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Determination of acoustic power outputs in the microwatt-milliwatt range
' l t r u ~ m m / m ,~,led & Biol., Vol. I, pp. 13 16. Pergamon Press, 1973. Printed in Great Britain,
DETERMINATION OF ACOUSTIC POWER OUTPUTS IN THE MICROWATT-MILLIWATT RANGE JAMES A. ROONEY* Physics Department, University of Vermont, Burlington, Vermont 05401, U.S.A. (Received 21 A ugust 1972: and in fina/jorm 13 Not,ember ]972) Abslract--A system using an electrobalance for radiation pressure measurements has been developed capable of determining acoustic powers in the microwatt-milliwatt range. Low background "noise" levels are achieved by effectiveisolation of the balance from building vibrations and shielding the target from convectioncurrents. The standard deviation for a power output of 1mW is typicallyless than 1per cent.
Key morals'. Acoustics, Pressure, Ultrasonics.
CURRENTLY with the increasing use of medical ultrasonics there is a need for accurate acoustic power measurements. A number of techniques by which the power output from an ultrasonic beam can be determined have been developed. In the megahertz frequency range both calorimetric and radiation pressure methods have been used in the past. The calorimetric techniques are usually based upon complete absorption of acoustic energy and are typically used to measure powers above 100 m W (Wells, 1969). In low acoustic power applications, radiation pressure techniques are used to measure the force upon a target which intercepts an entire sound beam. For a traveling plane wave impinging on a perfectly absorbing target suspended in an open vessel, the radiation force is equal to the acoustic power divided by the velocity o f sound (Rooney, 1972; Borgnis, 1953). F o r an acoustic power of 1 m W the radiation force is equivalent to the weight of 68 ~tg. Three systems capable of measuring such small forces have been reported. Wells e t al. (1964) measured deflections o f a reflecting vane upon which a sound beam impinged. The minim u m power which could be detected (although not measured) was o f the order o f 0.01 mW. * Present Address: Physics Department,
at Orono, Orono, Maine 04473, U.S.A.
Universityof Maine
They were able to measure a power output of 2 m W with a stated error of + 3 per cent. Kossoff (1965) used a modified analytical chemical balance to measure the radiation pressure. For his system he states that the m i n i m u m detectable acoustic power output was 0.04 mW. A third system developed by Wemlen (1968) consisted of a torsion balance with capacitive transducer attached to the balance arm, Wemlerj states that acoustic powers as low as 0.03 m W could be detected. In the 10 m W range, the error o f the balance was stated to be less than 5 per cent. We have developed a radiation pressure balance that is capable of power determinations in the microwatt range. The apparatus currently in use is shown schematically in Fig. 1 and consists o f a Cahn R G Electrobalance (Cahn Instrument Co., .Paramount, California) from one arm of which a cylindrical absorbing target (SOAB, B. F. Goodrich), 3 cm in diameter and 0.2 cm in height is suspended; appropriate tare weights are suspended from the other arm. The target is hung in the medium of interest within an inner vessel which is 4.3 cm in diameter. This small interior vessel is closed at the lower end with a stretched m e m b r a n e (25 la thick, Plastic Wrap) to shield the target from acoustic streaming. The electrobalance is calibrated by noting the deflection on the recorder corresponding to forces resulting from a series of calibrated 13
14
JAMES A.
ROONEY
\ \ \ N
\ \ N
\ \
S M
_
_
J
k.Trl L
Fig. 1. Schematic diagram of balance system. An acoustic signal supplied by the oscillator to transducer T passes by way of membrane M through the medium contained in the outer vessel 0. The sound passes through acoustic streaming shield S, continues through the medium within the inner vessel 1, and then impinges upon the absorbing target A. Changes in the voltage of the feedback system F are displayed on recorder R. W indicates the tare weights.
weights placed on the balance. The transducer element to be calibrated is brought into contact with a second stretched membrane at the base of the large vessel. A suitable coupling agent, in our case "Aquasonic 100" (Parker Laboratories, Irvington, N.J.), was used between the transducer and the membrane. The outer vessel containing water has a large volume (9.5 cm in dia. and 16 cm in height) so that thermal fluctuations in the inner vessel are reduced. When the transducer is activated, the target is deflected momentarily from equilibrium. This deflection changes the amount of light reaching a photocell which initiates a magnetic feedback system within the Cahn balance returning the target to its original position. A p o r t i o n of the feedback'voltage to the magnet i~ recorded on a Sanborn chart recorder (Model 296, Sanborn, Waltham, Mass.). We note that the use of the feedback system is advantageous because it eliminates errors which result from changes in surface tension forces on the suspending wire and minimizes those which are the result of other "surface" effects. The air gap between the balance and the large vessel is
enclosed to prevent effects of air currents on the suspending wire. The inner vessel proved to be important for the stability of the system. The vessel should have a diameter only slightly larger than the target in order to minimize drift in the signal which results from convection currents. Evidence for the degree of improvement in the measurements is shown in Fig. 2. Figure 2(a) shows the typical drift in the base line of the recorder output when the inner vessel is removed and replaced by a stretched plastic membrane whose diameter was that of the larger vessel. Fluctuations up to 0-51 mW are seen. The tracing in Fig. 2(b) is the recorder output resulting from 2 pulses of a 5 MHz signal whose power output is 1.03 mW when the inner vessel was present. In this figure the sound pulse begins at the point indicated by the upward arrow. Transients resulting partly from instrumentation decay within 6 sec. An equilibrium deflection is reached and the sound is then turned off as indicated by the downward arrow. Transients are again seen as the recorder out-
Determination of acoustic power outpuls in the microwatt milliwatt range
15
(a)
!
;
~
[ '
;i'
I
',
l
~
!
t ....
:
]
/
(b)
i! ....
/
4 see
Fig. 2. (a) Drift in recorder output as the result of convection currents. (b) Recorder output from 1-03 nfW pulses when inner vessel is used. In both cases 20 units corresponds to 0.1 mg (1.47 mW) and 2.5 units horizontally is 1 sec. Time progresses from right to left. p u t returns to the base line. W e note that f l u c t u a t i o n s in the base line u n d e r these cond i t i o n s (with the inner vessel present) are less t h a n 0.05 roW. The size o f the target also p r o v e d to be an i m p o r t a n t c o n s i d e r a t i o n for a c c u r a c y o f the m e a s u r e m e n t s . In c o n s i d e r i n g the a p p r o p r i a t e d i a m e t e r for the target a c o m p r o m i s e m u s t be made. T h e d i a m e t e r o f the t a r g e t m u s t be larger than the d i a m e t e r o f the b e a m to ensure that the s o u n d is c o m p l e t e l y a b s o r b e d but the v o l u m e o f the target s h o u l d be kept to a m i n i m u m to e l i m i n a t e excess noise in the system. T h e a b s o r b ing target must of course be thick e n o u g h to have g o o d a b s o r b i n g properties. F o r these studies S O A B p r o v e d to be g o o d m a t e r i a l a n d no a p p r e ciable s t a n d i n g waves could be detected for the
frequencies used. P r e l i m i n a r y e x p e r i m e n t s were c o m p l e t e d with a S O A B target 3 cm in dia. a n d 0.7 cm in height. The noise in the r e c o r d e r o u t p u t p r o v e d to be excessive (up to 1-03 roW) as can be seen in Fig. 3(a). Believing t h e r m a l fluctuations in the liquid to be the i m p o r t a n t cause o f the noise, we built a t h e r m a l l y c o m p e n sated target a l o n g lines suggested by K o s s o f f (1965). T h e target c o n s i s t e d o f a S O A B a b s o r b e r 3 cm in dia. a n d 0.2 cm in height glued to a plexiglas t h e r m a l c o m p e n s a t o r 3 cm in dia. a n d 0-7 cm in height. T h e noise present in the signal a c t u a l l y increased as s h o w n in Fig. 3(b). This noise a p p e a r s to be the result o f b u i l d i n g vibrations which set up pressure g r a d i e n t s in the liquid. In the presence o f these pressure gradients, the target is acted u p o n by a force p r o p o r t i o n a l
(o) r
' ~~
:-~
.........
:
! .....
i ......
i ¸ -
:
"-
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i: .....
i
-
o).
(b) r [:
"i
~- "I ........ T" ~" "r ..... ~!
i !
T
....
I
i
:
: .
.
I
(c)
.
.
.
.
.
i I
'
0
4sec
Fig. 3. Noise in recorder output for targets of various volumes. (a) Target with volume of 5.0 cm ~. On tracing 20 units is 0-2 mg. (b) Thermally compensated target with a volume of 6-4 cm 3. 20 units is 0,2 rag. (c) Target currently in use with volume of 1.4 cm 3. 20 units equals 0.1 rag. In all tracings 2.5 units corresponds to 1 sec.
16
JAMES A. ROONEY
to its volume. The reduction of noise in our system was achieved by using a target of minimum volume and isolating the experimental arrangement from the building. In our case we have found that mounting the arrangement on a heavy metal frame supported by eight hard rubber balls (singles squash balls) has allowed us to achieve the acceptable level of noise shown in Fig. 3(c). As examples of applications of the system we have measured the power output from two ultrasonic diagnostic units. Both operate in a cw mode and are Doppler type detectors. The first is the Hemosonde (Parke-Davis, Ann Arbor, Michigan) which operates at 5 MI-;Iz and has a power output of 1.03 mW at a distance of 3 cm from the transducer. The standard deviation in this determination is 0-7 per cent. The second unit is the Transcutaneous Doppler (Park Electronics Lab, Beaverton, Oregon) which used a 8.8 MHz signal and has a power output of 30 mW (standard deviation of 1.0 per cent) at the same distance. The beam configurations were studied using a hydrophone whose active element is a PZT-5 cylindrical ceramic (1.4 mm o.d., 1-4 mm length). Both units have well defined beams and no significant focussing. At 3 cm from the transducers the Hemosonde beam area is 0.8 cm 2 while that of the Transcutaneous Doppler is 0.32 cm 2. Here we define the limits of the beam to be the points where the pressure has been
reduced to 0.1 that of the pressure maximum in the beam. Thus the average intensities are respectively 1.29 and 93.8 mW/cm 2. If we use the half power points, the average intensities are respectively 4.35 and 300 mW/cm 2. Currently the balance allows us to measure power outputs of 30 laW with a standard deviation of 5 laW. Since the sensitivity of the balance is 0.1 lag (equivalent to 1-47 laW), further improvement should be possible by filtering the recorder input and more effective isolation of the equipment from the building. Acknowledgements The author would like to thank Dr. Robert A. Buchanan for his helpful suggestions and assistance. This research was supported in part by the National Institutes of Health via GM-08209 and by the HAS fund at the University of Vermont.
REFERENCES Borgnis, F. E. (1953) Acoustic radiation pressure of plane compressional waves. Rev. mod. Phys. 25, 653 664. Kossoff, G. (1965) Balance technique for the measurement of very low ultrasonic power outputs. J. acoust. Soc. Am. 38, 880 881. Rooney, J. A. and Nyborg, W. L. (1972) Acoustic radiation pressure in a travelling plane wave. Am. J. Phys. 40, 1825 1830. Wells, P. N. T., Bullen, M. A. and Freundlich, H. F. (I964) Milliwatt ultrasonic radiometry. Ultrasonics 2, 124 128. Wells, P. N. T. (1969) Physical Principles o/ UItrasmfic Diagnosis. Academic Press, New York. Wemlen, A. (1968) A milliwatt ultrasonic servo-controlled balance. Med. biol. Engng 6, 159 165.
DETERMINATION OF ACOUSTIC POWER OUTPUTS IN THE MICROWATT-MILLIWATT RANGE JAMES A. ROONEY* Physics Department, University of Vermont, Burlington, Vermont 05401, U.S.A. (Received 21 A ugust 1972: and in fina/jorm 13 Not,ember ]972) Abslract--A system using an electrobalance for radiation pressure measurements has been developed capable of determining acoustic powers in the microwatt-milliwatt range. Low background "noise" levels are achieved by effectiveisolation of the balance from building vibrations and shielding the target from convectioncurrents. The standard deviation for a power output of 1mW is typicallyless than 1per cent.
Key morals'. Acoustics, Pressure, Ultrasonics.
CURRENTLY with the increasing use of medical ultrasonics there is a need for accurate acoustic power measurements. A number of techniques by which the power output from an ultrasonic beam can be determined have been developed. In the megahertz frequency range both calorimetric and radiation pressure methods have been used in the past. The calorimetric techniques are usually based upon complete absorption of acoustic energy and are typically used to measure powers above 100 m W (Wells, 1969). In low acoustic power applications, radiation pressure techniques are used to measure the force upon a target which intercepts an entire sound beam. For a traveling plane wave impinging on a perfectly absorbing target suspended in an open vessel, the radiation force is equal to the acoustic power divided by the velocity o f sound (Rooney, 1972; Borgnis, 1953). F o r an acoustic power of 1 m W the radiation force is equivalent to the weight of 68 ~tg. Three systems capable of measuring such small forces have been reported. Wells e t al. (1964) measured deflections o f a reflecting vane upon which a sound beam impinged. The minim u m power which could be detected (although not measured) was o f the order o f 0.01 mW. * Present Address: Physics Department,
at Orono, Orono, Maine 04473, U.S.A.
Universityof Maine
They were able to measure a power output of 2 m W with a stated error of + 3 per cent. Kossoff (1965) used a modified analytical chemical balance to measure the radiation pressure. For his system he states that the m i n i m u m detectable acoustic power output was 0.04 mW. A third system developed by Wemlen (1968) consisted of a torsion balance with capacitive transducer attached to the balance arm, Wemlerj states that acoustic powers as low as 0.03 m W could be detected. In the 10 m W range, the error o f the balance was stated to be less than 5 per cent. We have developed a radiation pressure balance that is capable of power determinations in the microwatt range. The apparatus currently in use is shown schematically in Fig. 1 and consists o f a Cahn R G Electrobalance (Cahn Instrument Co., .Paramount, California) from one arm of which a cylindrical absorbing target (SOAB, B. F. Goodrich), 3 cm in diameter and 0.2 cm in height is suspended; appropriate tare weights are suspended from the other arm. The target is hung in the medium of interest within an inner vessel which is 4.3 cm in diameter. This small interior vessel is closed at the lower end with a stretched m e m b r a n e (25 la thick, Plastic Wrap) to shield the target from acoustic streaming. The electrobalance is calibrated by noting the deflection on the recorder corresponding to forces resulting from a series of calibrated 13
14
JAMES A.
ROONEY
\ \ \ N
\ \ N
\ \
S M
_
_
J
k.Trl L
Fig. 1. Schematic diagram of balance system. An acoustic signal supplied by the oscillator to transducer T passes by way of membrane M through the medium contained in the outer vessel 0. The sound passes through acoustic streaming shield S, continues through the medium within the inner vessel 1, and then impinges upon the absorbing target A. Changes in the voltage of the feedback system F are displayed on recorder R. W indicates the tare weights.
weights placed on the balance. The transducer element to be calibrated is brought into contact with a second stretched membrane at the base of the large vessel. A suitable coupling agent, in our case "Aquasonic 100" (Parker Laboratories, Irvington, N.J.), was used between the transducer and the membrane. The outer vessel containing water has a large volume (9.5 cm in dia. and 16 cm in height) so that thermal fluctuations in the inner vessel are reduced. When the transducer is activated, the target is deflected momentarily from equilibrium. This deflection changes the amount of light reaching a photocell which initiates a magnetic feedback system within the Cahn balance returning the target to its original position. A p o r t i o n of the feedback'voltage to the magnet i~ recorded on a Sanborn chart recorder (Model 296, Sanborn, Waltham, Mass.). We note that the use of the feedback system is advantageous because it eliminates errors which result from changes in surface tension forces on the suspending wire and minimizes those which are the result of other "surface" effects. The air gap between the balance and the large vessel is
enclosed to prevent effects of air currents on the suspending wire. The inner vessel proved to be important for the stability of the system. The vessel should have a diameter only slightly larger than the target in order to minimize drift in the signal which results from convection currents. Evidence for the degree of improvement in the measurements is shown in Fig. 2. Figure 2(a) shows the typical drift in the base line of the recorder output when the inner vessel is removed and replaced by a stretched plastic membrane whose diameter was that of the larger vessel. Fluctuations up to 0-51 mW are seen. The tracing in Fig. 2(b) is the recorder output resulting from 2 pulses of a 5 MHz signal whose power output is 1.03 mW when the inner vessel was present. In this figure the sound pulse begins at the point indicated by the upward arrow. Transients resulting partly from instrumentation decay within 6 sec. An equilibrium deflection is reached and the sound is then turned off as indicated by the downward arrow. Transients are again seen as the recorder out-
Determination of acoustic power outpuls in the microwatt milliwatt range
15
(a)
!
;
~
[ '
;i'
I
',
l
~
!
t ....
:
]
/
(b)
i! ....
/
4 see
Fig. 2. (a) Drift in recorder output as the result of convection currents. (b) Recorder output from 1-03 nfW pulses when inner vessel is used. In both cases 20 units corresponds to 0.1 mg (1.47 mW) and 2.5 units horizontally is 1 sec. Time progresses from right to left. p u t returns to the base line. W e note that f l u c t u a t i o n s in the base line u n d e r these cond i t i o n s (with the inner vessel present) are less t h a n 0.05 roW. The size o f the target also p r o v e d to be an i m p o r t a n t c o n s i d e r a t i o n for a c c u r a c y o f the m e a s u r e m e n t s . In c o n s i d e r i n g the a p p r o p r i a t e d i a m e t e r for the target a c o m p r o m i s e m u s t be made. T h e d i a m e t e r o f the t a r g e t m u s t be larger than the d i a m e t e r o f the b e a m to ensure that the s o u n d is c o m p l e t e l y a b s o r b e d but the v o l u m e o f the target s h o u l d be kept to a m i n i m u m to e l i m i n a t e excess noise in the system. T h e a b s o r b ing target must of course be thick e n o u g h to have g o o d a b s o r b i n g properties. F o r these studies S O A B p r o v e d to be g o o d m a t e r i a l a n d no a p p r e ciable s t a n d i n g waves could be detected for the
frequencies used. P r e l i m i n a r y e x p e r i m e n t s were c o m p l e t e d with a S O A B target 3 cm in dia. a n d 0.7 cm in height. The noise in the r e c o r d e r o u t p u t p r o v e d to be excessive (up to 1-03 roW) as can be seen in Fig. 3(a). Believing t h e r m a l fluctuations in the liquid to be the i m p o r t a n t cause o f the noise, we built a t h e r m a l l y c o m p e n sated target a l o n g lines suggested by K o s s o f f (1965). T h e target c o n s i s t e d o f a S O A B a b s o r b e r 3 cm in dia. a n d 0.2 cm in height glued to a plexiglas t h e r m a l c o m p e n s a t o r 3 cm in dia. a n d 0-7 cm in height. T h e noise present in the signal a c t u a l l y increased as s h o w n in Fig. 3(b). This noise a p p e a r s to be the result o f b u i l d i n g vibrations which set up pressure g r a d i e n t s in the liquid. In the presence o f these pressure gradients, the target is acted u p o n by a force p r o p o r t i o n a l
(o) r
' ~~
:-~
.........
:
! .....
i ......
i ¸ -
:
"-
t~t; ~h'~'~!!#~t t~##""~,~:~'~t"V~i~~,L~~;'?,~,~";~ E~' ! ~ ! i~i ~ i !~
i: .....
i
-
o).
(b) r [:
"i
~- "I ........ T" ~" "r ..... ~!
i !
T
....
I
i
:
: .
.
I
(c)
.
.
.
.
.
i I
'
0
4sec
Fig. 3. Noise in recorder output for targets of various volumes. (a) Target with volume of 5.0 cm ~. On tracing 20 units is 0-2 mg. (b) Thermally compensated target with a volume of 6-4 cm 3. 20 units is 0,2 rag. (c) Target currently in use with volume of 1.4 cm 3. 20 units equals 0.1 rag. In all tracings 2.5 units corresponds to 1 sec.
16
JAMES A. ROONEY
to its volume. The reduction of noise in our system was achieved by using a target of minimum volume and isolating the experimental arrangement from the building. In our case we have found that mounting the arrangement on a heavy metal frame supported by eight hard rubber balls (singles squash balls) has allowed us to achieve the acceptable level of noise shown in Fig. 3(c). As examples of applications of the system we have measured the power output from two ultrasonic diagnostic units. Both operate in a cw mode and are Doppler type detectors. The first is the Hemosonde (Parke-Davis, Ann Arbor, Michigan) which operates at 5 MI-;Iz and has a power output of 1.03 mW at a distance of 3 cm from the transducer. The standard deviation in this determination is 0-7 per cent. The second unit is the Transcutaneous Doppler (Park Electronics Lab, Beaverton, Oregon) which used a 8.8 MHz signal and has a power output of 30 mW (standard deviation of 1.0 per cent) at the same distance. The beam configurations were studied using a hydrophone whose active element is a PZT-5 cylindrical ceramic (1.4 mm o.d., 1-4 mm length). Both units have well defined beams and no significant focussing. At 3 cm from the transducers the Hemosonde beam area is 0.8 cm 2 while that of the Transcutaneous Doppler is 0.32 cm 2. Here we define the limits of the beam to be the points where the pressure has been
reduced to 0.1 that of the pressure maximum in the beam. Thus the average intensities are respectively 1.29 and 93.8 mW/cm 2. If we use the half power points, the average intensities are respectively 4.35 and 300 mW/cm 2. Currently the balance allows us to measure power outputs of 30 laW with a standard deviation of 5 laW. Since the sensitivity of the balance is 0.1 lag (equivalent to 1-47 laW), further improvement should be possible by filtering the recorder input and more effective isolation of the equipment from the building. Acknowledgements The author would like to thank Dr. Robert A. Buchanan for his helpful suggestions and assistance. This research was supported in part by the National Institutes of Health via GM-08209 and by the HAS fund at the University of Vermont.
REFERENCES Borgnis, F. E. (1953) Acoustic radiation pressure of plane compressional waves. Rev. mod. Phys. 25, 653 664. Kossoff, G. (1965) Balance technique for the measurement of very low ultrasonic power outputs. J. acoust. Soc. Am. 38, 880 881. Rooney, J. A. and Nyborg, W. L. (1972) Acoustic radiation pressure in a travelling plane wave. Am. J. Phys. 40, 1825 1830. Wells, P. N. T., Bullen, M. A. and Freundlich, H. F. (I964) Milliwatt ultrasonic radiometry. Ultrasonics 2, 124 128. Wells, P. N. T. (1969) Physical Principles o/ UItrasmfic Diagnosis. Academic Press, New York. Wemlen, A. (1968) A milliwatt ultrasonic servo-controlled balance. Med. biol. Engng 6, 159 165.