radar cross section measurements of frequency selective

Radar Cross Section Measurements of Frequency Selective Terahertz Retroreflectors

Richard J. Williams*, Andrew J. Gatesman, Thomas M. Goyette, and Robert H. Giles

Submillimeter-Wave Technology Laboratory, University of Massachusetts Lowell, Lowell, MA, USA 01854

ABSTRACT

The radar cross section of spherical retroreflectors operating at terahertz frequencies is investigated. Several spherical retroreflectors with diameters ranging from 2 mm to 8 mm were fabricated and their radar cross section was measured at 100 GHz, 160 GHz, and 350 GHz. A frequency selective surface was applied to the retroreflectors to demonstrate proof of concept of narrow-band terahertz retroreflection. Keywords: Radar cross-section, retroreflector, frequency selective surfaces, terahertz, novel structures, narrow-band, band-pass filter, dielectric, RCS, backscatter.

1. INTRODUCTION

A retroreflector is a device that reflects incident electromagnetic waves in the direction of the source. Retroreflectors have applications in a variety of diverse fields such as aviation, radar systems, antenna technology, communications, passive identification, and metrology. Specific retroreflector applications include optical identification systems [1], road safety devices such as reflective road signs [2], clothing for nighttime pedestrian visibility [3], and as laser trackers for GPS satellites [4]. A frequency selective surface (FSS) is a periodic structure serving as a filter of electromagnetic waves. We demonstrate the concept of frequency selective retroreflection by applying a band-pass FSS to a spherical lens reflector (SLR). The addition of an FSS exhibiting band-pass behavior creates a retroreflector that can be tailored to operate within a specific frequency band dependent on application. This paper analyzes the backscatter radar cross-section (RCS) and backscatter coefficient of retroreflectors across the millimeter-wave and submillimeter-wave regions as well as investigates frequency selective retroreflector behavior.

2. RETROREFLECTORS AND FREQUENCY SELECTIVE SURFACES

2.1 Retroreflectors Retroreflectors generally fall into one of two broad categories: corner reflectors, or spherical lens reflectors (SLRs). Corner reflectors, such as dihedral and trihedral reflectors, incorporate multiple reflections of the incident electromagnetic wave in order to direct it back towards the source. The second category of retroreflectors is the spherical lens reflector, which includes the cat’s eye and Luneburg lens reflectors (graded index SLR). Spherical lens reflectors use refraction to focus the incident electromagnetic wave onto a reflective cap, once reflected the wave is then refracted back into the direction of the source with minor deviation.

Terahertz Physics, Devices, and Systems VIII: Advanced Applications in Industry and Defense, edited by Mehdi F. Anwar, Thomas W. Crowe, Tariq Manzur, Proc. of SPIE Vol. 9102, 91020R

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Figure 1: Common retroreflector types illustrating retroreflection and displaying characteristic dimensions including a) the dihedral reflector, b) the trihedral reflector, and c) the spherical lens reflector.

Corner reflectors are perhaps the most well-known and readily available retroreflectors, however it has been shown that SLRs have a wider acceptance angle [5]. The acceptance angle is the angular extent over which the reflector backscatters toward the source. It is noted that the retroreflection phenomena for a dihedral is limited to the plane perpendicular to the corner crease. The trihedral performs similarly with the added benefit of retroreflection no longer being confined to the perpendicular plane. For an SLR on bore-sight, it has been suggested [6,7] that the RCS can be modeled as a circular metal plate. Off bore-sight, the capture area scales as the azimuth angle increases. The RCS as a function of azimuth angle for a dihedral, trihedral, and a circular metal plate, all of similar size, is shown in Figure 2 as described in [8].

Figure 2: RCS as a function of aspect angle for a dihedral, trihedral, and a circular metal plate where 45 degrees azimuth is bore-sight. The RCS is calculated at 10 GHz for a square dihedral with side length w=h=0.914 m, a trihedral with side length L=0.914 m, and a circular metal plate of diameter d=0.914 m.

A comparison of the peak RCS values for the three retroreflectors shows that although the approximated SLR (green line) has a larger RCS, it is the SLR’s larger aperture that leads to superior retroreflection for incident waves at oblique angles. The RCS of the corner reflectors drops an order of magnitude at approximately 30 degrees from bore-sight whereas the SLR drops an order of magnitude closer to 60 degrees from bore-sight.



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2.1.2 Spherical Lens Reflectors An SLR is a passive retroreflector comprised of a spherical ball lens with index of refraction n=2 and a highly reflective cap on the back hemisphere [9]. An incident wave is refracted by the lens and focused onto the reflecting surface on the back hemisphere; the wave is reflected and then refracted again at the boundary between the spherical lens and air. Due to the geometry and index of refraction of the lens, the exiting refraction steers the wave along a vector antiparrallel to the incident direction. The suggested RCS approximation for an SLR on bore-sight is given in Equation 1, where λ is the wavelength of the incident electromagnetic wave and d is the diameter of the spherical lens, expressed in units of m2.

σm 2 =π 3d4

4λ2 (1)

The backscatter coefficient σ0 is determined by normalizing the RCS to the illuminated area of the scattering body.

2.2 Frequency Selective Surfaces A frequency selective surface (FSS) is a periodic structure that functions as a filter of electromagnetic waves [10]. In general, a continuous metal sheet perforated by a periodic array of holes, known as an inductive mesh, transmits high frequencies while reflecting low frequencies. At sufficiently low frequencies, currents can be set-up in the mesh, the filter acts as a low impedance surface, and the incident wave is largely reflected [11]. At higher frequencies, sufficient current cannot be set-up in the mesh, the filter acts as a high impedance surface, and the incident wave is largely transmitted. With proper tailoring of the aperture shape and dimensions, an inductive FSS can be fabricated to behave as a band-pass filter. Further discussion of filter designs is given in [12]. The FSS utilized in this work consisted of periodic crossed-dipole apertures in a 12-micron-thick Nickel screen as described in Figure 3. As shown in Figure 3b, the FSS transmits greater than 50% between approximately 325 and 375 GHz, with a maximum transmittance of nearly 100% at 349 GHz [13].

Figure 3: a) Crossed-dipole aperture FSS made from electroplated Nickel. Inset shows the unit cell of the FSS with aperture dimensions and periodicity, w=68 microns, l=400 microns, and p=700 microns. b) Transmittance spectra of FSS band-pass filter. Image from Ref (13).



Crossed -DipoleBand -Pass FSS

Fused SilicaBall Lens

Aluminum Layer

3. DESIGN AND FABRICATION The spherical lens reflectors were fabricated from fused silica spheres due to the material being low-loss with an index of refraction of n=1.951 from 0.3-5 THz [14], and they’re commercially available. Six spheres ranging from 2 mm to 8 mm diameters were purchased, one hemisphere was masked, and the unmasked hemisphere was coated with approximately 1400 angstroms of aluminum via vacuum deposition. Aluminum was chosen as the reflective coating as it has a reflectivity of approximately 99% from 0.1-45 THz [15]. The method for achieving frequency selective retroreflection was the application of a 350 GHz band-pass filter to the front surface, or aperture, of a spherical lens reflector. The 350 GHz band-pass FSS was cut into small squares and affixed to the aperture of each SLR as depicted in Figure 4. With the band-pass filter applied to the front surface, only frequencies within the pass-band will transmit into the retroreflector while frequencies outside the pass-band are scattered away. Due to the size of the spheres and difficulty of application of the FSS, no special folding techniques were used to reduce sharp edges and as such the FSS did not conform perfectly to the sphere.

Figure 4: Cross-section diagram of a frequency selective spherical lens reflector showing the fused silica ball lens with the aluminized hemispherical cap and the cross-dipole FSS wrapped around the aperture.

4. BACKSCATTERING PREDICTIONS AND MEASUREMENTS 4.1 Backscatter Predictions For the THz SLRs to be observable in any real-world environment, their backscattering coefficient should exhibit significant contrast with its surroundings. Therefore, for comparison purposes, the SLRs in this study were measured on a rough dielectric ground plane whose backscattering coefficient approximated that of a rough concrete surface at 100 GHz [16] and was assumed to be approximately equal to concrete’s rough surface scattering behavior at 160 GHz and 350 GHz as well. RCS measurements of the ground plane without the retroreflectors were taken for comparison purposes.



Table 1 shows the predicted backscatter coefficients (log scale) of the six SLRs as determined by normalizing Equation 1 to the area of the scatterer. The rough dielectric ground plane’s measured backscatter coefficient is also given. The backscatter coefficient for a rough concrete surface is given for 100 GHz, but was not available for 160 GHz or 350 GHz. At 100 GHz, the predicted σ0 of the SLRs is greater than 32 dB above the σ0 of the ground plane. The SLRs are predicted to backscatter greater than 28 dB and 34 dB above the ground plane for 160 GHz and 350 GHz, respectively.

Table 1: Predicted backscatter coefficient σ0 (dB) for the six SLRs. Also shown are the measured backscatter coefficient of the rough dielectric ground plane and rough concrete sample from Ref. (16).

Freq./Diam. 8 mm 6 mm 5 mm 4 mm 3 mm 2 mm Ground Plane Concrete

100 GHz 18.5 dB 16 dB 14.4 dB 12.4 dB 9.9 dB 6.4 dB -26 dB -26.7 dB 160 GHz 22.6 dB 20.1 dB 18.5 dB 16.5 dB 14 dB 10.5 dB -18 dB N/A 350 GHz 29.3 dB 26.9 dB 25.3 dB 23.3 dB 20.8 dB 17.3 dB -17.5 dB N/A

4.2 Backscatter Measurements RCS data of six frequency selective spherical lens reflectors mounted on the rough ground plane were measured in compact radar ranges operating at center frequencies of 100 GHz, 160 GHz, and 350 GHz. Each RCS measurement consisted of a -70 to +70 degree azimuth sweep at a fixed elevation angle. Measurements were taken at 5, 15, 25, 35, and 45 degrees elevation with the retroreflectors oriented such that 25 degrees elevation coincided with bore-sight at 0 degrees azimuth. The range of orientation angles used yielded an almost complete picture of the backscattering phenomena of the retroreflectors.

Table 2: Comparison of ground plane elevation angle and SLR elevation angle. When the ground plane was positioned at 25 degrees elevation, the retroreflector was oriented such that the incident wave was on bore-sight.

Ground Plane Elevation Angle Reflector Elevation Angle

5 degrees -20 degrees 15 degrees -10 degrees 25 degrees 0 degrees (bore-sight) 35 degrees +10 degrees 45 degrees +25 degrees

4.2.1 ISAR Imagery An inverse synthetic aperture radar (ISAR) image is a two-dimensional, range versus cross-range, high-resolution image of an object. ISAR imagery is analogous to SAR imagery with the difference that the ISAR imagery is generated via the relative motion of the scattering target with the radar transceiver held fixed, whereas SAR imagery assumes a stationary target and data is collected as the transceiver is moved. ISAR images of the SLRs on the rough dielectric ground at 25 degrees elevation and 0 degrees azimuth are shown in Figures 5-7 for 100 GHz, 160 GHz, and 350 GHz respectively. The σ0 of each SLR was determined by boxing in a given scatterer (see the lower left scatterer in Fig. 5a), summing the RCS of the selected pixels, and then dividing by the area selected. In comparison to the area of the scatterers themselves, the area used to extract the RCS was slightly larger and as such the normalization somewhat underestimated the backscatter coefficient of the reflector.



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Figure 5: 100 GHz HH-polarized ISAR imagery of the rough ground plane with (Fig. 5a) and without (Fig. 5b) the six SLRs. Both images are at 25 degrees elevation and 0 degrees azimuth. The box shown around the 6 mm SLR indicates the approximate area chosen to determine each SLR’s backscattering coefficient.

In Figure 5a the SLRs have been labeled based on size and are visible above the ground plane return. The SLRs were removed and the RCS of the empty ground plane was measured (Fig 5b). A comparison of Fig 5a and Fig 5b show that at 100 GHz the SLRs backscatter substantially more than the ground plane. The backscatter of the SLRs at 160 GHz is shown in Figure 6a and compared to the backscatter of the empty ground plane in Figure 6b. It is shown that all except the 2 mm SLR backscattered higher than the ground plane. At 350 GHz all of the SLRs backscattered significantly more than the ground plane.

Figure 6: 160 GHz HH-polarized ISAR imagery of the rough ground plane with (Fig. 6a) and without (Fig. 6b) the six SLRs. Both images are at 25 degrees elevation and 0 degrees azimuth.



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Figure 7: 350 GHz HH-polarized ISAR imagery of the rough ground plane with the six SLRs at 25 degrees elevation and 0 degrees azimuth.

The backscatter coefficients for the SLRs in Figures 5-7 are presented in Table 3 along with the rough ground plane’s return for comparison. In general, the SLRs backscattered approximately an order of magnitude more than the rough ground plane.

Table 3: Measured backscatter coefficients of six SLRs at 100 GHz, 160 GHz, and 350 GHz. Measurements were taken for HH-polarization at 25 degrees elevation and 0 degrees azimuth.

Freq/Diam 8 mm 6 mm 5 mm 4 mm 3 mm 2 mm Ground Plane 100 GHz 7.9 dB -1.8 dB -7.1 dB -4.6 dB -3.9 dB -13.6 dB -26 dB 160 GHz 11.1 dB -1.7 dB -9.6 dB 1.3 dB -9.2 dB N/A -18 dB 350 GHz 19.4 dB 11.5 dB 8.1 dB 8.8 dB 9 dB 3.3 dB -17.5 dB

A comparison of the measured σ0 values in Table 3 with the predicted values in Table 1 show that the SLRs backscatter somewhat less than the predicted values. The discrepancy in measured versus predicted backscatter coefficients may arise from sphere orientation and material losses not accounted for in the prediction. 4.2.2 Spherical Lens Reflector RCS as a function of Azimuth and Elevation at 100 GHz The monostatic backscatter coefficients for the six SLRs and the ground plane at 100 GHz are shown in Figure 8 for HH polarization and 25 degrees elevation. Figure 8 shows that the SLRs backscatter between approximately 5 dB and 33 dB above the ground plane for the smallest to largest reflectors, respectively. The peak backscatter coefficient for the 5 mm, 4 mm, and 2 mm SLRs is shifted towards +40 degrees azimuth, which indicates those reflectors were somewhat misaligned when affixed to the ground plane.



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Figure 8: 100 GHz backscatter coefficient for six SLRs at 25 degrees elevation for HH polarization as a function of azimuth angle. 4.2.3 Spherical Lens Reflector backscatter coefficient as a function of Azimuth and Elevation at 160 GHz The backscatter coefficient for the SLRs as a function of azimuth angle at 160 GHz is shown in Figure 9 for HH polarization and 25 degrees elevation. Finding the 2 mm diameter reflector proved difficult and as such the backscatter coefficient is not reported. It is shown in Figure 9 that the 6 mm and 3 mm reflectors were misaligned towards -40 degrees azimuth and the 5 mm misaligned towards +60 degrees azimuth. The peak backscatter coefficients for the five reflectors reported varied from 5 dB to 30 dB above the ground plane.



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Figure 9: 160 GHz backscatter coefficient for five SLRs at 25 degrees elevation for HH polarization as a function of azimuth angle. The 2mm reflector is not reported due to difficulty of locating in the ISAR imagery.

4.2.4 Spherical Lens Reflector backscatter coefficient as a function of Azimuth and Elevation at 350 GHz The backscatter coefficient as a function of azimuth angle at 350 GHz is shown in Figure 10 for HH-polarization and 25 degrees elevation. The peak σ0 ranges from 22 dB (2 mm SLR) to 36 dB (8 mm SLR) above the ground plane. A quick inspection of Figure 10 shows that the 8 mm, 3 mm, and 2 mm SLRs were orientated such that the peak σ0 occurred at approximately 0 degrees azimuth, whereas the 4 mm SLR’s peak σ0 was closer to +40 degrees azimuth.



Backscatter Coefficient at 350 GHz

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Figure 10: 350 GHz backscatter coefficient for six SLRs at 25 degrees elevation for HH-polarization as a function of azimuth angle. 4.2.5 Frequency Selective SLR RCS RCS measurements at 160 and 350 GHz were repeated for the reflectors with the band-pass FSS and are shown in Figures 11 and 12. The 160 GHz data falls outside the pass-band of the filter and as such the backscatter coefficient is expected to be smaller than when measured at 350 GHz. Figure 11a shows 160 GHz retroreflector data without the band-pass filter (same as Figure 6a), whereas Figure 11b shows the retroreflectors with the band-pass filter. At 160 GHz, the addition of the band-pass filter causes the reflectors to be masked by the ground plane return. The measurement at 350 GHz, shown in Figure 12, corresponds to a frequency range of the pass-band exhibiting nearly 100% transmission. Though the returns from the SLRs are somewhat diminished by the addition of the FSS, they are still clearly visible above the rough ground terrain’s return.



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Figure 11: Comparison of the backscatter ISAR imagery for a) retroreflectors (without FSS) on the ground plane at 25 degrees elevation, and b) frequency selective retroreflectors on the ground plane at 25 degrees elevation. ISAR image is of the retroreflectors at 160 GHz and 0 degrees azimuth for HH polarization.

Figure 12: Backscatter ISAR image for the frequency selective retroreflectors at 350 GHz. Image taken at 25 degrees elevation and 0 degrees azimuth for HH polarization.

5. DISCUSSION 5.1 Backscatter Coefficient of SLRs The backscatter coefficient of six fused silica spherical lens reflectors were reported at 100 GHz, 160 GHz, and 350 GHz. As shown in Figure 8, the backscatter coefficient of the reflectors at 100 GHz ranges from 5 dB to 33 dB higher than the supporting rough ground plane. The intended orientation of the retroreflectors was to align bore-sight with 25 degrees elevation and 0 degrees azimuth. Analyzing the backscatter coefficient as a function of azimuth angle from Figures 8-10 shows that some of the SLRs were misaligned. Regardless of alignment, the SLRs still had a significantly larger backscatter coefficient than the ground plane.



Another potential source of error is the choice of material. It was discussed in [17] that for a solid sphere SLR, the index of refraction of the material should be n=2. For n≠2 the SLR should consist of two hemispheres of differing radii as described by

R1 = (n −1)R2 (2) where R1 is the radius of the hemisphere with the reflective coating and R2 is the radius of the aperture hemisphere. Fused silica was reported to have an index of refraction of n=1.951 in [14] for 0.3-5 THz, using Equation 2 this implies that the reflective coated hemisphere should have a radius 95.1% of the front hemisphere radius. As solid fused silica spheres were used the effective aperture of the reflector was not optimized. This reduction in effective aperture may have lead to smaller backscatter coefficients than predicted. Approximating a spherical retroreflector as a circular metal plate does not account for material losses or front surface reflections due to the sphere. The suggested RCS approximation does not take into account scattering from the opposite side of the reflective cap. At oblique angles the reflective cap is visible to the incident wave and therefore contributes to the RCS of the SLR. The approximation (green line) in Figure 2 only scales the capture area and as such does not include scattering due to the emergence of the reflective cap. 5.2 Frequency Selective SLRs The application of the 350 GHz band-pass FSS successfully masked the retroreflectors at 160 GHz as shown in Figure 11b. This masking was expected as the measurement frequency was outside of the pass-band of the filter. At 350 GHz the FSS-covered retroreflectors are visible to the radar as the measurement frequency is within the pass-band of the FSS. The RCS of the retroreflectors at 350 GHz was likely diminished somewhat due to the application of a planar FSS to the spherical surface. Due to their size it proved difficult to carefully wrap the FSS around the spheres without introducing sharp edges and folds. Inside the pass-band, the folds and sharp edges could cause unwanted reflections, reducing the transmission into the retroreflector and therefore its RCS. A modification to the fabrication methods is to etch the filter directly onto the sphere. It has been shown in [18] that 175 nm features can be patterned onto a sphere using topographically directed photolithography and near-field contact-mode lithography. Others have patterned 1 mm diameter spheres with micron-scale features [19], and 1 inch diameter spheres with nanometer-scale features [20]. Using these techniques it may be possible to etch the band-pass FSS directly onto the front hemisphere of the SLR. This device would function much like the design reported with the added benefit of conforming the filter to the sphere. This design would involve coating the entire sphere in a reflective coating and then etching the band-pass filter into one hemisphere. An alternative design for frequency selective retroreflection is the application of a band-stop filter as the reflecting surface. In this case only frequencies within the stop-band will be retroreflected whereas frequencies outside the stop-band will be transmitted. For frequencies outside of the stop-band, the reflector is expected to scatter like a homogeneous dielectric sphere. This design can be taken a step further by applying filter designs with multiple resonances to effectively encode a barcode signature [21]. The application of an FSS with multiple tailored resonances to an SLR would yield a reflector with a specific frequency signature that can be used as a method of passive identification similar to current RFID technology [22]. A potential application for an encoded frequency selective SLR operating at THz frequencies is the identification of drones (UAVs).

6. CONCLUSION The backscatter coefficient for six spherical lens reflectors has been reported for 100, 160, and 350 GHz. The measured σ0 values are within 10 dB to 20 dB of the predicted values and possible sources of the deviation were discussed. Even though the measured σ0 is lower than expected, it has been shown that the retroreflectors backscatter between 5 dB and 33 dB more than a generic rough ground plane. Proof of concept for a frequency selective retroreflector operating at 350 GHz has been shown through the addition of a band-pass filter to the reflector. Alternate designs for achieving frequency selective retroreflection have been discussed as well as their potential application to passive identification.



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radar cross section measurements of frequency selective

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