Acoustic Lens

The resolution of an acoustic lens is determined by diffraction limitations, and is 7 = 0.51 /N.A [95], where is the wavelength of sound in liquid, and N.A is the numerical aperture of the acoustic lens. For smaller (high-frequency) lenses, N.A can be about 1, and this would give a resolution of 0.5 Kyj. Thus a well designed lens can obtain a diameter of the focal spot approaching an acoustic wavelength (about 0.4 /Ltm at 2.0 GHz in water). In this case, the acoustic microscope can achieve a resolution comparable to that of the optical microscope. 

Since the aberrations of an acoustic lens can be much less than a wavelength, an alternative is not to think of them in geometrical terms, but rather to consider the phase aberrations introduced into the wavefront (Lemons and Quate 1979). In the absence of any aberration the wavefront after passing though the lens would be a sphere whose centre was at the focus. The difference between such a sphere and the actual wavefront is the aberration... 

The material for an acoustic lens should have a low attenuation, and a high velocity to minimize aberrations. Sapphire is an excellent material in both these respects. But the high velocity has a less desirable consequence. An acoustic impedance can be defined, which is equal to the product of the velocity and the density. The impedance of sapphire for longitudinal waves travelling parallel to the c-axis is thus 44.3 Mrayl, compared with the impedance of water which at room temperature is about 1.5 Mrayl, rising to 1.525 Mrayl at 60°C. When sound is transmitted across an interface between two materials of different impedance, the stress amplitude transmission coefficient is ( 6.4.1 Auld 1973 Brekhovskikh and Godin 1990)... 

Fig. 5.3. An acoustic lens for two-pulse response, with the second echo coming from a flat annular region around the lens (after Liang et al. 1986).

Fig. 7.3. Ray model of an acoustic lens with negative defocus aa is an arbitrary ray, which is reflected at such an angle that is misses the transducer (or else hits the transducer obliquely and therefore contributes little to the signal because of phase cancellation across the wavefront) bb is the axial ray, which goes straight down and returns along the same path cc is the symmetrical Rayleigh propagated wave, which returns to the transducer normally and so also contributes to the signal. The wavy arrow indicates the Rayleigh wave.

Fig. 7.4. Wave model of an acoustic lens focused on a surface the tangent to one of the wavefronts illustrates one of the family of plane waves of which the wavefront is...

Figure 10.4. (A) Acoustic lens focused on the front (left) and back (right) the acoustic waves. (B) Measured sound echoes from both zones. Above front and back echo with the lens focused on the sample s back. Below front echo with the lens focused on the sample front. (Reproduced with permission of the American Institute of Physics, Ref [34].)...

The SAM is a reflection mode technique that uses a transducer with an acoustic lens to focus the wave below the surface the transducer is scanned acro.ss the sample to create an image [36]. Images from SAM are formed through the interaction of sound waves by direct reflection of the longitudinal waves w ith the sample, or by mode conversion to surface acoustic waves that propagate and scatter. High-resolution images of the material surface... 

A sapphire cylinder combines the functions of a transducer and an acoustic lens. It features a thin ZnO coating on its top end and a cup-shaped indentation (formed by poUshing) on its front side. It produces, transmits, and receives brief sound pulses (Fig. 47). 

Li, J., Friedrich, C. R. and Keynton, R. S. (2002) Design And Fabrication Of A Miniaturized, Integrated, High-Frequency Acoustical Lens-Transducer System, J. Micromech. Microeng., 12, 219-28. 

The standard piece of equi( nent used in AMI is the C-Mode Scanning Acoustic Microscope (C-SAM ). The system is a pulse-echo (reflection type) microscope that generates images by mechanically moving a transducer back and forth, in a raster pattern, over the sample. The source transducer is a focused acoustic lens assembly and is coupled to the sample by fluid medium - usually de-ionized water or some type of inert fluid. The transducer has piezoelecoric properties, which allow it to aa as both a sender and receiver being electronically switched back and forth between transmit and receive modes (Figure 2). 

To form a 2D acoustic image, an acoustic lens and/or an X-Y stage is mechanically scanned across a given area of the specimen. 

The acoustic lens is able to translate axially along the z direction by variation of the distance between the specimen and the lens for subsurface visualization. That is, when the surface of the specimen is visualized, the acoustic lens is focused on the specimen (we denote z = 0 pm), and when a subsurface of the specimen is visualized, the acoustic lens is mechanically defocused toward the specimen (we denote z = -x pm, where x is the defocused distance). 

The paraxial focal distance of the acoustic lens (Fb) is approximately expressed as follows ... 

Referring to Fig. 3, we describe the spherical aberration of the acoustic lens below. 

Figure 3. Calculation of the spherical aberration of the acoustic lens. A(0) is the spherical aberration, Fq is the paraxial focal distance of the acoustic lens, F is the zonal focal distance, R is the radius of curvature of the surface of the lens, 9 is the incident angle of the acoustic wave, and O is the refracted angle of the acoustic wave.

For reference, a comparison of the ratio of the spherical aberration and the radius, A 9)/R, between the acoustic lens and the optical lens is shown in Fig. 4. The spherical aberration of the acoustic lens is much smaller than that of the optical lens. This is an important advantage. 

Figure 5. Resolution, (a) Optical image of a standard specimen having patterns for measuring resolution (i.e., resolution chart) for the scanning acoustic microscope in C-scan mode using a tone-burst wave (b) acoustic image. The acoustic lens is focused onto the surface of the resolution chart. The acoustic lens is operated at a frequency of 1.0 GHz.

Figure 6. Cross-sectional geometry of the spherical acoustic lens, explaining the mechanism of the V(z) curves. 

Figure 7. V (z) curve for fused quartz specimen fused quartz, coupling medium distilled water, temperature of the coupling medium 22.3°C (change less than 0.1°C). The parameters of the acoustic lens are as follows frequency 400 MHz, aperture angle 120°, and working distance 310 p.m.

Figure 8a shows the relation between the incident angle and the amplitude of the ultrasonic beam emitted from the acoustic lens... 

When the acoustic wave is focused onto the surface of the specimen, the phases of the acoustic waves traveling path I and path II are identical. Let this phase be denoted as phase changes of the waves traveling paths I and II are expressed, respectively, as... 

Equation (32) shows that the errors in the measmement of the surface acoustic wave velocity are the sum of the errors in the values of the velocity of the coupling medium, the frequency of the acoustic wave, and the distance of the period. Therefore, to minimize the measurement error, it is necessary to maintain constant temperature for the coupling medium to stabilize the frequency of the acoustic wave, and measure accurately the movement of the acoustic lens along the Z-axis. 

Figure 9. An acoustic lens for expressing the V(z) curve with an angular-spectrum approach to a nanoscaled thin film system, at is the radius of the transducer, zj is the distance from the transducer to the back focal plane, R is the radius of the aperture of the lens, / is the focal distance of the lens, and u is the acoustic field at the back focal plane.

The acoustic fields are expressed by uf or [7 (/ = 0, 1, 2, and 3), where uf is the spatial distribution and Uf is the frequency distribution, where numbers 0, 1, 2, and 3 represent the transducer plane, the back focal plane, the front focal plane, and the surface of the specimen, respectively. The superscripts indicate that the acoustic field travels in the direction from the acoustic lens to the specimen or from the specimen to the acoustic lens. 

When the acoustic waves are reflected back from the specimen, the pupil function must be considered within the region expressed as -Xa < X < Xa in accordance with the directions of wave propagation shown in Fig. 13b. Using the angular spectrum approach," we can express the intensity of the wave at the transducer of the acoustic lens as follows ... 

Based on (56) and (72), we have completed the computer simulation (see Figs. 14, 15). The simulation is implemented as the following conditions such as parameters of the acoustic lens and the specimen (see Tables 3,4). 

Figure 17. Acoustical image, (a) the acoustic lens is focused at the surface (denoted as Z = 0 j,m) (b) the acoustic lens is mechanically defocused by 3 j,m toward the specimen (denoted as Z = —3 pm). The acoustic lens is operated at a frequency of 1 GHz.

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