ISSN 1063-7842, Technical Physics, 2018, Vol. 63, No. 2, pp. 260–267. © Pleiades Publishing, Ltd., 2018. Original Russian Text © S.I. Ivashov, A.S. Bugaev, A.V. Zhuravlev, V.V. Razevig, M.A. Chizh, A.I. Ivashov, 2018, published in Zhurnal Tekhnicheskoi Fiziki, 2018, Vol. 63, No. 2, pp. 268–275.
OPTICS
Holographic Subsurface Radar Technique for Nondestructive Testing of Dielectric Structures S. I. Ivashov*, A. S. Bugaev, A. V. Zhuravlev, V. V. Razevig, M. A. Chizh, and A. I. Ivashov Bauman State Technical University, Moscow, 105005 Russia *e-mail:
[email protected] Received May 11, 2017
Abstract—Holographic subsurface radar method is compared with the conventional technology of impulse radars. Basic relationships needed for the reconstruction of complex microwave holograms are presented. Possible applications of the proposed technology are discussed. Diagnostics of polyurethane foam coatings of spacecrafts is used as an example of the efficiency of holographic subsurface radars. Results of reconstruction of complex and amplitude microwave holograms are compared. It is demonstrated that the image quality that results from reconstruction of complex microwave holograms is higher than the image quality obtained with the aid of amplitude holograms. DOI: 10.1134/S1063784218020184
INTRODUCTION Subsurface radars are employed in the study of optically opaque media [1, 2] in various applications. Note, for example, engineering geology [3], humanitarian demining operations [4–6], testing of building structures and objects of cultural heritage [7], and nondestructive testing of dielectric materials [8]. Conventional subsurface radars are impulse radars that emit signals the shape of which is close to one sine period. Almost all commercially available subsurface radars are based on such a technology due to several reasons. The main advantage of the devices lies in the fact that media with relatively high levels of electromagnetic wave attenuation can be studied at significant depths which is not possible for radars that emit continuous (modulated or unmodulated) signals. Such an advantage is reached owing to the emission of a pulse packet and the detection of pulses using a stroboscopic detector with a variable gain [1, 2]. The impulse radar also allows direct estimation of the depth of the subsurface object using the delay time of the received signal if, at least, approximate values of the propagation velocity of electromagnetic waves in the medium under study are available. A potential threat of the interference with alternative sources of electromagnetic signals (e.g., satellite navigation and mobile communication systems) can be considered as a disadvantage of the impulse systems. Federal Communications Commission has made an attempt at banning of the subsurface radars [9, 10].
Both continuous wave and impulse radars are applied in the subsurface measurements [1]. The former employ linear frequency modulation, step-frequency, or holographic detection, which is discussed in this work. The first works on the holographic subsurface radars date back to the 1980s [11, 12]. The efficiency of holographic radars appeared to be insufficient for the study of soils with a relatively high attenuation owing to a small penetration depth [12] in comparison with measurement depths of up to 10 m or more for impulse radars. RASCAN subsurface radars that were developed in the 1990s can be used in several applications in which relatively large penetration depths are unnecessary but relatively high spatial resolution is needed to determine shape of and identify subsurface objects using the reflected signal [5, 13]. Commercial production of the RASCAN radars has stimulated further study [6, 14]. 1. HOLOGRAPHIC SUBSURFACE RADARS The design of subsurface radars is based on the classical principles of radar technologies. The signal emitted by the transmitting antenna to the medium is reflected from a local inhomogeneity provided that the permittivity of such an inhomogeneity differs from the permittivity of the medium. The reflected signal is detected by the receiving antenna of the radar and amplified in the receiver.
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subsurface radar under study lies in the fact that the transmitting and receiving dipole antennas are located in a unit that represents an open-end circular waveguide. The waveguide diameter, antenna positions, and the remaining parameters are optimized with respect to the radar sensitivity [15]. Principles of microwave holography are similar to the principles of optical holography. We assume that a plane monochromatic wave with constant phase (reference wave) is incident on and scattered by an object. An interference pattern is formed on a plane screen that is located at a certain distance behind the object owing to the superposition of the reference and scattered waves (Fig. 2a). When the reference wave is incident on the screen along the normal, the interference results in the formation of the hologram that represents a Fresnel zone plate consisting of concentric rings and exhibits the properties of a focusing lens. A real image of object is obtained when the reference wave is diffracted by the hologram (Fig. 2b). A similar scenario is implemented when a microwave hologram of a point target in homogeneous medium is detected using a subsurface holographic radar [14]. However, optical holography substantially differs from the holography in the subsurface radar measurements. First, optical holograms are recorded in optically transparent media with insignificant or zero absorbance whereas the media that are studied with the aid of the subsurface radars exhibit relatively high attenuation coefficients of 25 dB/m or more in the wavelength range of the radar [1, 2]. This circumstance is
Radar antenna Scanned aperture
y z
x 0
Target point (x, y, z0)
Target Fig. 1. Scheme of the subsurface holographic radar measurements: (x, y, z) are the Cartesian coordinates, and z0 is the depth of the object relative to the radar plane.
As distinct from the measurements using an impulse radar, the single-point measurements using a monochromatic holographic radar do not yield informative results, so that the reflected signal must be detected at a certain fragment of the surface to obtain a microwave hologram (Fig. 1). The signal emitted by the transmitting antenna is reflected from the subsurface object (object wave) and is mixed in the detector with a reference wave that is obtained from a generator. The signal that is directly transmitted from the transmitting to the receiving antenna may also serve as the reference wave. Such a configuration is used in the measurements of amplitude holograms. A specific feature of the holographic (a)
(b)
Reference wave
Object
261
Object wave
h
Image plane r
0
Fresnel zone plate
h
Conjugate object wave
Reconstructed image
Fig. 2. (a) Recording and (b) reconstruction of the simplest optical hologram. TECHNICAL PHYSICS
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The third difference lies in the fact that complex or amplitude holograms can be obtained in the radio frequency band whereas in the optical band only amplitude holograms can be recorded. This circumstance makes it possible to get rid of the virtual image in the reconstruction of microwave holograms and to improve their quality.
5 3 2 1
4
Fig. 3. Experimental setup: (1) sample under study, (2) antenna, (3) cables, (4) electromechanical scanner, and (5) ZVA 24 vector network analyzer.
important for the measurements. When the attenuation factor is high, the subsurface object is observed only along the axis of the main lobe of the antenna pattern (AP). Deviation from the axis of the main lobe for the antenna pattern for all types of antennas that are used in the subsurface radars leads to a significant decrease in the antenna gain and the object is not observed at oblique angles, so that the interference pattern is not formed and the hologram is not recorded [16]. In particular the experiments with concrete yield shadow images (that are similar to the X-ray images) rather than microwave holograms [7, 14]. Second, the microwave holograms substantially differ from optical holograms by the ratio of size d of the system in which the hologram is obtained to wavelength λ. In optics, such a ratio may amount to d/λ ≅ 106. Such a parameter determines the number of interference fringes in the hologram. For the holograms that are obtained with the aid of subsurface radars, ratio d/λ is several units and can be used to determine the shape of the object under study even in the absence of the reconstruction procedures. As was mentioned, the image for media with relative high levels of attenuation is similar to shadow image and the interference fringes are missing.
2. EXPERIMENTAL SETUP The experimental setup consists of a ZVA 24 vector network analyzer (VNA) that is used for signal generation and measurement, antenna unit (AU), and electromechanical scanner (Fig. 3). The electromechanical scanner provides the computer-controlled movement of the samples under study relative to stationary AU that represents an open-end circular waveguide. The AU is connected using cables to the VNA. Such an experimental configuration provides the absence of cable bending influence on the detected signal, which is inherent in the configuration with the mobile AU. The VNA working range makes it possible to perform experiments at frequencies ranging from 10 MHz to 24 GHz, and the setup allows variations in the distance between the antenna and the surface of the sample under study. Thus, we can analyze the effect of such a distance on the experimental holograms and study samples with different thicknesses and surface roughnesses. The VNA can be used for the measurement of signal amplitude and phase, so that complex holograms can be obtained (as distinct from optical holography). Below, we prove that complex holograms are superior to amplitude holograms with respect to the reconstruction procedure. In the experiments, the VNA is used to measure the S parameters that represent coefficients of the scattering parameters matrix for a multiport device
⎡V1− ⎤ ⎡V1+ ⎤ ⎢ − ⎥ ⎡ S11 S12 ... S1N ⎤ ⎢ + ⎥ V ⎢V2 ⎥ = ⎢ S ⎥ ⎢ 2 ⎥, ⎢ ⎥ ⎢ 21 ⎥⎢ ⎥ SNN ⎦⎥ ⎢ ⎥ ⎢ − ⎥ ⎣⎢SN 1 ... + ⎢⎣Vn ⎥⎦ ⎢⎣Vn ⎥⎦ which establish relationships of the voltages of incident (Vn+ ) and reflected (Vn− ) waves [17]. In the experiments, we measure parameters S11 and S12 for the antennas connected to one and two ports, respectively. 3. ALGORITHM FOR THE RECONSTRUCTION OF MICROWAVE HOLOGRAMS Complex microwave holograms that result from the scanning need to be further processed with the aid of reconstruction algorithms. For the reconstruction, TECHNICAL PHYSICS
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and a factor that corresponds to the delay of the reflected wave relative to the reference wave:
A−A
5
1
40
Polyurethane foam
400 200 ∅50 3 positions
30
60
200
A
100
85
500
A
E ( x, y) =
∫∫ r( x ', y ')e
e
=
Fig. 4. Schematic drawing of the sample made of polyurethane foam provided by the NPO Tekhnomash.
we employ the algorithm that has been proposed for processing of acoustic holograms and improved in [18, 19]. The advantage of such an algorithm lies in the fact that the far-field approximation is not needed. Transverse resolution δx is determined only by the diffraction relationships and represented in the following way for the lossless medium: (1)
Here, λ is the radiation wavelength and d is the effective size of the synthesized aperture with allowance for the antenna pattern. Parameter d can be significantly less than the size of the scanning region, since the former is determined by the angles at which the signal reflected by the object is detected by the antenna. The details of the reconstruction algorithm are as follows. We consider a plane object that is parallel to the scanning plane and located at distance z0 from such a plane (Fig. 1). Complex signal E(x, y) that is detected by the antenna detector at each point of the scanning plane can be represented as an integral of the product of signals reflected from each point of object TECHNICAL PHYSICS
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2
2
2
dx ' dy '. (2)
(3) v = c . |ε| Here, c is the speed of electromagnetic wave in vacuum and ε is the complex permittivity of the medium. Expression (2) is written with disregard of the effect of AP and signal attenuation in the medium, which affect the amplitude of the detected signal, since the corresponding amplitude dependences are less important than the phase dependences in the reconstruction procedure [18]. The exponential term in the integrand in expression (2) corresponds to a spherical wave that propagates from point (x, y) and can be represented as a superposition of plane waves [20]:
Welded seam
z δx ≈ λ 0 . 2d
−i 2k ( x − x ') +( y − y ') + z0
Here, r(x', y') is the function that describes the reflectivity of the surface of the object (ratio of the complex amplitudes of the reflected and incident waves), k = 2πf/v is the wave number, v is the speed of electromagnetic wave in the medium under study, f is the frequency of the radar signal, and a factor of 2 in the exponent results from the double passage of the wave (from the antenna to the object and in the opposite direction). Speed v is related to the material parameters:
Aluminium sheet
∅270
263
∫∫
e
−i 2k ( x − x ')2 +( y − y ')2 + z02
(4)
i(k x ( x − x ')+ k y ( y − y ')+ kz z0 )
dk x dk y ,
where kx, ky, and kz are the projections of the wave vector along the corresponding coordinate axes. Substituting expression (4) in formula (2), we obtain
E ( x, y) =
∫∫ r( x ', y ')e
×e
−i(k x x '+ k y y ')
dk x 'dk y '
i(k x x + k y y + kz z0 )
(5)
dk x dk y .
It is seen that the underlined term in this expression is the 2D Fourier transform of function r(x, y):
F (k x , k y ) =
∫∫ r( x, y)e
−i(k x x + k y y )
dxdy = Φ 2D{r ( x, y)}. (6)
We represent expression (5) as
E ( x, y) =
∫∫ F (k , k )e x
y
ikz z0 i(k x x + k y y )
e
−1 = Φ 2D {F (k x , k y )}e
dk x dk y
ikz z0
(7)
and employ the properties of the Fourier transform
F (k x , k y ) = Φ 2D{E ( x, y)}e
−ikz z0
−1 r ( x, y) = Φ 2D {F (kz , k y )}
,
(8) (9)
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(a)
(b)
(c)
Fig. 5. Result of scanning at a frequency of 20.3 GHz for the sample of Fig. 4: (a) Q quadrature, (b) I quadrature, and (c) amplitude hologram.
(a)
(b)
Fig. 6. Results of the reconstruction of the holograms of Fig. 5: (a) reconstructed complex hologram and (b) reconstructed amplitude hologram.
to derive the following expression for the reflectivity function of the object: −1 r ( x, y) = Φ 2D {Φ 2D{E ( x, y)}e
−ikz z0
(10)
}.
With allowance for the relationships of the wave vector and its projections
k x2 + k y2 = kz2 = (2k )2;
kz = 4k 2 − k x2 − k y2, (11)
we obtain the final expression that is used for the reconstruction of holograms: −1 r ( x, y) = Φ 2D [Φ 2D{E ( x, y)}e
i 4 k 2 − k x2 − k y2 z0
].
(12)
Normally, the object depth is unknown in the subsurface radar measurements. Thus, a layer-by-layer reconstruction of hologram can be performed with a
certain step with respect to depth. Then, the depth that corresponds to the most distinct image of the object can be chosen. Such a procedure may yield the best focusing at the object under complicated conditions (e.g., inhomogeneous media with a relatively high electromagnetic wave attenuation). Note a problem that is inherent in the subsurface radar measurements and lies in the fact that the determination of the position of a subsurface object using measurements at the surface of half space with unknown permittivity of medium ε always implies solution of inverse ill-posed problem.
4. EXPERIMENTAL RESULTS As was mentioned, microwave holograms can be recorded and reconstructed only for media with relatively low attenuation in the working wavelength TECHNICAL PHYSICS
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promising launchers. Two samples of coatings provided by Russian and Indian aerospace research centers were used in the experiments. Figure 4 presents a schematic drawing of the Russian sample.
B
A
A 30
20
40
75
60
E F
10
40 20 30
B 10
300
45
C
C 15
80
D
10 50
D 25
50
20
60
Bonded surface
300
265
Metal plate PUF
Fig. 7. Schematic drawing of the sample with defects provided by the Vikram Sarabhai Space Center.
range. Most media that are studied with the aid of subsurface radars do not satisfy such a requirement. However, composite materials based on glass and quartz fibers [21, 22] and polyurethane foam [8, 23] can be considered as exceptions. The interest in the study of the polyurethane foam coatings has been driven by the fatal accident of Space Shuttle Columbia (2003). Such coatings with extremely low thermal conductivity and low density [23, 24] had been used for thermal insulation of the outer fuel tank with cryogenic agents. Production defects related to the deposition of coating had been the reason for detachment of a fragment of coating and the subsequent destruction of the reentry module [25]. Several experiments using the experimental setup (Fig. 3) have been performed for aerospace industry. The experiments were aimed at the nondestructive testing of dielectric coatings of cryogenic tanks of
A sample with artificial defects represents a thermally insulating package that is fabricated with the aid of gluing of the polyurethane foam layer with a thickness of 40 mm on the AMg6 aluminum–magnesium plate with a thickness of 5 mm. A layer consisting of primer and glue (0.2 mm) is deposited on the metal plate under the thermally insulating layer. The outer side of the thermally insulating layer is mechanically processed to obtain a smooth surface. A cylinder with a diameter of 270 mm is cut in the polyurethane layer. Voids with a diameter of 50 mm and a depth of 1 mm are made on the inner surface of the cylinder. Then, the cylinder is glued to the metal substrate. The glue layer is absent on the metal plate at the locations of the voids, and the primer and glue are deposited on the inner surface of the voids. Such a sample serves as a model of detachment of the thermally insulating layer from the surface of the cryogenic tank. The total area of the sample with the thermally insulating layer is 400 × 500 mm. The sample is scanned using the experimental setup (Fig. 3). The scanning area (350 × 350 mm) is less than the sample area and covers the region with defects. The scanning step is 5 mm, the antenna–surface distance is 30 mm, and the holograms are detected at a frequency of 20.3 GHz. Figure 5 shows the experimental complex and amplitude holograms. The measured holograms are processed using the reconstruction algorithm of Section 3 (expressions (1)–(12)). The algorithm is used for general reconstruction of complex holograms. However, it is expedient to compare the quality of reconstructed complex and amplitude microwave holograms. The reconstruction of the amplitude microwave holograms has been considered in [26].
A B
C D (a)
(b)
(с)
Fig. 8. Result of scanning for the sample of Fig. 7: (a) Q quadrature, (b) I quadrature, and (c) reconstructed hologram. TECHNICAL PHYSICS
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In the reconstruction of the holograms, we assume that focusing depth Z0 (70 mm) corresponds to the distance between the edge of antenna and metal substrate with defects. In accordance with the results of [23], the permittivity of the polyurethane foam of Space Shuttle is ε = 1.05 – i0.003. With allowance for identity of requirements on thermally insulating materials, we use such a permittivity for the samples under study. The imaginary component of the permittivity that is related to conductivity is relatively small, and the real part slightly differs from the permittivity of air. Thus, we assume that ε = 1 in the reconstruction algorithm. Figure 6 shows the reconstructed holograms that correspond to the experimental results of Fig. 5. The comparison of the complex and amplitude holograms shows that the image quality for the former is significantly higher than the image quality for the latter. Such a result is due to the fact that the real and virtual images are superimposed upon reconstruction of the amplitude holograms. The effect is missing in the reconstruction of the complex holograms. The fringes at the edges of the images result from the reflection of electromagnetic wave from the edges of the metal plate. The second sample of the thermally insulating coating with a size of 300 × 300 mm and a thickness of 40 mm is provided by the Vikram Sarabhai Space Center. The samples are similar to each other. However, the defects of the Indian sample are made in a different way. Voids of different shapes and sizes are made in the polyurethane layer on the side that is glued to the metal substrate. Figures 8a and 8b show the results of scanning of such a sample and the complex hologram at a frequency of 22.5 GHz. Figure 8c presents the reconstructed hologram. Relatively large defects A–D are detected in the reconstructed image. However, small defects E and F (with sizes not shown in Fig. 7) are not detected. Note also that the image of Fig. 8c shows inhomogeneities the origin of which is unclear. Such specific features may result from roughness of the inner surface of the polyurethane or adhesive layer. CONCLUSIONS The experimental results show that the proposed method for nondestructive testing of thermally insulating polyurethane foam coatings of spacecrafts based on the gigahertz-range holographic subsurface radar can be used to supplement alternative (e.g., ultrasonic and thermographic) diagnostic procedures. The method can be implemented using specific sensors equipped with devices for scanning of relatively large items (e.g., cryogenic fuel tanks). A system with working frequencies ranging from 20 to 24 GHz must be used to reach the needed sensitivity with respect to
defects and inhomogeneities in the thermally insulating coatings. ACKNOWLEDGMENTS Support for this work was provided by the Russian Science Foundation under project no. 15-19-00126. Authors are grateful to NPO Tekhnomash and Vikram Sarabhai Space Center for the samples of thermally insulating coatings. REFERENCES 1. D. J. Daniels, Ground Penetrating Radar, 2nd ed. (IEE, London, 2004). 2. M. I. Finkel’shtein, V. I. Karpukhin, A. V. Kutev, and V. N. Metelkin, Ground Penetrating Radar, Ed. by M. I. Finkel’shtein (Radio i Svyaz’, Moscow, 1994). 3. M. I. Finkel’shtein, V. A. Kutev, and V. P. Zolotarev, The Use of Ground Penetrating Radar in Geotechnical Engineering, Ed. by M. I. Finkel’shtein (Nedra, Moscow, 1986). 4. L. Nuzzo, G. Alli, R. Guidi, N. Cortesi, A. Sarri, and G. Manacorda, in Proc. 15th Int. Conf. on Ground Penetrating Radar, Brussels, Belgium, 2014, p. 969. 5. S. I. Ivashov, V. I. Makarenkov, V. V. Razevig, V. N. Sablin, A. P. Sheyko, and I. A. Vasiliev, in Proc. 8th Int. Conf. on Ground Penetrating Radar, Gold Coast, Australia, 2000, p. 36. 6. X. J. Song, Y. Su, C. L. Huang, M. Lu, and S. P. Zhu, in Proc. 16th Int. Conf. on Ground Penetrating Radar, Hong Kong, China, 2016. https://doi.org/10.1109/ ICGPR.2016.7572660 7. V. V. Razevig, S. I. Ivashov, A. P. Sheyko, I. A. Vasilyev, and A. V. Zhuravlev, Prog. Electromagn. Res. Lett. 1, 173 (2008). 8. S. Ivashov, V. Razevig, I. Vasiliev, T. Bechtel, and L. Capineri, NDT&E Int. 69, 48 (2015). 9. Federal Communications Commission, Report and Order No. FCC 02-48 (Washington, 2002). 10. D. J. Johnson, GPR—The Impact of New FCC Regulations (GSSI, 2002). 11. G. Junkin and A. P. Anderson, in Proc. 16th European Microwave Conf., Dublin, Ireland, 1986, p. 720. 12. G. Junkin and A. P. Anderson, IEE Proc. F 135, 321 (1988). 13. I. A. Vasiliev, S. I. Ivashov, V. I. Makarenkov, V. N. Sablin, and A. P. Sheyko, IEEE Aerosp. Electron. Syst. Mag. 14 (5), 25 (1999). 14. S. I. Ivashov, V. V. Razevig, I. A. Vasiliev, A. V. Zhuravlev, T. D. Bechtel, and L. Capineri, IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 4, 763 (2011). 15. V. V. Razevig, I. A. Vasil’ev, A. I. Ivashov, S. I. Ivashov, and V. I. Makarenkov, RF Patent No. 2482518 (2013). 16. V. V. Razevig, S. I. Ivashov, I. A. Vasiliev, A. V. Zhuravlev, T. Bechtel, and L. Capineri, in Proc. XIII Int. Conf. on Ground Penetrating Radar, Lecce, Italy, 2010, p. 657. 17. D. M. Pozar, Microwave Engineering, 4th ed. (Wiley, 2012). TECHNICAL PHYSICS
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HOLOGRAPHIC SUBSURFACE RADAR TECHNIQUE 18. D. M. Sheen, D. L. McMakin, and T. E. Hall, IEEE Trans. Microwave Theory Tech. 49, 1581 (2001). 19. V. V. Razevig, A. S. Bugaev, S. I. Ivashov, I. A. Vasil’ev, and A. V. Zhuravlev, Usp. Sovrem. Radioelektron., No. 9, 51 (2010). 20. L. M. Brekhovskikh, Waves in Layered Media (Nauka, Moscow, 1973). 21. S. I. Ivashov, V. V. Razevig, T. D. Bechtel, I. A. Vasiliev, L. Capineri, and A. V. Zhuravlev, in Proc. IEEE Int. Conf. on Microwaves, Communications, Antennas and Electronic Systems, Tel-Aviv, Israel, 2015, p. 1.
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22. T. Lu, C. Snapp, T.-H. Chao, A. Thakoor, T. Bechtel, S. Ivashov, and I. Vasiliev, Proc. SPIE 6555, 65550S1 (2007). 23. S. Kharkovsky and R. Zoughi, IEEE Instrum. Meas. Mag. 10 (2), 26 (2007). 24. B. A. Dombrow, Polyurethanes (Reinhold, New York, 1957). 25. F. Morring, Jr., Aviat. Week Space Technol., 31 (2003). 26. D. Ya. Sukhanov and K. V. Zav’yalova, Tech. Phys. 57, 819 (2012).
Translated by A. Chikishev
