Proceedings of the Eighth International Conference on Ground Penetrating Radar, pp.718-722, Gold Coast, Australia, 23-26 May, 2000.
DIRECTIONAL BOREHOLE RADAR USING A DIPOLE ANTENNA ARRAY S.Ebihara and M.Sato Center for Northeast Asian Studies, Tohoku University Kawauchi, Sendai, 980-8576, Japan
[email protected]
. ABSTRACT In this paper, we propose to introduce an electric field sensor using LiNbO3 optical modulator to an array type directional borehole radar. Advantage of the sensor is accuracy of measurement of fields with no electromagnetic disturbance, no battery and small space to transfer electrical signals to optical signals. If the sensor is used as array elements of the directional borehole radar, we might accurately measure electric fields at several points, and determine directions of arrival waves with the data set. We did experiment that the sensor in a borehole is illuminated from a slot antenna as a source outside the borehole. Transmission between the transmitter and the electric field sensor in a borehole was measured, and we got array data set with the sensor. The array data was analyzed by cross-spectrum analysis, and coherence, time delay and relative amplitude among the array elements was estimated. Experimental results gave good agreement with theoretical results. This is because we could accurately measure electric fields with the optical modulator, and accuracy of the data was enough to determine directions of arrival waves in a borehole. We think that the experimental results show possibility to realize a directional borehole radar using the dipole array with an optical modulator. Keywords : Optical modulator, Dipole antenna, Directional borehole radar
borehole radar. We can transfer received electrical signals of the dipole antenna element to optical signals with small space and no battery by the modulator. If we use the antenna in a borehole, we could measure field with no electrical disturbance, since there is no conducting part. Also it may be easy to increase number of elements. In this paper, we will examine how suitable a dipole antenna with the optical modulator is for an array type directional borehole radar. We will show accuracy of measurement of fields at many positions in a borehole with the dipole antenna. EXPERIMRNT USING AN OPTICAL MODULATOR Dipole Antenna Element And Optical Modulator We arranged a dipole antenna element using an optical modulator on an acrylic pipe for a receiving antenna. A picture of the antenna is shown in Figure1. Light through Mach-Zehnder waveguide is modulated by received voltage of the dipole antenna with Pockels effect, and the received signals are transmitted by an optical fiber. Length of the dipole antenna is 0.2m, and the diameter of the pipe is 0.07m. There is no conductor around the antenna, except for the antenna element by itself. Bandwidth of the optical modulator is 0.3-1GHz.
INTRODUCTION Most conventional borehole radar use dipole antenna, which are ominidirectional. However, in many engineering applications, three-dimensional positions of targets should be accurately determined. Since used wave length, which is more than 0.3m, is much larger than the space available for antennas, we have proposed to apply super-resolution technique to array data in order to estimate three-dimensional positions of targets in a borehole (Ebihara et al., 1996 and 1998a). When we use the super-resolution technique, accurately measuring fields in many positions in a borehole is essential. For the accurate measurement, we will introduce a dipole array with an optical modulator (Kuwabara et al., 1992, Kondo et al., 1994) such as Mach-Zehnder interferometry to directional
Experiments The following experiments were carried out in order to examine time delay and amplitude of the dipole antenna in a borehole. Measurement system and arrangement of antennas are shown in figure 2. We set the dipole antenna with an optical modulator at 1.5m depth inside a borehole, in which there is no fluid. Also we set a slot antenna, of which slot length is 0.1m, as the transmitting antenna at 1.5m depth on a wall of a cave. The wall is 0.8m apart from the borehole. We can assume that a vertically polarized wave illuminates the dipole antenna, since a horizontal slot antenna is chosen. There is no guided wave in a borehole (Ebihara, 1998b), since the transmitter and receiver in
different holes. Cross section of the borehole is shown in Figure 3. We rotated the pipe around z-axis, and we got received signals every φ=15 degree. Although number of the sensor is only one, we can get a kind of array data set because of the rotation. Measurement was carried out with a network analyzer. The time domain signals are shown in Figure 4, which were got by inverse Fourier transform. Also Fourier transform of a window function in frequency domain is shown. We can see that waves from the transmitter arrive around 108 ns. In the direction of 0 degree, a transmitter is actually located.
Sxy (ω )
H (ω ) =
Sxx (ω )
af
τg ω =
a f=
∆θ xy ω ∆ω
af
coh ω =
As we can see in Figure4(a), time delay difference and relative amplitude among the signals are small. Here, we introduce cross-spectrum analysis to analyze the signals. We can see which frequency is credible data with coherency, and time delay and relative amplitude can be estimated with the cross-spectrum analysis. Using Blackman-Tukey method (Kay,1988), power-spectrum Sxx of a signal x(t) and cross-spectrum Sxy between a signal x (t) and y(t) were estimated. Relative amplitude between the two is estimated as
(1)
Also group delay between the two signals τg and coherency coh2 are
2
Cross-spectrum Analysis
.
∆ arg( Sxy (ω )) . ∆ω
af . aω fS aω f 2
Sxy ω Sxx
In Figure 5(a)-(c), we show results of the analysis with solid lines. In this analysis, we used the signal, which was received at φ=0 degree, for x(t), and the signal at φ=180 degree for y(t). Also, in Figure 6 (a)-(c), we show results of cross-spectrum analysis between the signal at φ=0 degree and each signal received every 15 degree at 150MHz with solid lines.
air x
φ
ρ
φ0.07m
z
φ 0.11m
dipole antenna( φ0.001m)
Azimuth(degree)
Figure 3. Cross section of the borehole
0 180 345 104
106
108
110
112
114 116 Time(ns)
118
120
122
124
6
8
10
amplitude(V)
(a) Received signals 0.04 0.02 0 -10
-8
-6
-4
-2
0 time(ns)
(3)
yy
soil(εr=20)
E
(2)
2
4
(b) An incident signal Figure 4. Cross section of the borehole
1
coherency
coherency
1
0.5
0
0
200
400
600
800
0.5
00
1000
90
180 270 Azimuth(degree)
Frequency(MHz) (a) Coherency
(a) Coherency measured theory
Measured Theory
1 Relative amplitude
Relative amplitude
1
0.5
00 0
0.9
0.8
0.7 1
2 200
3
4 400
6 600
8 800
9
10 1000
0
Frequency(MHz)
90
180 270 Azimuth(degree)
(b) Relative amplitude
(b) Relative amplitude 1.2
8 6 4
0.8
Group delay(ns)
Group delay(ns)
measured theory
Measured Theory
2 0 -2 -4 -6 -8
0.4
0 0
0
200
400
600
800
1000
Frequency(MHz) (c) Group delay Figure 5 Cross-spectrum analysis between the signal at φ=0 degree and φ=180 degree.
90
180 270 Azimuth(degree)
(c) Group delay Figure 6 Cross-spectrum analysis between the signal at φ=0 degree and each signal received at φ=0-345 degree. Frequency =150MHz.
DISCUSSION In this section, we will show the time delay and relative amplitude is reasonable. We use a theoretical model that TM uniform plane wave propagating in the –x direction in homogenous medium (εr=20) is incident normally on a vacuum circular cylinder of diameter a=0.11m as shown in Figure3. Such field can be theoretically calculated using cylindrical functions (Balanis, 1989, Chew, 1995). We assume that calculated z-component of electric field at ρ=0.035m is proportional to received voltage of the dipole antenna. Current is induced on the dipole antenna, but we ignore the current for simplicity. This assumption may be valid, because we will consider that only relative amplitude and group delay between two signals received at two different azimuth, and that diameter 0.001m of the dipole antenna is very thin. The theoretical curves are also shown in Figure 5 (b)-(c) by a dotted line. Also we solved nonlinear curve-fitting problems in the least-squares sense, and we fitted the theoretical lines to figure 6 (b)-(c) with a dotted line. In Figure 5(a), we find that coherence is high around frequency 100-200MHz, 500MHz and 600-700MHz. Especially in 100-200MHz in Figure 5(b)-(c), and we can see that the measured relative amplitude and group delay are near the theoretical line. Therefore we think that the theoretical model represents the experimental results around 150MHz well. In figure 6 (b)-(c), tendency of the relative delay and amplitude among azimuth is almost same as the theoretical results in 150MHz. This means that there is possibility to estimate direction of arrival waves with some proper array synthesis using the theoretical model in the frequency band-width, if we put the dipole antenna elements on a circle in a borehole. CONCLUSIONS AND FUTURE WORK In this paper, we proposed a dipole antenna element with a LiNbO3 optical modulator for a directional borehole radar. We did experiments with the optical modulator, and we got circular array data set in a borehole. Cross-spectrum analysis was used to estimate time delay and relative amplitude among the signals. We found that a plane wave incidence model to dielectric cylinder gives good agreement with the delay and amplitude of the experimental results. This means possibility to realize the directional borehole radar with the optical modulator. If we put multiple antenna elements in a borehole, there will be mutual coupling between them. We have to consider the influence to analyze the array signals. We will try to use Method of Moment to calculate influence of the coupling in a borehole.
ACKNOLEDGEMENTS
This work was partly supported by Secom Science and Technology Foundation, and Grant-in-Aid of Encouragement of Young Scientists (A) 11750802 and Scientific Research (A) 11355041, Japan Society for the Promotion of Science. REFFRENCE Balanis,
C.A., 1989. electromagnetics.
Advanced
engineering
Chew, W.C., 1995. Waves and Field in Inhomogeneous Media, IEEE Press. Ebihara, S., Sato, M., and Niitsuma, H., 1996. Estimation of reflector position by a directional borehole radar using a cylindrical conformal array antenna, Proceedings of 6th International Conference on Ground Penetrating Radar, Sendai, Japan, Sept. 30-Oct. 3, pp.411-416. Ebihara, S., Sato, M., and Niitsuma, H., 1998a. MUSIC algorithm for a directional borehole radar using a conformal array antenna, Proceedings of 7th International Conference on Ground Penetrating Radar, Kansas, USA, May 27- 30, pp.13-18. Ebihara, S., Sato, M., and Niitsuma, H., 1998b. Analysis of a guided wave along a conducting structure in a borehole, Geophysical prospecting, 46, pp.489-505. Kay, S.M., 1988. Modern spectral estimation. Kondo, M., Tokano, Y., Tanabe T., and Muramatsu, R., 1994. Conference paper. Proceedings of EMC Symposium ’94, Sendai, Japan, 16-20 May, pp.774-777. Kuwabara, N., Tajima, K., Kobayashi, R., Amemiya, F., 1992. Development and analysis of electrical field using LiNbO3 optical modulator, IEEE Trans. Electromagn. Compat., Vol.34, No.4.
optical modulator(Modified version of TOKIN OEFS1)
dipole antenna
Figure 1. Dipole antenna with an optical modulator
Network Analyzer(HP8752A)
Laser Diode (TOKIN TG007) Coaxial cable
Photo-detector (TOKIN TG007) Single mode fiber
rotating
Polarization maintaining fiber Cavity backed slot antenna
0.8m BR2
Dipole antenna
wall of the cave
1.5m slot antenna dipole antenna
Altered version of TOKIN OEFS1 optical modulator
(a) Block diagram
(b) Arrangement of antennas
Figure 2. Experiment using the optical modulator
