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To be published in: IEEE Computer Society, Proceedings of the 34th Applied Imagery Recognition Workshop (AIPR ’05), Washington, D.C. Terahertz Laser Based Standoff Imaging System Kurt J. Linden, William R. Neal Spire Corporation [email protected], [email protected] Jerry Waldman, Andrew J. Gatesman, Andriy Danylov University of Massachusetts Lowell, Submillimeter Wave Technology Laboratory [email protected], [email protected], [email protected] Abstract Definition and design of a terahertz standoff imaging system has been theoretically investigated. Utilizing terahertz quantum cascade lasers for transmitter and local oscillator, a detailed analysis of the expected performance of an active standoff imaging system based on coherent heterodyne detection has been carried out. Five atmospheric windows between 0.3 THz and 4.0 THz have been identified and quantified by carrying out laboratory measurements of atmospheric transmission as a function of relative humidity. Using the approximate center frequency of each of these windows, detailed calculations of expected system performance vs target distance, pixel resolution, and relative humidity were carried out. It is shown that with 1.5 THz laser radiation, a 10m standoff distance, 1 m x 1m target area, and a 1cm x 1cm pixel resolution, a viable imaging system should be achievable. Performance calculations for various target distances, target pixel resolution, and laser frequency are presented. 1. Introduction There is strong interest in developing standoff methods for detecting hidden weapons and explosives. At the present time it is virtually impossible to detect concealed weapons and explosives on people or in containers at a distance. Close-proximity detection schemes utilizing x-ray imaging techniques and hand searches are widely used at airports and in some government buildings, but such close proximity detection is often too late to prevent terrorists from firing weapons or detonating explosives in crowded areas. What is needed is a method whereby concealed weapons and explosives can be detected at distances such that use of the weapons or detonation of the explosives are far enough away to prevent or greatly reduce human injury. Currently existing hidden weapon detection schemes such as x-ray imaging or trace gas spectroscopy do not work at large distances. Visible and infrared detection schemes have limited capability because this radiation cannot easily distinguish between different materials such as clothing, paper, metals, or a human body. Beyond the far-infrared spectral region however, in the sub-millimeter wavelength region (known as the terahertz region because the frequencies are between 0.3 and 4 THz), radiation is strongly absorbed by polar molecules such as water and certain explosives. Terahertz radiation is reflected by metals and heavy organic molecules (such as contained in certain explosive materials), but materials such as clothing, paper, and most packaging materials are relatively transparent to it. The energy of this radiation is very low (in the meV range), being orders of magnitude below that of x-rays, and is therefore non-ionizing. Thus, with no anticipated safety issues at power levels well below 1 W, it is an ideal type of electromagnetic radiation for detection of concealed weapons and explosives. Terahertz technology involves electromagnetic radiation with wavelengths ranging approximately from 1000 µm to 75 µm (corresponding to frequencies ranging from 0.3 THz to 4 THz). Also known as the submillimeter wavelength spectral region, the technology of terahertz radiation has been extensively investigated, and a number of sources and detectors of such radiation have evolved over the past 50 or so years [1]. Current and prior terahertz technology applications include astronomy, plasma fusion diagnostics and gas diagnostics based on terahertz spectroscopy, and scaled radar simulation. Scaled radar simulation using terahertz laser radiation has been extensively carried out over the past 25 years [2]. One of the primary problems that kept the terahertz technology from being more widely used has been the lack of convenient and affordable terahertz radiation sources. There are currently a number of sources of terahertz radiation, but all of the current sources have disadvantages such as large size, high cost, complex equipment, or the need for cryogenic cooling [3]. Terahertz frequencies occur in the most underdeveloped region of the electromagnetic spectrum, even though their potential applications are promising for biological and medical imaging, as well as for detection of chemical and biological agents. This underdevelopment is primarily due to the lack of coherent solid-state terahertz sources that can provide convenient radiation intensities (greater than a mW) and continuous-wave (CW) operation. The terahertz frequencies fall between the microwave and the infrared regions of the electromagnetic radiation spectrum, two regions in which conventional semiconductor devices are well developed. In the microwave region, semiconductor electronic devices (such as transistors, Gunn oscillators, IMPATT devices, Schottky-diode frequency multipliers, and photomixers) have operating frequencies that are usually limited by carrier transit times or parasitic RC time constants. Consequently, the power level of these classical devices decreases as 1/f4, or even faster, as the frequency f, increases above 1 THz. In the infrared region, semiconductor optoelectronic devices based on quantum-mechanical interband transitions are limited to frequencies higher than those corresponding to the semiconductor energy gap, which is higher than 4 THz even for the narrowest-bandgap materials. Thus, the frequency range of 0.3-4 THz is generally inaccessible for conventional microwave and infrared semiconductor devices. A list summarizing currently available terahertz radiation sources is shown in Table 1. In this table, coherent implies that the listed source is appropriate for use in a coherent heterodyne transmitter/receiver system. The quantum cascade laser has the favorable attributes of small size (similar to diode lasers), potentially low manufacturing cost (using standard semiconductor foundry operations with thousands of devices on a single wafer), low power requirements, and frequency tunability. The remaining challenge is to obtain thermoelectric temperature (250 K) or room temperature (300 K) operation. Several laboratories and companies (including Spire) are currently working in this area. 2. Identification of atmospheric terahertz transmission windows Atmospheric transmission measurements were carried out at the University of Massachusetts Lowell, Submillimeter-wave Technology Laboratory (UMLSTL) using a 1.7 m FTIR interferometer. Atmospheric relative humidity (RH) values ranged from 5 % to 58 % with air temperatures ranging from 25.5˚C to 28.7˚C. The results obtained from these measurements (the details of which are to be published elsewhere) are summarized in Figure 1. Lower terahertz windows, even though they clearly have higher transparency, were not considered in the calculations for two reasons: (a) the longer wavelengths require unrealistically large antenna dish sizes, and (b) from basic physical reasons it is expected to be very difficult to obtain efficient quantum cascade lasers operating at frequencies below 1.5 THz. Optical radiation loss as a function of propagation distance through a medium can be calculated using the Beer-Lambert law, which states that radiation intensity decreases exponentially with distance according to (1) I = I0 exp (- αx) where I is the intensity of the radiation at a position, x, I0 is the intensity of the radiation for x = 0, and α is the optical absorption coefficient (with dimensions of 1/distance). Since the measured atmospheric transmission values shown in Figure 1 were measured for atmospheric path lengths of 1.7 m, it is possible to calculate α for x = 1.7 m for any terahertz frequency and RH value. From these values, it is then possible to extrapolate the atmospheric attenuation for any distance. For example, the calculated optical loss in the five identified atmospheric windows for a 50 m path is summarized in Table 2. The entries for α correspond to the atmospheric attenuation values (m-1), while the dB values are the calculated radiation loss due primarily to the absorption of terahertz radiation by the atmospheric water content over a distance of 50 m. Table 2 illustrates the expected tradeoff between lower terahertz frequency (with expected larger antenna size and greater difficulty in quantum cascade laser fabrication) and improved atmospheric transmission. It is because of this trade off that the method of heterodyne detection is selected as the most favorable choice of detection mechanisms. Table 1 List of some currently available terahertz radiation sources. None of these sources has all the attributes of low cost, convenience, coherence, and adequate (mW or greater) power. The quantum cascade laser appears as a strong candidate for a low-cost, mass-produced terahertz radiation source. THz source Details Characteristics Mercury lamp Mercury arc lamp in water cooled housing Low pressure (1E-3 Torr), 75 - 150 W Sciencetech SPS-200, 300, low spectral power density. Low cost - used in THz spectroscopy. Optically pumped gas laser Grating-tuned CO2 laser and far-IR gas cell. Most mature device. > 100 mW, 0.3 - 10 THz, discrete lines, CW or pulse Commercially avail., coherent rad'n, large footprint Optically pumped PC switch Mode locked Nd:YAG pumped, low-temp photoconducting InGaAs-antenna shaped Imaging apparatus produced, 0.1 to 3 THz Commercially avail, low ave. power/spectral density Photomixing of near-IR lasers ErAs:GaAs photomixer Four-wave mixing, two-color 835 nm diode Room temp, frequency tunability,< 1 uW THz output Room temp, sub nW power out, 2-3.5 THz output Optical parametric oscillator Phase matching in GaP with YAG laser Not commercial. GaP gave 480 mW @ 1.3 THz and OPO. Difference freq generation GaSe crystal, Nd:YAG/OPO difference freq Tunable 58-3540 um (5.17 - 0.1 THz), 209 W pulsed Electrically pumped Ge Electric field injects electrons, magnetic field splits hole levels for low-E transitions Requires electric and magnetic fields Up to hundreds of mW, cryo cooled, multi-mode Direct multiplied mm waves multiplied to low-THz region Microwatt level, commercially available (VA Diodes) Coherent, heterodyne local oscillators in astronomy Quantum cascade (QC) laser First announced in 2002, semiconductor, AlGaAs/GaAs-based, MBE (presently) 3-4 THz region, mW power level, to 165K (MIT) Coherent, not yet commercially available Transistor InGaAs channel HEMT with 60 nm gate Plasma waves provide oscillation Under development at Inst. Elec. Micro, Lille, France and U. Illinois - InGaAs/InP (600-650 GHz) Backward-wave oscillators Vacuum tube, requires homogeneous mag Tunable output possible. Homogeneous magnetic field of ~ 10 kG field awkward. Commercially available Traveling Wave Tube (TWT) Difficult to get small dimensions, MEMS in Si being explored Theoretical, 1-100 mW to 0.5 THz, U. WI Free electron laser Benchtop design at Univ. Essex, UK Brookhaven/Lawrence Berkeley/Jefferson: Tunable over entire THz region, limited avail., large Achieved 20 W Synchrotron Coherent synchrotron produces very high photon flux, including THz region Very broadband source, limited instrument availab., 40 MeV elec bent in H-field = 20 W pulsed, large 3. Terahertz imaging system candidates and system selection The standoff imaging system being considered is intended to be capable of detecting hidden objects approx. the size of a hand weapon (gun, knife, or hidden explosives) on a person ideally at distances of approx. 50 m. Candidate system designs include single detector systems operating in either scanning mode with homodyne detection, or scanning mode with heterodyne detection, as well as 2-dimensional detector array detection methods with full-scene illumination. These options are summarized in Table 3. Heterodyne detection, though somewhat more complex, increases system sensitivity by approximately 8 to 9 orders of magnitude. Such terahertz detection systems have been previously demonstrated at UML-STL using terahertz, CO2-optically-pumped gas lasers [4]. Substitution of a large, bulky gas laser with a miniature quantum cascade semiconductor laser will significantly reduce system size and cost. Quantum cascade lasers can operate at voltages below approx. 20 V, and are very small. They have been operated at temperatures of up to approx. 165 K, and could reach thermoelectric temperatures of approx. 250K in the near future. Thermoelectric coolers are small and inexpensive, and readily available. 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9 Frequency (THz) Fig. 1 Atmospheric terahertz spectral transmission (0.3 – 4.0 THz), normalized to 1 at 0.3 THz, under RH values ranging from 5 % (upper plot) to 58 % (lowest plot). The five identified atmospheric windows are 1.47 – 1.56 THz, 1.96 – 2.0 THz, 2.09 – 2.12 THz, 2.51 – 2.55 THz, and 3.39 – 3.47 THz. The instrument spectral resolution is 0.15 cm-1 Table 2 Calculated values of terahertz attenuation over a distance of 50 m, for laser frequencies corresponding to the five measured atmospheric window regions, as a function of RH. THz Window Region 3.39 – 3.47 THz 2.51 – 2.55 THz 2.09 – 2.12 THz 1.96 – 2.0 THz 1.47 – 1.56 THz RH = 6.4% α = 0.062 - 13.5 dB α = 0.062 - 13.5 dB α = 0.049 - 10.6 dB α = 0.038 - 8.2 dB α = 0.012 - 2.6 dB RH = 11.8% α = 0.069 - 15 dB α = 0.077 - 16.8 dB α = 0.075 - 16.3 dB α = 0.049 - 10.64 dB α = 0.021 - 4.56 dB RH = 25.9% α = 0.110 - 23.9 dB α = 0.131 -28.5 dB α = 0.117 - 25.4 dB α = 0.072 - 15.6 dB α = 0.0333 - 7.23 dB RH = 39.4% α = 0.131 - 28.51 dB α = 0.161 - 35.05 dB α = 0.1462 - 31.75 dB α = 0.103 - 22.28 dB α = 0.0555 - 12.05 dB RH = 52% α = 0.193 - 41.95 dB α = 0.218 - 47.40 dB α = 0.218 - 47.40 dB α = 0.139 - 30.12 dB α = 0.0819 - 17.78 dB RH = 58% α = 0.359 - 78 dB α = 0.359 - 78 dB α = 0.359 - 78 dB α = 0.218 - 47.4 dB α = 0.15 - 32.6 dB Table 3 Three candidate system designs for terahertz imaging of objects at standoff distances of 50 m. THz imaging instrument option Single detector, scanning mirror, with heterodyne detection Single detector, scanning mirror, without heterodyne detection 2-D array detector with laser source as illuminator Attributes High sensitivity but also high level of complexity Simplicity in design, but reduced system sensitivity Reduced system complexity and sensitivity Terahertz detector types and associated sensitivity values have been reviewed, and a number of detector options will be investigated [1]. A wide variety of terahertz detectors are available. Room temperature detectors such as Schottky diodes and bismuth or tellurium composite bolometers have been extensively used, as have microbolometers and Golay cells. More recently, cooled germanium-on-silicon bolometers and metal tunnel junction composite bolometers have demonstrated noise equivalent power (NEP) values of 10-17 to 10-18 W Hz-1/2. Superconducting bolometers have demonstrated NEP values as low as 10-20 W Hz-1/2. A major advantage of the heterodyne detection system described here is that room temperature Schottky diode detectors can be used. Beam shaping and signal gathering optics will be required to direct the master oscillator laser beam to the subject and to collected the terahertz radiation reflected from and scattered by the target object. The most promising candidate heterodyne detection system type is one consisting of a laser transmitter antenna whose diameter is designed to flood illuminate the 1 m x 1 m target area. This antenna will accordingly be relatively small. The receiver antenna is designed to scan the target area with a 1 cm x 1 cm imaging resolution (pixel size). The receiver antenna will therefore be much larger than the transmitter antenna, as discussed in the following section. Data shown in Figure 1 indicate the existence of five distinct terahertz window regions between 1.4 and 4 THz. These window regions are centered around 1.488 THz, 1.979 THz, 2.11 THz, 2.52 THz, and 3.42 THz. Good terahertz transmission windows at currently-achievable cascade laser emission wavelengths (2 – 4 THz), exist at 2.11 THz, 2.52 THz, and 3.42 THz. It is anticipated that terahertz quantum cascade lasers emitting in the 1.488 THz and 1.979 THz regions will soon become available as well. For RH values of 52% or less, the 2.11, 2.2, and 3.42 THz window regions appear reasonable, although at much higher humidity values, there may be detection problems. The 1.488 THz window is expected to provide the best system performance. 4. Terahertz imaging system design and system sensitivity calculations This section contains estimates of achievable system performance and sensitivity for the selected 1.488 THz atmospheric window, using ideal Gaussian beam approximations for optical and infrared laser resonators as outlined by Kogelnik and Li [5]. The candidate terahertz standoff detection system design is illustrated in Figure 2. Fig. 2 Schematic illustration of a candidate terahertz standoff detection system for a 50 m target distance, with an assumed suicide bomber target. The heterodyne detection system includes two frequency-locked terahertz quantum cascade lasers, one master oscillator (MO), and one local oscillator (LO). The detector is a Schottky barrier diode mixer operating at room temperature. This figure describes the candidate terahertz standoff imager. Representative target distances of 50 m and 10 m are analyzed and described, and the design tradeoffs are presented. The heterodyne detection system incorporates a master oscillator (MO) cascade laser and a local oscillator (LO) cascade laser, and these lasers are frequency locked at a given frequency separation. The Schottky detector mixer operates at room temperature, and feeds a 15 GHz (down-converted from 1.5 THz) signal to a conventional microwave IF strip, video detector and video amplifier. The video signal is then digitized and computer processed to form a real-time display. The terahertz reflectance properties of explosives of the type commonly used by suicide bombers, cyclotrimethylenetrinitramine (RDX) for example, have been measured and their imaging properties have been discussed by Federici, et. al [6]. RDX has a fairly high reflectivity in the 1.5 THz spectral region [7]. This material, when hidden, should therefore be distinguishable under clothing, similar to a metal. The initial 1.5 THz system performance calculations (for 1 cm x 1 cm resolution, and 1 m x 1 m target size) are shown in Figure 3. This figure shows the power received by the receiver antenna as it scans the target area as a function of distance to target and atmospheric RH level. The specific atmospheric ab- sorption coefficient values used in the calculations of Figure 3 are taken from the third-order least-squares curve fit to measured data points shown in Figure 4. Fig. 3 Terahertz standoff imager performance (received power) vs distance to target for various atmospheric RH levels. Scene pixel size is 1 cm x 1 cm. A video bandwidth of 0.5 MHz is assumed. Fig. 4 Atmospheric absorption coefficient vs. RH for the 1.5 THz atmospheric window. The shown data points are used for Figure 3 and later for Figure 5. The calculations summarized in Figure 3 assume a terahertz cascade laser power of 10 mW. Future quantum cascade laser devices may well have 100 mW or higher output power, shifting the curves of received power up by 10 dB or more. The lower, horizontal line of Figure 3 indicates the purely thermal noise floor for a video bandwidth of 0.5 MHz. To this thermal noise floor one must add a receiver noise figure, typically about 10 dB. In addition, one must add 10 to 20 dB of loss to account for clothing attenuation. Accordingly, the effective noise floor can range from 20 to 30 dB above the indicated thermal noise line of Figure 3. Therefore, for example in Figure 3, it can be seen that at a target distance of 50 m, the 20 dB above thermal noise floor would accommodate a system operating at 30% relative humidity, and the 30 dB above thermal noise floor would accommodate a system operating at only 10% relative humidity. In order to achieve viable standoff detection system operation, it is necessary to either reduce target distance or reduce system resolution. As the distance to target is reduced, higher RH values can be accommodated. The second parameter that could be relaxed to provide increased system sensitivity is the imaging resolution. Reduced resolution results from increased pixel size. Increasing the pixel size while operating at the same scan rate leads to reduced video bandwidth. A reduction in video bandwidth leads to a reduction in the thermal noise floor (horizontal line in Figure 3). In order to achieve system sensitivities more in line with the original goal (i.e., 50 m standoff distances), the target linear pixel size was increased by a factor of 10 (from 1 cm to 10 cm). This however would make it difficult to detect a hand weapon, for example, but is expected to be adequate to detect an explosive belt. Increasing the pixel size and decreasing the scene scan rate to yield a 1 kHz video bandwidth results in a factor of 500 in bandwidth reduction and thereby a 27 dB increase in system sensitivity. It also has the additional important benefit of significantly reducing the required size of the receiver antenna. Since the receiver antenna must be horizontally and vertically rocked to produce a raster scan of the target, its size and weight reduction are expected to be important benefits in terms of minimizing system size, weight, and cost. System sensitivity calculations were carried out for the reduced resolution pixel size of 10 cm x 10 cm. The imager performance (received power) calculations under these conditions are presented in Figure 5. From this figure it can be seen that significant improvement in system performance is obtained. For example, at a 50 m target distance, with 10 dB receiver noise figure and 10 to 20 dB clothing attenuation, it is possible to obtain an image with 20% to 35% relative atmospheric humidity. The standoff imager performance plots for both high imaging resolution (1 cm x 1 cm pixel size) and lower resolution (10 cm x 10 cm pixel size) shown in Figures 3 and 5, respectively, were generated with the assumption that the antenna dish diameters were optimized for each target distance for the following reason. If a given divergent transmitter beam just flood-illuminates a target at a given distance, then bringing the target closer to the source results in only the inner portion of the target being illuminated. Fig. 5 Terahertz standoff imager received power vs distance to target for various atmospheric RH levels, for an assumed scene pixel size of 10 cm x 10 cm. A video bandwidth of 1 kHz is assumed. This results in a system thermal noise floor reduction of 27 dB (500 x) below that shown in Figure 3. Accordingly, for optimal performance, the transmitter antenna size (and thus the flooding angle) must be modified for each target distance considered. Similar considerations hold for the receiver antenna. The impact of these considerations for both the 1 cm x 1 cm and 10 cm x 10 cm pixel imaging resolution and for both transmitter and receiver antennas is shown in Figure 6. Fig. 6 Calculated optimal transmitter and receiver antenna dish diameter vs. distance to target for a high-resolution (1 cm x 1 cm pixel size with 1 m x 1 m target area) and lower resolution (10 cm x 10 cm pixel size with 1 m x 2 m target area) system. Comparable system sensitivity calculations were also carried out for the case of reduced target distances, but with the original pixel imaging resolution of 1 cm x 1 cm. The imager performance calculations under these conditions are presented in Figure 7. Fig. 7 Terahertz standoff imager performance vs. distance to target for various relative humidity levels. Pixel resolution is 1 cm x 1 cm. For a 10 m target distance predicted system performance is 37 dB above the thermal noise floor for a 50 kHz bandwidth. At a target distance of 10 m, if one includes a receiver noise figure of 10 dB and clothing losses of 20 dB, there is still a noise margin of approx. 10 dB for a relative atmospheric humidity level of 60%. This suggests acceptable system performance. The optimal size of the transmitter and receiver antennas as a function of distance to target for this scenario, is shown in Figure 8. Fig. 8 Transmitter and receiver antenna dish diameter vs distance to target for 1 m x 1 m target size and 1 cm x 1 cm pixel size, in a standoff imaging system designed for use around 10 to 20 meter target distances. For a system designed for 10 m target distances, a 2.5 mm transmitter antenna diameter and a 25 cm receiver antenna diameter is optimal. The slopes of the two curves reflect the previously-noted fact that different target distances require different optimal antenna sizes. Use of antennas of sizes that deviate from these values can be expected to result in system performance degradation. For example, for a system designed for operation at a 10 m target distance, operation at shorter distances results in a reduction in the area of the illuminated target, while operation at longer distances results in a reduction of flood illumination intensity. This does not mean that the system will not operate at distances other than those for which it is designed. It means that the system performance will be somewhat degraded according to the degree of deviation from the design distance. Since moderate to high atmospheric humidity levels must realistically be dealt with, two possible tradeoffs were investigated. Reducing either imaging resolution or operational target distance results in improved system sensitivity. A reduction in imaging resolution from 1 cm x 1 cm to 10 cm x 10 cm, results in acceptable sensitivity at 50 m target distances, whereas maintaining the 1 cm x 1 cm image resolution results in the achievement of adequate sensitivity at distances of about 10 m. Intermediate target resolution/target distance combinations could also provide adequate system sensitivity. For hidden hand weapon detection, the higher (1 cm x 1 cm) imaging resolution will be required. 5. Summary and conclusions The authors are indebted to Thomas Goyette and Jason Dickinson of UML-STL for technical input on antenna design issues. This work was supported by the Homeland Security Advanced Research Projects Agency (HSARPA). The authors are grateful to Peter Costianes of AFRL for his support and encouragement of this work. Atmospheric transmission measurements of terahertz radiation over the 0.3 – 4.0 THz spectral range were carried out at sea-level for RH values ranging from 5 % to 58 %. These previously unpublished terahertz atmospheric absorption coefficient data are needed to enable accurate estimation of terahertz standoff imager performance, and are of value to the general scientific community. Five transmission windows were found to occur in the spectral regions between 3.39 – 3.47 THz, 2.51 – 2.55 THz, 2.09 – 2.12 THz, 1.96 – 2.0 THz, and 1.47 – 1.56 THz. A performance tradeoff study involving atmospheric attenuation, antenna size, and terahertz laser technology suggests that the 1.5 THz atmospheric window region is the most promising, if lower frequency windows are excluded. Portable standoff imaging system definition was carried out, and a comparison of general imaging system performance for several basic imaging system designs was completed and tabulated. A detailed analysis of standoff imaging system performance was carried out for a system based on the ultra-sensitive heterodyne detection technique, wherein both the transmitter and the local oscillator in the receiver utilize terahertz quantum cascade lasers. Such lasers have demonstrated power levels adequate for the proposed system. This standoff detection system appears to be the most promising for detection of hidden weapons and explosives on individuals at standoff distances. The 1.5 THz design, which involved a 1 cm x 1 cm target imaging resolution (pixel size) at a target distance of 50 m, does not provide adequate system sensitivity at normal atmospheric humidity levels. Acknowledgment References [1] Peter H. Siegel, “Terahertz Technology,” IEEE Trans. Microwave Theory and Techniques 50, 910 (2002). [2] J. Waldman, H.R. Fetterman, P.E. Duffy, T.G. Bryant, and P.E. Tannenwald, “Submillimeter model measurements and their applications to millimeter radar systems,” Proc. 4th Int. Infrared Near-Millimeter Waves Conf., 49 (Dec. 1979.) [3] J.M. Chamberlain, “Where optics meets electronics: recent progress in decreasing the terahertz gap,” Phil. Trans. R. Soc. Lond. A 362, 199-213 (2004). [4] D.R. Culkin, G.B. DeMartinis, T.M. Goyette, J.C. Dickinson, J. Waldman and W.E. Nixon, “W-Band Polarimetric Scattering Features of a Tactical Ground Target Using a 1.56 THz 3D Imaging Compact Range,” Proc. SPIE 4382, 241 (2001). [5] H. Kogelnick and T. Li, “Laser Beams and Resonators,” Appl. Opt. 5, 1550 (1966). [6] J.F. Federici, D. Gary, B. Schulkin, F. Huang, H. Altan, R. Barat, and D. Zimdars, “Terahertz imaging using an interferometric array,” Appl. Phys. Lett. 83, 2477 (2003). [7] M.C. Kemp, P.F. Taday, B.E. Cole, J.A. Cluff, A.J. Fitzgerald, and W.R. Tribe, Proc. SPIE 5070, 44 (2003).