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Abstract
Terahertz (THz) radar imaging has gained great interests in various applications due to its capability of deep penetration in some specific contents such as plastic and non-conductive materials without water. However, the image quality would be highly degraded by the scattering of the rough surfaces, which remains a challenge in the area. Here, we propose a confocal terahertz synthetic aperture radar (SAR) to alleviate the scattering issues with both improved signal-to-noise ratio (SNR) and resolution. Inspired by the confocal non-line-of-sight imaging in visible wavelength, a convex lens is added into the conventional SAR system to localize the effect of scattering within each spatial sampling point by the confocal configuration. Then, the random phase aberration caused by scattering could be corrected through a simple shift in temporal domain. The performance of the proposed method under different roughness occlusions is evaluated through experiments. All the results demonstrate great enhancements in both resolution and SNR over the conventional methods.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Terahertz (THz) radar imaging is one of the most promising technologies in personnel security, non-invasive inspection, medical imaging, etc. [1,2]. In addition to the general advantages of millimeter waves (MMW), such as penetration and non-ionizing radiation in specific contents like plastic and non-conductive materials without water, THz waves feature high spatial resolution in imaging due to short wavelength. In recent years, different systems and algorithms of THz radar imaging have been proposed to increase the imaging speed [3,4], resolution [5] and extend its application fields [6-8]. However, previous studies rarely consider the problem of the image quality degradation caused by the occlusions, which cannot be penetrated for visible light. Although these occlusions can be penetrated by THz waves, their rough surfaces will introduce additional scattering and aberration for THz imaging, which is quite common for clothing, radome, and medicine gauze, etc. Neglecting these low-scattering occlusion effects are reasonable in MMW radar because the roughness is much smaller compared with the long wavelength. When the frequency increases to THz band, the wavelength becomes too short to maintain the phase stability under these low-scattering occlusions. Especially, in the situation of occlusions with very rough surfaces, severe scattering would occur [9-11]. And it can partially or fully obscure the image of hidden objects with traditional reconstruction methods.
A few studies have been reported on imaging through smooth occlusions in THz band. For example, multi-beam interference in digital holography [12] and phase retrieval techniques [13] in coherent imaging were proposed to improve the imaging quality. A time-gated spectral technique in THz time domain spectroscopy (TDS) was introduced to solve the case of multi-layer occlusions in [14]. Unfortunately, these techniques cannot be directly used in THz radar because they require different imaging models and setups. Furthermore, it’s getting more complicated when considering the rough surfaces of the occlusion with strong scattering to THz wave. To our best knowledge, it remains a great challenge in THz radar imaging with rough-surface scattering and no systematic studies have been ever reported.
Generally, there are two main types of THz radar imaging systems, namely quasi-optical systems [15-18] and synthetic aperture radar (SAR) systems [19-21]. Quasi-optical systems employ a parabolic mirror to focus the beam into a small spot, while SAR systems utilize a wide-angle beam and focus it by aperture synthesis with coherent information. Traditional methods for both types of systems ignore the scattering effects of the occlusions, thus resulting in reduced imaging quality. Recently, a confocal non-line-of-sight (CNLOS) imaging technique was proposed to deal with scattering by transient information [22,23]. Although it is implemented in visible wavelength system, it can also be extended to systems with longer wavelength, especially THz radars due to its quasi-optical feature. Inspired by the idea, a confocal terahertz SAR imaging technique is proposed in this paper to improve the image quality under scattering situations caused by rough surfaces. Compared with conventional THz SAR imaging system, the proposed confocal THz system introduces additional convex lens to focus the light on the rough surface. With the confocal setup, the random phase modulation induced by the scattering can then be corrected with a simple shift in temporal domain for each sampling point in the spatial domain.
The remainder of the paper is organized as follows. The proposed imaging system with the proposed algorithm is introduced in details in Section 2. Section 3 designs various experiments in the situation of different stochastic rough surfaces to evaluate the performance of the proposed method. Quantitative metrics including image contrast, signal-to-noise ratio (SNR) and spatial resolution are analyzed to demonstrate the superior performance of the proposed system and algorithm. Section 4 discusses the limitations and future work with a special case incorporating a uniformly rough surface. The conclusion is made in Section 5.
2. Methods
2.1 Conventional THz SAR system
A brief review of the conventional rectilinear monostatic THz SAR system is presented here as the fundamental of the study. The geometric model of THz SAR imaging, also called THz holography imaging, is shown in Fig. 1. Based on the scalar diffraction model in wave optics, the echo signal neglecting attenuation can be expressed as
2.2 Confocal THz SAR system
The confocal THZ SAR system is proposed in this section to account for the impact of occlusions which is not included in the conventional system. The occlusion gives an extra phase aberration ${\varphi _{x^{\prime},y^{\prime}}}$ to the echo, which can be represented as
Due to the broad coverage of the occlusion in traditional system, the random phase aberration will significantly degrade the reconstruction performance. A straight-forward strategy to reduce the influence of such random phase aberration is to reduce the coverage of the occlusion for each spatial sampling point. Then the phase aberration will only introduce a phase shift for the confocal point, which can be removed easily by a temporal delay.
Figure 2 illustrates the proposed confocal THz SAR imaging system. The vector network analyzer (VNA) connected with two THz extenders is used to generate a wide-band frequency stepped signal. Horn antennas are installed on the extenders to transmit and receive the THz waves in the free space. Between the transceivers, a beam splitter is installed with 45 degree to align the transmitter and receiver in conjugated planes. A convex lens is introduced to focus the beam to the spot on the occlusion, forming a confocal configuration. The wave penetrates the occlusion with scattering and illuminates the hidden object. After that, the reflected signal is scattered again, and then collected by the receiver. Finally, the data is captured by scanning the target to simulate the confocal scanning system.
In the confocal configuration, the THz wave can be regarded as transmitting and receiving at a rough surface. Therefore, the range migration algorithm (RMA) can be applied with a simple pre-processing step to calibrate the phase aberration in temporal domain. Figure 3 demonstrates the data processing procedure with the simulated data. The low-scattering occlusion can be any materials which could be penetrated by THz waves. The hidden object is a letter ‘T’ in the example of Fig. 3(a). For each spatial sampling point with the frequency stepped signal [Fig. 3(b)], the inverse Fourier transform is implemented to get the range profile in temporal domain [Fig. 3(c)]. It can be noticed that both the occlusion in the front and the hidden object in the back can be visualized in the range profile. Considering the wide-band advantage of THz signal, it’s easy to get a high temporal resolution to distinguish the occlusion and the hidden object. Different phase aberrations will create different temporal delay for the whole profile, while the distance between the occlusion and the hidden object is fixed. Therefore, the occlusion can be treated as a new transceiver. Similar to the wavefront shaping, the signal for each spatial sampling point can be shifted to the position of occlusion [Fig. 3(d)], which can also remove the signal of the occlusion. After that, Fourier transform is taken to get the signal after descattering in frequency domain back [Fig. 3(e)]. Finally, the conventional RMA can be directly used to reconstruct the image of the hidden object [Fig. 3(f)].
Fig. 3. The procedure of signal processing in the confocal THz imaging system. (a) Illustration of the simulated scene. (b) Raw echo signal. (c) Inverse Fourier transform is taken to get the range profile. (d) Temporal wavefront shaping by searching the first peak and shifting the signal for each spatial sampling point. (e) Another Fourier transform to get back the signal in frequency domain after descattering. (f) Reconstruction of the hidden object with traditional RMA algorithm.
3. Experimental results
3.1 Setup
The experimental setup is shown in Fig. 4 with the conventional system in lower right and the proposed confocal system in lower left. All the components in the two systems are the same except for the TPX convex lens introduced in the confocal system. The diameter of the lens is about 50mm and the focal length is 60 mm.
Fig. 4. Experimental imaging systems. The lower left is the confocal system with a convex lens, while the lower right is the conventional system without the convex lens.
The linear frequency sweep from 280 GHz to 320 GHz with 200 sampling points is applied in the system. The bandwidth of 40 GHz leads to the range resolution of 3.75 mm. The horn antennas with 20°full beam width are used to transmit and receive the signal. The occlusion and the target are around 210 and 260 mm away from the antennas respectively. Note that ‘4f’ configuration is not strictly required due to the coherent effect. The diameter of the light spot on the occlusion is about 1 mm for the confocal system and 74 mm for the conventional system. In order to achieve a synthetic aperture, the target is installed on a 2D scanner. The intermediate frequency is set as 1kHz. It costs about 300 ms to collect the data of one point and totally 40 min to complete an 80 ${\times} $ 80 points scanning. The sampling interval and resolution step size are both set to 1 mm on each axis.
3.2 Sample preparation
Since the output power of our VNA is as low as 10 dBm, it is necessary to reduce the power loss of scattering for enough SNR. Moreover, the roughness of the occlusion should be controllable to implement the experiments. Therefore, the occlusion constituent should be carefully selected. In the experiments, polyethylene is used because of its low loss property in THz frequency [25] and its roughness can be easily controlled with 3D printing techniques. By doing this, enough SNR can be obtained even under very limited power and it is convenient to get the desired rough-surface model. It should be noticed that the proposed method also fits for other low-loss materials and more challenging cases with strong scattering loss will be investigated in the future.
The surfaces with RMS larger than 0.05 times of the wavelength can be considered as the rough surface as defined similarly in [9]. 3D printing technique is adopted to control the roughness exactly. The diameter of the sheets is 100 mm and their thickness is about 1 mm. Figure 5 denotes the images in visible wavelength of the surfaces and its CAD model with different samples I-III. Due to the craft limitations, sample III is roughest one that can be processed by 3D printing. In order to get a rougher sample, sample IV is made by pasting double sample III together. The RMS of sample IV can be roughly estimated to be twice that of sample III. The roughness parameters are calculated from the CAD model and shown in Table 1. Since the wavelength used in the system is around 1 mm, sample I could be regarded as slightly rough and sample IV could be thought as very rough.
Fig. 5. Occlusion samples with different roughness. (a1, a2) Sample I and its CAD model. (b1, b2) Sample II. (c1, c2) Sample III.
Table 1. Roughness parameters of occlusion samples
3.3 Imaging results and evaluation
In this section, two experiments are carried out including a resolution chart and some common items for inspection.
Different occlusion cases are evaluated with both the conventional and the proposed system. The resolution chart contains vertical and horizontal bars at four different feature sizes: 0.5 mm, 1 mm, 2 mm and 4 mm. The imaging field of view is 80 ${\times} $80 mm2. The reconstruction result is shown in Fig. 6. The whole reconstruction result is three dimensional, but only the range gate containing the target is shown here. With the conventional system, it can be observed that the images get more and more blurred as the occlusions get rougher as denoted from Figs. 6(a1) to 6(a5). Especially for the case occluded by sample IV [Fig. 6(a5)], the bars get totally indistinguishable with severe reconstruction artefacts due to the phase aberration introduced by scattering. In contrast, there is neglectable difference for sample I-III with the proposed system. Moreover, slight impact can be found in the worst case [Fig. 6(c5)], which may be caused by the focal point misaligned with the occlusion sample. Such condition is common in THz imaging and the proposed system presents higher robustness to scattering rather than previous ones.
Fig. 6. Comparison of reconstructions through occlusions with different roughness. The conventional method is shown on the first row and proposed method on the third row. (a1)(c1) no occlusion. (a2)(c2) occluded by sample I. (a3)(c3) sample II. (a4)(c4)sample III. (a5)(c5)sample IV. (b)(d) the corresponding redline intensity profile. (e) ground truth. (f) contrast. (g) SNR. (h) resolution. Scale bars:1 cm.
A quantitative comparison including contrast, SNR, and resolution is shown in Figs. 6(f)–6(h). The contrast is calculated by $C = {{({{I_{\max }} - {I_{\min }}} )} \mathord{\left/ {\vphantom {{({{I_{\max }} - {I_{\min }}} )} {({{I_{\max }} + {I_{\min }}} )}}} \right.} {({{I_{\max }} + {I_{\min }}} )}}$, where ${I_{\max }}$ and ${I_{\min }}$ are the maximum and minimum of the red profile. Figure 7(e) shows the ground truth ${\textrm{U}_{\textrm{gt}}}$, and the SNR of the reconstruction ${U_{\textrm{test}}}$ is evaluated by $SNR = 10 \times {\log _{10}}[{\mathop{\rm var}} ({\textrm{U}_{\textrm{gt}}})/{\mathop{\rm var}} ({U_{test}}\textrm{ - }{\textrm{U}_{\textrm{gt}}})]$. The resolution is calculated by knife edge method [26] using the pixels indicated by the blue square. It is clear that our method outperforms the conventional method in all the contrast, SNR, and resolution.
Fig. 7. Reconstruction of a key and a scissor hidden by sample III. (a) Front view. (b) Side view. (c) In-focus results reconstructed by the proposed system. (d) In-focus results reconstructed by the conventional system. Scale bar: 1 cm.
There are two interesting phenomena also been revealed in the study. First, even without occlusion, the proposed method produces higher image quality than conventional method. This is because the lens focuses the light spot on the occlusion, thus ‘shortening’ the distance R between the radar and the target. As the received power scales as R-4, the proposed method has a higher SNR and contrast. The cross-range resolution is given by
where ${\lambda _\textrm{c}}$ is the center frequency, ${{\theta }_\textrm{b}}$ is the lesser of the full beam width of the antenna or the angle subtended by the aperture. In the experiments, the resolution is mainly limited by the angle of the scanning aperture. In confocal setup, the angle can be seen as subtended from the focal point on the occlusion, which is naturally larger than the angle subtended from the antenna. In addition, for both the proposed and the conventional system, the imaging quality decreases as the distance increases because of a relatively smaller synthetic aperture. Secondly, it can be concluded that the resolution of reconstruction occluded by sample III is the highest in confocal system, because the scattering of the occlusion makes the focal spot form a larger beam width. Such behavior takes the advantage of scattering, which is similar to the situation described in [27]. By the way, it is worth mentioning that the performance of the confocal system is slightly concerned with the focal point.To further evaluate the performance of the design in practical application, the cases with a key and a scissor occluded by sample III shown in Fig. 7 are tested. Both of the items are commonly used in security inspection applications, which can’t be seen in visible wavelength range as shown in Figs. 7(a1) and 7(a2). The imaging field of view is 80 ${\times} $ 80 mm2 for the key, and 120 ${\times} $ 80 mm2 for the scissor. Compared with the proposed system, the image of the conventional system is degraded by the scattering with lots of reconstruction artefacts. Moreover, some parts are not reconstructed correctly, such as the key head and the scissor handle.
4. Discussion
Compared with the conventional system, the proposed confocal THZ SAR imaging system is more robust to the scattering introduced by the rough occlusion. Both spatial resolution and reconstruction SNR are improved significantly with the design. However, there are still following limitations. The system works well for the fixed occlusion occasion with high scattering but the reconstruction quality will reduce due to speckles when the non-uniform rough occlusion moves with the target. It is caused by the effect of stochastic rough surface [28], as the phase of THz wave will be disturbed irregularly with large variance of scattering angles.
Fortunately, for most applications of THz imaging, the texture is common then can be usually regarded as a rough surface with uniform distribution. On the other hand, the speckle effect can be mitigated by dithering the occlusion or scanning the illumination source. And then the proposed method can be applicable.
To verify the above idea, the following test of imaging through a specific uniform rough surface is implemented. The rough surface developed with 3D printing consists of regular slopes with both width and height to be 1 mm. The RMS and correlation length are 308 µm and 280 µm respectively, which is comparable with sample III. The sheet size is about 13 cm × 13 cm and the imaging field of view is 60 × 60 mm2. The sheet is pasted on a frame tightly to keep flat and the target is right behind the sheet. As shown in Fig. 8, the results obtained with the conventional system are very blurry due to the scattering. In contrast, the edges of the plate by the proposed system are much clearer, even with high roughness. The results obtained by the proposed system also have higher resolution and SNR than the results without occlusions by the conventional system. Because of the uniform distribution of the roughness, there are almost no speckles in the figure. To evaluate the imaging quality quantitatively, the 20 × 20 pixels indicated by the red square are used to calculate the resolution with knife edge method. For the three cases, the resolutions are 1.5 mm, 5.65 mm and 2.9 mm, respectively.
Fig. 8. Reconstruction results of a plate hidden by the media with uniformly rough surface. (a) The CAD model of the uniform rough surface. The slopes are regularly ranked with width and height of both 1 mm. (b) Front view. The sheet is pasted on a plastic frame and keep flat. (c) Side view. The object plate is hidden right behind the occlusion, and both installed on the scanner. (d) Proposed system (e) Conventional system (f) Conventional system without occlusion. Scale bar:1 cm.
Furthermore, the case of a curved occlusion is investigated. In the experiment, the occlusion sheet is not totally flat, so the scanning focal plane is not conjugated to the scattering plane. Such condition is quite common in practical security inspections since parts of the clothing are always curved. The imaging field of view in this experiment is 80 × 80 mm2. As shown in Fig. 9(c), the image reconstructed from the conventional method is severely distorted. In contrast, there are almost no artefacts in the reconstructed images with proposed method owing to the wavefront-shaping process in temporal domain which can correct the tilting phase introduced by the curved plane.
Fig. 9. Reconstruction results of a plate hidden by a curved uniform rough surface. (a) Side view. The sheet is not totally flat. (b) Results obtained by the proposed system (c) Results obtained by the conventional system. Scale bar:1 cm.
5. Conclusion
In summary, a confocal THz SAR imaging technique is proposed to deal with the high scattering introduced by rough surfaces in THz imaging. With a simple convex lens introduced into the conventional system, the confocal system leads to both enhanced SNR and resolution. Inspired by the confocal NLOS imaging in visible wavelength, the scattering process in THz imaging can be modelled as random phase delays in temporal domain at different spatial points. Such phase aberration can be corrected easily in the confocal setup with simple shift operation at each point in spatial domain during pre-processing. Experiments with occlusions of different roughness are implemented and the proposed method outperforms the conventional method in terms of reconstruction accuracy, SNR, and resolution.
The proposed method paves the way to various applications including radar imaging through radome, security imaging through clothing, and medical imaging through gauze, etc. In the future, the work on more complicated models with multiple scattering, strong speckles, or large loss for different practical applications would be explored.
Funding
National Natural Science Foundation of China (61575103, 61675111, 61927804); National Key Research and Development Program of China (2016YFC0801200).
Disclosures
The authors declare no conflicts of interest.
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