Frequency domain (top) and time domain (bottom) characterization of a wideband delay line (a) and a dual-resonator sensor (b), both compatible with differential measurement approaches.
Experimental measurement of the response of a delay line ((a), green) and a 100 MHz fundamental frequency resonator ((a), red) as probed by a Malå RAMAC GPR unit. (b) A radargram is made of multiple A-scan RADAR traces (fast time vertical, trace number horizontally). The sequence of experiments is with the delay line and resonator (both), resonator only, delay line and resonator, delay line only, and again delay line and resonator (both), resonator only, delay line and resonator. Bottom (b): Fourier transform of the recovered signal in the various configurations just described: the peaks of equal areas whatever the sensor configuration emphasizes that both resonators and delay line exhibit similar efficiency to returning energy when excited by the wideband incoming RADAR pulse. The value next to each legend entry is the integral below each curve, representative of the returned power (arbitrary units).
Result of applying the LASSO estimator algorithm using the sparse sine wave distribution in the spectrum. Top: the frequency estimate as a function of trace number. Each estimate is independently computed and the standard deviation is 7.8 kHz, with a result independent of the dimension for values larger than 218 (here shown for 218 and 220). The frequency resolution is thus 100-fold improvement with respect to the Fourier transform (613 MHz sampling rate, 800 sampled points). Notice that the frequency estimate loss between traces 25 and 41 is consistent with the removal of the resonator from the GPR interrogation range. Bottom: estimate of the standard deviation of the additive noise .
Top: raw measurements recorded by a GPR operating at 200 MHz, with a HBAR sensor located at a fixed distance between the emitting and receiving antennas (bistatic configuration, the antennas being separated by 50 cm). Bottom: results of the cross-correlation computation between the segments indicated by horizontal lines on the top graph (first and fourth reflections, selected for maximum separation and thus maximum delay while keeping acceptable signal to noise ratio). The cross-correlation maximum, locally fitted by a parabolic fit for sub-pixel resolution, provides an accurate estimate of the time delay between the two returned pulses, and thus, the physical quantity changing the acoustic velocity. Notice the cross correlation maximum position varying as a function of the HBAR temperature.
Interrogation of a HBAR sensor buried at varying distances from the surface in a snow drift assumed to remain at constant temperature during the measurement. The HBAR response is considered in the time domain as multiple reflections of the incoming GPR pulse. Top: time domain returned signals. Bottom: the cross correlation of two returned signal echos performs a matched filter identification providing both efficient signal extraction from noise and accurate delay identification through the position of the cross-correlation. Using both 100 and 200 antennas on the same transducer acting as remote cooperative target, the device was still visible while buried as deep as 5 m below the surface at which the GPR antennas were located. (a) Measurements of the HBAR using a 100 MHz antenna. (b) Measurements of the same device using a 200 MHz antenna. Notice the cross correlation maximum value decay with distance, but most significantly the cross-correlation maximum position varying as a function of the target distance to the GPR antennas. The distance value next to each legend entry is the depth of the sensor with respect to the antennas located on the snow drift surface, ranging from 55 cm to 460 cm.
(a) Top, GPR based interrogation of a HBAR sensor subject to temperature variations using a resistance as a heater and located at a fixed distance from the antennas. Bottom: the temperature of the acoustic sensor was simultaneously measured using a Pt100 reference probe. In this example, the distance between HBAR and RADAR is kept constant and the temperature is varied. (b) Time delay vs. temperature between two pulses relationship as observed on this particular device. Considering the slope of the temperature vs delay dependence (left) is and the delay standard deviation (right), the temperature measurement standard deviation is 4.6 K, with 8 stack averaging on the GPR trace acquisition and no sliding average on the temperature estimated values. Inset: electrode layout for a coupled resonator configuration, with a typical chip size of 1 × 1 mm2 and electrode diameter of 900 μm.
Simulation of the evolution of the first order temperature coefficient of a HBAR made of a (YXl)/165° lithium niobate thin single-crystal piezoelectric layer over a 50 μm thick (YXl)/35° quartz as a function of overtone number. The thinner the piezoelectric active layer, the lower the temperature coefficient variation as a function of overtone number, providing easier data processing when using the sensor with various GPR antennas (the same temperature coefficient is used whatever the operating frequency), but preventing a differential approach in a restricted frequency range for which different temperature sensitivities of the various echos is needed.
The device used earlier (Fig. 6 ) as a dipole was used as a 4-pole coupled oscillator. The second port was either loaded by a 50 Ω load, or opened. The switch behavior probed through a wireless link is dominant over the temperature variation in the 20-80 °C range.
(a) geometrical model considered, with 3 perfectly conducting cylinders (black) 1.9 m deep and separated by 50 cm, in dry sand ( , white), the middle rebar being fitted with an acoustic transducer delaying its echo by 450 ns (air above the surface is indicated as a grey area). (b) raw modelled response, (c) Stolt migration of the previous graph assuming a velocity of 163 m/μs. While the hyperbolas from the reflection on the rebars converge towards a blurred set of reflections from the three conducting cylinders (time before 80 ns), the hyperbola located near 500 ns delay does not converge since its curvature does not fit the expected shape from an electromagnetic delay at such a large distance. (d) Separate migration of the three reflections from the rebars as in the middle graph, and in addition the delayed echo is manually migrated by shifting the time origin by 450 ns. In this case, the hyperbola translated by 450 ns converges to a single reflector well identified with the middle rebar, at abscissa 2.70 m (arrow). This basic simulation only assumes that the direct wave reaching the sensor generates an acoustic signal which is returned to the GPR receiver without additional reflections on other buried dielectric interfaces.
(a) Geometry of the modelled configuration, in which two water ( ) filled pipes (white) are buried 0.9 and 0.6 m deep in dry sand (grey, ). The acoustic transducer is assumed to be located atop the deepest pipe. (b) Top: RADARgram obtained by scanning the transmitter and the receiver over the surface, at the air (black)-sand (grey) interface. The hyperbola generated by the shallowest tube nearly overlaps the hyperbola generated by the deepest tube, making the identification process of the buried structure complex. Bottom: the signal recorded by the acoustic transducer located on top of the deepest tube records the incoming signal, and re-emits the recorded sequence after some delay representative of the acoustic wave propagation in the transducer. The hyperbola related to the deepest tube in now well resolved (vertical arrow). Since the electromagnetic signal propagation from the surface to the sensor step and the propagation from the sensor to the surface step are separate, the direct air-wave from emitter to receiver is no longer visible on the bottom graph.
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