Ultrasound in Med. & BioL, Vol. 2, pp. 219-220. Pergamon Press, 1976. Printed in Great Britain
TECHNICAL NOTE USE
OF A SPHERE
RADIOMETER BEAM
TO MEASURE
ULTRASONIC
POWER
(Received 18 September 1975) Abstract--Making use of the theoretical work of Hasegawa and Yosioka, it is demonstrated that errors associated with either of the sound velocities in the spherical target can significantly shift the resonance dips in the variation of the radiation force function Y, with ka. Without a knowledge of these acoustic parameters of the target, uncertainties may therefore occur in the computation of Y~.
Key Words: Ultrasonics, Acoustics, Radiometry. In the design of a radiation force method for absolute measurement of the average acoustic power associated with a medical ultrasonic beam, the choice of spherical geometry for the target is desirable because it is only in this case that calculation of the inevitable diffraction effects is theoretically tractable. The use of this type of device is valuable in biomedical work (Dunn and Fry, 1973) and it is the purpose of this note to point out some of the problems that may arise in such applications. The basis of the practical application of the sphere radiometer is that there is a factor Yp which can he calculated from theory and which expresses the ratio between the forward force experienced by a spherical target and the acoustic energy density in the beam which it intercepts. Computations of values of Yp have been carried out by Hasegawa and Yosioka (1969) in terms of the variation with ka (k = wave number of the acoustic wave in the target medium and a = radius of the sphere) and their values for steel (extended by us for the range of ka values between 8 and 26) are shown by the solid line in Figs. 1 and 2. For certain applications, particularly those where the use of a sphere radiometer constitutes a primary standard (e.g. Hill, 1975), it is desirable to work in conditions where ka > 5 and here it is important to note the influence of uncertainties in the knowledge of the longitudinal and shear sound velocities. The effect of such possible errors is illustrated by the dotted curve in Fig. 1, which is the result of re-running the computation for conditions identical apart from a reduction of 5% in the value assumed for shear mode velocity. A similar, although rather less 1.0
0.8 0.6 0.4
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10 12 14 16 1B 20 22 2Z, 26 28 kct ---->
Fig. 1. Variation of the radiation force function Yp with ka for a steel sphere in water. Solid line: shear wave sound velocity in steel=3252ms -1. Dotted line: shear wave sound velocity in steel=3089.4ms -t. In both cases, longitudinal velocity= 5949 m s -t. UMB
Vol. 2, No. 3--E
219
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Fig. 2. Variation of Yp with ka for a steel sphere in water. Solid line: longitudinal wave sound velocity = 5949 m s -1. Dotted line: longitudinal wave sound velocity = 5647.7 m s -1. In both cases, shear velocity = 3252 m s -1.
severe, shift in the curve can be shown to result from a 5% reduction in the value of the longitudinal mode velocity (Fig. 2). (Changes in Poisson's Ratio, due to the changes in the sound velocities, are accounted for in the computation). The magnitude of the variation in velocity values considered here is somewhat arbitrary but not unrealistic. The quoted values of the sound velocities for similar but non-identical materials can vary by comparable amounts, due perhaps, to variation in composition coupled with the expected experimental uncertainties. We do not wish to make any comment on the validity of the velocity values that appear in the literature hut merely to point out that such variations can cause the resonance dips in the Yp curve to shift. It is noteworthy that attempts to verify experimentally the variation of Y~ with ka that have been reported make quite specific statements as to the nature of the target. Both Averbuch et aL (1973) and Hasegawa and Yosioka (1969) report results which are applicable to a well-defined steel. However, if the two sound velocities of the target material are not known with sufficient accuracy, then a precise computation of Yp may not be possible. For the future, a useful advance will be to introduce an appropriate attenuation correction into the calculations, since one would expect this to have the effect of damping down the oscillations in the Yo values, particularly at the larger values of ka. By use of an attenuating target material it may then be possible to reduce the magnitude of the uncertainty in the value of Yp. Bearing in mind these points, we feel that the accuracy claimed
220
Technical Note
for measurements of beam power using a sphere radiometer should reflect the uncertainties outlined in this note.
Acknowledgement--The authors wish to acknowledge the helpful comments made by Professor F. Dunn regarding this note.
Physics Department, H.R. STOCKDALE University of Surrey, Guildford, Surrey, U.K. Physics Division, Institute of Cancer Research, Sutton, Surrey, U.K.
C. R. HILL
RgFERF,NCES
Averbuch, A. J., Fry, F. J. and Dunn, F. (1973) Absolute determination of acoustic intensity by the method of radiation force on a solid elastic sphere. J. acoust. Soc. Am. 53, 340-341. Dunn, F. and Fry, F. J. (1973) Ultrasonic field measurement using the suspended ball radiometer and thermocouple probe. In Interaction of Ultrasound and Biological Tissues, pp. 173-176, U.S. Govt. publication DHEW(FDA) 73-8008. Hill, C. R. (1975) Proposed facility for ultrasound exposimetry and calibration. Ultrasound Med. Biol. 1, 476. Hasegawa, T. and Yosioka, K. 0969) Acoustic radiation force on a solid elastic sphere. J. acoust. Soc. Am. 46, 1139-1143.
TECHNICAL NOTE USE
OF A SPHERE
RADIOMETER BEAM
TO MEASURE
ULTRASONIC
POWER
(Received 18 September 1975) Abstract--Making use of the theoretical work of Hasegawa and Yosioka, it is demonstrated that errors associated with either of the sound velocities in the spherical target can significantly shift the resonance dips in the variation of the radiation force function Y, with ka. Without a knowledge of these acoustic parameters of the target, uncertainties may therefore occur in the computation of Y~.
Key Words: Ultrasonics, Acoustics, Radiometry. In the design of a radiation force method for absolute measurement of the average acoustic power associated with a medical ultrasonic beam, the choice of spherical geometry for the target is desirable because it is only in this case that calculation of the inevitable diffraction effects is theoretically tractable. The use of this type of device is valuable in biomedical work (Dunn and Fry, 1973) and it is the purpose of this note to point out some of the problems that may arise in such applications. The basis of the practical application of the sphere radiometer is that there is a factor Yp which can he calculated from theory and which expresses the ratio between the forward force experienced by a spherical target and the acoustic energy density in the beam which it intercepts. Computations of values of Yp have been carried out by Hasegawa and Yosioka (1969) in terms of the variation with ka (k = wave number of the acoustic wave in the target medium and a = radius of the sphere) and their values for steel (extended by us for the range of ka values between 8 and 26) are shown by the solid line in Figs. 1 and 2. For certain applications, particularly those where the use of a sphere radiometer constitutes a primary standard (e.g. Hill, 1975), it is desirable to work in conditions where ka > 5 and here it is important to note the influence of uncertainties in the knowledge of the longitudinal and shear sound velocities. The effect of such possible errors is illustrated by the dotted curve in Fig. 1, which is the result of re-running the computation for conditions identical apart from a reduction of 5% in the value assumed for shear mode velocity. A similar, although rather less 1.0
0.8 0.6 0.4
0.2 o
.
o
2
.
.
4
.
6
.
J
8
.
.
.
.
.
.
.
10 12 14 16 1B 20 22 2Z, 26 28 kct ---->
Fig. 1. Variation of the radiation force function Yp with ka for a steel sphere in water. Solid line: shear wave sound velocity in steel=3252ms -1. Dotted line: shear wave sound velocity in steel=3089.4ms -t. In both cases, longitudinal velocity= 5949 m s -t. UMB
Vol. 2, No. 3--E
219
t
1.0"
vo 0.8
0.6
0,4"
0.2" .
0 0
. 4
.
.
6
.
8
.
.
.
.
.
.
.
.
.
m
10 12 14 16 18 20 22 24 26 28 ko ----->
Fig. 2. Variation of Yp with ka for a steel sphere in water. Solid line: longitudinal wave sound velocity = 5949 m s -1. Dotted line: longitudinal wave sound velocity = 5647.7 m s -1. In both cases, shear velocity = 3252 m s -1.
severe, shift in the curve can be shown to result from a 5% reduction in the value of the longitudinal mode velocity (Fig. 2). (Changes in Poisson's Ratio, due to the changes in the sound velocities, are accounted for in the computation). The magnitude of the variation in velocity values considered here is somewhat arbitrary but not unrealistic. The quoted values of the sound velocities for similar but non-identical materials can vary by comparable amounts, due perhaps, to variation in composition coupled with the expected experimental uncertainties. We do not wish to make any comment on the validity of the velocity values that appear in the literature hut merely to point out that such variations can cause the resonance dips in the Yp curve to shift. It is noteworthy that attempts to verify experimentally the variation of Y~ with ka that have been reported make quite specific statements as to the nature of the target. Both Averbuch et aL (1973) and Hasegawa and Yosioka (1969) report results which are applicable to a well-defined steel. However, if the two sound velocities of the target material are not known with sufficient accuracy, then a precise computation of Yp may not be possible. For the future, a useful advance will be to introduce an appropriate attenuation correction into the calculations, since one would expect this to have the effect of damping down the oscillations in the Yo values, particularly at the larger values of ka. By use of an attenuating target material it may then be possible to reduce the magnitude of the uncertainty in the value of Yp. Bearing in mind these points, we feel that the accuracy claimed
220
Technical Note
for measurements of beam power using a sphere radiometer should reflect the uncertainties outlined in this note.
Acknowledgement--The authors wish to acknowledge the helpful comments made by Professor F. Dunn regarding this note.
Physics Department, H.R. STOCKDALE University of Surrey, Guildford, Surrey, U.K. Physics Division, Institute of Cancer Research, Sutton, Surrey, U.K.
C. R. HILL
RgFERF,NCES
Averbuch, A. J., Fry, F. J. and Dunn, F. (1973) Absolute determination of acoustic intensity by the method of radiation force on a solid elastic sphere. J. acoust. Soc. Am. 53, 340-341. Dunn, F. and Fry, F. J. (1973) Ultrasonic field measurement using the suspended ball radiometer and thermocouple probe. In Interaction of Ultrasound and Biological Tissues, pp. 173-176, U.S. Govt. publication DHEW(FDA) 73-8008. Hill, C. R. (1975) Proposed facility for ultrasound exposimetry and calibration. Ultrasound Med. Biol. 1, 476. Hasegawa, T. and Yosioka, K. 0969) Acoustic radiation force on a solid elastic sphere. J. acoust. Soc. Am. 46, 1139-1143.
