Transcript
Terahertz imaging using an interferometric array John F. Federici*a, Dale Garya, Robert Baratb, David Zimdarsc a Department of Physics, New Jersey Institute of Technology, Newark, NJ 07102 b Department of Chemical Engineering, New Jersey Institute of Technology, Newark, NJ 07102 c Picometrix, Inc, 2925 Boardwalk, Ann Arbor, MI 48113
ABSTRACT It has been suggested that interferometric/ synthetic aperture imaging techniques, when applied to the THz regime, can provide sufficient imaging resolution and spectral content to detect concealed explosives and other weapons from a standoff distance. The interferometric imaging method is demonstrated using CW THz generation and detection. Using this hardware, the reconstruction of THz images from a point source is emphasized and compared to theoretical predictions. Keywords: Terahertz, imaging, stand-off, interferometric, synthetic aperture
1. INTRODUCTION Over the past several years, there has been an increased interest in the potential of terahertz (THz) detection for imaging of concealed weapons, explosives, chemical and biological agents. There are three major factors contributing to this interest: (a) Terahertz radiation is readily transmitted through most non-metallic and non-polar mediums, thus enabling THz systems to "see through" concealing barriers such as packaging, corrugated cardboard, clothing, shoes, bookbags, etc. in order to probe the potentially dangerous materials contained within. (b) Many materials of interest for security applications including explosives, chemical agents, and biological agents have characteristic THz spectra that can be used to fingerprint and thereby identify these concealed materials. For example, many explosives (for example C-4, HMX, RDX, TNT) have characteristic transmission/ reflection spectra in the THz range1,2 that could be distinguishable from other materials such as clothing, coins, and human skin. In essence, these materials should appear as different “colors” to the THz detector as compared to non-hazardous items. (c) Terahertz radiation poses either no or minimal health risk to either a suspect being scanned by a THz system or the system's operator. The simplest method of THz imaging is to use a single transmitter and detector - i.e. line-of-sight detection. An image is obtained on a point-by-point basis by scanning the transmitter/detector pair over the sample under test and recording the THz phase and amplitude at each point. Using this method, THz images of macroscopic objects have been obtained3 and extended to THz tomography4 and synthetic phased-array techniques.5,10 Close range (<3m) imaging offers solutions to a wide variety of applications.6,7,8,9 Over short distances, atmospheric attenuation and scattering is minimal. Screening of mail, packages and baggage is a close range application, whereas detection of explosives, weapons, and illicit drugs on people approaching a check-point or portal are a standoff application. Close range imaging has been greatly studied. The three main techniques, each having different meritorious properties10, are •
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Raster scanning – A tightly focused THz beam is scanned across the surface of a thin sample. The reflected, 11 or transmitted12 THz is measured and an image is produced on a pixel-by-pixel basis.
[email protected]; http://physics.njit.edu/~federici
Terahertz for Military and Security Applications III, edited by R. Jennifer Hwu, Dwight L. Woolard, Mark J. Rosker, Proceedings of SPIE Vol. 5790 (SPIE, Bellingham, WA, 2005) 0277-786X/05/$15 · doi: 10.1117/12.603864
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Impulse scanning13 – Time-delayed THz signals are used to stack an image. This technique provides fine transverse resolution. Electro-optic imaging14,15 – THz images are shifted into visible light, allowing conventional CCD cameras to acquire images at a very rapid rate. The trade-off for the speed is low dynamic range; small or weakly reflecting signals cannot be imaged.
Two imaging methods that have potential for standoff imaging are focal plane array imaging and interferometric imaging. The focal plane array method is similar to a standard digital camera, for which each detector denotes a pixel in the image. Due to the high expense of THz detectors and limited detector packing density, it may not practical to fabricate an array of 1,920,000 (1600x1200) pixels. Instead, a line camera, equivalent to a flatbed scanner, could be scanned over a region comprising the mega-pixel imaging element. The scanning action decreases the frame rate dramatically, rendering a real challenge for real-time detection. Interferometric imaging, unlike digital camera-like pixel arrays, utilizes intensity and phase information between pairs of detectors. The distance between each pair is referred to as a baseline, and the image quality is strictly dependant on utilizing a wide range of unique baselines. For N detectors, there are N(N-1)/2 detector pairs corresponding to N(N-1)/2 pixels in a reconstructed image. Consequently, fewer detectors and faster frame rates may be needed for the interferometric approach as compared to the focal plane array approach. For applications to the Terahertz (THz) range, the basic technique of radio interferometry17 is employed for which signals at two or more points in space (the aperture plane at which the detectors of the array are located) are brought together with the proper delay and correlated both in phase and in quadrature to produce cosine and sine components of the brightness distribution. From the phase delay in wavefront arrival at the sensor positions the direction and location of the source can be determined.16 The instantaneous response of an interferometer to point sources can be analyzed by knowing the signal paths.17 Each THz detector measures the amplitude and phase of incoming THz radiation. As a wave front of THz radiation encounters the array, each pair of detectors measures one spatial Fourier component of the incoming THz radiation as determined by the separation (baseline) of the detector pair. Each spatial Fourier component is represented as a point in the Fourier transform plane (also known as the u-v plane). In order to image the source, additional measurements from other baselines must be carried out. An image is generated from the spatial Fourier components of all the different pair combinations. The quality of an image depends on the coverage of the u-v plane, i.e. the number of different points generated in the u-v plane. This in turn depends on the arrangement of the detecting elements of the interferometer. The primary concern in designing the configuration of antennas is to obtain an efficient coverage of the u-v plane over a range determined by the required angular resolution. For astronomical applications, the interferometric imaging array is typically operated in the far field. In this limit, the curvature of the incoming wave fronts is neglected. However, for stand-off detection of concealed weapons, the object to be image is in the near-field region of the imaging array. Consequently, the far-field image reconstruction18 must be modified19 to account for the curvature of the wave fronts in the near-field. To date, THz interferometric imaging and its application to detection of concealed explosives and weapons has been limited to simulations and calculated performance.1,18,19 In this paper, a CW THz generation and detection method is used to demonstrate the reconstruction of a THz image using the interferometric technique.
2. EXPERIMENTAL CONFIGURATION 2.1 THz Photomixing System To demonstrate THz image reconstruction using interferemetric imaging, a CW THz generation and detection method is employed. Continuous wave generation of THz radiation by photomixing has a long history. CW generation of THz radiation by photomixing (beating) of two infra-red laser sources commenced in the 1990’s through the seminal work of Brown, McIntosh, and Verghese.20 The technology for growth, design, and characterization of the Low Temperature Grown (LT) GaAs photomixers has improved dramatically20,21 enabling the use of CW THz systems for sensing, spectroscopy, 22,23 and imaging applications.24,25,26,27,28 The key materials component of LT-GaAs and higher power ErAs:GaAs photomixers is the presence of nanoparticulates that reduce the charge carrier lifetime in the material to the sub-picosecond level thereby enabling optical mixing to the THz range. While there has been improvements in photomixer performance with ErAs:GaAs materials,29 the photomixer approach has been limited by the achievable
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output power and device reliability. 30 To circumvent the carrier lifetime limits of the GaAs system, several groups utilized p-i-n photodiode structures.30 Terahertz photomixing by resonant excitation of plasma oscillations in quantum well structures has also been considered.31 While the GaAs system uses infrared lasers at ~800nm wavelengths, the InAlAs/InGaAs system can utilize inexpensive telecommunications lasers operating near 1.5µm.32 In addition to semiconductor based systems, CW THz generation and detection has been demonstrated using non-linear optical crystals.33 A conceptual diagram of the receiving array is shown in Fig. 1. Two infrared lasers are mistuned to ~1THz to power the fiber-optically coupled THz photomixer receivers. Due to the relatively low power requirements of the receiver, the optical power fromm a single set of lasers can distributed using a fiber-optical splitter to power each element of the imaging array. The receiving array is tunable by simply adjusting the difference frequency of the infrared lasers.
Fig. 1: Schematic representation of interferometric imaging array receiver. Two infrared lasers power the THz photomixer receivers through fiber-optic cables.
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Fig. 2: (left) Schematic diagraph of CW Photomixing apparatus. (right) Optical spectrum showing the tuning of the two ECDL lasers (0.lnm bandwidth).
The experimental system which is used to demonstrate the concept of interferometric imaging in the THz range is shown in Fig. 2. Two External Cavity Diode Lasers (Sacher Laser Technik) in the Littrow configuration are used as the infrared laser sources. The ECDL lasers can be electronically tuned from 778 to 782 nm. The linewidth of the laser is ~2 MHz with an output power of ~ 100 mW. The lasers are very sensitive to feedback. Consequently, an optical isolator is incorporated to an extended chamber. In addition, the fiber launch assembly is designed such that the back reflection from the fiber front surface is not reflected back into the laser cavity. Since the photomixing process requires that the electric fields of the optical sources be aligned collinearly, polarization maintaining fiber is used to deliver the optical
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power to the fiber-pigtailed THz transmitter and receiver.6 A 2x2 fiber coupler is used to combine the infrared laser beams into fibers for delivery to the THz transmitter (Tx) and receiver (Rx) modules. The THz Tx and Rx modules are Low Temperature Grown GaAs photomixers. The THz radiation is emitted within a 15 degree angle34 using a hyperhemispheric lens that is attached to the THz module. For the current experiments, only one THz Rx is used. As will be explained below, using even only one receiver, the THz electric field amplitude and phase can be measured at multiple detector positions. By acquiring the amplitude and phase at different locations, the electric field correlation can be calculated for each “pair” of detector positions thereby mimicking the performance of an N element detector array. The CW THz radiation is generated by tuning the difference frequency of the ECDL lasers to a difference frequency of approximately 0.3THz. The amplitude of the THz radiation is chopped at 100kHz by modulating the electronic bias to the THz Tx. Using a lock-in amplifier, the modulated THz electric field is detected. The location of the THz Rx is positioned by two translation stages. One stage, which translates the Rx towards the receiver, is used to measure the phase and amplitude of the THz electric field. The second stage, which translates the Rx laterally, is used to position the Rx at different locations corresponding to different “detectors” in the interferometric imaging array. The Tx and Rx are initially configured so that the n=0 detector position corresponds to the Tx directly illuminating the Rx, perpendicular to the plane of the imaging array. The initial spacing between the Rx and Tx is 11.16cm. 2.2 Generation of Homodyne Waveform The configuration of Fig. 2 is commonly referred to as a homodyne configuration. The homodyne waveform is determined by recording the THz electric field as a function of separation between the Tx and Rx. By fitting the homodyne wave form data, such as Figure 3, to a sinusoidal function, the amplitude, phase and wavelength (frequency) of the THz electric field can be determined. By tuning the difference frequency of the two ECDL lasers, once can alter the frequency of the THz wave.
THz Ampl. (Arb. Units)
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Figure 3: (left) Homodyne waveform as acquired by changing the separation between the Tx and Rx in Fig. 2. The solid line shows a numerical fit to the data. The extracted E field amplitude and phase are 2.78×10-3 and 0.9113 radians, respectively. The extracted frequency, 0.354THz, compares well to the expected frequency based on the frequency difference of the two ECDL lasers (780.2nm and 779.5nm). (right) Similar waveform obtained with an ECDL difference frequency of 0.236 THz.
3. RECONSTRUCTION OF THE THZ IMAGE The detector positions that are used in the experiment are given by the formula d = 5 (1.1 − 1) where d is in units of millimeters, and n=0,1..7 is the corresponding label for each detector position. At each detector position, a homodyne waveform is recorded and the THz amplitude, phase, and frequency extracted from the data. The data is shown in Fig. 4 shows the measure THz phase and amplitude compared to theoretical predictions. The left figure compares the n
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measured THz amplitude to that expected for a point source at infinity (eg. a planar plane wave). The curved solid line corresponds to the expected THz amplitude for the hyperhemispheric lens design of the THz Tx. This lens design restricts the THz radiation to a ~15o cone. The figure on the right compares the measured phase to two limits: The first is a plane wave limit corresponding to incoming planar waves whose wavefronts are parallel to the plane defined by the positioning of the detectors in the imaging array. The second solid line corresponds to the expected phase for a point source emitting spherical wavefronts a distance Zo=11.16cm from the Rx. Clearly, the incoming wavefronts, based in particular of the measured phase, are curved rather than planar. Therefore one might expect near-field distortions to the reconstructed image, particularly if the detector positions exceed ~5mm.
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Fig. 4: (left) The measured THz amplitude as a function of position. The diamond symbols represent the measured data. The pink line corresponds to the theoretical amplitude assuming that the source is a point source located at infinity (ie. incoming plane waves of constant amplitude). The blue line corresponds to the predicted THz amplitude as inferred by previous measurements of the photomixer Tx.34 (right) The measured phase as a function of detector position. The pink line corresponds to the predicted value for a point source at infinity (constant phase), while the blue line corresponds to the theoretical value for a point source 11.16cm from the detector. The THz image is reconstructed1,19,18 using the following formulas
σ E (ξ ) =
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where σ E is the brighness distribution (image), ξ = x / Z o , xn and xm are the detector positions, and the iteration of n and m is choosen such that each baseline combination (from the N(N-1)/2 possible) is included. C(ui ) is the correlation function given by
C (ui ) = Ai 2 cos(∆φi )
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where Ai and φi represent the product of the electric field amplitudes and change in phase for each baseline pair combination. The summation over i includes in the reconstructed image the contribution from each spatial fourier component corresponding to each unique baseline separation. The above equations represent the simplest reconstruction of the image: the correlation function is assumed to be zero for each possible baseline pair combination that was not measured.
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The reconstructed THz images of the Tx source are shown in Fig. 6. From theoretical considerations,18,19 the angular resolution of a planar array can be approximated as θ min = λ / b . At a distance Zo away, the lateral spatial resolution is
∆Llat θ min Z o λ Z o / b . For the distribution of baseline values b shown in Fig 5, one can estimate the lateral and angular resolution to be ±0.9cm and ±5o, respectfully. Note that the full-width at half maximums for the reconstructed images are close to these values indicating a good correspondence between the reconstructed image and theoretical predictions. As a further test, the THz Tx source is moved 10o from its initial perpendicular orientation (ie. perpendicular to the plane of the imaging array. When the measured THz homodyne waveforms are analyzed and the THz image is reconstructed, the reconstructed image position have shifted 10o (Fig. 6b) as expected.
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Fig. 6: (a) Reconstructed image of THz source located directly in front of the detector a distance of 11.16cm away. The dashed line is the expected image reconstruction assuming a point source at infinity. (b) A similar figure plotted as a function of angle. The solid blue curve is the reconstructed image of the source physically located 10 degrees from the center axis. The angular width of the reconstructed image (~ ±5o) is comparable to the theoretically expected width.
4. CONCLUSION In summary, interferometric reconstruction of a point source THz image has been demonstrated. The expected angular resolution compares well with theoretical predictions. The angular resolution can be further improved by increasing the size of the baselines used in the imaging array. In the future, this technique will be expanded to the imaging of extended sources. Moreover, the THz spectral content of the source can be easily imaged by tuning the difference frequency of the ECDL lasers.
ACKNOWLEDGEMENTS The authors gratefully acknowledge the support of the US Army SBIR contract (DAAD19-03-C-0038) and TSWG-ED (N41756-04-C-4163). Helpful discussions with Prof. J. M. Joseph are acknowledged.
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