Received 10 December 2015; accepted 4 February 2016; published 22 April 2016
Acoustic shadow method is an efficient ultrasound imaging technique for diagnosis of inner and outer state for target object, which utilizes acoustic shadow of the object backward. The shadow occurs at the area where acoustic signal intensity is lower than other area due to the high acoustic impedance differences at the medium interface of the target. It has higher signal intensity than acoustic images obtained by pulse echo method because of low attenuation of sound in medium material. It is also known that the acoustic shadow method can be applied to rough surface that causes the acoustic scattering where the target detection using pulse echo method is difficult to apply for the limitation of critical angle of reflection to the target  -  . For these better acoustic characteristics, it has been applied to a detection of flaw defects and a characterization of materials  -  . However reverberation artifact is repeatedly occurred in the measurement due to the acoustic impedance difference between the target and water, especially when transducer and hydrophone receiver are located vertical to the surface of the target and it causes virtual image of the target material  . In order to reduce the reverberation artifact in acoustic shadow imaging, the sound pressure of the transmitter can be reduced or the transducer can be inclined to the target surface, while the signal amplitude of imaging is reduced and causes lower SNR (signal to noise ratio) in acoustic shadow imaging. Therefore, the reducing reverberation artifact is an important topic in the application to underwater measurement and material characterization in comparison with the medical application due to higher environmental and machinery noise. Furthermore, it is difficult to estimate the incident angle of the beam to the target in the underwater measurement.
The purpose of this paper is to study the experimental technique using the secondary waves generated by nonlinear interaction of ultrasonic wave emitted from parametric array for reducing reverberation artifact in acoustic shadow imaging. Then, the results are compared with those of the conventional acoustic shadow method that utilizes the primary waves.
We introduced secondary wave generated from parametric array to reduce reverberation artifact of acoustic shadow imaging in water. When two different frequency of sound waves (primary waves) are transmitted in the same direction, the secondary wave such as sum and difference frequencies are generated by nonlinear interaction of finite amplitude waves   . This acoustic technique has been reported by many previous papers for its acoustic characteristic such as high directivity with low side-lobe beam. Especially, it has been used with pulse echo method in underwater imaging  -  and underwater acoustic communication  .
The experiments were carried out for acoustic shadow imaging of square cylinder made of aluminum, which is summarized in Figure 1(a), Figure 1(b). The water tank was 600 mm long and 500 mm wide with 500 mm deep, and the water temperature was maintained at 298 K by temperature control unit. Both the transducer and hydrophone used in the experiment were circular type with flat surface. The size of the transducer was 12 mm in diameter and that of the hydrophone was 6 mm in diameter. It should be mentioned that hydrophone potentially has space averaging error in measurement, and such error may be reduced by smaller size of the hydrophone. However smaller size hydrophone also reduces the sensitivity and has difficulty in measuring the secondary waves which has lower signal level than that of the primary waves. The center point of the square cylinder was located at the axial position z = 85 mm from the transducer in water and the hydrophone was located at z = 200 mm from the transducer on beam axis. The transducer and hydrophone were traversed in the same direction
Figure 1. Noninvasive detection of square cylinder in water (unit in mm). (a) Top view of experimental setup; (b) Side view of square cylinder.
across the square cylinder and the hydrophone was set a) vertical to the square cylinder and b) 45 degree to square cylinder, which allows the detection of the acoustic signal from the transducer influenced by the presence of the square cylinder and reconstructs two-dimensional acoustic image as shown in Figure 2(a), Figure 2(b), respectively. The sampling of the acoustic signal was carried out by traversing the transducer and hydrophone for every 1 mm across the target by three-dimensional positioning stage. Then, the shadow image of signal amplitude distribution was generated.
The transducer was excited by two different frequencies of primary waves and the driving signal s is written by the following equation,
where s0 is the signal amplitude of primary waves and t is a time. The two frequency of primary waves were set f1 = 2 MHz and f2 = 2.4 MHz with transmittance time of tr = 2.5 μs. The signal was observed by the digital storage oscilloscope, where the spurious reflections were eliminated using the time gate, and the received signal was averaged over 64 times at each position to minimize the white noise in this measurement. The sound pressure was measured using the receiver hydrophone which had flat frequency response within ±3 dB over the frequency range from 2 MHz to 8 MHz. Note that the initial time of signals recorded by hydrophone is set as a time when acoustic wave is transmitted from transducer.
3.1. Nonlinear Sound Propagation through Square Cylinder
Figure 2. Arrangement of square cylinder and hydrophone (unit in mm). (a) Vertical to square cylinder; (b) 45 degree to square cylinder.
Figure 3. Frequency spectrum of parametric sound detected at z = 200 mm. (a) With square cylinder; (b) Without square cylinder.
at z = 200 mm with and without square cylinder, respectively. The center of the square cylinder is on the beam axis and the hydrophone is set behind the square cylinder, which is the vertical case in Figure 2(a). The same input voltage was applied to the transducer in both cases and the frequency spectrum of the sound wave was evaluated using discrete Fourier transform, and the frequency spectrum is normalized by each maximum signal amplitude of the signal. Note that the signal level of the primary waves is reduced to 1/5 by the influence of the square cylinder, while that of the secondary wave is reduced more strongly. The results of the normalized pressure amplitude show the generation of secondary wave at the sum frequency (centered at f = 4.4 MHz) due to the nonlinear interaction of finite amplitude sound propagation. It should be mentioned that the relative pressure amplitude of the secondary wave with square cylinder is almost half amplitude of the case without square cylinder. Furthermore, the pressure amplitude at higher harmonics (centered at f = 6.8 MHz) shows a similar trend as the secondary wave with and without square cylinder. These results indicate that acoustic shadow imaging using secondary wave can be applied to eliminate the small amplitude phenomena in imaging, such as the reverberation artifact in acoustic shadow method, when the secondary wave is properly amplified.
3.2. Nonlinear Acoustic Shadow Imaging
To verify the application effects of nonlinear acoustic shadow method, we investigated the noninvasive detection of the square cylinder using nonlinear acoustic shadow method that utilizes secondary wave in water. For the comparative purposes, linear acoustic shadow imaging was carried out by removing secondary wave by low-path filter with the cut-off frequency 3.3 MHz. Note that the linear acoustic shadow imaging corresponds to the conventional acoustic shadow method that utilizes primary waves. Finally, the two-dimensional acoustic shadow images were reconstructed by traversing the transducer and hydrophone across the square cylinder after detecting the envelope of each waves by Hilbert transformation  -  . These images were normalized by each maximum amplitude that corresponds to the direct wave.
Figure 4(a) and Figure 4(b) show the linear acoustic shadow images of two different arrangements of hydrophone to square cylinder, respectively. These are the cases of beam axis vertical to square cylinder (Figure 4(a)) and 45 degree to square cylinder (Figure 4(b)). There are three kinds of signal distributions, which are numbered in 1, 2 and 3 in Figure 4(a). These are the penetration wave through square cylinder, reverberation waves inside the square cylinder and the direct waves, respectively, while Figure 4(b) shows no reverberation artifact in acoustic shadow image due to large incident angle of the beam to the square cylinder.
Figure 5(a) and Figure 5(b) show the nonlinear acoustic shadow images of two different arrangements of square cylinder and hydrophone, respectively. These are vertical to square cylinder (Figure 5(a)) and 45 degree to square cylinder (Figure 5(b)). There is a tendency of nonlinear acoustic shadow image to have shaper outline compared to linear acoustic shadow image due to the shorter wave length of the secondary wave than that of the primary waves  , which are commonly observed in these results. The signal level of penetration wave and reverberation wave are greatly suppressed in the image using nonlinear acoustic shadow method in Figure 5(a) compared to that of linear acoustic shadow method shown in Figure 4(a). This is true for the case of 45 degree to square cylinder in Figure 5(b).
In order to verify the size measurement accuracy of nonlinear acoustic shadow method, the error of measurement is introduced as follows,
where Ls and L0 are the side lengths measured by acoustic shadow method and actual size, respectively. Note that the shadow is defined by 10% amplitude of the direct wave. Figure 6(a) and Figure 6(b) illustrate the signal amplitude distributions along traversed direction of two different arrangements of hydrophone to square cylinder, respectively. These are the cases of vertical to square cylinder (Figure 6(a)) and 45 degree to square cylinder (Figure 6(b)). The error of measurement ε is 4.1 mm in nonlinear acoustic shadow method and it is 9.0 mm in linear acoustic shadow method of Figure 6(a), while the ε is 4.0 mm in nonlinear case and it is 9.3 mm in linear case in Figure 6(b). These results indicate that the image using nonlinear acoustic shadow method shows sharper distribution, and the error is almost half in the non-linear acoustic shadow method compared to that of the linear acoustic shadow method. This is due to the smaller refraction effect and higher directivity of secondary wave propagation than that of the primary waves. It should be mentioned that the nonlinear shadow method offer better measurement accuracy by eliminating the reverberation artifacts in imaging.
Figure 4. Linear acoustic shadow image of square cylinder (1: penetration wave; 2: reverberation wave; 3: direct wave). (a) Vertical to square cylinder; (b) 45 degree to square cylinder.
Figure 5. Nonlinear acoustic shadow image of square cylinder. (a) Vertical to square cylinder; (b) 45 degree to square cylinder.
Figure 6. Signal amplitude along traversed direction. (a) Vertical to square cylinder; (b) 45 degree to square cylinder.
Nonlinear acoustic shadow method that utilizes the secondary wave of parametric array is newly developed for the noninvasive detection of solid structure in water. The experiments are carried in water with and without square cylinder and the result shows that larger variation of relative signal is observed through structure in the secondary wave than the primary waves. It is also observed that the reverberation artifact is reduced and the measurement accuracy is improved in the nonlinear acoustic shadow method using the secondary wave. These results show the capability of lower artifact with higher accuracy for the target object detection by nonlinear acoustic shadow imaging using parametric array, and might lead to a wider application of ultrasound in underwater imaging.
f: frequency [Hz]
f1, f2: two frequency of primary waves [Hz], Equation (1)
L0: side length of square cylinder [mm]
LS: side length measured by acoustic shadow method [mm]
s: driving signal [V] , Equation (1)
s0: signal amplitude [V]
t: time [s]
tr: transmittance time [s]
x, y, z: coordinates [mm], Figure 1
ε: error, Equation (2)
*Part of the paper was presented at the 12th International Conference on Flow Dynamics, Sendai, Japan (2015-10).