On the beam deflection method applied to ultrasound
absorption measurements
K. Giese
To cite this version:
K. Giese. On the beam deflection method applied to ultrasound absorption measurements.
Journal de Physique IV Colloque, 1994, 04 (C7), pp.C7-461-C7-464. <10.1051/jp4:19947107>.
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JOURNAL DE PHYSIQUE IV
Colloque C7, supplement au Journal de Physique 111, Volume 4, juillet 1994
On the beam deflection method applied to ultrasound absorption
measurements
K. Giese
Institut fur Medizinische Physik und Biophysik, Georg-August-Universitat, Gosslerstrasse 10, 37073 Gottingen, Germany
Abstract. The beam deflection method has been used for the detection of ultrasound absorption
in a plane sample of silicon rubber which in a water bath is exposed to a beam of ultrasound. Parallel scanning of the laser beam across the pump beam cross section yields the acoustic power transmitted to the absorber. Measurements in dependence on ultrasound frequency show the mirage signal to correlate well with the absorption coefficient of the material.
1, INTRODUCTION
Photothermal techniques have been applied to study the absorption of electromagnetic waves at wavelengths ranging from the X-ray up to the microwave regions. In medicine, these spectroscopic techniques in particular have been applied to study in vitro and in vivo the optical and thermal properties of skin [1,2]. Recent developments in diagnostic ultrasound have demonstrated that by use of frequencies up to about 50 MHz the spatial resolving capacity of pulse echo-imaging systems can be increased to a level which allows promising applications in the field of dermatological diagnosis. At these high frequencies ultrasound is effectively absorbed by soft tissues: as with optical radiation, the acoustic penetration depth is comparable to the diffusion length of thermal waves at audio frequencies. Therefore, photothermal techniques can hold as an interesting new tool for performing measurements in the field of ultrasonic exposimetry and spectroscopy.
Optical techniques have been applied to the investigation of ultrasonic fields since many years 131.
They utilize the diffraction and deflection of light passing a sound field in a transparent medium, typically water, where the index of refraction n is spatially modulated by the acoustic pressure p. For the deflection of a narrow light beam traversing a sound field normally to the acoustic axis an exact solution has been given by Lucas and Biquard in 1932
141.
At room temperature, the pressure coefficient of the refraction index of water is given by dn/dp = 1.2 10-lo pa-'.Thermal techniques utilize acoustic absorption for determining ultrasound field paramters. A good spatial resolution is obtained by measurement procedures based on evaluating the temperature response of small thermocouples with sound absorbing coating [5]. If aimed at the absolute determination of local sound intensity or of the sound power of a transducer, thermal techniques suffer from the complex dependence of temperature elevation on heat deposition, thermal properties, and boundary conditions. In a recent experimental study, where some of these aspects have been discussed in detail, we have evaluated the sound power of transducers by measuring the time of flight of short ultrasound pulses, which sensitively reflect changes in absorber temperature [6]. In this paper we report on results of experiments which have been performed by applying the beam deflection method to ultrasound absorption measurements. Highly absorbing samples with small acoustic penetration depths were used. The measurements were performed at such modulation frequencies where one has to encounter a pronounced dependence of the mirage signal on the relative magnitudes of acoustic penetration depth, thermal diffusion length and diameter of the laser beam.
JOURNAL DE PHYSIQUE IV
2. EXPERIMENTAL SET-UP
The experimental set-up is outlined in Figure 1. From a circular, piston-like broadband transducer of diameter 2a = 12.7 cm and center frequency f, = 5 MHz (V 309, Panametrics), intensity modulated ultrasound is transmitted via a water bath of adjustable length to a plane absorber manufactured from silicon rubber (Z 435, Wacker Chemie). This absorber material is acoustically matched to water so that the sound field in the cell essentially is a propagating wave. High values of the absorption coefficient
P
were achieved by suspending fie-grained corundum before adding the hardening agent to the silicon rubber. Within the bandwidth of the transducer, the absorption coefficient of the material was determined to be given by the power lawP
= 6.6-
(f/fc)1.2 cm-l, corresponding to an acoustic penetration depth of 1.7 mm at ultrasonic frequency f = 5 MHz [6]. The thermal diffusivities of silicon rubber and water are nearly the same. At a modulation frequency of 5Hz,
as used in our experiments, the thermal diffusion length in both materials is about 100 pm. The lateral distribution of oscillating surface temperature reflects the intensity profile of the ultrasound beam, the shape of which depends on the transducer radius a, the acoustic wavelength h (which equals 300 pm in water at 5 MHz), as well as on the axial distance z between transducer and absorber. At a modulation frequency of 5 Hz, transmission of sound of power 50 mW yields temperature oscillations of about 1 mK at the absorber surface. The corresponding modulation of the index of refraction within the adjacent water layer is controlled by the temperature coefficient dn/d6 = -1.1.104 K-I.The detector used for the measurement of the normal deflection mirage-signal has been described in detail elsewhere [2]. The probe beam is focused near the absorber surface where its diameter is about 120 pm. In water this beam diameter is close to the thermal diffusion length at 5 Hz so that the quantitative description of the mirage signal requires to take into account beam size effects as discussed in literature [71.
3. RESULTS AND DISCUSSION
The ultrasound beam transmitted to the water bath shows a complex spatial structure. This holds true especially for the near field, which for a circular piston source covers a range of axial distances up to the value zo = a2/h. In Figure 2 is plotted a beam profile in a cross-sectional plane at normalized distance s = z/zo = 0.25. Local values of the squared acoustic pressure, which is proportional to the local intensity, are plotted versus the transversal coordinates. With the absorber positioned in this plane, the intensity profile of Figure 2 reflects the corresponding lateral distribution of temperature at the absorber surface. Figure 3 shows calculated values of the normal beam deflection signal to be obtained by scanning the laser beam across the ultrasound beam in cross-sectional planes at normalized distances s = 0.25, 0.5 and 1.0. At distance s = 1 the width of the ultrasound beam passes through its minimum value, which is clearly demonstrated by the course of the corresponding scan.
I
US-Transducer PSD&
I
Chopper, GeneratorFig. 1: Schematic diagram of the experimental set-up used for the mirage-detection of the absorption of ultrasound
1.6 t I
s
=
I Piston Radiator,ka=125
Homogeneous Beam
-
0.0 0.5 1.0 1.5
Lateral Distance
x/a
Fig. 2: Calculated three-dimensional profile of Fig. 3: Normalized magnitude of the normal the squared acoustic pressure at distance s = 0.25 deflection mirage-signal as calculated in in front of a circular, piston-like transducer of dependence on lateral distance between laser radius a = 6 mm operating at frequency f = 5 beam and acoustic beam-axis in cross-sectional MHz (k-a = 2 n a = 125). planes at distances s = 0.25, 0.5 and 1.0 between
transducer (a = 6 mm, f = 5 MHz) and absorber.
With the absorber positioned close to the transducer surface, scanning across the temperature profile yields a course of the beam deflection signal as it is characteristic to a homogeneous pump beam, with constant intensity inside a cylinder of diameter 2a and zero intensity outside. For comparison, this limiting curve is contained in Figure 3. In applications of the beam deflection technique aimed at determining the sound power of a transducer, measurements are in general performed at such small distances. Figure 4 shows a curve obtained by scanning across the ultrasound beam in the cross-sectional plane at s = 0.2, which corresponds to a distance of 2.7 cm at 5 MHz. In contrast to the distance transducerlabsorber, which in case of an acoustically matched material is uncritical, due to the comparatively small thermal diffusion length in water an exact adjustment of the distance between absorber surface and probe beam axis is required. The steep decrease of thermal waves yields large gradients and, correspondingly, large beam deflection signals. On the other hand, for the reproducible determination of data the error made in adjusting the distance absorber surfacelprobe beam axis must not exceed a few pm. For an automatic fine adjustment we use computer-controlled step motors acting on the supports of laser and position detector.
Figure 5 shows data obtained in dependence on ultrasound frequency, with the absorber positioned at a fixed distance of about 2 cm in front of the transducer. By varying the frequency within the bandwidth of the transducer, the corresponding normalized distances s cover the range 0.1 < s < 0.25. It has been mentioned above that at these small values the spatial structure of the sound field is of low influence on the mirage signal. The frequency dependence of the transmitting current response of the transducer was known from field measurements with a broad band hydrophone, which allowed the transducer to be operated at constant sound power. In Figure 5 the normalized representation of the frequency dependences of the mirage signal and of the absorption coefficient (see section 2.) show both quantities to be proportional to each other. This dependence is not unexpected, as the experimental conditions were such that the thermal diffusion length was much smaller than the acoustic penetration depth.
The results of this study demonstrate that it is possible to detect the absorption of ultrasound by the beam deflection technique as long as the ratio of thermal diffusion length and acoustic penetration depth is not too small. With soft tissue-like absorbing materials this condition is fullfilled only at relatively high ultrasound frequencies. As can be seen from measurements in dependence on distance between absorber
C7-464 JOURNAL DE PHYSIQUE IV
Lateral Distance x [mm] Frequency [MH~]
Fig. 4: Normal deflection mirage-signal as Fig. 5: Normal deflection mirage-signal as measured in dependence on lateral distance measured at distance z = 10 mm and absorption between laser beam and acoustic beam-axis in a coefficient of the absorber material plotted versus cross-sectional plane at distance s = 0.2 between ultrasound frequency. The data are normalized to transducer (a = 6.3 mm, f =
5
MHz) and absorber. the respective values measured at f = 5 MHz.surface and laser beam axis, the sensitivity of the method is restricted due to interactions between the acoustic and the thermal modulation of the index of refraction in water. As the first effect increases with acoustic pressure and the second with intensity, the thermal effect gains importance with increasing intensity.
References:
[I] Sennhenn B., Giese K. Plamann K., Harendt N. and Kijlmel K., Skin Pharmacol6(1993)152-160 [2] Werner U., Giese K., Sennhenn B., Plarnann K. and Kolmel K., Phys. Med. Biol. 37(1992)21-35 [3] Reibold R., PTB-Mitteilungen 85(1975)109-119
[4] Lucas R. and Biquard P., J. Phys. Radium. 10(1932)464-477
[5] Fry W. J. and Fry R. B., J. Acoust. Soc. Am. 26(1954)294-310; 311-317 [6] Ueing B. and Giese K., Z. Med. Phys. 1(1991)33-37
