Results are presented for the first imaging system that combines the high power of terahertz quantum cascade lasers with three-dimensional image reconstruction based on filtered back-projection. Images of various phantoms have been successfully reconstructed revealing both their external and internal structures.
©2006 Optical Society of America
Since the first work on imaging using terahertz (THz) radiation, published in 1995 , the field has undergone rapid development and has attracted much international interest owing to its application areas which range from security screening to medical imaging [2–8]. For example, it has been demonstrated that THz radiation can be used to (i) distinguish healthy and diseased skin tissue; (ii) obtain spectroscopic signatures of pharmaceutical compounds, drugs-of-abuse, and explosives; (iii) penetrate many packaging materials, such as plastics and paper; and (iv) allow spatial resolutions in the 100 μm range [4,5], owing to the relatively short wavelengths compared with microwave radiation. To date the vast majority of THz images have been recorded using a pulsed photoconductive THz generation/detection technology [5–8], with this technology currently employed in commercial imaging systems used for research on online quality control . The advent of THz quantum cascade lasers (QCLs) has opened up further opportunities for THz technology , these semiconductor laser sources offering the advantage of both compactness and the ability to generate continuous wave (CW) powers of several tens of mW [10,11]. QCLs with emission frequencies between 2.0 and 4.4 THz and maximum CW operating temperatures of 117 K [12,13] have already been reported.
To date, the majority of work on THz imaging has focused on two-dimensional (2D) scanned images of thin samples , although other imaging modalities appropriate to thin 2D samples have also been reported [14,15]. As yet, there have been few reports of true three-dimensional (3D) THz images of real 3D structures; although 3D images of a dielectric sphere, a turkey bone and various polystyrene phantoms have been reported  using computed tomography reconstruction techniques similar to those used at shorter wavelengths . An overview of such THz tomographic techniques can be found in Wang et al. .
Other imaging modalities developed for 2D applications also have the potential for extension to 3D imaging [19,20]. The first report of imaging using THz QCLs  presented a 2D scanned image of a slice of rat brain tissue. More recently, 2D scanned images of a bank note, spots of protein evaporated on a piece of polyimide, a leaf and a flex circuit  and a razor blade  have been demonstrated using THz QCLs.
The need for high power sources to study samples of realistic thickness has been identified as one of four principal challenges for THz-tomography . In this article, we demonstrate for the first time the combination of the high power of THz QCLs with a 3D image reconstruction, based on filtered back-projection, and use this technology to study exemplar samples made from two forms of polystyrene. There are a wide range of other materials which are well suited for tomographic study at 3 THz, having absorption coefficients in the range 0-10 mm-1 at 3 THz, and these include a range of polymeric materials (e.g. polypropylene, polyethylene, nylon, polyester), various organic compounds such as vitamins, and silicon. Potential applications of the imaging system under construction include characterisation of pharmaceutical products, security and quality control of packaged products.
2. Image reconstruction
The experimental protocol used in this work is directly based on that typically applied in X-ray computed tomography, and is illustrated in Fig. 1a. A reconstruction algorithm is used to produce an image of a cross-section through the sample at a given height. Subsequently, a 3D image is obtained by stacking such cross-sections, acquired at different heights, together.
The underlying theory required for reconstruction is the Fourier slice theorem, which states that: “The 1D Fourier transform of a parallel projection of an object equals the 2D Fourier transform of that object”. In practice, the Fourier slice theorem is used to derive algorithms suitable for image reconstruction [17,24]. The most efficient and widely used is the filtered back-projection algorithm, on which this work is based. This algorithm involves a Fourier transform of the raw absorption data, multiplication with a filter, an inverse Fourier transform and regridding into the object Cartesian domain .
3. Experimental set-up
The THz QCL used in this work  is based on a GaAs-Al0.15Ga0.85As heterostructure grown by molecular-beam epitaxy. The laser was operated in pulsed mode, typically with 250 ns long pulses at a repetition rate of 80 kHz. In order to match the detector response time, the pulse train was then usually gated with a 15 Hz, 50% duty cycle slow modulation; i.e. giving an overall duty cycle of the order of 1%. Under these conditions the device yielded a 70 mW peak pulsed power at 2.9 THz (λ = 103 μm) with a high-stability single mode operation. L-I-V characteristics demonstrated a threshold current density of 112 A/cm2.
The experimental apparatus is shown in Fig. 1b. The QCL was mounted on the cold finger of a continuous-flow helium-cooled cryostat (Janis Research Co. Inc, model: ST – 300) maintaining a heat-sink temperature of 4.2 K. The emitted radiation was collected with a 2″ f/1 off-axis parabolic mirror, and then focused by a 2″ f/6.43 parabolic mirror onto the sample. The sample was mounted on a motorised rotation stage (Newport, model: SR50CC), which was itself mounted on a motorised linear stage (Newport, model: VP-25XA). The linear stage was mounted on a lab jack (Newport, model: 281) allowing control of the 3D motion of the sample. The transmitted beams were detected by a Golay cell (Cathodean Ltd, model: IR50). The power incident on the sample, including the effects of the transmission of the cryostat window, was typically ~35 mW (peak). The signal-to-noise ratio in the absence of a sample in the beam was 20 dB.
In the present experiment, the resolution is determined by the shape of the focused THz beam at the position of the sample and is limited by the optical design. To characterise the beam, the sample was removed and a pin hole with a diameter of 0.5 mm was put in front of the Golay cell; the Golay cell was then moved in the y and z directions to map out the beam shape in the focal plane. The cross-section of the beam (Fig. 2) was found to be relatively circular, with a full-width-half-maximum (FWHM) varying between 800 μm (y) and 1100 μm (z). The optics were designed to give a compromise between resolution and depth of field over the typical depths of the samples. The centre of the sample was positioned 32 cm from, and at the focus of, the f/6.43 mirror. The distance between the rear surface of the sample and the Golay cell was 5 mm.
Figure 3 shows photographs and the reconstructed cross-sections, derived from the absorption coefficients, for a range of phantoms made from expanded polystyrene. The step size for linear translation was 0.2 mm, the rotational angle was 1°. The reconstructed images reveal both the internal and the external structures of the phantoms. The artefacts observed outside the region of the image are common artefacts of the filtered back projection reconstruction algorithm: in the present case we believe that non-negligible surface refraction dominates the error in the reconstruction. The somewhat ragged appearance of the surface in the reconstructed images is mostly real and is representative of the significant spatial density variations of the material at the sample surface.
A quantitative comparison of the features within the samples to those in the corresponding visible images is achieved by determining the FWHM of the spatial variation in absorption coefficient in the reconstructed image. For the sample with the triangular cross-section the diameter of the hole in the reconstructed image (Fig. 3d) is 2.5±0.7 mm compared with the measurement taken from the actual sample (Fig. 3a) of 2.6±0.3 mm. For the sample with square cross-section, the minimum and maximum diameters of the hole are 5.9±0.2 mm and 5.1±0.3 mm (Fig. 3b), compared with the values of are 6.0±0.6 mm and 5.4±0.6 mm determined from the reconstructed image (Fig. 3e). The quantitative agreement between features in the real sample and the reconstructed image is less good for the case of the metal needle inserted into the cylindrical phantom (Figs. 3 c,f). The region occupied by the metal insert appears qualitatively as a region of high absorption (shown by the grey dots, identifying the FWHM in variation in absorption coefficient, in Fig. 3f). The size of the needle determined from the reconstructed image is 1.7±0.6 mm, compared with the real needle diameter of 0.813 mm. The worse agreement arises from the strong reflection especially at grazing incidence of the THz radiation at the surface of the needle which causes problems with the reconstruction algorithm. The absorption coefficient for the type of polystyrene used in the objects in Fig. 3 was measured to be 0.19 mm-1 at 2.9 THz using a THz time domain spectroscopy system, and established analysis algorithms. The absorption coefficients in the reconstructed images are indicated by the scale bars in Fig. 3, and are consistent with this value, hence confirming the quantitative accuracy of our measurements.
A phantom made of low density polystyrene in the shape of a clown’s head (Fig. 4) was used to demonstrate the 3D imaging capability of the system. As for the data in Fig. 3, an independent measurement of the absorption coefficient was obtained with a THz time domain spectroscopy system. For this type of polystyrene, the coefficient was found to be 0.04 mm-1 at 2.9 THz. The phantom had complicated external features; furthermore, a hole with a diameter of 10 mm was introduced inside the phantom, and hence was not visible from the outside. The phantom was imaged from bottom to top at twelve different heights, 5 mm apart. The linear step was 0.2 mm, and the rotation angle was 10°. The reconstructed cross-sections were stacked together in the correct order to generate the 3D image of the phantom (Fig. 5). The reconstructed image reveals the general shape of the phantom, as well as the nose and cheek features; the inherent under-sampling by taking 10° angular steps does, though, cause some features on the surface of the phantom not to be detected. The diameter of the hole is measured to be 9.8±0.5 mm from the reconstructed image, compared with 10.1±0.2 mm determined directly from the sample, giving excellent agreement once again.
Imaging of phantoms made from polytetrafluoroethylene (PTFE) was less successful. Fig. 6 compares the reconstructed image of two solids; an expanded polystyrene cylindrical phantom (diameter = 12 mm) and a solid cylindrical PTFE phantom of a similar size (diameter 16 mm). Whilst the cross-section of the polystyrene phantom is correctly reconstructed, the reconstructed image of the PTFE phantom shows the erroneous presence of a central hole. The reason for this lies in the high refractive index of PTFE, i.e. 1.50, compared with 1.02 for expanded polystyrene. The filtered back-projection algorithm used extensively in X-ray tomography, and employed here, assumes pure absorption within the sample. For PTFE, the high refractive index leads to significant refraction at the surface invalidating the assumptions of the reconstruction algorithm. We are currently implementing modifications to the experimental protocol and developing a new reconstruction algorithm in order to address the problems posed by both reflection and refraction through the sample volume so as to extend our imaging capability to a wider range of materials.
Data integration times can be reduced by using a more sensitive detector such as a helium-cooled composite-silicon bolometer. An alterative approach would be to use an imaging array of, for example, micro-bolometers  which would require less motion of linear stages. Further increases in THz QCL power are also anticipated, which can be expected to decrease data acquisition times by a factor of ~2.
We have reported the first results for a true 3D imaging system using a THz QCL that emits at 2.9 THz, with subsequent image reconstruction based on the filtered back-projection technique. Images of a range of phantoms made from polystyrene have been successfully reconstructed revealing both their external and internal structures, with high contrast levels obtained between different materials. The reconstructed images are also shown to be in good quantitative agreement with features characteristic of the phantoms. The FWHM resolution of the experimental apparatus is 800-1100 μm.
Ongoing research aims to increase the range of samples that can be studied in two main areas. First, developments in QCL technology mean that the operating frequency of QCLs continues to decrease and lower frequency QCLs will be used in our imaging system; as discussed earlier QCL operation at 2 THz has already been achieved. Second, modifications are under development to both the experimental protocol and reconstruction algorithm to better account for both THz radiation reflection and refraction. This will improve image quality for high refractive index samples, and increase the speed of data acquisition.
We thank the Research Councils UK “Basic Technology Programme” and the European Community Framework VI Integrated project “Teranova”, and EPSRC for funding aspects of this work. K.L. Nguyen also thanks the Gates Cambridge Trust for financial support.
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