding incident angles from −25° to 25°.
3.2 Image reconstruction under bistatic scheme
In bistatic measurement imaging, the CAS algorithm can be applied but with a quasi-monostatic approximation. The quasi-monostatic approximation assumes that the signals measured by the bistatic antenna pair are the same as those measured at the equivalent phase center (EPC). In circular imaging, the EPC position is at the center angle of the bistatic antenna pair. If the range difference between the bistatic antenna pair and the EPC position, while measuring an arbitrary position in the imaging scene, is smaller than the imaging resolution, the quasi-monostatic approximation is available and the influences on the image focusing performance will be negligible. As shown in Fig. 8, the path of monostatic measurement and the path of bistatic measurement are different. And we quantify this difference by the EPC error, which is described by (3)
Where θEPC = (θt + θr)/2.To find the effective region where the quasi-monostatic approximation is available, the EPC error in different positions is shown in Fig. 9. The bistatic angle in this scenario is 50°, and the effective region is considered as positions where EPC error is smaller than resolution. For example, the effective region is 0.025m for bandwidth from 12GHz to 24GHz. The effective region looks like the shape of a crescent moon, as shown in Fig. 9. It is shown that point-like targets within the effective region can be reconstructed correctly. Outside this region, image resolution is reduced while object can be smeared in the reconstruction.
Fig. 9 Distribution of the EPC error and the corresponding imaging result of point-like targets inside and outside of the effective region.
Based on the echo signal distribution in Fig. 4, it is possible to find a suitable set of bistatic angles and incident angles to achieve improved imaging results. For both 90° and 60° dihedral, we propose to prevent the incident angles from −25° to 25° in order to avoid receiving multiple reflection signals. And we choose to measure at 0°, 10°, 20°, 30° bistatic angles to rebuild a more complete image of the concave target.
Figure 10(a) shows the illustration of the near-field bistatic cylindrical imaging geometry. The bistatic angle is fixed and the receiving antenna rotates with the transmitting antenna. The images are obtained by adding the outlines of the multiple bistatic images together, as shown in Fig. 10(b). It is obvious that for the 90° dihedral, the strong artifact at the vertex appearing in the image of conventional monostatic reconstruction in Fig. 1(b) has disappeared, and the two edges of the dihedral are recovered correctly. For the 60° dihedral, it can be seen that the artifact shaped like a straight line in monostatic result is now significantly reduced. The image of the dihedral inner part is still weaker than the outer part. This is because most of the multiple reflection signals are avoided in the proposed bistatic approach and these high-order scattering signals are mainly produced by the inner part of the concave structure.
Fig. 10 Illustration of the proposed bistatic cylindrical imaging geometry and reconstruction of dihedral (with 90° and 60° opening angle) using bistatic cylindrical aperture synthesis algorithm. In contrast to the monostatic results presented in Fig. 1(b), image artifacts due to high-order scattering from the concave structure are now significantly reduced.
Comparing with the monostatic results in Fig. 1(b), the high-order artifacts due to concave structures are now greatly reduced and the shape of the reconstructed surface is much more complete. The proposed approach is capable of reducing artifacts for concave structures with different opening angles. For dihedrals larger than 90°, although there exists two times reflection, the multiple reflection echos will be rarely received, thus posing less influences on the resulting image. For dihedral with opening angles lower than 30°, the artifacts can still be reduced by avoiding larger incident angles, but greater inner sections of the concave structure will be missing due to the fact that significant portion of backscattered waves have experienced multiple-scattering paths.
4. Experimental verification
The proposed bistatic cylindrical imaging approach was further verified with experimental data. Near-field imaging experiments were carried out in an anechoic chamber with a vector network analyzer (VNA) and mechanical turntable. The setup is shown in Fig. 11. Data acquisition was performed in the frequency domain with the VNA connected with antipodal Vivaldi antennas [22] through a multi-port RF switch. The middle pairs of the array were used to achieve the monostatic circular imaging geometry; the middle antenna and several antennas within the array formed pairs of 10 o to 30° bistatic transceivers; the two antennas at the edges of the array formed a pair of 30° bistatic transceivers. The measurement frequency band was from 12GHz to 24GHz, the cylindrical rotation radius was 0.6m, with a rotation step of 1°.
Fig. 11 Pictures of experimental setup in anechoic chamber and the object made by foam covered with aluminum foil.
A complex shaped object containing 90° and 60° dihedrals was made using foam and further covered with aluminum foil as shown in Fig. 11(b). The distance between two parallel planes of the object was 20 cm. The edge length of two 90° dihedrals was 7cm, and the edge length of the 60° dihedral was 10cm. Both conventional monostatic imaging results and the proposed bistatic imaging results are shown in Fig. 12.
Fig. 12 Experimental imaging results of the complex shape object using both (a) conventional monostatic cylindrical approach and (b) the proposed bistatic scheme.
To quantify the improvement of the proposed bistatic approach, intensity of artifacts and actual target surfaces are marked as position A, B and C in both of the images in Fig. 12. In the monostatic result, the strength of the strong scattering point A is 0dB, the strength of the edges of the object at B is −18.67dB, and the strength of the 60° dihedral artifact at C is −18.23dB. The strong scattering point artifact caused by the 90° dihedral is a serious problem, which is 18dB stronger than other parts of the target surface, therefore covering all the details of the target. Meanwhile the artifacts caused by the 60° dihedral exhibit almost the same intensity as the edges of the object. Applying the proposed method, the strong scattering artifact at position A is completely eliminated with only 3.09dB difference when compared with the image intensity at position B. In addition, the artifact at position C caused by the 60° dihedral has disappeared with −19.97dB intensity, which is about 17dB less than the edges of the object.
To verify the effectiveness of the proposed approach in real targets, a pair of needle nose pliers was further measured, as shown in Fig. 13. The antenna separation was larger than the previous experiment (Fig. 11) due to increased cylindrical rotation radius in this experiment. The angle of opening of the pliers’ mouth was about 50°, and the angle of the inner part of the pliers’ handles was approximately 90°.
The pliers were first measured by monostatic transceivers. Both the pliers’ mouth opening and its handles form concave outlines and can produce high-order artifacts when conventional monostatic scheme is applied. Visible artifacts are formed on both sides of the pliers as shown in Fig. 14(a). Then, the pliers were further measured by bistatic transceivers with 0°, 10°, 20°, 30° bistatic angles while avoiding the incident angles when directly facing the concave structure (−25° to 25° for both the mouth and handle side of the pliers), and the result is shown in Fig. 14(b).
Fig. 14 Experimental imaging results of a pair of needle nose pliers using both (a) conventional monostatic cylindrical approach and (b) the proposed bistatic scheme.
The two artifacts are marked at position A and B in Fig. 14 for comparison. In Fig. 14(a) under conventional monostatic scheme, the strength of artifacts at A caused by the handle and the artifacts at B caused by the mouth of the pliers are −8.52dB and −5.27dB, respectively. In contrast, these artifacts are reduced to −13.35dB and −13.01dB in Fig. 14(b) using the proposed method.
To further investigate the feasibility of the proposed method under practical conditions, imaging experiments on the lower section of a human-sized manikin was performed. This mimics a typical imaging scenario during security screening at the airport. The picture of the manikin and imaging results from both the conventional and the proposed methods are presented in Fig. 15. Under this scenario, the body region where the legs join the torso forms concave surfaces with opening towards the front of the person. And the opening angle is approximately 80° as shown in the cross section of the resulting 3D reconstruction (indicated in Fig. 15(d)). As we analyzed the scattering behavior of a 90° dihedral in section 2, 80° concave structure exhibits similar strong point-like artifact around the vertex of the structure due to double bounces between the legs. These high-order scattering artifacts appears as phantom objects between the legs in the resulting image under conventional monostatic cylindrical scanning (region marked by the white circles). In order to reduce the level of artifacts, the proposed method is applied where multiple bistatic angles at 0°, 20°, and 40° are acquired while avoiding incident angles from −25° to 25°. It is evident in Fig. 15 (c) that the strong point-like artifact at position A is now significantly reduced. Quantitatively the image intensity of this artifact is suppressed from 0dB to −9.47dB in artifact level. This also makes other parts of the body more prominent due to reduced artifact level, which is also visible when comparing the cross sections in Fig. 16 (d) and (e). In general, the artifacts in the region between two legs are largely reduced by approximately 6dB in average. These results show that the proposed technique is feasible when imaging complicated concave objects under practical conditions.
Fig. 15 Reconstruction of the lower half of a human-sized manikin using conventional monostatic cylindrical approach (b)(d) and the proposed bistatic scheme (c)(e). (a) Picture of the target during imaging, (b) (c) front view of the 3D reconstructions, (d) (e) horizontal cross sections from the 3D reconstructions.
5. Conclusion
In this paper, high-order scattering artifacts caused by high-contrast concave object in near-field imaging are investigated. By using ray-tracing analysis, it is found that high-order scattering echoes often exhibit strong incident and scattering directivity. Based on this analysis, a new bistatic imaging scheme is proposed to reduce artifacts by avoiding multiple reflection components in the scattered waves while combining bistatic measurement angles in order to reconstruct a more precise outline of the concave surface. Both simulation and measurement results show that the proposed method is capable of effectively reducing high-order artifacts, especially for objects including significant concave surfaces. This study can be instructive for arriving at specific arrangement of antenna arrays to achieve more accurate near-field imaging of concave targets with pre-known main scattering directions.
Funding
National Natural Science Foundation of China (NSFC) (41531175, 61731001); Beihang 100 Talents Plan; Beihang Top Young Scholars Program; Excellence Foundation of BUAA for PhD Students (2017013).
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