## Abstract

We demonstrate a 2D radar system for the THz region using a leaky parallel-plate waveguide, which can support real-time object tracking. The system can track a target within 200 ms with an accuracy of 1 mm in range and 1.4° in angle. Because the system is based on broadband excitation, it can locate multiple objects simultaneously. The broadband excitation also enables sensing of objects for which there is no direct line-of-sight path to the waveguide, via detection of a non-line-of-sight path.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Commercial radars typically operate at frequencies ranging from 0.1 GHz to 100 GHz. The development of radar systems at higher frequencies is motivated by the performance improvements that can be achieved. Both range resolution and cross-range (angular) resolution can be improved by increasing the frequency. These THz radar systems also can have smaller aperture sizes, and therefore a smaller form factor. Therefore, there has been growing interest in radar systems that operate in the terahertz (THz) range, above 100 GHz. One key challenge is the attenuation of a received signal back-scattered from a target, as a result of increased free-space path loss at higher frequencies. This effect, in addition to increased atmospheric absorption, will ultimately limit the range over which such radar systems could be employed. Nevertheless, many of the envisioned applications do not require long range, and instead would benefit tremendously from improvements in the location accuracy that result from the use of higher frequencies. These advantages have spurred discussions of THz radar applications in many areas, including the automotive industry [1,2], security screening [3,4], health monitoring [5–7] and numerous other examples [8–13].

In this paper, we describe a radar system based on the excitation of a leaky waveguide with broadband THz pulses. The characteristic frequency-dependent emission of radiation from a leaky parallel-plate waveguide (PPWG) has been exploited in THz communication systems for frequency division multiplexing and demultiplexing [14,15]. Using a similar concept, a radar system for the THz region has recently been introduced [16,17]. In this work, a narrowband swept-frequency source was employed to scan the field of view of the radar, extracting information from the back-scattered signals using coherence tomography. In this approach, the object location is derived through inverse Fourier transform of the frequency spectrum. As a result, the range resolution (time of flight) and cross range resolution (frequency) are entangled. An alternative approach is to employ a broadband (low-coherence) source [18] which can be measured with high (sub-cycle) temporal resolution, such as the signals generated by a THz time-domain spectrometer. In this case, the range and cross-range information can be obtained independently from each other, using a time-windowed Fourier transform. We show experimentally that this method can be used to rapidly locate individual objects or multiple objects within the radar’s field of view, with the minimum resolvable distance between them dependent on the pulse dispersion [19]. We also demonstrate the detection of a hidden object, via a non-line-of-sight signal path, a possibility which relies on the broadband capabilities of the transceivers.

The operating principle of our object detection system can be described as follows. By opening a slot in one plate of a PPWG, we can allow the guided THz wave to leak energy into free space, or to receive energy from free space. The frequency dependence of the emitted radiation pattern originates from the phase-matching requirement for the coupling between the guided mode and free space. For the lowest-order transverse-electric (TE_{1}) mode of a PPWG, the frequency-dependent propagation constant is given by [20]

*c*is the vacuum light velocity,

*b*is the plate separation,

*f*is the operating frequency, and ${k_0}$ is the wave-vector in free space, ${k_0}$= $2{\pi }f/c$. Radiation can couple from the guided mode to free space, or vice versa, provided the phase matching condition ${k_0}cos\varphi = {k_{PPWG}}$ is satisfied. Here, $\varphi $ is the propagation angle of the free-space wave relative to the PPWG’s propagation axis (so $\varphi = 0$ corresponds to the direction parallel to

*k*). Because of the frequency dependence of ${k_{PPWG}}$, this condition results in an angle-dependent emission frequency from the slot, given by Since the THz pulse propagating in the PPWG consists of a broad frequency spectrum (0.1 THz – 3 THz), the leaked energy spreads out in a fan-like beam. According to Eq. (2), high frequencies have lower emission angles, while low frequencies have higher emission angles. If this fan interacts with a target, part of the energy can retro-reflect along the same path and couple back into the same (but reversed) guided mode though the slot. This recoupled signal emerges back out of the input end of the waveguide, and can then be detected. The frequency of this retro-reflected signal is determined by the angular position ($\varphi $) of the target from which it was reflected, while its time-of-flight delay encodes the target’s range information (

_{PPWG}*R*).

## 2. Experimental setup

A schematic of the experimental arrangement is shown in Fig. 1(a). We use a stainless steel PPWG with a tapered input, similar to a one-dimensional version of a horn antenna, to optimize the efficiency of input coupling [21]. The curvature of the taper is sufficiently smooth so as to avoid exciting higher-order modes in the waveguide. A vertical Teflon cylindrical lens inserted into the flared end of the waveguide further improves this coupling. In the straight (non-tapered) section of the PPWG, we use a plate spacing of 1 mm (which imposes a cutoff frequency of *f*_{c}∼150 GHz for the TE_{1} mode). A larger plate spacing would diminish the angular variation per frequency [from Eq. (2)] which would decrease the angular resolution. A smaller spacing would shift the cutoff frequency of the TE_{1} mode to higher frequencies, limiting the usable THz bandwidth and also reducing the coupling efficiency into the waveguide. We note that Eq. (2) is strictly valid only in the limit that the top waveguide plate (the one with the slot) has zero thickness. We have determined that a plate thickness of 1 mm results in only a small deviation from the theoretical radiation pattern predicted by Eq. (2) [14,22]. In all of our measurements, the slot width is chosen to be 2 mm [shown in Fig. 1(b)]. This is large enough to ensure that nearly all of the energy contained in the TE_{1} guided mode underneath the slot is radiated out of the waveguide within a relatively short propagation distance (not more than a few mm). In other words, the radiation emerging from the PPWG is not emitted along a distributed region defined by the entire 2 cm slot length, but rather emerges from a relatively small (wavelength-scale) region at the beginning of the slot. This high emission rate is a somewhat unusual regime for typical leaky waveguides [23]. However, it is important for the radar operation, as it provides a reasonably well-defined location for coupling between the slot and free space, which reduces the error in both range and angle measurements. A second cylindrical Teflon lens is pressed against the upper waveguide plate, parallel to the slot, to facilitate the formation of a sheet-like fan of radiation in the plane of the slot, as well as optimize the recoupling of back-scattered radiation from a target back into the waveguide.

The experiments are carried out using a fiber-coupled THz time-domain-spectroscopy system. The input Gaussian beam is vertically (*z*) polarized in order to excite the TE_{1} mode in the PPWG. Two confocal polyethylene lenses were used to form the input beam to a size of 1 cm at the tapered waveguide input. To collect the beam emerging back out of the waveguide, we used a high resistivity Si slab (5 mm thick) as a beam splitter to divert this reflected beam from the original optical path to a perpendicular path where it is focused onto the THz receiver.

## 3. Signal processing

Real-time signal processing is required to track an object with high accuracy at high rate. We have therefore developed a signal processing protocol which is relatively straightforward, and could be implemented in real time, for example with a high-speed FPGA. The first issue concerns background subtraction. In the detected time domain signal, we observe a pulse reflected from the waveguide’s input facet due to the small but unavoidable coupling mismatch. This signal is a small replica of the generated time-domain waveform, consisting of an approximately single-cycle pulse followed by persistent low-amplitude ringing which results from the characteristic electrical and optical response of the THz-TDS system. This ringing is quite small, and usually has little impact on TDS measurements. However, it can give rise to fluctuations in the measured signal which persist for hundreds of picoseconds after the main single-cycle pulse. In our measurements, these fluctuations are superposed coherently on the back-reflected radar signal, which can have similar amplitude. Therefore, it is difficult to extract position information directly from the received signal. We therefore use a reference procedure, acquiring a waveform with no object in the field of view and using this to perform coherent background subtraction in the time domain. An example of the resulting background-subtracted waveform is shown in Fig. 2(a). The signal at ∼1450 ps is the signature of the back-reflection from an object placed in the leaky waveguide’s field of view. The smaller signal at ∼1550 ps is a replica of the same signal, which results from the fact that the input waveform has an echo at a delay of ∼100 ps following the main pulse, due to the inherent system response.

As the next step, we apply a windowed FFT to these time-domain signals, using a moving window which has a tapered cosine profile (Tukey window). This generates a measure of the spectral content of the signal as a function of time delay, generally referred to as a short-time Fourier transform (STFT). First, we keep the length of the moving window constant at 27 ps, and slide the window from the beginning of the time scan to the end with a step size of 78 fs. At each step, we obtain the largest value of the spectrum which we define as Max-FFT. Because of the pulse broadening, the pulse width for higher frequencies can be as small as 20 ps (for, e.g., 477 GHz) and for lower frequencies can be as high as 100 ps (for 195 GHz) [this effect is illustrated in Fig. 4(a), below]. Therefore, in order to increase the accuracy, we modify the window length to accommodate the pulse broadening according to the frequency corresponding to the highest peak in the Max-FFT values by inspection. Then we repeat the time-windowed FFT with the optimized window length. A plot of the resulting Max-FFT value versus time delay is shown in Fig. 2(b), corresponding to the waveform shown in Fig. 2(a). The spectrum corresponding to the highest peak is shown in Fig. 2(c). After obtaining the frequency corresponding to the peak, we can use Eq. (2) to determine the angular position ($\varphi $) [Fig. 1(a)].

Additional signal processing is required to determine the range information [*R* in Fig. 1(a)], because of the group velocity dispersion experienced by the signals inside the waveguide. We can calibrate the effective one-way path length for signals inside the waveguide (${{\boldsymbol {s}}_{\boldsymbol {w}}}$), which is 18.5 mm in our experiment. (This is an effective value because of the tapered region of the waveguide.) When the pulse propagates along this path length, it broadens due to group velocity dispersion. The group velocity (${{\boldsymbol {v}}_{\boldsymbol {g}}}$) in the TE_{1} mode of a PPWG is given by [24]

*t*depends on frequency due to the range of angles for rays of different frequency propagating through this cylindrical lens. The path length inside the lens for different frequencies can be calculated using Snell’s law together with Eq. (2).

_{l}## 4. Experimental results

#### 4.1 Real-time object tracking

The time domain signal shown in Fig. 2(a) has a relatively high SNR because of the higher number of signal averages (an average of 10000 waveforms, which requires an averaging time of 100 seconds). An important question is by how much this value can be reduced, while maintaining an acceptable SNR. To demonstrate the possibility of real-time object tracking, we explore the accuracy of extracted angle and range values when the averaging time is reduced. Our target object is a cylindrical metallic rod with a 10 mm diameter, oriented vertically [i.e., perpendicular to the plane of the diagram shown in Fig. 1(a)]. This object is translated along a pre-defined triangular path using an xy-translation stage with a step size of 0.1 mm. At each step, we acquire one measurement, consisting of a time-domain waveform such as shown in Fig. 2(b), except with a reduced averaging time. Each of these waveforms is processed off-line, using the procedure described above.

The results are shown in Fig. 3, for the case where waveforms are averaged only 20 times (i.e., only 200** **ms of data acquisition per location point). The estimated range and angle are translated into an x-y position, and plotted (red dots) on top of the actual center location of the metal rod (blue line) in Fig. 3(a). We compute the angular and distance errors for each point, and plot these results as histograms in Figs. 3(b) and 3(c). The widths of these histograms are a reasonable measure for the measurement accuracy, which can be interpreted as the range and cross-range resolution of our radar system. Both error distributions are approximately symmetric and zero-mean, with variances of 1.38° and 1** **mm, respectively. Of course, a smaller object would produce less back-scattered signal, and could therefore require additional averaging to reach equivalent accuracy. Nevertheless, we conclude that real-time object tracking at a rate of 5** **Hz is feasible with this experimental configuration. Since the noise is limited by pulse-to-pulse amplitude fluctuations of the THz source, longer averaging time leads to narrower error histograms and improved resolution.

#### 4.2 Simultaneous multiple object detection

An interesting advantage of the use of broadband signals, which would be a much more challenging task for a narrowband radar system [16,17], is the possibility to simultaneously detect multiple objects within the field of view, each at a different angular location. To explore this, we assembled a test consisting of three different metal rods. The rods have diameters of 6 mm, 10 mm, and 16 mm, and each is located at a unique angle and range [as illustrated in Fig. 4(b)]. The detected time-domain signal corresponding to this static configuration is shown in Fig. 4(a). We used the same signal processing technique as before to process this signal, identifying three peaks using the STFT. We note that the waveform illustrates the importance of optimizing the window length when computing the time-windowed FFT; here, one can clearly see that the low-frequency (blue) signal [resulting from the object at largest angle, labeled “1” in Fig. 4(b)] is much more extended in the time domain when compared to the other two, as a result of the more pronounced dispersive effects for signals that are closer to the waveguide’s cutoff frequency. For this measurement, we optimize the window length for the highest value in Fig. 4(f) (located at a delay of about 1180 ps). The resulting spectra corresponding to the three peaks are shown in Figs. 4(c), 4(d), and 4(e). Evidently, this one waveform can be used to obtain both range and angle values for all three objects. We estimate that their ranges are 30.3 mm, 49.3 mm, and 56.3 mm (compared to actual ground-truth values of 30 mm, 49 mm, and 56 mm), while their estimated angular locations are 50.4°, 20.9°, and 31.5° (compared to actual angles of 50°, 21°, and 31°). In addition, we can also roughly estimate the relative object sizes based on the amplitude of the Max-FFT values. The three peak heights in Fig. 4(f) have a ratio of 6:10.3:18.6, which corresponds reasonably well to the ratio of object diameters, which is 6:10:16.

Another important note about these spectra involves the change in spectral bandwidth, which increases from lower frequencies [Fig. 4(c)] to higher frequencies [Fig. 4(d)]. Changes in the bandwidth can occur for several reasons, including the fact that the objects have different size and the nonlinear variation of the emission frequency with angle (Eq. (2); also see [14,15]). Yet, even with this bandwidth variation, we can always determine a particular angle for each object by extracting the frequency at which the measured spectrum peaks. This shows that, in sharp contrast with the performance of a traditional radar operating at a single frequency, even if the single-frequency beam width is large, the angular resolution afforded by our approach is not degraded.

#### 4.3 Object detection with no line of sight

One of the concerns pertaining to many THz applications is that they are unable to operate well unless there is a direct line-of-sight path for beam propagation [25]. However, the leaky-wave architecture offers the unique possibility of detecting and identifying non-line-of-sight signals through their distinct spectral signatures. Therefore, it is interesting to explore the possibility of non-line-of-sight radar. As a simple demonstration, we created the experimental setup shown in Fig. 5(a). Here, a passive reflector (mirror) is located within the field of view of the leaky-wave device. An object is situated at a location such that it can be illuminated by both a line-of-sight (blue dashed line) and a non-line-of-sight (red dashed line) path. These two signals emerge from (and recouple into) the waveguide at different angles, so they correspond to different frequency components of the broadband input. A measured waveform therefore contains two peaks [Fig. 5(d)]. Using the same signal processing protocol as before, we extract the Max-FFT values [Fig. 5(b)]. The difference in the time delay of the two signals in Fig. 5(b) (which is about 185 ps) corresponds well with the two-way difference in lengths of the two paths, estimated to be 52** **mm. We also see that the two signals have different spectral content, corresponding well to the different angles of emission for the two paths, which are 26**°** and 43.5**°**. We can then insert a wave blocker (in this case, a piece of Eccosorb rf-absorbing foam) to eliminate the line-of-sight path. The resulting waveform then contains only the non-line-of-sight signal [Fig. 5(e) and corresponding Max-FFT signal in Fig. 5(c)]. Here, the remaining signal has the same spectral content which is identical to the red part of the signal in Fig. 5(d) (both spectra peak at 365** **GHz). This demonstrates that the non-line-of-sight path is unaffected by the wave blocker that was inserted into the line-of-sight path. As in the demonstration shown in Fig. 3 above, real-time tracking of moving objects may also be feasible in this case. Thus, one can envision the detection and tracking of obscured objects using this non-line-of-sight radar capability. This ability to track moving hidden objects is unique among radar systems, and is complementary to recent demonstrations employing incoherently scattered light [26].

## 5. Conclusions

We have implemented a high-resolution object detection system using a leaky THz waveguide. The system can track a cylindrical object of 10** **mm diameter at a rate of 5** **Hz with an accuracy of 1** **mm in range and 1.4° in angle. With only 200** **ms of averaging time, the detection region for this proof-of-concept demonstration is 20° to 45° in angle (cross-range) and 10** **mm to 40** **mm in range. These ranges are both limited by the signal-to-noise ratio of our low-power measurement system, which offers the possibility for further optimization.

Although THz radar will have less range compared to millimeter-wave radar, the use of higher frequencies (and larger bandwidth) can improve the range and cross range resolution significantly. Due to the smaller wavelength, such devices can have a smaller form factor, which may make them more compatible with certain applications where size and weight are significant considerations. We have also demonstrated that we can detect multiple objects in a scene simultaneously, via a single waveform, which cannot be accomplished using a conventional narrowband swept-frequency approach. Finally, we also show that we can use this system to detect and track an object even if there is no direct line-of-sight path from the waveguide to the object, using an alternative specular non-line-of-sight path. This radar system may prove valuable in applications such as gesture sensing and health monitoring, where improved resolution is more important than an extended sensing range.

## Funding

National Science Foundation.

## Acknowledgments

This work has been supported in part by the US National Science Foundation.

## Disclosures

The authors declare no conflicts of interest.

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