We report on acoustic phase imaging of objects using terahertz radiation. The sensitivity of the technique is sufficient to detect objects at oscillation amplitudes down to about 300 nm. Such acoustic amplitudes are comparable to the human physiological perception level, which offers novel opportunities in security imaging.
© 2007 Optical Society of America
The development of terahertz (THz) technology [1, 2, 3] has indicated many applications for sensing concealed objects. Recent works on THz imaging include continuous wave (CW) techniques [4, 5] or quantum cascade lasers . The potential of passive imaging  and reflection imaging  is investigated for security applications, and many works use THz techniques for sensing illicit substances [9, 10]. However, these approaches are only sensitive to specific materials such as metals or few organic substances.
This paper presents the fundamental physics of an alternative approach, which is promising for detecting concealed objects due to its sensitivity to virtually all objects. Items are detected by forcing them to perform a minute acoustic oscillation and by imaging their acoustic phase with THz radiation. Objects are not identified by their specific optical properties because the technique provides no spectral information.
It exclusively answers the question whether or not an object is present, which is the most relevant information in many areas of application. The advantage of our technique is its sensitivity to every object with mass.
In the following section we discuss the fundamental properties of our approach and present two experimental methods for imaging the acoustic phase of driven vibrations. The experimental data shown in section 3 demonstrate that THz imaging provides the acoustic phase of an object even at submicron oscillation amplitudes. In section 4, we discuss the technique with respect to possible applications for security imaging.
Mechanically coupled objects respond to a driving acoustic vibration with a phase lag that is given by their masses, their individual coupling constants, and the damping of the system. The two objects illustrated in Fig. 1a) respond with oscillation amplitudes D 1,2 and acoustic phase ϕ 1,2. These quantities can be measured by detecting electromagnetic waves reflected from the surface of oscillating objects. It can be shown that the amplitudes are rather difficult to track in particular when the imaging radiation is subject to absorption in covering materials or when the optical signal is corrupted due to imaging aberrations in general. In contrast, the optical measurement of the acoustic phase is much more robust regarding optical absorption or imaging aberrations. Therefore, we exclusively focus on the spatial mapping of ϕ in order to sense the presence of objects by their phase lag.
Coherent imaging techniques provide access to the acoustic phase, as for example in optical holographic interferometry . For our purposes radiation wavelengths are suitable that penetrate covering materials while providing sufficient spatial resolution. These requirements are fulfilled by few-cycle THz radiation or CW radiation in the upper GHz range. Shorter wavelengths may be absorbed or Mie scattered by covering materials, while longer wavelengths may not allow for sufficient spatial resolution. In particular, radiation of about 100 GHz is advantageous, because it can be generated using commercially available GHz devices such as Gunn oscillators. In order to highlight fundamental properties of acoustic phase imaging, we focus in the following on CW techniques. One straightforward approach for measuring the acoustic phase is homodyne mixing of the reflected radiation with a CW reference as it can be achieved for instance with a Michelson interferometer. As illustrated in Fig. 1b) the acoustic oscillation of the object has an amplitude of Dacoust, which changes the path length difference and leads to a modulation amplitude Amod. Integrating the mixing signal over time intervals larger than the optical oscillation period yields
where Δ is the difference in optical path length and Iobj and Iref are the intensities of the beam reflected from the object and of the reference beam, respectively. The oscillation of the object is described by amplitude Dacoust, angular frequency ωacoust, and phase ϕ. Since Dacoust/λ ≈ 0 the 1st order Taylor series expansion of the cosine at leads to
when considering only the fundamental harmonic of ωacoust. This is equivalent to using a notch filter at the fundamental frequency of the acoustic drive. Most conveniently a lock-in amplifier can be used, which uses the driving frequency as reference. However, it has to be noted that in Eq. 3 the amplitude of the modulation signal Amod is a function of sin(…Δ). Taking into account that Amod by definition is greater than or equal to zero, yields the following relation between the measured phase Φ and the acoustic phase ϕ:
Most important of Eq. (4) is that the measured acoustic phase Φ does neither depend on spectral properties of the object, nor on optical properties of the environment. In particular, the phase is not affected by the reflectivity of the oscillating objects or by the absorption due to cover materials or air moisture.
The only requirement is that the amplitude of the sampling beam is sufficient for a phase measurement. The measured phase depends in a highly nonlinear manner on the difference in path length Δ yielding only two values. This is advantageous since many imaging aberrations are associated with a change in Δ. One example is a changing distance between object and imaging optics. The fact that only two phase values are possible makes the technique extremely robust. Both properties, the robustness of the technique and that the measured phase cannot be corrupted by absorption, facilitate the sensing of concealed objects.
Our experimental results were achieved using two techniques: i) a homodyne technique utilizing CW radiation (Figure 2a) and ii) a time-resolved THz technique (Figure 2b). For the CW technique we used a Gunn diode, which emits about 30 mW radiation at 87 GHz. Homodyne mixing is achieved using a Michelson interferometer with an arm length of about 0.5 m. In one arm of the interferometer the radiation is reflected by the object, which is acoustically driven by a piezo. The reflected beam and the reference beam are mixed in an amplified Schottky detector. The lock-in amplifier is referenced to the acoustic drive frequency of the piezo. Typical oscillation frequencies are of the order of 200 Hz. A maximum amplitude of the modulation signal Amod is obtained when the difference in path length is Δ = (2n - 1)λ/4. Additionally, the oscillation amplitude Dacoust of the object is estimated from the maximum modulation amplitude Amod and the amplitude of the steady state interferogram given by Aifg. Using the approximation , we deduced for the presented experiments oscillation amplitudes between 300 nm and 1.5 μm.
The time-resolved experiments were performed using a standard setup for electro-optic sampling . The setup has a bandwidth of about 3 THz and is described in detail in Ref. . Imaging optics with a numerical aperture NA = 0.16 give a resolution of about 4λ, which corresponds to 600 μm, when considering a THz spectrum with a center frequency of 2 THz.
Fundamental properties of acoustic phase imaging become visible by homodyne interferometry with CW radiation as illustrated in Fig. 2a). In this experiment, a metal mirror serves as object and performs oscillations with an amplitude of 300 nm at 400 Hz. The diameter of the unfocused beam is about 5 cm. Data were recorded with an integration time of 0.1 s. The dependence of the measured acoustic phase on the path difference Δ is shown in Fig. 3. As expected from Eq. (3), only two phase values are possible. Besides this, there is an additional phase offset in the lock-in detection, which however is constant and is therefore irrelevant for phase-contrast imaging. Deviations from the expected two-valued behavior occur when the steady state interference signal exhibits an extremum. The deviations are not related to noise, which is in this measurement of the order of 0.2 degree. We attribute the differences to the fact that positions on the object have different Δ across the beam width. This problem can be reduced by focusing the spot onto the test object. In recent experiments, we verified that an Abbe-Rayleigh limited resolution can be achieved even if the object is covered with textiles in mechanical contact with the object.
We investigated imaging properties such as spatial resolution or the required oscillation amplitude applying time resolved THz imaging. The temporal observation window of the electro-optic sampling technique was set to a delay where the THz signal exhibits a zero-crossing, maximizing the differential signal due to oscillations of the object in a similar manner as illustrated in Fig. 1b. Figure 4 shows two-dimensional THz data of an oscillating metallic membrane. The quadrants of the membrane are driven individually from the backside by four piezos. For both modes shown in Figure 4 alternating voltages with different phases are applied to the piezos, which translates to different acoustic phases of the quadrants. The spatial structure of the oscillation mode is reproduced by the THz data. The plot shows the oscillation amplitude instead of the acoustic phase, allowing for estimating the oscillation amplitude Dacoust from the modulation amplitude Amod and the THz field amplitude as discussed above. From the data and the noise floor, we conclude that oscillations of about 300 nm are well distinguishable at an integration time of 0.1 s per point.
The image at the right side of Fig. 4 was recorded through a linen covering the object at a distance of about 5 mm. Despite the two passes through the textile the modal structure is still visible at an oscillation amplitude of about 500 nm. Absorption and scattering in cover materials affect the measurement of the acoustic phase only indirectly: While the determination of the acoustic phase does not depend on the oscillation amplitude or the reflected THz intensity, the error of the measurement does scale with the inverse oscillation amplitude. However, at sufficient acoustic oscillation amplitudes cover materials have no significant impact on the phase because every measurement results either in ϕ or ϕ - π.
In order to investigate the spatial resolution of acoustic phase imaging, we recorded images of a lamella structure as shown in Fig. 5 using time resolved THz measurements. The metallic structure has an overall size of 20 mm by 20 mm. The middle lamella is loaded with a weight on its back side and the lower lamella is stiffened at the end. The top finger of the lamella structure is unmodified for reference. Terahertz images were recorded from the front side. The finger structure is well reproduced in the image showing the field amplitude of the reflected THz radiation when the structure is at rest (Fig. 5 bottom left). All fingers appear similar and a spatial resolution of about 1 mm can be deduced from the image. As expected this image gives no clue about the items behind the fingers. In contrast (see Fig. 5 bottom right), the acoustic phase image unveils the mechanical differences between the fingers. The load of the middle lamella changes the acoustic response. The stiffening of the lower lamella leads to a completely different acoustic vibration. Along this finger the acoustic phase changes by nearly 180 degrees. Both examples show that different mechanical properties can be located by THz imaging of the acoustic phase. Although it may be impossible to identify the objects by their specific material properties, the phase data indicate the presence of objects behind two of the lamellas. Generally, the spatial phase pattern depends on the shape of the object, its orientation with respect to the incoming beam, and also on its acoustic mode. Therefore, the acoustic phase provides primarily information about the presence of an object and its coupling to the environment. The object’s shape becomes visible by phase jumps, which appear at the borderline to another object that oscillates with different phase. One example is the lamella’s finger tips oscillating at different phase. The phase image of the lamella structure shows a spatial resolution of about 2 mm, which is somewhat coarser as compared to the reflection image. The image indicates an acoustic phase even in the gaps between the fingers, which we attribute to the spatial wings of the signal reflected by the nearby fingers.
Techniques for THz imaging of the acoustic phase promise applications in material characterization, but the main potential of the technique may be in security imaging. Many imaging technologies currently used for security applications are highly sensitive, such as metal detectors or X-ray scanners, but respond only to few materials or cannot be applied on humans because of health risks. The most important factors that make THz techniques attractive for contactless screening are : i) Terahertz radiation is transmitted by many packaging materials and by common clothing [15,16]. ii) Illumination by terahertz radiation causes no genotoxic effects because of the low photon energy [17, 18]. iii) According to Rayleigh’s criterion, the wavelength of THz radiation is small enough to image objects with sufficient spatial resolution.
The major hurdle towards the development of future contactless scanners results from the vast number of potentially dangerous materials and items. The goal of many THz approaches in the field is to expand the number of detectable materials by sensing their spectral properties in the far infrared. However, sensing of specific material properties by their spectral response will cover only a fraction of all objects one could think of. Such technologies may not give sufficient confidence that any object with known or unknown properties is concealed. Another hurdle is that real life applications have to overcome corruptions of the signal, which may result from different cover materials that absorb or reflect part of the spectral information required for identifying a material. Optical aberrations of the imaging optics may also alter the spectral response of the system. Finally, it can be expected that the characteristic spectral signals of concealed objects may be minute compared to background and signal corruptions. Differential detection techniques would be helpful in order to enhance the signal quality, but require the modulation of the relevant signal. To the best of our knowledge, no applicable techniques exist for modulating the spectral properties in security applications.
According to the above considerations acoustic phase imaging differs from most THz techniques by the following properties:
- 1. Completeness: The method is sensitive to all objects with mass subjected to a driving vibration. Acoustic phase imaging is not suited to identify an object by spectral information. It only provides insight into whether or not an object is concealed.
- 2. Sensitivity: Acoustic phase imaging is a modulation technique. Differential detection methods allow for efficient suppression of noise and background signals, which may arise for instance due to covering materials.
- 3. Robustness: The measured phase does not depend on the optical properties of cover materials, or water absorption in air. Additionally, the measured phase information depends on aberrations in a highly nonlinear manner and can take only two discrete values. Thus, different objects are easily distinguishable.
Applications for personnel inspection would require to couple vibrations into the human body, which could be achieved for instance by an oscillating ground plate. Transmission measurements have shown that in this configuration the acoustic amplitude is attenuated to a few percent along the body for frequencies below 100 Hz . The international standard ISO 2631  addresses the exposure of humans to vibrations and recommends to limit oscillation amplitudes to about 30 μm at frequencies of about 100 Hz for exposure times of about 10 minutes. In our experiments on membranes the oscillation amplitudes were as small as 300 nm, which is about two orders of magnitude smaller than the values recommended by ISO 2631. Such submicron amplitudes are comparable to the physiological perception level .
We have shown that THz imaging can be used to measure the acoustic phase of vibrating objects with resolutions comparable to those expected from the Abbe-Rayleigh diffraction criterion. An outstanding property of the developed technique is the capability of detecting virtually all objects. While the technique gives no insight into the object’s material properties it is capable of determining whether a concealed object is present. Differential detection schemes allow for a nearly background free signal and for efficient noise suppression. The measured acoustic phase depends only in a discrete manner on signal corruptions, which facilitates future applications.
The authors acknowledge technical help by C. Lang and thank Radiometer Physics GmbH for support. The work of G.A. is funded by the Deutsche Forschungsgemeinschaft (contract KE 516/1-1).
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