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Abstract
We demonstrate a bar code sensing system for the THz region using leaky parallel plate waveguide and an off-axis parabolic mirror. The bars of the bar code are made from metal with air as gaps between them. We use up to 6 bars in the barcode system which can store up to 64 bits. Because the system employs coherent detection, we can further increase the bit density by adding Teflon strips to the barcode, encoding information in both amplitude and phase delay. These bar codes can be manufactured easily and inexpensively, offering a versatile alternative to RFID tags.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The Internet of Things (IoT) promises to connect many devices together in an intricate network of physical objects and virtual machines. At the core of this network, identification technologies are crucial components to allow the automatic recognition and metadata collection of target objects [1]. In recent years, identification techniques have progressed tremendously in that regard. The most widely used techniques include barcodes [2] and quick response (QR) codes [3] that can be used in the visible range with cameras. Here, one key challenge is information leakage in which anyone with a camera can access the code and obtain the information.
Another important class of technique is the radio-frequency identification (RFID) that uses electromagnetic waves in the radio and microwave band [4]. Two types of RFID tags exist: active chipped RFID tags with an integrated source of energy (e.g., battery), and passive chipless RFID tags that use the energy of the interrogating wave [5]. Active RFID tags can store more information, are more secure and have wider range, but they are also expensive compared to other techniques. Passive RFID tags are inexpensive, but they can only store little data, and their size is limited by the size of a rf antenna, which scales with the wavelength.
In the meantime, the terahertz spectrum (0.1–10 THz) has recently been subject to increased interest for applications in wireless communications [6–10]. THz communication systems promise ultra-high speed data transmission thanks to the large available bandwidths at higher carrier frequencies, that may incorporate the IoTs.
In that regard, there are few works in the literature that uses the THz region for tag identification purposes. Due to the inherent challenges of THz generation, with few exceptions [11], the THz tags discussed in the literature are all passive. They can be categorized in two groups. One category is raster scan identification [12–15] in which one scans a code from beginning to end using a moving beam. Raster scan identification techniques cannot be employed in wider use as a small beam size (∼ 1 mm) and precision positioning are required.
The second category of THz tags use single shot identification [11,16–19] in which a code is scanned rapidly. To our knowledge, almost all the single shot THIDs can be further classified as passive volume THIDs. That means the information is stored into a volume of the tag instead of the surface. Also, all of them have used some form of absorption spectra to identify the codes.
In this work, we introduce a novel type of THz passive tag that can be secure, cheap, easy to manufacture and easy to handle. This THID is similar in form to an optical barcode, in the sense that a discrete set of reflecting and non-reflecting regions produce a recognizable signature. In order to produce a large contrast between these regions, our first example THz barcodes are made of bulk metal strips. However, we also demonstrate that these metallic regions can be formed using a conventional printer and laminator, a rapid and inexpensive fabrication procedure.
In this paper, we use an experimental configuration of the leaky-wave transceiver similar to our previous work [20], in which a broadband THz pulse is spectrally spread in space (in the form of a rainbow), and the leaky-wave antenna is used both to broadcast the outgoing wave and to receive the back-reflected signals. We first describe this leaky-wave THz barcode detection system and the detection algorithm. Then we describe several different types of bar code structures, to produce both amplitude and phase variations on the detected signal. Finally, we consider improvements of the THz bar code reader to further increase its bit density, security and robustness.
2. THz barcode reader
For the THz barcode detection system, we use a leaky waveguide radar system introduced in [20]. By opening a narrow rectangular slot in one plate of a parallel plate waveguide (PPWG), we allow the guided THz wave to leak energy into free space, or to receive energy from free space. This type of antenna has recently been demonstrated for various communication applications in the THz range, including frequency-division multiplexing [21,22], link discovery [23] and radar and object tracking [20,24–26]. The frequency dependence of the emitted radiation pattern originates from the phase-matching constraint between the guided mode and the free space mode. For the lowest-order transverse-electric (TE1) mode of a PPWG filled with air, the frequency-dependent propagation constant is given by [27]
Fig. 1. (a) Schematic diagram of the experimental arrangement, view from above. (Here, the electric field polarization is normal to the view). (b) Photograph of the THz barcode with the code (111111)
The experiments are carried out using a fiber-coupled THz time-domain-spectroscopy (TDS) system. The input Gaussian beam is vertically (z) polarized in order to excite the TE1 mode in the PPWG. Two confocal polyethylene lenses are used to form the input beam to a size of 1 cm at the tapered waveguide input [29]. A tapered input is used to focus the incoming beam in order to improve the coupling and increase the SNR. In all of our measurements, the slot width is chosen to be 2 mm. This is large enough to ensure that nearly all of the energy contained in the TE1 guided mode underneath the slot is radiated out of the waveguide within a relatively short propagation distance (not more than a few mm) [28]. In other words, the radiation emerging from the PPWG is not emitted along a distributed region defined by the entire 2 cm slot length; rather, most of it emerges from a relatively small (wavelength-scale) region at the beginning of the slot. As a result, the positioning of the off-axis parabola is reasonably well defined, as the focus of the parabola can be situated at the center of this small emission region. In order to have a high SNR, the barcode is kept close to the parabolic mirror. To collect the retro-reflected beam out of the waveguide, we used a beam splitter made of a high resistivity silicon slab (5 mm thick) to divert the beam to a perpendicular path where it is focused in the THz receiver.
Figure 1(b) shows an example of barcode that we have used in our experiment. Here, we use metal pins as bars for the barcode, providing a strong reflection signal. Since this realization of a bar code effectively produces a digital signal (either there is a reflection, or not), we interpret each bar as representing one digital bit. In this example, each pin is separated by constant distance of 4 mm. Hence the bar code shown in Fig. 1(b) represent the identification code (111111) (i.e., all six pins are present).The non-uniform width of the bars (getting wider from left to right) compensates for the nonuniform power distribution in the spectrum, which results from the characteristic spectrum of our TDS system, and also because of higher signal diffraction at lower frequencies.
3. THz barcode decoding algorithm
3.1 Four amplitude bars
We now present the algorithm we use to decode the barcode from the measurements. To illustrate this concept, we use up to 4 metallic pins in the THz beam path to generate a ${2^4} = 16$-bit encoding scheme. As described above, if there is a metal surface in front of the beam path, the THz radiation at that position is retroreflected. In our encoding, this corresponds to a bit of 1, while a 0 indicates the absence of a reflection.
To decode the measured signal, we use a strategy based on the measurement obtained in the time domain. First, we denoise these signals using an empirical Bayesian method with Cauchy prior [30,31]. The measurements are then written as vectors $\vec{y}$ of length ${N_t}$ where ${N_t}$ is the number of points measured in the time domain (in our case ${N_t} = 1800$ for a time window of 140 ps). We consider that any measurement is a linear combination of the 4 elementary bit patterns ({1000}, {0100}, {0010}, {0001}). Their time domain waveforms are shown in Fig. 2(a). As can be seen from the corresponding spectra in Fig. 2(b) (and as expected from Eq. (2)), the four elementary vectors have unique frequency peaks. However, these peaks become broader as the frequency increases, which is a consequence of the fact that Eq. (2) is nonlinear with respect to angle. Consequently, when there is more than one bar present, the different peaks cannot be easily distinguished, and an approach based on the frequency domain signals does not work well. Moreover, as we show below, we can take advantage of the time-domain processing to encode more information and increase the bit density.
Fig. 2. (a) Windowed time domain signals of all the elementary signals. (b) Corresponding frequency spectrums for time signals from Fig. 1(a). (c) Original time domain signal (dashed black) for the pattern 1010 and its reconstructed signal form the algorithm (red). (d) target of all combinations of code with 4 bars (white represents zero and black represents one). (e) Heatmap of the decoded signals. The grey scale indicates the magnitude of the elements of the recovered vector, for comparison with the target values illustrated in (d).
From the measurements of the four elementary vectors ({1000}, {0100}, {0010}, {0001}), we construct a matrix C of dimensions ${N_t} \times 4$. Then, any measurement $\vec{y}$ can be written as a linear combination of these 4 vectors:
where $\vec{x}$ is a vector corresponding to the 4 coefficients of the linear combination. To solve for $\vec{x}$ in Eq. (3), we rewrite the problem as and find $\vec{x}$ that minimizes the left-hand side in a least-squares sense: where the second-order Euclidean norm is used. Ideally, the $\vec{x}$ coefficients$\; $in (Eq. (5)) should be either zero (absent) or one (present). But in reality, because of noise in the measurement, the value of $\vec{x}$ coefficients vary from zero to one. Figure 2(c) shows an example of decoding. A measurement of the bit pattern 1010 is shown as a black curve. We use (Eq. (5)) to find $\vec{x} = [{0.941,\; 0.133,\; 0.955,\; 0.0103} ]$. To compare our extracted result to the raw measurement, we can reconstruct the initial time-domain waveform $\vec{y}$ using the product $C\vec{x}$ (red curve in Fig. 2(c)). We define the error in reconstruction asIn this example, the error is 0.0537 and results in a good agreement between the measurement and our decoding. We test the validity of our approach by measuring the complete set of 16-bit patterns that can be generated with 4 pins. Figure 2(d) shows the 16 target bits, while Fig. 2(e) shows the reconstructed coefficients from $\vec{x}$. In all cases, the error is less than 0.065, with one exception: the error is greater for the special case of {0000}, because there is only noise for that signal (so the denominator in (Eq. (6)) is small). In this case of four bars, to correctly identify the bits, we set the decision threshold at 0.85 for the ceiling and 0.15 for the floor, meaning that the algorithm infers that the bit is a 1 only when the value of the corresponding coefficient is greater than 0.85 and a zero when value is less than 0.15. With this approach, we can identify the 16 different bits with an accuracy of 100%. We also measure the average error for all the combinations to be 0.045.
3.2 Six amplitude bars
We now turn to increasing the bit density by using 6 bars in the THz path, thus leading to an encoding scheme of ${2^6} = 64$-bits. For that purpose, we decrease the width of the bars as well as the space between them. Following a similar approach as discussed above, we create a basis matrix C formed of the 6 elementary bit patterns: {(100000), (010000), (001000), (000100), (000010), (000001)} shown in time domain in Fig. 3(a).
Fig. 3. (a) Windowed time domain signals of all the elementary signals. (b) target of some of the complex combinations of code with 6 bars (white represents zero and black represents one). (c) Heatmap of the decoded signal for the particular combination in Fig. 3(b), as in Fig. 2(e). (d) Orthogonality matrix for 4 bars. (e) Orthogonality matrix for 6 bars.
To certify the validity of the decoding process in this case, we decode complex combinations of 6 bars using Eq. (5). Figure 3(b) shows the target bit patterns while Fig. 3(c) shows the reconstructed coefficients. Compared to the case of 4 bars, the errors for 6 bars are larger, which is a manifestation of the fact that different elementary vectors are “less” orthogonal with each other. Indeed, our decoding algorithm works best if the elementary vectors form an orthogonal set, i.e., ${\vec{c}_i} \cdot {\vec{c}_j} = 0$ for $i \ne j$ where i and j correspond to any two vectors of the elementary set. In Fig. 3(d), we plot the orthogonality matrix where the matrix element ${a_{i,j}}$ correspond to the scalar product of any two vectors ${\vec{c}_i}$ and ${\vec{c}_j}$ of the matrix $C$: ${a_{i,j}} = {\vec{c}_i} \cdot {\vec{c}_j}$. We compute this for both the cases of 4 bars and 6 bars. In a true orthogonal set of vectors, the average of the off diagonal of this matrix would yield 0. Here, we obtain a value of -0.016 for the case of 4 bars, and -0.19 for 6 bars, meaning that the orthogonality is less respected for the case of 6 bars compared to 4 bars. Indeed, our decoding algorithm works best if the elementary vectors form an orthogonal set, i.e., ${\vec{c}_i} \cdot {\vec{c}_j} = 0$ for $i \ne j$ where i and j correspond to any two vectors of the elementary set. This implies that their waveforms do not overlap in time domain. Nevertheless, for 6 bars, we can still decode the tested bit patterns with 100% accuracy using a decision threshold of 0.75 for the ceiling and 0.25 for the floor. We see that the space between the threshold values shrinks from 0.7 to 0.5, a reflection of the reduced orthogonality of the basis set. The average of the error for the combinations shown in Fig. 3(c) is 0.103.
3.3 Four phase bars
As mentioned above, our decoding algorithm performs best when the temporal traces of the elementary bits are orthogonal, as assessed by the orthogonality matrix. Another way to evaluate the performance of the set of elementary bits is to look at the spectrogram. In Fig. 4(a) and Fig. 4(b), we plot the sum of the spectrograms of the elementary bits (in power) for the case of 4 and 6 amplitude bars respectively. These graphs were obtained using a short-time Fourier transform of the temporal traces. They reveal the spectral content as a function of time. Both spectrograms show an inverse relationship between time and frequency with a cutoff frequency at 150 GHz. This is a signature of the dispersion of the parallel-plate waveguide with a 1 mm plate separation, excited in the lowest-order TE mode. We also plot the contour maps of the individual elementary bits. As one can see, the elementary bits are well separated in the spectrogram for 4 amplitude bars, while they are more tightly packed for 6 amplitude bars.
Fig. 4. (a) Spectrogram of the individual elementary patterns graphed together for 4 amplitude bars. (b) Spectrogram of the individual elementary patterns graphed together for 6 amplitude bars. (c) Spectrogram of the individual elementary patterns graphed together for 4 phase bars.
The spectrograms also suggest an additional strategy to pack more information in the bit patterns. By using bits which exploit both amplitude and phase, we can shift some of the bits in the time domain. We realize this experimentally by using 5-mm thick Teflon (PTFE) pads attached to one or more of the metal bars shown in Fig. 1(b). Due to the increased optical path, the pulses returning from these bars arrive at a later time $\mathrm{\Delta }t = ({n - 1} )\; 2d/c$, where d is the Teflon pad thickness and n is its refractive index (which is virtually constant at 1.434 in the relevant spectral range [32]). Consequently, these phase bits introduce ∼23 ps delay, without otherwise significantly altering the signals. It is worth noting that the Fresnel reflection from the Teflon material is small (∼3% in power assuming normal incidence), thus we do not observe a reflection at the air/Teflon interface in the time domain traces. However, if one were to use a material with a larger refractive index, this reflection would have to be taken into account when designing the decoding algorithm. Therefore, each bar can now store 3 levels of information: 0 is without any bar, 1 is with a metal bar and 2 is with a metal bar and a Teflon pad. With these 3 levels for each of the 4 bars, we now have ${3^4} = 81$ possible bit patterns. Figure 4(c) shows the sum of the spectrograms of the elementary bits for the case of 4 phase bits. Compared to the pure amplitude bits, one can see that the phase bits are distributed over a wider area in the spectrogram, which offers a greater range of possibilities for information storage and retrieval.
Using the same algorithm as discussed earlier, we now decipher these amplitude / phase bit patterns. Figure 5(a) shows a photograph of the bar code for the case {2222}, corresponding to all 4 metal bars covered by Teflon pads. In Fig. 5(b), the temporal traces of a pure amplitude bit (4 metal bars, 0001) and the corresponding phase bit (4 bars and Teflon strips, 0002) are shown; their frequency spectra are shown in Fig. 5(c). While their spectra are quite similar, the signals can be clearly distinguished in the time domain. This is also confirmed by computing the orthogonality matrix between the different elementary bits (Fig. 5(d)). We find that the average of the off-diagonal elements is now -0.22, which is close to the case of 6 amplitude-only bits. Finally, we demonstrate that our analysis can successfully decode some of the most complicated bit patterns. Figure 5(e) shows the target reconstruction while Fig. 5(f) shows the results of our decoding. The average error calculated for the combinations shown in Fig. 5 (f) is 0.092, slightly lower than the case shown in Fig. 3.
Fig. 5. (a) Photo of the barcode with 4 bars present with the Teflon bars. b) Comparison between two time domain signals for bit patterns 0001 and 0002. (c) Corresponding frequency spectra for time signals from (b). (d) Orthogonality matrix of the base vectors. (e) target of some of the complex combinations of code with 6 bars. (f) Heatmap of the decoded signal for the particular combination in (e) (Here, zero {0} represent {00}, only metal bar {1} represents {10} and metal bar with Teflon bar {2} represent {01}).
4. Discussion
In our measurements, the barcode was kept at a constant distance from the parabolic mirror throughout the experiment. Because of the approximate collimation of the beam after the parabolic mirror, we are able to detect similar time-domain waveforms when this location is changed; however, the system is sensitive to some misalignment which affects the propagation direction of the retro-reflected beam. Advanced machine learning methods could be used to improve the detection sensitivity in order to make the system more robust against such misalignment errors. In addition, one could use a single bar as an alignment marker, against which the other bars could be calibrated. This procedure would also improve the system robustness, at the cost of decreased information capacity.
We also note that, in our experiment we use metal pins as bars. However, other more low-profile and light-weight alternatives are also possible. For example, one could use a hot stamping technique [33] to create the bar code by patterning thin metal layers directly on paper with a conventional printer. After printing a pattern on normal paper, one could even flip the paper over, so the barcode is not visible to the naked eye from the point of view of the incident THz beam. We have verified that this approach works just as well as the bulk metal bar codes discussed above. This suggests the possibility of covert tagging and information storage, as well as the ability to rapidly and inexpensively produce customized bar codes in volume.
5. Conclusions
We have implemented a novel bar code system for the THz region using a leaky parallel plate waveguide. The bars of the bar code are made from metal pins with air as gaps between them. We demonstrate the effectiveness of this approach using 4 bars (to provide 16 bits of information) and 6 bars, which can store up to 64 bits. Because the system employs coherent detection of the THz field, we can also encode data using the phase, in addition to the amplitude, of the signal. This enables us to increase the bit density even further. Finally, we demonstrate that this bar code can be manufactured easily from paper with metal laminating, providing a route for inexpensive and rapid prototyping.
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.
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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