- Email: [email protected]
Thallium arsenic sulfide (Ti3AsS4) Bragg cells for acousto-optic spectrum analysis
Volume 57, n u m b e r 2
OPTICS COMMUNICATIONS
15 February 1986
T H A L L I U M ARSENIC SULFIDE (TI3AsS4) BRAGG CELLS FOR A C O U S T O - O P T I C S P E C T R U M ANALYSIS A.P. GOUTZOULIS, D.K. DAVIES and M. GOTTLIEB Westinghouse R& D ('enter, Pittsburgh, PA 15235, USA Received 1 October 1985
Thallium arsenic sulfide Bragg cells are considered for use in bulk acousto-optic spectrum analyzers. Various design and fabrication issues are discussed and experimental results for high efficiency-bandwidth single transducer cells are presented. Experimental data for the third order intermodulation products are also presented and reveal that the intermodulation level is due to acoustic nonlinearities.
1. Introduction
Recently we reported the first experimental results for thallium arsenic sulfide (TASL), longitudinal wave, isotropic diffraction Bragg cells [1 ]. In such a configuration TASL has some very interesting acoustooptic properties which include an M 2 value of 525 associated with a sound velocity of 2.15 X 105 cm/s and an acoustic attenuation of 7 dB//as (GHz)2 . Optimized design for this configuration reveals that for realistic crystal lengths (less than 2.5 cm) the maximum time-bandwidth product is about 1000. This is achieved using a 3 dB bandwidth of 100 MHz, centered at 200 MHz, and a time aperture of 11/as. With a less optimized design, we can realize cells with a 3 dB bandwidth of 200 MHz, centered at 400 MHz, and an aperture of 2.5/as. We have demonstrated that such devices have a diffraction efficiency that exceeds 400%/W. Thus, this device configuration is very appropriate for a number of imaging applications which include time-integrating and space-integrating correlators [2] as well as triple product processors [3]. Similar applications can be handled by anisotropic diffraction configurations which include: (1) a fast shear mode with a sound velocity of 1.21 X 105 cm/s and a birefringence minimum that occurs at 550 MHz and (2) a slow shear mode with a sound speed of 6 X 104 cm/s and a birefringence minimum that occurs at 285 MHz.
In this paper we consider TASL for another class of applications, namely, spectrum analysis. Specifically, we consider longitudinal acoustic wave, isotropic diffraction, TASL designs, and present experimental results appropriate for moderate bandwidth (500 MHz) non-heterodyne bulk spectrum analyzers. We consider this application mostly because of the material's high figure of merit M 2 and the possibility that the level of the 3rd order intermodulation products (IMP) may be limited by acousto-optic diffraction [4] rather than nonlinear acoustics [5]. If this is the case, TASL may be used for an enhanced dynamic range, highly sensitive spectrum analyzer of moderaie resolution. In section 2 we discuss various design factors and fabrication issues. Experimental data describing the efficiency and bandwidth are presented in section 3. In section 4 we present detailed measurements of the third order intermodulation products.
2. Design and fabrication The acousto-optic properties of TASL permit the realization of 500 MHz bandwidth (BW) Bragg cells with an isotropic diffraction, longitudinal wave cell configuration. For such a configuration the acoustic propagation is along (100), the optical beam propagation is along (010), and the polarization along (100). The useful optical aperture is determined by the ma93
Volume 57, number 2
OPTICS COMMUNICATIONS
terial's acoustic attenuation along with the operating center frequency (fc)" Since the acoustic attenuation is relatively high [7 dB/t~s (GHz) 2 ] the value o f f c , for all practical purposes, cannot exceed 1 GHz. Thus, f o r f c = 1 GHz and a bandwidth of 500 MHz the useful optical aperture is about 0.9 mm which corresponds to a time aperture of 0.4/as. For such a design the resolution is 200 spots. Increased resolution (~400 spots) can be achieved for an fc of 750 MHz. In this case the optical aperture is 1.8 mm or 0.8/as. We note that for some spectrum analyzer scenarios the desired time aperture is smaller than the apertures o f the above two cases. This situation occurs, for example, when high performance detection o f pulsed waveforms is desired where the time aperture is about 100 ns. For TASL this corresponds to an aperture o f 215/am. In practice, such apertures are used with focused rather than collimated optical beams. Once the fc and BW of the device has been determined, we need to determine the top electrode dimensions: length (L) and height (H). Since we consider single transducer cells, we need to choose L to be small enough to allow sufficient acoustic beam spread in order to satisfy the Bragg requirements over the desired BW (for a fixed incident optical angle). An optimum value o f L can be obtained from the relation [6] L = 1.8 no 2 c o s O / k f c B W
(1)
where n is the index of refraction, o is the speed o f sound, 0 is the Bragg angle and ~ is the optical wavelength. From (1) and for ~ = 830 nm we find that L = 53/am (fc = 1 GHz) and L = 72 tam (fe = 750 MHz). These are rather small widths and are due to the low speed of sound in TASL. Because o f the problems associated with the fabrication of such small electrodes, we have implemented only the latter design. The transducer height H determines the amount of acoustic diffraction, while the transducer area determines the transducer impedance as well as the maximum rf power that can be applied. For our experimental devices, we have used H values o f 2 0 0 - 2 8 0 / m a . These values, in conjunction with an L of about 70/am, have allowed us to apply up to 50 mW of power without damaging or heating the crystals. More power can be safely applied if heat sinks are used. Once L and H are determined, we use a generalized computer program to achieve a transducer-bond struc94
15 February 1986
ture compatible with the rf requirements. Tin is used as a bonding layer in conjunction with a LiNbO 3 transducer. The top electrode is gold to which gold wires are bonded. The fabricated cells have an almost constant impedance of 15 ~2 over the full BW. Impedance matching to 50 f2 can then be achieved via a variety o f well established techniques. The transducer structure is made by bonding a 36 ° y-cut LiNbO 3 plate to the (100) face of the cell. This is accomplished by simultaneously depositing the metal layers onto the mating surfaces of the crystal and transducer plate in a vacuum compression system. Immediately after the chrome and tin layers are complete, the transducer and crystal are brought into contact, and suitable pressure is applied. This is accomplished without breaking the vacuum by manipulating the fixtures from outside the vacuum system. High quality bonds are achieved if the metal layers are kept free of any contamination. Only modest pressures are required for such a bond. This is important for TASL because it is a soft material. This procedure offers the advantage over heat bonding procedures that no thermal strains are generated which may degrade cell performance. The transducer is then mechanically lapped to a thickness o f about 7 / a n and the final thinning is done to high accuracy by ion milling. Once this is done we deposit the top electrode and wedge bond the gold wire connection.
3. Experimental results Two experimental TASL devices have been fabricated and tested. The diffraction efficiency (7/) and bandwidth are measured using a HeNe laser (k = 633 nm) beam with dimensions 0.4 mm (along the direction o f sound propagation) and 150/am (perpendicular to the sound-light plane). The laser beam is positioned about 200/am from the transducer face in order to
Table 1 TI3AsS 4 Bragg cell characteristics (for h = 633 nm)
Device number fc (MHz)
3-dB BW (MHz)
LXH (#m X #m)
r~ (%/W)
TASL 27 TASL 26
460 500
70 X 200 70 × 270
210 70
730 800
Volume 57, number 2
OPTICS COMMUNICATIONS TASL 27
20(
15 February 1986
profiles under conditions similar to the ones described in ref. [1 ]. We discuss the IMP measurements in the following section.
IOO 4. IMP measurements 500
730 f (MHz) (a)
960
TASL 26
7C
35
550
800
1050
f (MHz)
(b) Fig. 1. TI3AsS4 Bragg cell frequency response.
avoid reflections. The measured 77and BW of the cells are shown in table 1. From this table we see that cell 27 has an extraordinarily high ~7which is the result of the material's high M 2 . The efficiency-bandwidth product is 96.6%/W GHz, which is higher than that reported earlier [1] (83%/W GHz). The improvement is attributed to the improved quality of the crystal used. Note that cell 27 has a lower r/than cell 26 (by a factor of 3) because of: (1) the larger H value used and (2) differences in the bond. The BW response of the two devices is shown in fig. 1. The differences in device response smoothness are attributed to differences in crystal (transducer face) polishing procedures as well as possible contamination of the metal layers during tranducer bonding. The zero order scattering in the devices in the vicinity of the first order is about - 4 6 dB. This figure reflects the current state of development of the crystal material. Thus, the single tone dynamic range of the devices is about 35 dB (assuming operation at about 10% diffraction efficiency). The two tone dynamic range depends on both first order scattering sidelobes and 3rd order intermodulation products (IMP). The former is currently about - 3 2 dB at a separation of 25 MHz from a single tone peak. This value is obtained from several first order
In order to efficiently measure the IMP for the single transducer TASL devices we have used the interferometric system of fig. 2, as suggested in ref. [7]. In this arrangement the cell under test is fed with two equal amplitude RF tones (830 and 838 MHz respectively), at a level such that a predetermined diffraction efficiency is produced. The two-tone diffracted beam is interfered with the diffracted beam from a reference TASL cell driven by a 800 MHz cw signal. The output is detected by a high gain, low noise detector/amplifier system and then analyzed by an RF spectrum analyzer. In order to ensure a low RF IMP level from the RF source tones, the two tone signal is analyzed using an RF spectrum analyzer before application to the test cell. The RF IMP level is found to be better than - 5 5 dB. The test cell is first operated at an 77of 0.05 per tone. The result (shown in fig. 3) suggests that the 3rd order IMP is about - 1 9 dB below the desired two tone signal. This is about 22 dB higher than the level predicted by multifrequency acousto-optic diffraction theory [4]. This implies that the origin of the observed IMP is nonlinear acoustics triggered by the high acoustic power density used. The latter is due to the small L used which, in turn, is necessary in order to achieve the desired bandwidth. By reducing the input power and monitoring the IMP
Beam Splitter ~ Reference ~
~
( ~o ~z~ ~
~ I h,\
Test
1800MHzl I k\
Mirror ',r'r- Beam" v Combiner
Photo -
VLo w Noise Amplifier
Fig. 2. Interferometric system for IMP measurement.
95
Volume 57, number 2
OPTICS COMMUNICATIONS 0
15 February 1986 t
i
i
f
i
/ i
I
i
-10 -20 -30 -40 "o
I~°
-50 -60 -70
;~0 Fig. 3. TlsAsS4 IMP level ffl = 830 MHz, f2 = 838 MHz, = 0.05, h = 633 nm). Vertically 10 dB/division, horizontally 5 MHz/division. level we can plot the IMP level as a function o f acoustic power. Such a plot is shown in fig. 4. As expected [5] reduction o f the input power results in reduction o f the IMP level. To achieve a desirable IMP level o f - 4 0 dB we need to drive the cell with no more than - 6 dBm (0.25 mW) which corresponds to the low r? value o f 0.005. To maintain the above IMP level at a higher r? we need to enhance [5,7] the interaction length L. For TASL, in conjunction with isotropic diffraction operation, this can be done only by the use o f phased array transducers [7].
t
i
-40
-30
-20 -10 Input Power (dBm)
/ 10
20
Fig. 4. IMP level as a function of input RF power. the material's high M 2 . Experimental data for the third order intermodulation products are also reported which show that for a diffraction efficiency o f 5% the intermodulation level is 19 dB below the desired signals. This value suggests that the intermodulation level is limited by nonlinear acoustics rather than b y multifrequency diffraction. For optimum operation ( - 4 0 dB IMP level and 6% diffraction efficiency) enhancement of the interaction length is necessary.
References 5. Summary and conclusions In this paper we consider thallium arsenic sulfide acousto-optic Bragg cells suitable for application to spectrum analysis. We discuss b o t h the design and fabrication of such Bragg cells and show that the maximum bandwidth one can expect from this material is about 500 MHz. Experimental results are presented which show an extraordinarily high diffraction efficiency (210%/W) associated with 460 MHz bandwidth. This is the highest e f f i c i e n c y - b a n d w i d t h product (96.9%/W GHz) ever reported and is due to
96
[1 ] A. Goutzafis, M. Gottlieb, D.K, Davies and Z. Kuy, Thallium arsenic sulfide (TI3 ASS4) aeousto-optie Bragg cells, submitted to Appl. Optics. [2] R.A. Sprague, Opt. Engineering (1977)467. [3] P. Kellman, Opt. Engineering (1980) 370. [4] D.L. Heclit, IEEE Trans. Sonics and Ultrasonics SU-24 (1977) 7. [5 ] I.C. Chang and R.T. Weverka, 1983 Ultrasonics Symposium Proceedings, Vol. 1 (1983) p. 445. [6] I.C. Chang, IEEE Trans. Sonics and Ultrasonics SU-23 (1976) 2. [7 ] M.L. Shah and P.S. Zerwekh, 1983 Ultrasonics Symposium Proceedings, Vol. 1 (1983) p. 441.
OPTICS COMMUNICATIONS
15 February 1986
T H A L L I U M ARSENIC SULFIDE (TI3AsS4) BRAGG CELLS FOR A C O U S T O - O P T I C S P E C T R U M ANALYSIS A.P. GOUTZOULIS, D.K. DAVIES and M. GOTTLIEB Westinghouse R& D ('enter, Pittsburgh, PA 15235, USA Received 1 October 1985
Thallium arsenic sulfide Bragg cells are considered for use in bulk acousto-optic spectrum analyzers. Various design and fabrication issues are discussed and experimental results for high efficiency-bandwidth single transducer cells are presented. Experimental data for the third order intermodulation products are also presented and reveal that the intermodulation level is due to acoustic nonlinearities.
1. Introduction
Recently we reported the first experimental results for thallium arsenic sulfide (TASL), longitudinal wave, isotropic diffraction Bragg cells [1 ]. In such a configuration TASL has some very interesting acoustooptic properties which include an M 2 value of 525 associated with a sound velocity of 2.15 X 105 cm/s and an acoustic attenuation of 7 dB//as (GHz)2 . Optimized design for this configuration reveals that for realistic crystal lengths (less than 2.5 cm) the maximum time-bandwidth product is about 1000. This is achieved using a 3 dB bandwidth of 100 MHz, centered at 200 MHz, and a time aperture of 11/as. With a less optimized design, we can realize cells with a 3 dB bandwidth of 200 MHz, centered at 400 MHz, and an aperture of 2.5/as. We have demonstrated that such devices have a diffraction efficiency that exceeds 400%/W. Thus, this device configuration is very appropriate for a number of imaging applications which include time-integrating and space-integrating correlators [2] as well as triple product processors [3]. Similar applications can be handled by anisotropic diffraction configurations which include: (1) a fast shear mode with a sound velocity of 1.21 X 105 cm/s and a birefringence minimum that occurs at 550 MHz and (2) a slow shear mode with a sound speed of 6 X 104 cm/s and a birefringence minimum that occurs at 285 MHz.
In this paper we consider TASL for another class of applications, namely, spectrum analysis. Specifically, we consider longitudinal acoustic wave, isotropic diffraction, TASL designs, and present experimental results appropriate for moderate bandwidth (500 MHz) non-heterodyne bulk spectrum analyzers. We consider this application mostly because of the material's high figure of merit M 2 and the possibility that the level of the 3rd order intermodulation products (IMP) may be limited by acousto-optic diffraction [4] rather than nonlinear acoustics [5]. If this is the case, TASL may be used for an enhanced dynamic range, highly sensitive spectrum analyzer of moderaie resolution. In section 2 we discuss various design factors and fabrication issues. Experimental data describing the efficiency and bandwidth are presented in section 3. In section 4 we present detailed measurements of the third order intermodulation products.
2. Design and fabrication The acousto-optic properties of TASL permit the realization of 500 MHz bandwidth (BW) Bragg cells with an isotropic diffraction, longitudinal wave cell configuration. For such a configuration the acoustic propagation is along (100), the optical beam propagation is along (010), and the polarization along (100). The useful optical aperture is determined by the ma93
Volume 57, number 2
OPTICS COMMUNICATIONS
terial's acoustic attenuation along with the operating center frequency (fc)" Since the acoustic attenuation is relatively high [7 dB/t~s (GHz) 2 ] the value o f f c , for all practical purposes, cannot exceed 1 GHz. Thus, f o r f c = 1 GHz and a bandwidth of 500 MHz the useful optical aperture is about 0.9 mm which corresponds to a time aperture of 0.4/as. For such a design the resolution is 200 spots. Increased resolution (~400 spots) can be achieved for an fc of 750 MHz. In this case the optical aperture is 1.8 mm or 0.8/as. We note that for some spectrum analyzer scenarios the desired time aperture is smaller than the apertures o f the above two cases. This situation occurs, for example, when high performance detection o f pulsed waveforms is desired where the time aperture is about 100 ns. For TASL this corresponds to an aperture o f 215/am. In practice, such apertures are used with focused rather than collimated optical beams. Once the fc and BW of the device has been determined, we need to determine the top electrode dimensions: length (L) and height (H). Since we consider single transducer cells, we need to choose L to be small enough to allow sufficient acoustic beam spread in order to satisfy the Bragg requirements over the desired BW (for a fixed incident optical angle). An optimum value o f L can be obtained from the relation [6] L = 1.8 no 2 c o s O / k f c B W
(1)
where n is the index of refraction, o is the speed o f sound, 0 is the Bragg angle and ~ is the optical wavelength. From (1) and for ~ = 830 nm we find that L = 53/am (fc = 1 GHz) and L = 72 tam (fe = 750 MHz). These are rather small widths and are due to the low speed of sound in TASL. Because o f the problems associated with the fabrication of such small electrodes, we have implemented only the latter design. The transducer height H determines the amount of acoustic diffraction, while the transducer area determines the transducer impedance as well as the maximum rf power that can be applied. For our experimental devices, we have used H values o f 2 0 0 - 2 8 0 / m a . These values, in conjunction with an L of about 70/am, have allowed us to apply up to 50 mW of power without damaging or heating the crystals. More power can be safely applied if heat sinks are used. Once L and H are determined, we use a generalized computer program to achieve a transducer-bond struc94
15 February 1986
ture compatible with the rf requirements. Tin is used as a bonding layer in conjunction with a LiNbO 3 transducer. The top electrode is gold to which gold wires are bonded. The fabricated cells have an almost constant impedance of 15 ~2 over the full BW. Impedance matching to 50 f2 can then be achieved via a variety o f well established techniques. The transducer structure is made by bonding a 36 ° y-cut LiNbO 3 plate to the (100) face of the cell. This is accomplished by simultaneously depositing the metal layers onto the mating surfaces of the crystal and transducer plate in a vacuum compression system. Immediately after the chrome and tin layers are complete, the transducer and crystal are brought into contact, and suitable pressure is applied. This is accomplished without breaking the vacuum by manipulating the fixtures from outside the vacuum system. High quality bonds are achieved if the metal layers are kept free of any contamination. Only modest pressures are required for such a bond. This is important for TASL because it is a soft material. This procedure offers the advantage over heat bonding procedures that no thermal strains are generated which may degrade cell performance. The transducer is then mechanically lapped to a thickness o f about 7 / a n and the final thinning is done to high accuracy by ion milling. Once this is done we deposit the top electrode and wedge bond the gold wire connection.
3. Experimental results Two experimental TASL devices have been fabricated and tested. The diffraction efficiency (7/) and bandwidth are measured using a HeNe laser (k = 633 nm) beam with dimensions 0.4 mm (along the direction o f sound propagation) and 150/am (perpendicular to the sound-light plane). The laser beam is positioned about 200/am from the transducer face in order to
Table 1 TI3AsS 4 Bragg cell characteristics (for h = 633 nm)
Device number fc (MHz)
3-dB BW (MHz)
LXH (#m X #m)
r~ (%/W)
TASL 27 TASL 26
460 500
70 X 200 70 × 270
210 70
730 800
Volume 57, number 2
OPTICS COMMUNICATIONS TASL 27
20(
15 February 1986
profiles under conditions similar to the ones described in ref. [1 ]. We discuss the IMP measurements in the following section.
IOO 4. IMP measurements 500
730 f (MHz) (a)
960
TASL 26
7C
35
550
800
1050
f (MHz)
(b) Fig. 1. TI3AsS4 Bragg cell frequency response.
avoid reflections. The measured 77and BW of the cells are shown in table 1. From this table we see that cell 27 has an extraordinarily high ~7which is the result of the material's high M 2 . The efficiency-bandwidth product is 96.6%/W GHz, which is higher than that reported earlier [1] (83%/W GHz). The improvement is attributed to the improved quality of the crystal used. Note that cell 27 has a lower r/than cell 26 (by a factor of 3) because of: (1) the larger H value used and (2) differences in the bond. The BW response of the two devices is shown in fig. 1. The differences in device response smoothness are attributed to differences in crystal (transducer face) polishing procedures as well as possible contamination of the metal layers during tranducer bonding. The zero order scattering in the devices in the vicinity of the first order is about - 4 6 dB. This figure reflects the current state of development of the crystal material. Thus, the single tone dynamic range of the devices is about 35 dB (assuming operation at about 10% diffraction efficiency). The two tone dynamic range depends on both first order scattering sidelobes and 3rd order intermodulation products (IMP). The former is currently about - 3 2 dB at a separation of 25 MHz from a single tone peak. This value is obtained from several first order
In order to efficiently measure the IMP for the single transducer TASL devices we have used the interferometric system of fig. 2, as suggested in ref. [7]. In this arrangement the cell under test is fed with two equal amplitude RF tones (830 and 838 MHz respectively), at a level such that a predetermined diffraction efficiency is produced. The two-tone diffracted beam is interfered with the diffracted beam from a reference TASL cell driven by a 800 MHz cw signal. The output is detected by a high gain, low noise detector/amplifier system and then analyzed by an RF spectrum analyzer. In order to ensure a low RF IMP level from the RF source tones, the two tone signal is analyzed using an RF spectrum analyzer before application to the test cell. The RF IMP level is found to be better than - 5 5 dB. The test cell is first operated at an 77of 0.05 per tone. The result (shown in fig. 3) suggests that the 3rd order IMP is about - 1 9 dB below the desired two tone signal. This is about 22 dB higher than the level predicted by multifrequency acousto-optic diffraction theory [4]. This implies that the origin of the observed IMP is nonlinear acoustics triggered by the high acoustic power density used. The latter is due to the small L used which, in turn, is necessary in order to achieve the desired bandwidth. By reducing the input power and monitoring the IMP
Beam Splitter ~ Reference ~
~
( ~o ~z~ ~
~ I h,\
Test
1800MHzl I k\
Mirror ',r'r- Beam" v Combiner
Photo -
VLo w Noise Amplifier
Fig. 2. Interferometric system for IMP measurement.
95
Volume 57, number 2
OPTICS COMMUNICATIONS 0
15 February 1986 t
i
i
f
i
/ i
I
i
-10 -20 -30 -40 "o
I~°
-50 -60 -70
;~0 Fig. 3. TlsAsS4 IMP level ffl = 830 MHz, f2 = 838 MHz, = 0.05, h = 633 nm). Vertically 10 dB/division, horizontally 5 MHz/division. level we can plot the IMP level as a function o f acoustic power. Such a plot is shown in fig. 4. As expected [5] reduction o f the input power results in reduction o f the IMP level. To achieve a desirable IMP level o f - 4 0 dB we need to drive the cell with no more than - 6 dBm (0.25 mW) which corresponds to the low r? value o f 0.005. To maintain the above IMP level at a higher r? we need to enhance [5,7] the interaction length L. For TASL, in conjunction with isotropic diffraction operation, this can be done only by the use o f phased array transducers [7].
t
i
-40
-30
-20 -10 Input Power (dBm)
/ 10
20
Fig. 4. IMP level as a function of input RF power. the material's high M 2 . Experimental data for the third order intermodulation products are also reported which show that for a diffraction efficiency o f 5% the intermodulation level is 19 dB below the desired signals. This value suggests that the intermodulation level is limited by nonlinear acoustics rather than b y multifrequency diffraction. For optimum operation ( - 4 0 dB IMP level and 6% diffraction efficiency) enhancement of the interaction length is necessary.
References 5. Summary and conclusions In this paper we consider thallium arsenic sulfide acousto-optic Bragg cells suitable for application to spectrum analysis. We discuss b o t h the design and fabrication of such Bragg cells and show that the maximum bandwidth one can expect from this material is about 500 MHz. Experimental results are presented which show an extraordinarily high diffraction efficiency (210%/W) associated with 460 MHz bandwidth. This is the highest e f f i c i e n c y - b a n d w i d t h product (96.9%/W GHz) ever reported and is due to
96
[1 ] A. Goutzafis, M. Gottlieb, D.K, Davies and Z. Kuy, Thallium arsenic sulfide (TI3 ASS4) aeousto-optie Bragg cells, submitted to Appl. Optics. [2] R.A. Sprague, Opt. Engineering (1977)467. [3] P. Kellman, Opt. Engineering (1980) 370. [4] D.L. Heclit, IEEE Trans. Sonics and Ultrasonics SU-24 (1977) 7. [5 ] I.C. Chang and R.T. Weverka, 1983 Ultrasonics Symposium Proceedings, Vol. 1 (1983) p. 445. [6] I.C. Chang, IEEE Trans. Sonics and Ultrasonics SU-23 (1976) 2. [7 ] M.L. Shah and P.S. Zerwekh, 1983 Ultrasonics Symposium Proceedings, Vol. 1 (1983) p. 441.