We realize a compact two-dimensional tomographic terahertz imaging experiment involving only one photoconductive antenna (PCA) simultaneously serving as a transmitter and receiver of the terahertz radiation. A hollow-core Teflon cylinder filled with α-Lactose monohydrate powder is studied at two terahertz frequencies, far away and at a specific absorption line of the powder. This sample is placed between the antenna and a chopper wheel, which serves as back reflector of the terahertz radiation into the PCA. Amplitude and phase information of the continuous-wave (CW) terahertz radiation are extracted from the measured homodyne self-mixing (HSM) signal after interaction with the cylinder. The influence of refraction is studied by modeling the set-up utilizing ZEMAX and is discussed by means of the measured 1D projections. The tomographic reconstruction by using the Simultaneous Algebraic Reconstruction Technique (SART) allows to identify both object geometry and α-Lactose filling.
© 2015 Optical Society of America
In recent years, a multitude of applications for terahertz radiation have been developed for industrial as well as research tasks [1–4]. The field of terahertz applications ranges from fundamental semiconductor research  over quality control in food processes  to tomographic imaging . A great benefit of terahertz imaging is the opacity of many materials and the specific spectral finger-prints of a multitude of molecules in the terahertz region. These properties are utilized for example in security imaging, where the opacity of textiles and synthetic materials and the absorption of metal is used to detect hidden objects  or the spectral finger-print of explosives reveal directly and doubtless the presence of these substances . In the field of terahertz imaging a plurality of concepts for the generation and detection of terahertz radiation exist. Approaching from the low-frequency regime of the terahertz-gap, a common approach is the all-electrical detection of terahertz radiation using silicon MOSFET and CMOS technology [10, 11], where room-temperature operation with a good signal to noise ratio is realized. Furthermore, this concept offers detector arrays in the size of several millimeters, allowing high resolution pictures in real time mode . A second approach covers the optoelectronic terahertz generation and detection using photoconductive antennas (PCAs). Advantages of this technique include robustness, phase sensitivity and a good signal-to-noise ratio, which makes it an ideal option for many scientific and industrial tasks . Here both, the pulsed broadband terahertz generation by femto-second lasers and CW photomixing involving two single-mode lasers and a photomixer are well-established for terahertz imaging [14,15]. Both approaches use a second PCA for phase-sensitive detection on which optical radiation from the femto-second laser or the two lasers are superimposed together with the terahertz signal. Promising progress towards improving the compactness of terahertz imaging systems has already been achieved by combining the terahertz source (transmitter) and detector (receiver) into one device as realized for example by self-mixing of a quantum cascade laser . Very recently, a similar approach for the generation and detection of broadband terahertz pulses has been reported involving a set-up that includes a femto-second laser and a photoconductive switch . For CW terahertz radiation a combination of terahertz transmitter and receiver is studied experimentally in a novel concept based on one single PCA only .
In this paper this homodyne self-mixing approach is explored towards a proof-of-concept two-dimensional terahertz tomography. This leads to a significantly reduced degree of complexity and cost of the terahertz imaging set-up.
2. Experimental set-up
As in a conventional CW heterodyne set-up, the output of two single-mode semiconductor lasers at frequency ν1 and ν2 are superimposed to generate an optical beat signal at a difference frequency of νTHz = ν2 −ν1. As schematically depicted in Fig. 1, the lasers are two tunable external-cavity diode lasers (ECDLs) with a band-pass filter as frequency selective element, emitting at wavelengths of around 794 nm and providing an optical output power of approximately 80 mW each . After coupling each laser beam into a single-mode fiber, they are superimposed via a fiber-based 50 : 50 beam combiner. One part of the beat signal is analyzed with an optical spectrum analyzer (OSA) and a power meter, while the other part impinges on a fiber-coupled PCA (FC-PCA: GaAs-based photomixer, model EK-000831, TOPTICA Photonics). The FC-PCA features an interdigitated finger structure and a logarithmic spiral antenna with three turns, which emits the terahertz radiation at the difference frequency of the two laser frequencies. A hyperhemispherical silicon lens (SiL), with a theoretical focal length of 40 mm focuses the terahertz beam behind the PCA, resulting in a focus diameter of around 5 mm. The PCA is electrically connected to a 9 V battery that provides a constant bias voltage. Within the Rayleigh length of the terahertz radiation, which we estimate to be 18.7 mm for a terahertzwave frequency of 0.3 THz, a revolving chopper wheel is placed. The terahertz radiation is back reflected by the surface of this chopper wheel onto the FC-PCA. The chopper wheel is modulated at the chopping frequency of up to 2.6 kHz and is mounted on a linear translation stage (ESP300, Newport Inc.), which allows a variation of the phase between the laser beat signal and the back reflected THz radiation. The back-reflected terahertz radiation gives rise to the HSM intensity signal I(z) , which is proportional to
Here λ is the wavelength of the terahertz field and z the displacement of the RCW. In order to perform two-dimensional tomographic terahertz imaging a hollow-core Teflon cylinder filled with α-Lactose monohydrate powder (Acros Organics) is placed in between the FC-PCA and the RCW. The dimensions of the cylinder are height h = 20 mm, cylinder diameter d = 18.5 mm and wall-thickness t = 4.25 mm, as indicated in Fig. 1. This sample is mounted on a second linear translation stage allowing for a movement orthogonal to the terahertz beam (Δx direction) related to the RCW. A further rotation around the center axes of the Teflon cylinder is realized by a rotation platform. In this manner the sample can be scanned over a range of 27 mm in 1 mm steps in x-direction and for 6 rotation angles Θy between 0° and 150° in 30° iterations.
3. Experimental results and discussion
The two ECDLs are tuned to 795.92 and 797.07 nm, which results in a difference frequency of 0.539 THz. First, we investigate the empty Teflon cylinder. For each x-position of the cylinder displacement, the HSM signal is recorded over a RCW displacement Δz of 1200 μm. Figure 2 shows the measured HSM signals at two selected sample x-positions, which correspond to no sample between PCA and RCW (x = 0 mm, left) and the position, where the center of the PCA and Teflon cylinder are congruent (x = 14 mm, right). From these two measurements the total wall thickness of the hollow-core Teflon cylinder can be determined by a curve fitting to the set of two equations:
Here, z0 denotes the start displacement of the RCW, I0,x=0mm and I0,x=14mm the intensity of the HSM signals for the two positions, λ the terahertz wavelength, d the geometric wall-thickness of the hollow-core Teflon cylinder and n the refractive index of Teflon at 0.539 THz, which is assumed to be 1.44 . The curve fitting yields a terahertz wave frequency of 0.542 THz and a wall-thickness of the hollow-core Teflon cylinder of d = 8.8 mm. Both values are in good agreement with the calculated difference frequency (see above) and two times the wall-thickness of the hollow-core Teflon cylinder as determined by a caliper measurement (Fig. 1).
In order to perform two-dimensional imaging of the filled hollow-core Teflon cylinder, a complete set of measurements for all rotation angles Θy of the sample is performed. The total measurement time depends on the investigated terahertz wavelength. For longer wavelengths the RCW displacement increases, leading to longer measurement times. In the case of a terahertz frequency of 0.19 THz, one HSM signal measurement, i.e. at one specific angle Θy and one x-position, lasts roughly 40 seconds which results in an overall time duration of two hours for one tomographic measurement of 6 angles with 27 x-positions each. After measuring all HSM signals, a curve fitting to Eq. (1) for each HSM signal yields the HSM signal intensity I0 for each x-position and rotation angle Θy, considering different DC offsets by an additional constant factor in Eq. (1). This fitting is done in order to perform an automated data processing and to avoid false signals with the wrong wavelength at low signal amplitudes. Besides the signal amplitude, the curve fitting provides also the signal phase, which may be useful in future investigations. An normalized example of these measured signal intensities I0 for Θy = 0° at each x-position are shown in Fig. 3 for the two selected terahertz frequencies of 0.19 THz (left) and 0.539 THz (right). As a guide to the eye a photograph of half of the investigated Teflon cylinder is scaled to the axis dimensions and shown in the background in both graphs. The filled circles in blue represent a scan of the Teflon cylinder filled with α-Lactose monohydrate powder, whereas the empty circles in red show a scan of the empty hollow-core Teflon cylinder. The hollow-core Teflon cylinder filled with powder clearly shows negligible transmission through the whole sample at a terahertz frequency of 0.539 THz (Fig. 3 right, blue circles). Only in the periphery outside the Teflon cylinder, from x = 0 to x = 4 mm and from x = 22 to x = 26 mm marked as regions I, a considerable transmission is observed. In contrast for the empty cylinder at a terahertz frequency of 0.539 THz (Fig. 3 right, red empty circles) and for the filled cylinder for a terahertz frequency of 0.19 THz (Fig. 3 left, blue filled circles) a high transmission through the center of the sample can be seen (region III), whereas no transmission through the side walls of the Teflon cylinder (x = 6 to x = 10 mm and x = 15 to x = 20 mm) is observed in both cases (region II). Responsible for the absence of any signal in case of the filled cylinder at 0.539 THz is not the scattering by the powder, but rather the characteristic absorption line of α-Lactose near the selected frequency of 0.539 THz . In case of 0.19 THz three different transmission regions are identified and marked in Fig. 3, left.
- A normalized HSM signal amplitude of approximately 0.4 is observed in the case of no sample between PCA and RCW.
- By moving the sample into the THz beam path a region of no transmission is observed.
- A surprisingly high signal of around twice the amplitude according to (I) is found at the position, in which the center of the PCA and sample are congruent.
Coming from the well established x-ray tomographic imaging, the measured projections of the Teflon cylinder showing these three regions appear unusual, since a smooth attenuation of the signal depending on the thickness of the Teflon cylinder is expected when moving it into the terahertz beam path . As x-rays only experience a small refraction at boundary surfaces, the path from the source of the radiation to the detector can be approximated as a straight line. Hence, the measured signal amplitude at the detector only depends on the attenuation of the sample between source and detector. In contrast, optical effects like refraction and diffraction play an important role for terahertz radiation [22, 23]. Therefore, the experimental set-up from Fig. 1 is studied by ray tracing using the software ZEMAX in the non-sequential mode. The investigated geometrical set-up is depicted on the left side of Fig. 4 for different displacements of the Teflon cylinder filled with α–Lactose, representing the regions (I), (II) and (III). The source is a circular Gaussian source with a radius of 4 mm followed by a paraxial lens with a focal length of 21 mm. The sample is modeled by two cylinders with refractive indices of 1.44 (Teflon)  and 1.79 (α–Lactose)  and are displaced in x-direction. At a distance of 40 mm from the source a mirror back-reflects the calculated rays to the detector, which is located at the source position. By summing up the total power of the incident rays at the detector for different x-positions of the Teflon cylinder, one projection of the cylinder is simulated. The projection is shown on the right side of Fig. 4. The intensity has been normalized with respect to the maximum calculated intensity at the detector and is shown over a total displacement of 26 mm in 1 mm steps. As in the experimentally obtained data, the simulated projection exhibit the same three regions.
In region (I) there is no sample placed between the PCA and the RCW respectively the mirror. Here the loss of intensity derives from the deviation of the focal point position at 0.19 THz compared to the theoretical distance of 40 mm from the PCA. This deviation arises from the ’active region’ of the logarithmic spiral antenna, which emits the major part of the terahertz radiation. Due to constructive and destructive interference of the radiation, the size of this region turns out to be frequency-dependent. With increasing wavelength respectively lower frequency, the area of this region increases [24, 25], which leads to a more distant virtual point source. In combination with the mounted SiL, this contributes to a shift of the focal point of the terahertz radiation towards the SiL. The absence of any signal in region (II) of both the simulated and experimentally obtained projection of the Teflon cylinder becomes evident by regarding the second set-up in Fig. 4. The emitted terahertz radiation gets strongly refracted by the curved surface of the Teflon cylinder, resulting in the total loss of the radiation. In contrast, region (III) exhibits an amplitude of approximately twice the amplitude in (I) in accordance with experimental and simulated data. Here the Teflon cylinder acts like a lens making sure that the whole terahertz radiation gets back reflected to the PCA.
After this developed understanding of a central line scan we now proceed to the reconstruction using all 6 projection angles Θy for the tomographic 2D image of the Teflon cylinder. In order to avoid aliasing in the rasterisation of the projections, necessary for the 2D reconstruction, the received transmission projections for every rotation angle Θy are up-scaled by a linear interpolation. After that up-scaling, the two-dimensional image of the Teflon cylinder is calculated. The back projection is performed using a multitude of algorithms, which are well-established in the field of tomography. In agreement with literature , we observe that the inverse radon transformation suffers from the small number of performed projections. It is well accepted that iterative algorithms are superior to Back Fourier algorithms on low numbers of projections . Here the Simultaneous Algebraic Reconstruction Technique (SART)  implemented in the ASTRA Tomography Toolbox  provides the best image quality and therefore is chosen. By even considering the Gaussian beam shape of the terahertz radiation, it would be possible to further improve the quality of the reconstructed image . This also becomes clear by viewing the smooth transition between air and Teflon cylinder in Fig. 3, where the absence of the expected sharp transition indicates a Gaussian beam profile. However, for simplicity of this proof of concept experiment, we have assumed parallel beams in our reconstruction method.
The reconstructed two-dimensional images of the Teflon cylinder filled with α-Lactose monohydrate powder for both investigated terahertz frequencies of 0.19 THz (left) and 0.539 THz (right) is depicted in Fig. 5. In case of a terahertz frequency of 0.19 THz a transmission through the surrounding air can be seen at the edges of Teflon cylinder by the yellow and orange region. The side-walls of the Teflon cylinder are defined by a blue area of no transmittance, due to strong refraction on the curved surface of the Teflon cylinder. The transition region from air to the Teflon cylinder appears to be a little bit blurry. In contrast the 1D-projections for both frequencies and the reconstructed 2D image at 0.539 THz (Fig. 5 right) exhibit a sharp transition between air and the Teflon cylinder. Therefore, it seems likely that this blurring effect is a consequence of the refraction of the terahertz radiation at the curved surface. A part of the outer Teflon ring appears transparent for measurements in a configuration shown in Fig. 4 III. But under a rotation of the Teflon cylinder the same part of the outer Teflon ring seems to be highly absorbing like illustrated in Fig. 4 II. These two contradictory transmission behaviors may result in a blurring effect in the reconstruction. The center of the reconstructed image at 0.19 THz (Fig. 5) clearly shows a high transmission despite the α-Lactose inside the Teflon cylinder, which confirms our assumption that the scattering at the terahertz wavelength does not affect our transmission experiment. The right hand side of Fig. 5 shows a large blue region of no transmission, from which the outer shape of the Teflon cylinder is recognized. Here only a transmission through the air surrounding the cylinder can be seen. A comparison of the two images received from the chosen terahertz frequencies reveal the hollow core of the Teflon cylinder, since a high transmission in case of a terahertz frequency of 0.19 THz is observed, whereas no transmission is measured at 0.539 THz. With the knowledge about the absorption line of α-Lactose at 0.539 THz, finally the filling of the hollow core Teflon cylinder can be identified. In this manner frequency dependent imaging can be used to identify substances or even to indicate specific regions in tomographic images, which would be unrecognized in single frequency imaging.
4. Summary and conclusion
In conclusion, we have studied HSM using only one PCA for two-dimensional spectrally resolved terahertz imaging. The PCA serves simultaneously for the generation and the detection of the CW-terahertz radiation thus simplifying enormously the set-up. We could show that the phase information of the HSM signals can be used to determine the wall-thickness of a hollow-core Teflon cylinder. The optical effects of refraction on the experimentally determined 1D projections of the sample could be clearly identified by the modeling of the experimental set-up in ZEMAX. These results show a very good agreement between experiment and theory and allow for a better understanding of the refraction effects. Consequently, two-dimensional tomographic measurements for two different terahertz frequencies were performed for a Teflon cylinder filled with α-Lactose. Even for a small number of data points we successfully received the 2D image of the cylinder by choosing a proper reconstruction algorithm. This image revealed the dimensions of the Teflon cylinder and allowed us to identify the α-Lactose filling by its specific absorption line. The developed frequency-resolved imaging shows promises for security and quality control applications in the near future. This simple and compact terahertz imaging set-up allows a significant cost reduction and relaxes the demand on high power lasers as only one PCA is needed. The proposed method allows for the realization of compact terahertz imaging assemblies.
We thank TOPTICA Photonics AG for the excellent photomixers, particular A. Deninger for productive discussions and acknowledge the support from “ Sensors Towards Terahertz” within the LOEWE platform ( 1502-2995-11). We acknowledge the support of the COST Action MP1204 “TERA-MIR”. Further we thank S. Patel for technical support and M. Simonetta for active discussions, R. Walser and M. Sturm for support with the ZEMAX modeling and G. Birkl, M. Schlosser and F. Stopp for support regarding the ECDLs. We also thank the anonymous reviewer for recommending us the superior reconstruction method for the 2D image reconstruction, which finally allowed for an improved image quality and his continuous questioning support. S. Breuer also acknowledges support through the Adolf Messer Foundation.
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