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Measurement of the ultrasonic energy radiated by transducers used in echography
Ultmsound in Med. & Biol., Vol. 5. pp. 7542 Pcrgamon Press Ltd.. 1979. Printed in Great Britain
MEASUREMENT OF THE ULTRASONIC ENERGY RADIATED BY TRANSDUCERS USED IN ECHOGRAPHY J. C. BABOUX, F. LAKESTAN~ and M. PERDRIX Laboratoire D’Ultrasons, Bat. 502, INSA 69621, Villeurbannc, Fraoce
(First received 5 June 1978, and in final form 2 November 1978) Abmtmd-A method based on the response of a thick piezoelectric disc to an ultrasonic plane wave and enabling the measurement of the energy in short pulses is described. The energy characteristics of three transducers, differing in frequency and diameter, are given. Theii mean acoustic intensities are respectively 0.08, 0.26 and 14mW/cm2 for repetition rates of 1 kHz, 1kHz and 2.4 kHz. Key words: Ultrasonic pressure. Acoustic transducer, Power measurement.
intensity, Ultrasonic energy calibration, Ultrasonic
with transducers radiating continuous or pulsed sinusoidal waves; the variations of the ultrasonic signal with time being perfectly known, it is then possible to deduce the temporal characteristics of the ultrasonic energy. On the contrary, with transducers radiating short pulses, the instantaneous values of the acoustic intensity cannot be extracted although the in5uence of parameters, such as the temporal peak intensity, would be worth taking into account for the study of the ultrasonic hazards. The radiation force and calorimetric methods being ,,then inadequate, the temporal distribution of the acoustic energy is derived from the measurement of either the particle velocity (Etienne, 1976) or the instantaneous ultrasonic pressure. When the pressure determination is chosen as a preliminary step, it is obtained with transducers calibrated by the reciprocity or self reciprocity method (Ebaugh, 4947; Cartensen, 1947). Very often however, the spectral response of a standard receiver varies with frequency and the information provided is thus approximate since the deconvolution which, in that case, would be necessary is generally not carried out. Besides .the pressure scale is determined by considering the sensitivity of the standard receiver at the nominal frequency of the transmitter which is not a very well de&red value, especially when the ultrasonic pulse is short. This problem is even more critical if the ultrasonic field is investigated by a small probe, its sensitivity varying considerably with frequency, as shown by Brendel(l976). In our method, the energetic characteristics
INTRODUCTION
Ultrasonic echography is now also used in numerous medical fields e.g. cardiology, ophtalmology, obstetrics, gynaecology. The characteristics of the ultrasonic beam used for tissue investigation must be known for the following two reasons: the ultrasonic energy must not reach a dangerous threshold for the patient, and the good working order of the apparatus must be checked. These characteristics are usually obtained by immersing the transducer in a liquid and measuring the ultrasonic pressure or energy on a limited area around a point, or determining an average value of these quantities over a section of the beam. Based on the existence of the radiation pressure, the measurement of the force exerted on a reflector or an absorber subjected to an ultrasonic field leads to the determination of either the total output power when the target is large, or the spatial distribution of the ultrasonic intensity when the target is a small steel ball (Gazanhes et al., 1966; Hill, 1970; Haran et al., 1975; Carson et al., 1978; Farmery et al., 1978). The heat produced by the absorption of ultrasound may also be used to measure ultrasonic power; recently, with a constant flow calorimeter, the sensitivity has been improved to 1 mW(Torr et al., 1977). Because of the inertia of the mechanical or thermal phenomena, the two previous techniques integrate, with respect to time, the acoustic energy and therefore, they can only provide temporal average values of power or intensity. This restriction is not troublesome 75
76
J. C. BABOUX, et al.
of the ultrasonic beam and, in particular, the instantaneous values are calculated from the ultrasonic pressure, p(f). This pressure is measured by means of calibrated receiver, which consists principally of a thick piezoelectric disc and a fairly simple electronic circuit (differentiator). It is shown that this apparatus provides, directly and without distortion, the absolute value of the pressure as a function of time. It should be noted that the use of this device is restricted to transducers radiating rather short pulses (less than a few microseconds), a field where the conventional methods can only give partial or approximate results. On the other hand, it is assumed that the ultrasonic wave to be studied is plane, which implies the following conditions: (1) The energy radiated by focused transducers cannot be measured. (2) The standard receiver must be placed close to and facing the transmitter, so that this set up cannot provide any information about the spatial distribution of the ultrasonic energy.
tic impedance pc) giving the front particle velocity
a
2PO)
at at =
PiCi + pC
hence a displacement
E(t) =.pici : pc [ PO’)a’. As long as the wave has not reached the back face of the standard receiver (duration of about 2.5 ps in our set up), a voltage u(t) appears between its faces
where h is the piezoelectric coefficient of the thick ceramic disc. Thus it is su5cient to differentiate the voltage u(t) to obtain the instantaneous Mrasonic pressure in the liquid p(t)
*
face
=
PiC;i PC du(t). dt
PRINCIPLE OF THE MRT’IfOD (1) Measurement of the instantnneous If the area of the transmitter surface, S,, is ultrasonic pressure p(t) less than that of the receiver surface, S, a This method has already been partly des- correction is necessary and the ultrasonic cribed (Lakestani, 1976; Baboux, 1977) and pressure is given as therefore will only be summarized here. A thick piezoelectric disc poled parallel to its p(t) = S,E&pg@ axis-called the standard receiver-was Se 2h dt placed just in front of the transmitter to be calibrated; the axes of the two transducers The previous formulae show that, by were aligned and both were immersed in a means of an analog circuit able to differenliquid. If the standard receiver is placed close tiate the voltage appearing across the faces of to the transmitter to be calibrated (between 1 a thick piezoelectric element, the instanand 3 mm), the diffraction phenomenon can taneous pressure can directly be obtained. be neglected and the wave impinging on the The terms used to express p(t) in terms of standard receiver can be considered plane. (du(t)/dt) being independent of frequency, The theoretical model assumes that the the main advantage of the device is the fact receiver diameter satisfies the following that the incident pressure is faithfully conditions: reproduced. The absolute value of the pres(a) It is much greater than the ultrasonic sure and its accuracy depend upon an acwave length in the liquid. curate knowledge of the different terms of (b) It is less than or equal to the diameter the proportionality coefficient (PC, pici, h, S,,, of the transducer to be calibrated (so that the S,). The specific acoustic impedance of the ultrasonic wave is inciderit upon the entire media are easy to determine. Since the surface of the standard receiver). piezoelectric coefficient h is seldom given by After the transmitter has been excited, it the manufacturer, it has been measured using generates a wave, whose pressure is p(t), an original, method developed in our laborawhich propagates through the liquid (of tory (Lakestani, 1975). With the ceramics specific acoustic impedance pici) and then used, h equals 14.0 X lo* V/m and this value is into the standard receiver (of specific acousalmost independent of temperature between
Measurement of the ultrasonic energy radiated by transducers used in echography
77
15” and 40°C. In the particular case when the wave does not cover the whole surface of the standard receiver, the area of the transmitter surface must be known. To do this, the dimensions of the active element, generally given by the manufacturer, can be used or they can be measured by moving a small probe across, and, in front of the transmitting face. (2) Calculation of the energetic characteristics of the ultrasonic beam From the instantaneous values of the ultrasonic pressure p(t) the following energetic quantities can be derived: (a) The instantaneous intensity I(t) = (p*(t)/pici) (in W/m’) and in particular, its maximum value I,,,, called the instantaneous peak intensity. (b) The energy per unit area carried by each pulse of duration T : WT = 107I(t) dt (in J/m’). (c) The average intensity per pulse IP = (Wdr) (in W/m*), where 7 is the duration for which the ultrasonic pressure exceeds a certain level and in which almost all the energy of the ultrasonic impulse is concentrated. This threshold is not standardized, and only the pressure oscillations whose amplitude are greater than a tenth of the temporal peak pressure were taken into account to define this duration 7. (d) The temporal average intensity I, the average value of the intensity over a duration T, = (I/f,), where fr is the repetition rate of the ultrasonic pulses: Z = fiW, (in W/m*). The ultrasonic wave is supposed to be plane, so the intensities may be considered uniform inside a cross section of the beam; from the area S, of the transmitting transducer it is also possible to calculate: (a) The total energy contained in a pulse W,, = W& (in J); (b) The total ultrasonic power P = IS, (in W) which may be compared with the value directly obtained from the calorimetric or radiation force methods.
Fig. 1. Experimental set up used for the measurement of the instantaneous ultrasonic pressure.
(d) to be measured is fastened to a circular lid (e) whose axis is orientable by means of three screws (f), which allows the transmitter to be adjusted in front of the receiver, so that the front face of the thick receiver is parallel with the incident plane wave. This adjustment is achieved when the amplitude of the electrical signal s(t), displayed on the oscilloscope and proportional to the pressure p(t) has reached its maximum value. (2) An amplifier, a differentiator and an oscilloscope. The signal measured by the oscilloscope probe across the faces of the standard receiver is first amplified (one of the two amplifiers of a two channel oscilloscope is used), then, after differentiation and further amplification, displayed on the screen of the oscilloscope. The electrical part of this measuring device (amplifier and electronic differentiator) was calibrated, using sinusoiamplitude and dal signals of known frequency. This electronic system is capable of displaying ultrasonic pressure pulses, whose spectra range from 0.5 MHz to 20 MHz, without distortion. Also, the absolute value of the pressure is given with satisfactory accuracy (about 5%). It should be noted that with the receiver disc used, 12 mm in thickness, it is possible to measure the ultrasonic pressure radiated by transducers whose decay time is less than or equal to 2.4 11s. If longer ultrasonic signals were to be studied, it would suffice to increase the thickness of the standard receiver. Experiments have been carried out recently EXPERIMENTALARRANGRMRNTFOR THE MRASURE- using a disc allowing measurements up to MENTOF THE ULTRASONICPRES!W~ 4ps, a value which is acceptable for most of Figure 1 shows the experimental set up. It the pulse echo instruments used in echoconsists of: graphy. (1) A perspex tank (a) filled with the liquid EWERIMENTALRESLJLTS (b) and at the bottom of which the thick piezoelectric disc (c) used as standard The energetic characteristics of the receiver is fixed. The transmitting transducer ultrasonic beams produced by three different
J. C. Bmoux,
78
Table 1. Characteristics of the three transducers studied Transducer
Nominal frequency
Diameter
(a) (b) (cl
1s MHZ 4MHz 8MHz
12.7mm 12.7 mm Smm
transducers were determined. Two of them, (a) and (b) were part of an ultrasonic apparatus designed for non destructive testing (similar to those generally used in medical diagnosis); the third, (c) was the probe of an echograph used in ophthalmology*. The nominal frequencies and the diameters of these transducers are listed in Table 1. (1) Measurement of the instantaneous ultrasonic pressure From Fig. 2(a)-(c), which shows the variations of the ultrasonic pressure as a function of time, for the three above-mentioned transducers, it is possible to draw the following conclusions: (i) Transducer (a) transmits very short ultrasonic pulses and is particularly well damp&d. (ii) Transducers (b) and (c) transmit longer oscillations and the pulses of several frequency of these oscillations is different from the nominal frequency given by the manufacturer; the deviation from the expected value is quite large ?or transducer (c) (5 MHz instead of 8 MHz). (iii) The greatest ultrasonic pressure is radiated by transducer (c). So, the mere examination of the instantaneous pressure already provides interesting information on the transducer. It would also be particularly easy to study the influence of ditPerent parameters, such as the duration and the amplitude of excitation electrical pulses on the shape and level of the ultrasonic pressure. (2) Methods of calculating the intensity, power and energy only the instantaneous intensity can be readily derived from the time dependent pressure; the determination of the other energetic values requires the integration over time of the square of the pressure. This calculation was conducted in two different ways.
*We are grateful to Professor Ravaud (Hbpitai Edouard Heniot) for the loan of this apparatus.
d al.
In method 1, a computer was used to control the sampling of the time signal proportional to the pressure and then to make the various calculations. This fast method was profitably used to determine the minimum number of samples leading to an accurate value of the time integral of p*(t). However, such a complex equipment is not necessary and a satisfactory evaluation of the previous quantities can also be obtained from an oscillogram of the pressure, p(t) (method 2). Method 1. For real time calculation of the energy by means of a computer, it is necessary to know the digital values of the pressure at regular time intervals. Owing to the rapid variation of p(t) with time, a complex apparatus was needed. Only a brief description of this set up, mainly used for ultrasonic spectroscopy studies, in our laboratory, will be given here. Since the pulsed ultrasonic signal is repetitive, it was displayed on a sampling oscilloscope acting as a stroboscope. The vertical output of this oscilloscope was slowed down to be compatible with the conversion and storage times of an ordinary data acquisition system controlled by a mini computer. Once the pressure has been stored in the computer memory, various mathematical operations can easily be performed. The minimum sampling rate of the time signal, p(t), could have been deduced from its frequency spectrum. A more empirical method was chosen; the time interval between the samples was reduced until the result of the numerical integration of p2(t) becomes constant. As an illustration of this process, the energy per unit area contained in each pulse, was estimated for different sampling rates. The results obtained show that the sampling interval must be less than 20ns for transducer (a) and less than 4011s for transducer (b) (Table 2). Method 2. The integration of p2(t) can be obtained by reading the series of successive pressure values on a magnified display of the p(t) signal. If a sufficiently small sampling interval is respected, this rather long and tedious process leads to the same result as the previous automated method. A more rapid but approximate calculation can also be developed. The pressure, p(t), is replaced by a signal of a known mathematical shape, as close as possible to the real signal, for which the integral to be performed is directly given
Measurement
of the ultrasonic
energy radiated by transducers
used in echography
Fig. 2. Ultrasonic pressure wave forms of different transducers: (a) and (b): transmitters used in non destructive testing: (c): probe used in ophtalmology.
79
81
Measurement of the ultrasonic energy radiated by transducers used in echography Table 2. Intluence of sampling interval on calculated ultrasonic energy Transducer Samplii interval (ns) Ultrasonic energy per unit area in each pulse ( 1Ow3J/m*)
Transducer (a)
I
Transducer (b)
I
4
8
20
40
8
20
40
80
0.80
0.78
0.77
0.51
2.23
2.18
2.21
1.32
Table 3. Complete energy characteristics of the three transducers studied For each pulse
Transducer
Repetition rate f, (k=)
:; (c)
1 1 2.4
Temporal peak Intensity UW/m*) 2.0 x lo’ 3.0 x 104
Average intensity
Energy per unit area
J,(W/m*) 2.4 x ld
46X10’
by an analytical formula. Thus, for the ultrasonic pressure radiated by transducer (a) and (b), each positive and negative alternation, whose duration is At and amplitude is pm, was replaced by a semi-sinusoid of the same duration and amplitude; hence, the integral I:+“’ p2(t) dt becomes 1/2p,2At. The results obtained were fairly close to the exact value previously computed (relative error of about lQ-20%). (3) Results All the previously defined energetic characteristics were calculated, for transducer (a), (b), (c) utilizing the simpler method just described (Table 3). Our measurements of the total ultrasonic power and of the average intensities near the transducer face, fall into the range of values published by other authors (Carson et al., 1978; Farmery et aI., 1978).
CONCLUSION
A calibrated receiving .transducer is described, which is easy to build and to use, and which allows an accurate measurement of the instantaneous ultrasonic pressure generated by pulsed transducers. The main advantage of this set up lies in the fact that it gives the time dependence and the absolute value of the ultrasonic pressure, directly and without distortion. This first measurement already brings interesting information on the working
Wz(J/m*) 0.81 x lo-’ 2.6 x lo-’ 58 x lo-’
Temporal average value Total energy
Intensity
Power
W,(J)
I(W/m’)
PO
1.0 x lo-’ 3.3 x 10-7 11 x lo-’
0.81 2.60 140
0.1 x lo-’ 0.33 x lo-’ 2.6 x IO-’
order of a pulse echo instrument and of its transducer. The ultrasonic pressure can also be used to evaluate various energy characteristics, and in particular instantaneous values, for the purpose of studying ultrasonic toxicity. For three transducers, diBerent quantities such as the temporal peak intensity, the intensity in each pulse, the average intensity, the energy per pulse and the total ultrasonic power have been calculated. Our method, which is based on the measurement of the pressure close to the transmitting face of a transducer, gives the temporal distribution of the ultrasonic energy but is not adapted to a study of its spatial distribution. There are not many devices enabling the accurate measurement of the instantaneous pressure at a spatial point. The interferometric method developed by Konstantinov (1974) seems to meet these two requirements of adequate resolution both in time and space. However his equipment is complex and probably not sensitive enough in the case of short ultrasonic pulses. We plan to determine the acoustic intensity at spatial points where the energy is concentrated (last axial maximum or focus) by means of small calibrated probes which are now being built in our laboratory. In order to keep a satisfactory accuracy in the measurement of the instantaneous intensities, it is intended to correct the distortions due to the remaining resonances of the probes by numerical deconvolution.
J. C. BMOUX, et ai.
82 REFERENCES
Baboux, J. C., Lakcstani, F., Fkischma~, P. and Perdrix, M. (1977) Calibration of ultrasonic transmitters. NDT International 10, 135-138. Brendel. K. and Ludwig, G. (1976) Calibration of uhrasonic standard probe transducers. Acustico 36, 203-8. Carson, P. L.. FischeRa, P. R. and Gughton, T. V. (1978) Ultrasonic power and intensities produced by diagnostic ultrasound equipment. Ultrasound Med. Biol. 3, 34 I-350. Carstensen, E. L. (1947) Self reciprocity calibration of clectroacoustic transducers. I. Acoust. Sot. Am. 19. %l-%5. Ebaugh, P. and Mueser, E. (1947) The practical application of the reciprocity theorem in the calibration of underwater sound transducers. J. Acoust. Sot. Am. 19,695-700. Etienne. J., Fihpczynski, L., Firek. A., Gronowski, J., Kretowicz. U. and Salkowski. J. (1976) Intensity determim&on of ultrasonic f&used ‘beams used in ultrasonography in the case of gravid uterus. ~tMSOU#ld hh?d. Bid. 2, 119-122. Farmery, M. J. and Wbittmgham. T. A. (1978) A portable radiation force balance for use with diagnostic ultrasonic equipment. Ulrrasound Med. Biol. 3, 373-
379. Gazanhes. C.. Gamier, J. L. and Reinier, G. (1966) Detectem enregistreur de la pression de radiation ultrasonore. Acustica 16, 142-149. Haran, M. E., Cook, B. D. and Stewart, H. F. (1975) Comparison of an acousto-optic and a radiation force method of measuring ultrasonic power, X Acoust. Sot. Am. 57. 14361442. Hill, C. R. (1970) Calibration of ultrasonic beams for biomedical applications. Phys. Med. Biol. 15, 241-248. Konstantinov, V. A. and Panin, V. I. (1974) Absolute calibration of piewelectric transducers. Sov. I. N.D.T. 10. 35-39. Lakestani. F.. Baboux, J. C., Fleischmann, P. and Perdrix, hf. (197s) Mesura, par une m&ode impuisionnelle, de certaines constantes Clastique. pitzdlectrique et di&ctrique d’un transducteur. I. Phys. D. Appl. Phys. 8, 1863-1870. Lakestani. F., Baboux, J. C. and Perdrix, M. (1976) G&ttration d’une onde uhrasonore plane en forme d’tchelon: application a I’ttalonnage de rCcepteurs pi&oClectriqu& I. Phys. D. Appl. Whys. 9, 547-556. Torr. G. R. and Watmough. D. J. (1977) A constant flow calorimeter for the measurement of acoustic power at megahertz frequencies. Phys. Med. Biol. 22, 444-450.
MEASUREMENT OF THE ULTRASONIC ENERGY RADIATED BY TRANSDUCERS USED IN ECHOGRAPHY J. C. BABOUX, F. LAKESTAN~ and M. PERDRIX Laboratoire D’Ultrasons, Bat. 502, INSA 69621, Villeurbannc, Fraoce
(First received 5 June 1978, and in final form 2 November 1978) Abmtmd-A method based on the response of a thick piezoelectric disc to an ultrasonic plane wave and enabling the measurement of the energy in short pulses is described. The energy characteristics of three transducers, differing in frequency and diameter, are given. Theii mean acoustic intensities are respectively 0.08, 0.26 and 14mW/cm2 for repetition rates of 1 kHz, 1kHz and 2.4 kHz. Key words: Ultrasonic pressure. Acoustic transducer, Power measurement.
intensity, Ultrasonic energy calibration, Ultrasonic
with transducers radiating continuous or pulsed sinusoidal waves; the variations of the ultrasonic signal with time being perfectly known, it is then possible to deduce the temporal characteristics of the ultrasonic energy. On the contrary, with transducers radiating short pulses, the instantaneous values of the acoustic intensity cannot be extracted although the in5uence of parameters, such as the temporal peak intensity, would be worth taking into account for the study of the ultrasonic hazards. The radiation force and calorimetric methods being ,,then inadequate, the temporal distribution of the acoustic energy is derived from the measurement of either the particle velocity (Etienne, 1976) or the instantaneous ultrasonic pressure. When the pressure determination is chosen as a preliminary step, it is obtained with transducers calibrated by the reciprocity or self reciprocity method (Ebaugh, 4947; Cartensen, 1947). Very often however, the spectral response of a standard receiver varies with frequency and the information provided is thus approximate since the deconvolution which, in that case, would be necessary is generally not carried out. Besides .the pressure scale is determined by considering the sensitivity of the standard receiver at the nominal frequency of the transmitter which is not a very well de&red value, especially when the ultrasonic pulse is short. This problem is even more critical if the ultrasonic field is investigated by a small probe, its sensitivity varying considerably with frequency, as shown by Brendel(l976). In our method, the energetic characteristics
INTRODUCTION
Ultrasonic echography is now also used in numerous medical fields e.g. cardiology, ophtalmology, obstetrics, gynaecology. The characteristics of the ultrasonic beam used for tissue investigation must be known for the following two reasons: the ultrasonic energy must not reach a dangerous threshold for the patient, and the good working order of the apparatus must be checked. These characteristics are usually obtained by immersing the transducer in a liquid and measuring the ultrasonic pressure or energy on a limited area around a point, or determining an average value of these quantities over a section of the beam. Based on the existence of the radiation pressure, the measurement of the force exerted on a reflector or an absorber subjected to an ultrasonic field leads to the determination of either the total output power when the target is large, or the spatial distribution of the ultrasonic intensity when the target is a small steel ball (Gazanhes et al., 1966; Hill, 1970; Haran et al., 1975; Carson et al., 1978; Farmery et al., 1978). The heat produced by the absorption of ultrasound may also be used to measure ultrasonic power; recently, with a constant flow calorimeter, the sensitivity has been improved to 1 mW(Torr et al., 1977). Because of the inertia of the mechanical or thermal phenomena, the two previous techniques integrate, with respect to time, the acoustic energy and therefore, they can only provide temporal average values of power or intensity. This restriction is not troublesome 75
76
J. C. BABOUX, et al.
of the ultrasonic beam and, in particular, the instantaneous values are calculated from the ultrasonic pressure, p(f). This pressure is measured by means of calibrated receiver, which consists principally of a thick piezoelectric disc and a fairly simple electronic circuit (differentiator). It is shown that this apparatus provides, directly and without distortion, the absolute value of the pressure as a function of time. It should be noted that the use of this device is restricted to transducers radiating rather short pulses (less than a few microseconds), a field where the conventional methods can only give partial or approximate results. On the other hand, it is assumed that the ultrasonic wave to be studied is plane, which implies the following conditions: (1) The energy radiated by focused transducers cannot be measured. (2) The standard receiver must be placed close to and facing the transmitter, so that this set up cannot provide any information about the spatial distribution of the ultrasonic energy.
tic impedance pc) giving the front particle velocity
a
2PO)
at at =
PiCi + pC
hence a displacement
E(t) =.pici : pc [ PO’)a’. As long as the wave has not reached the back face of the standard receiver (duration of about 2.5 ps in our set up), a voltage u(t) appears between its faces
where h is the piezoelectric coefficient of the thick ceramic disc. Thus it is su5cient to differentiate the voltage u(t) to obtain the instantaneous Mrasonic pressure in the liquid p(t)
*
face
=
PiC;i PC du(t). dt
PRINCIPLE OF THE MRT’IfOD (1) Measurement of the instantnneous If the area of the transmitter surface, S,, is ultrasonic pressure p(t) less than that of the receiver surface, S, a This method has already been partly des- correction is necessary and the ultrasonic cribed (Lakestani, 1976; Baboux, 1977) and pressure is given as therefore will only be summarized here. A thick piezoelectric disc poled parallel to its p(t) = S,E&pg@ axis-called the standard receiver-was Se 2h dt placed just in front of the transmitter to be calibrated; the axes of the two transducers The previous formulae show that, by were aligned and both were immersed in a means of an analog circuit able to differenliquid. If the standard receiver is placed close tiate the voltage appearing across the faces of to the transmitter to be calibrated (between 1 a thick piezoelectric element, the instanand 3 mm), the diffraction phenomenon can taneous pressure can directly be obtained. be neglected and the wave impinging on the The terms used to express p(t) in terms of standard receiver can be considered plane. (du(t)/dt) being independent of frequency, The theoretical model assumes that the the main advantage of the device is the fact receiver diameter satisfies the following that the incident pressure is faithfully conditions: reproduced. The absolute value of the pres(a) It is much greater than the ultrasonic sure and its accuracy depend upon an acwave length in the liquid. curate knowledge of the different terms of (b) It is less than or equal to the diameter the proportionality coefficient (PC, pici, h, S,,, of the transducer to be calibrated (so that the S,). The specific acoustic impedance of the ultrasonic wave is inciderit upon the entire media are easy to determine. Since the surface of the standard receiver). piezoelectric coefficient h is seldom given by After the transmitter has been excited, it the manufacturer, it has been measured using generates a wave, whose pressure is p(t), an original, method developed in our laborawhich propagates through the liquid (of tory (Lakestani, 1975). With the ceramics specific acoustic impedance pici) and then used, h equals 14.0 X lo* V/m and this value is into the standard receiver (of specific acousalmost independent of temperature between
Measurement of the ultrasonic energy radiated by transducers used in echography
77
15” and 40°C. In the particular case when the wave does not cover the whole surface of the standard receiver, the area of the transmitter surface must be known. To do this, the dimensions of the active element, generally given by the manufacturer, can be used or they can be measured by moving a small probe across, and, in front of the transmitting face. (2) Calculation of the energetic characteristics of the ultrasonic beam From the instantaneous values of the ultrasonic pressure p(t) the following energetic quantities can be derived: (a) The instantaneous intensity I(t) = (p*(t)/pici) (in W/m’) and in particular, its maximum value I,,,, called the instantaneous peak intensity. (b) The energy per unit area carried by each pulse of duration T : WT = 107I(t) dt (in J/m’). (c) The average intensity per pulse IP = (Wdr) (in W/m*), where 7 is the duration for which the ultrasonic pressure exceeds a certain level and in which almost all the energy of the ultrasonic impulse is concentrated. This threshold is not standardized, and only the pressure oscillations whose amplitude are greater than a tenth of the temporal peak pressure were taken into account to define this duration 7. (d) The temporal average intensity I, the average value of the intensity over a duration T, = (I/f,), where fr is the repetition rate of the ultrasonic pulses: Z = fiW, (in W/m*). The ultrasonic wave is supposed to be plane, so the intensities may be considered uniform inside a cross section of the beam; from the area S, of the transmitting transducer it is also possible to calculate: (a) The total energy contained in a pulse W,, = W& (in J); (b) The total ultrasonic power P = IS, (in W) which may be compared with the value directly obtained from the calorimetric or radiation force methods.
Fig. 1. Experimental set up used for the measurement of the instantaneous ultrasonic pressure.
(d) to be measured is fastened to a circular lid (e) whose axis is orientable by means of three screws (f), which allows the transmitter to be adjusted in front of the receiver, so that the front face of the thick receiver is parallel with the incident plane wave. This adjustment is achieved when the amplitude of the electrical signal s(t), displayed on the oscilloscope and proportional to the pressure p(t) has reached its maximum value. (2) An amplifier, a differentiator and an oscilloscope. The signal measured by the oscilloscope probe across the faces of the standard receiver is first amplified (one of the two amplifiers of a two channel oscilloscope is used), then, after differentiation and further amplification, displayed on the screen of the oscilloscope. The electrical part of this measuring device (amplifier and electronic differentiator) was calibrated, using sinusoiamplitude and dal signals of known frequency. This electronic system is capable of displaying ultrasonic pressure pulses, whose spectra range from 0.5 MHz to 20 MHz, without distortion. Also, the absolute value of the pressure is given with satisfactory accuracy (about 5%). It should be noted that with the receiver disc used, 12 mm in thickness, it is possible to measure the ultrasonic pressure radiated by transducers whose decay time is less than or equal to 2.4 11s. If longer ultrasonic signals were to be studied, it would suffice to increase the thickness of the standard receiver. Experiments have been carried out recently EXPERIMENTALARRANGRMRNTFOR THE MRASURE- using a disc allowing measurements up to MENTOF THE ULTRASONICPRES!W~ 4ps, a value which is acceptable for most of Figure 1 shows the experimental set up. It the pulse echo instruments used in echoconsists of: graphy. (1) A perspex tank (a) filled with the liquid EWERIMENTALRESLJLTS (b) and at the bottom of which the thick piezoelectric disc (c) used as standard The energetic characteristics of the receiver is fixed. The transmitting transducer ultrasonic beams produced by three different
J. C. Bmoux,
78
Table 1. Characteristics of the three transducers studied Transducer
Nominal frequency
Diameter
(a) (b) (cl
1s MHZ 4MHz 8MHz
12.7mm 12.7 mm Smm
transducers were determined. Two of them, (a) and (b) were part of an ultrasonic apparatus designed for non destructive testing (similar to those generally used in medical diagnosis); the third, (c) was the probe of an echograph used in ophthalmology*. The nominal frequencies and the diameters of these transducers are listed in Table 1. (1) Measurement of the instantaneous ultrasonic pressure From Fig. 2(a)-(c), which shows the variations of the ultrasonic pressure as a function of time, for the three above-mentioned transducers, it is possible to draw the following conclusions: (i) Transducer (a) transmits very short ultrasonic pulses and is particularly well damp&d. (ii) Transducers (b) and (c) transmit longer oscillations and the pulses of several frequency of these oscillations is different from the nominal frequency given by the manufacturer; the deviation from the expected value is quite large ?or transducer (c) (5 MHz instead of 8 MHz). (iii) The greatest ultrasonic pressure is radiated by transducer (c). So, the mere examination of the instantaneous pressure already provides interesting information on the transducer. It would also be particularly easy to study the influence of ditPerent parameters, such as the duration and the amplitude of excitation electrical pulses on the shape and level of the ultrasonic pressure. (2) Methods of calculating the intensity, power and energy only the instantaneous intensity can be readily derived from the time dependent pressure; the determination of the other energetic values requires the integration over time of the square of the pressure. This calculation was conducted in two different ways.
*We are grateful to Professor Ravaud (Hbpitai Edouard Heniot) for the loan of this apparatus.
d al.
In method 1, a computer was used to control the sampling of the time signal proportional to the pressure and then to make the various calculations. This fast method was profitably used to determine the minimum number of samples leading to an accurate value of the time integral of p*(t). However, such a complex equipment is not necessary and a satisfactory evaluation of the previous quantities can also be obtained from an oscillogram of the pressure, p(t) (method 2). Method 1. For real time calculation of the energy by means of a computer, it is necessary to know the digital values of the pressure at regular time intervals. Owing to the rapid variation of p(t) with time, a complex apparatus was needed. Only a brief description of this set up, mainly used for ultrasonic spectroscopy studies, in our laboratory, will be given here. Since the pulsed ultrasonic signal is repetitive, it was displayed on a sampling oscilloscope acting as a stroboscope. The vertical output of this oscilloscope was slowed down to be compatible with the conversion and storage times of an ordinary data acquisition system controlled by a mini computer. Once the pressure has been stored in the computer memory, various mathematical operations can easily be performed. The minimum sampling rate of the time signal, p(t), could have been deduced from its frequency spectrum. A more empirical method was chosen; the time interval between the samples was reduced until the result of the numerical integration of p2(t) becomes constant. As an illustration of this process, the energy per unit area contained in each pulse, was estimated for different sampling rates. The results obtained show that the sampling interval must be less than 20ns for transducer (a) and less than 4011s for transducer (b) (Table 2). Method 2. The integration of p2(t) can be obtained by reading the series of successive pressure values on a magnified display of the p(t) signal. If a sufficiently small sampling interval is respected, this rather long and tedious process leads to the same result as the previous automated method. A more rapid but approximate calculation can also be developed. The pressure, p(t), is replaced by a signal of a known mathematical shape, as close as possible to the real signal, for which the integral to be performed is directly given
Measurement
of the ultrasonic
energy radiated by transducers
used in echography
Fig. 2. Ultrasonic pressure wave forms of different transducers: (a) and (b): transmitters used in non destructive testing: (c): probe used in ophtalmology.
79
81
Measurement of the ultrasonic energy radiated by transducers used in echography Table 2. Intluence of sampling interval on calculated ultrasonic energy Transducer Samplii interval (ns) Ultrasonic energy per unit area in each pulse ( 1Ow3J/m*)
Transducer (a)
I
Transducer (b)
I
4
8
20
40
8
20
40
80
0.80
0.78
0.77
0.51
2.23
2.18
2.21
1.32
Table 3. Complete energy characteristics of the three transducers studied For each pulse
Transducer
Repetition rate f, (k=)
:; (c)
1 1 2.4
Temporal peak Intensity UW/m*) 2.0 x lo’ 3.0 x 104
Average intensity
Energy per unit area
J,(W/m*) 2.4 x ld
46X10’
by an analytical formula. Thus, for the ultrasonic pressure radiated by transducer (a) and (b), each positive and negative alternation, whose duration is At and amplitude is pm, was replaced by a semi-sinusoid of the same duration and amplitude; hence, the integral I:+“’ p2(t) dt becomes 1/2p,2At. The results obtained were fairly close to the exact value previously computed (relative error of about lQ-20%). (3) Results All the previously defined energetic characteristics were calculated, for transducer (a), (b), (c) utilizing the simpler method just described (Table 3). Our measurements of the total ultrasonic power and of the average intensities near the transducer face, fall into the range of values published by other authors (Carson et al., 1978; Farmery et aI., 1978).
CONCLUSION
A calibrated receiving .transducer is described, which is easy to build and to use, and which allows an accurate measurement of the instantaneous ultrasonic pressure generated by pulsed transducers. The main advantage of this set up lies in the fact that it gives the time dependence and the absolute value of the ultrasonic pressure, directly and without distortion. This first measurement already brings interesting information on the working
Wz(J/m*) 0.81 x lo-’ 2.6 x lo-’ 58 x lo-’
Temporal average value Total energy
Intensity
Power
W,(J)
I(W/m’)
PO
1.0 x lo-’ 3.3 x 10-7 11 x lo-’
0.81 2.60 140
0.1 x lo-’ 0.33 x lo-’ 2.6 x IO-’
order of a pulse echo instrument and of its transducer. The ultrasonic pressure can also be used to evaluate various energy characteristics, and in particular instantaneous values, for the purpose of studying ultrasonic toxicity. For three transducers, diBerent quantities such as the temporal peak intensity, the intensity in each pulse, the average intensity, the energy per pulse and the total ultrasonic power have been calculated. Our method, which is based on the measurement of the pressure close to the transmitting face of a transducer, gives the temporal distribution of the ultrasonic energy but is not adapted to a study of its spatial distribution. There are not many devices enabling the accurate measurement of the instantaneous pressure at a spatial point. The interferometric method developed by Konstantinov (1974) seems to meet these two requirements of adequate resolution both in time and space. However his equipment is complex and probably not sensitive enough in the case of short ultrasonic pulses. We plan to determine the acoustic intensity at spatial points where the energy is concentrated (last axial maximum or focus) by means of small calibrated probes which are now being built in our laboratory. In order to keep a satisfactory accuracy in the measurement of the instantaneous intensities, it is intended to correct the distortions due to the remaining resonances of the probes by numerical deconvolution.
J. C. BMOUX, et ai.
82 REFERENCES
Baboux, J. C., Lakcstani, F., Fkischma~, P. and Perdrix, M. (1977) Calibration of ultrasonic transmitters. NDT International 10, 135-138. Brendel. K. and Ludwig, G. (1976) Calibration of uhrasonic standard probe transducers. Acustico 36, 203-8. Carson, P. L.. FischeRa, P. R. and Gughton, T. V. (1978) Ultrasonic power and intensities produced by diagnostic ultrasound equipment. Ultrasound Med. Biol. 3, 34 I-350. Carstensen, E. L. (1947) Self reciprocity calibration of clectroacoustic transducers. I. Acoust. Sot. Am. 19. %l-%5. Ebaugh, P. and Mueser, E. (1947) The practical application of the reciprocity theorem in the calibration of underwater sound transducers. J. Acoust. Sot. Am. 19,695-700. Etienne. J., Fihpczynski, L., Firek. A., Gronowski, J., Kretowicz. U. and Salkowski. J. (1976) Intensity determim&on of ultrasonic f&used ‘beams used in ultrasonography in the case of gravid uterus. ~tMSOU#ld hh?d. Bid. 2, 119-122. Farmery, M. J. and Wbittmgham. T. A. (1978) A portable radiation force balance for use with diagnostic ultrasonic equipment. Ulrrasound Med. Biol. 3, 373-
379. Gazanhes. C.. Gamier, J. L. and Reinier, G. (1966) Detectem enregistreur de la pression de radiation ultrasonore. Acustica 16, 142-149. Haran, M. E., Cook, B. D. and Stewart, H. F. (1975) Comparison of an acousto-optic and a radiation force method of measuring ultrasonic power, X Acoust. Sot. Am. 57. 14361442. Hill, C. R. (1970) Calibration of ultrasonic beams for biomedical applications. Phys. Med. Biol. 15, 241-248. Konstantinov, V. A. and Panin, V. I. (1974) Absolute calibration of piewelectric transducers. Sov. I. N.D.T. 10. 35-39. Lakestani. F.. Baboux, J. C., Fleischmann, P. and Perdrix, hf. (197s) Mesura, par une m&ode impuisionnelle, de certaines constantes Clastique. pitzdlectrique et di&ctrique d’un transducteur. I. Phys. D. Appl. Phys. 8, 1863-1870. Lakestani. F., Baboux, J. C. and Perdrix, M. (1976) G&ttration d’une onde uhrasonore plane en forme d’tchelon: application a I’ttalonnage de rCcepteurs pi&oClectriqu& I. Phys. D. Appl. Whys. 9, 547-556. Torr. G. R. and Watmough. D. J. (1977) A constant flow calorimeter for the measurement of acoustic power at megahertz frequencies. Phys. Med. Biol. 22, 444-450.