1. Introduction

In recent years many studies exploited the potential of millimeter wave technology for security imaging, in particular for personnel screening. The technological endeavors in this field are motivated by unique advantages of the so called terahertz range: Many covering materials such as textiles are transmittive in the upper gigahertz (GHz) or lower terahertz (THz) band [1, 2, 3, 4]. Additionally, imaging resolutions of the order of 1 mm can be achieved, and finally, the radiation is understood to cause no genotoxic health risks [5, 6], which makes it suitable for instance for passenger screening. A variety of different techniques were developed, some of which intend to identify hidden materials by their spectral properties [7, 8, 9, 10], while others measure the reflected radiation either of coherent illumination [11, 12, 13] or of ambient far infrared light [14, 15]. However, many approaches have to cope with conceptual difficulties, such as the vast number of spectrally similar materials, signal corruptions by atmospheric influences, or ambiguities of the image introduced by absorption in covering materials. These metrological challenges frequently sidetrack the attention from the ultimate question in security imaging, namely whether or not an object is present behind an opaque barrier.

Far infrared imaging of the vibrational properties of objects can provide decisive information for answering this question. Recently, we have presented the fundamental physics of a measurement scheme, which detects the presence of concealed objects, by imaging the phase of their acoustic vibrations [16]. Similar conclusions were drawn by Chen and Kaushik [17] in an independent work, published at the same time. In this Letter we present an experimental study proving the applicability of the technique.

2. Experimental method

The basic idea behind imaging the acoustic phase is that mechanically coupled objects in general respond to a driving force with different phase lags. In the context of a future application this means that an object carried underneath a textile responds with a different phase lag than the body to which the object is coupled mechanically. In consequence, imaging the acoustic phase reveals a contrast between object and body, which allows for locating the object.

We discussed the fundamental properties of imaging acoustic phases with THz radiation in Ref. [16]. In the experiments described here, we use a non-commercial GHz transceiver based on a voltage controlled oscillator and a frequency mixer circuit. This approach has the advantage that the same horn antenna is used for emission and detection (Fig. 1). The frequency of the transceiver can be tuned in the range of 69–78 GHz, providing typical emission powers of about 10 mW. The output voltage of the transceiver is proportional to the homodyne mixing signal.

In our experiments we fixed several metallic and dielectric items (labeled ”Object 1” in Fig. 1) with a Velcro-type hook and loop tape to the front side of a board (labeled ”Object 2”). This board serves as a reference for the acoustic phase measurements. It consists of a 1 cm thick wood panel topped with a 0.8 cm layer of neoprene. The board is wrapped in natural leather, which is kept moist in order to achieve a realistic reflectivity in the far-infrared, even though the exact amount of reflected radiation is irrelevant for acoustic phase measurements. Acoustic vibrations are launched from the backside into the board using a loudspeaker operated at frequencies between 15–80 Hz. In consequence, both the board as well as ”Object 1” performs a driven vibration. In our experiments the vibration amplitudes of the test objects are typically in the range of D_acoust = 0.07–10 μm.

 

Fig. 1. Schematic of the setup used for spatially resolved phase measurements employing homodyne detection.

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The acoustic phase lag of an object’s oscillation, driven at an angular frequency ω is

where m is the object’s mass, k is the elastic coupling constant between the object and the drive, and γ is the damping. Thus, even under strong damping (large γ) and a negligible elastic coupling (vanishing k) a nonzero phase lag will be observed. As outlined in Ref. [16] the acoustic phase of the objects can be measured by homodyne mixing of the electromagnetic radiation reflected from the objects. As it is known from interference phenomena, such mixing signals depend on the path length. Hence, if the reflecting object oscillates, this results in a modulation of the detected signal. The phase of this oscillation is extracted using a lock-in amplifier referenced to the drive signal. We distinguish between the actual acoustic phase ϕ_ac and the measured phase Φ_meas, as detected by the lock-in amplifier [16 ]:

where Δ_z stands for the optical path length minus an odd multiple of λ_GHz/4.

Most remarkable about Eq. (2) is that the measured phase relates to the acoustic phase in a two-valued manner, which depends exclusively on the distance between emitter and object. Two further properties of acoustic phase imaging are worth mentioning: The measured phase does neither depend on the oscillation amplitude nor on the intensity of the detected radiation. Both properties make the technique very robust against corruptions of the signal.

 

Fig. 2. Interferogram (a), the measured acoustic phase (b) depending on changes of the optical path length, and the acoustic phase (c) calculated by equating ϕ_calc = mod(Φ_meas + π,π). The oscillation amplitude for the phase measurement was about 750 nm.

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3. Results

The two-valued behavior is verified in experiments that are performed just on the vibrating board (”Object 2”) in dependence of the optical path length. Figure 2 shows an interferogram of the detected intensity (a), the measured phase (b) as well as the calculated acoustic phase (c) depending on the distance between transceiver and object. The interferogram shows the expected oscillations with maxima when the distance equals $\frac{2n+1}{4}{\lambda }_{\mathrm{GHz}}$. Whenever the spatial slope of the interferogram (a) is positive, a small modulation of the optical path length has a phase ϕ_ac while for negative slopes one detects ϕ_ac - π. Accordingly, the measured phase jumps by 180° whenever the intensity of the mixing signal exhibits an extremum as discussed in more detail in [16].

In the following, we show that concealed objects can be located by spatially resolved detection of the acoustic phase. For this experiments we use different items as ”Object 1”: i) an aluminum plate, ii) a cell phone, iii) a chocolate bar, iv) a piece of soap, and v) a 1 cm thick slice of Bavarian spam-meat (”Leberkäse”). All objects were attached to the plate using hook-and-loop tape, thus oscillating with equal frequency but different phase, depending on their individual mass, coupling, and damping, Eq. (1). The force of the fixation was sufficient in order to hold the items on the vertical back plate. In order to mimic random covering conditions in real world applications, all objects were at least covered with one textile layer of linen or wool.

The spatial resolution was achieved by scanning the objects in y-direction through the focus of the GHz-beam (Fig. 1). Figure 3 shows the phase contrasts for different items along with gray bars indicating their spatial extension. The drastic phase changes at the edges allow for locating the objects. In general the phase contrast exceeds 25°. The precise value however, rather depends on the individual coupling conditions of each object rather than on its material properties. The data recorded on chocolate and soap illustrate that not only metallic objects but also dielectrics can be detected. Additionally, we found that even multiple textile layers have no significant impact on locating the objects correctly.

There are three effects contributing to the measured phase in Fig. 3, namely i) the physical acoustic phase lag, Eq. (1), ii) the two-valued dependence of the measured phase on the optical path length, Eq. (2), and iii) the signal processing of the lock-in, which projects all phase values to a range between -180° and +180°. While effect i) is the quantity to be measured the other effects account for the deviations of some traces from the expected behavior. For instance the additional phase flip observed at the center of the cell phone position or in the chocolate pattern can be explained by ii), while in the case of the soap, the phase contrast exceeding 180° is the cumulated contribution of i) and ii). For the spam meat, we attribute the dramatic phase change at the second edge to contribution iii), while the phase structure in between is due to acoustic modes of this rather flexible material. Even though such flabby materials show complicated phase patterns, the data clearly indicate the presence of some object.

 

Fig. 3. Phase contrast of items coupled to a vibrating plate by hook-and-loop tape. For clarity all phase values are shifted. The objects were scanned across the focus of the GHz beam as depicted in Fig. 1. All objects were covered by textiles. The gray bars indicate the position of the respective items.

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In order to further investigate the applicability of the technique we performed an analysis of the measured noise. Figure 4 shows the noise of the phase measured on the leather wrapped back-plate in dependence on the oscillation amplitude. We deduce a nearly inverse proportionality between the noise and the vibration amplitude. As we stated above, the phase measurement is independent of the strength of the detected signal, i.e. independent of the GHz power, the reflectivity of the object, absorption in covering materials or the amplitude of the oscillation. However, the accuracy of the phase measurement is proportional to the modulation ampiltude and thus to the quantities mentioned before, which explains the scaling behavior illustrated in Fig. 4. For a realistic assessment of the noise level the measurement was performed through a linen towel, which turned out not to influence the accuracy of the measurement significantly.

4. Discussion

Several properties of acoustic phase imaging have to be analyzed for assessing the limitations of future applications. One is the spatial resolution that can be achieved. In our experiments using 70 GHz radiation we achieve a diffraction limited spatial resolution of about 1.2 cm, which roughly corresponds to 3λ. This resolution is certainly sufficient for detecting most objects of relevance. Another important property is the time required for recording a meaningful image, which can be estimated by an analysis of the measurement noise. In all cases shown in Fig. 3 the phase jumps exceed 25°. Therefore, a signal to noise ratio larger than 10 can be achieved as long as the phase noise is kept < 2.5°. For an oscillation amplitude of 3 μm such signal to noise ratios translate into an integration time of about $T_{\mathrm{int}}={\left(\frac{\frac{0.08°}{\sqrt{\mathrm{Hz}}}}{2.5°}\right)}^2$ ≈ 1 ms per pixel. Thus recording an image of about 200 × 200 pixels would take 0.4 s, if a 100 fold parallelization of the signal detection is assumed.

 

Fig. 4. Dependence of the phase noise on the oscillation amplitude of the back plate.

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One limitation of the technique arises, when the object moves with significant speed, which can lead to phase jumps of 180° during the integration time for a single pixel. For the conditions described here, more than 90% of all datapoints remain unaffected as long as the velocity is ≤ 0.1 m/s, [18]. Future developments will have to address this aspect. The application of acoustic phase imaging for personnel screening would require launching vibrations into the human body. The oscillation amplitudes discussed above are comparable to the physiological perception level, which is of the order of 1 μm [19]. However, acoustic vibrations are strongly damped along the human body. Typically, acoustic oscillations introduced by floor vibrations into the human body are attenuated at the shoulders to a few percent of the initial amplitude [20]. Altogether, we expect that reliable phase measurements are possible at floor oscillation amplitudes smaller than 100 μm. Such amplitudes are below the limits recommended by ISO 2631 for a 10 minute exposure of humans to vibrations [21].

5. Conclusions

In summary, we developed an experimental technique, which facilitates the detection of objects concealed under textile layers. It turns out that sensing the acoustic phase is extremely robust and insensitive to signal corruptions. We found that for realistic conditions, oscillation amplitudes of 3 μm are sufficient for detecting the acoustic phase of a concealed object. Such amplitudes are physiologically inoffensive and close to the human perception level. Experiments were performed on concealed items such as cellular phones, metal objects, and also on dielectric materials such as chocolate or soap. All items were successfully detected even when concealed by several layers of textiles. Further developments of the technique toward applications in security imaging appear reasonable.