Focused acoustic beams

In geometrical optics the numerical aperture of a lens is given by first-order theory and spherical aberrations are given by third-order theory (Jenkins and White 1976 Hecht 2002). In first-order theory the approximation is made 

The particular case of parallel rays from infinity incident on the spherical surface is illustrated in Fig. 2.2. In this case 1/si = 0, and s2 becomes equal to the focal length 

The aberrations may be calculated using third-order theory, in which sin 6 is approximated by 6 — (P/3. Rays from an object on the axis in medium 1 are refracted to cross the axis again in medium 2 at a distance that now depends on the distance h from the axis at which they pass through the lens surface (Hecht 2002) such that 

The term in curly brackets describes the deviation from the first-order theory. For paraxial rays h = 0 and that term vanishes this is the first-order result. But for other values of h the rays do not cross the axis at the same point as the paraxial rays, and this causes aberration. When parallel rays are incident from infinity as illustrated in Fig. 2.2, 1 /s y = 0. If the aberration is not too big, then in the term in the curly brackets the approximation Si q can be made. With n = nyjni, (2.4) then reduces to 

The magnitude of the aberration is proportional to h2, but it decreases as n2, the square of the relative refractive index. Once again, it is apparent that a small refractive index is beneficial. 

---

Kushibiki, J., Ohkubo, A., and Chubachi, N. (1981i>). Linearly focused acoustic beams for acoustic microscopy. Electron. Lett. 17, 520-2. [56,133]... 

Piezoelectric Microdispenser, Fig. 4 Focused acoustic beam ejection technology by Elrod and associates at Xerox PARC. Using a piezoelectric element with electrodes immersed in a tliin layer of fluid below a nozzle (a), an electrical impulse will induce an acoustic wave that,... 

Acoustic droplet ejection refers to the process whereby a focused acoustic beam directed toward a liquid-air interface can cause the ejection of discrete droplets of the liquid. Use of surface acoustic waves (SAW) on a solid upon which sessile droplets are attached can cause the migration of those droplets along the solid surface. Finally, standing acoustic waves in flow channels... 

Elrod SA, Hadimioglu B, Khuri-Yakub BT, Rawson EG, Richley E, Quate CF, Mansour NN, Limdgren TS (1989) Nozzleless droplet fmmation with focused acoustic beams. J Appl Phys 65 3441-3447... 

For conventional probes, acoustic verification aims at characterizing the beam pattern, beam crossing, beam angle, sensitivity, etc., which are key characteristics in the acoustic interaction between acoustic beam and defect. For array transducers, obviously, it is also a meaning to check the acoustic capabilities of the probe. That is to valid a domain (angle beam, focus, etc.) in which the probe can operate satisfactorily. 

These intensity levels are modest compared with the intensity of the beam at the focus of an acoustic microscope. From 3.1.2, the peak power in the beam at focus can be —10 dBm. At 2 GHz the focused beam area is about 1 pm2, giving a peak intensity of 0.1 mW pm 2. But the pulse length is usually less than 1 per cent of the interval between the pulses, and any one spot on the specimen experiences the acoustic beam for less than 1/250 000 of the total scan time (for a 512 x 512 scan). The temperature rise due to the acoustic power will usually be less than 1°C, and in most cases very much less than that (Maev and Maslov 1991). It is not clear how to relate these parameters predictively to the experiments on the effects of ultrasound, but in any case no adverse effects have been observed in an acoustic microscope. 

It should be readily formed into curved shapes and subdivided into acoustically and electrically isolated subsections for focusing and steering the acoustic beam. 

Doppler Flow Meters. Doppler flow meters sense the shift in apparent frequency of an ultrasonic beam as it is reflected from air bubbles or other acoustically reflective particles that ate moving in a Hquid flow. It is essential for operation that at least some particles ate present, but the concentration can be low and the particles as small as ca 40 p.m. CaUbration tends to be influenced by particle concentration because higher concentrations result in mote reflections taking place neat the wall, in the low velocity portion of the flow profile. One method used to minimize this effect is to have separate transmitting and receiving transducers focused to receive reflections from an intercept zone neat the center of the pipe. 

The line-focus-beam technique with its associated analysis has been more extensively used than any other method for quantitative acoustic microscopy. 

There are considerable difficulties in comparing theory and experiment even in such model experiments. The theoretical calculations are subject to the approximations inherent in the method, and also to uncertainties in the pupil function used to characterize the lens and in the two parameters used to characterize the crack. The experiments are subject to the difficulties of making a crack that is straight and flat to a fraction of the acoustic wavelength used, over the length measured by the line-focus-beam lens, and to the sensitivity of the results in some cases to small changes in x or z. Nevertheless, when all these considerations are taken into account it does seem... 

Kushibiki, J. and Chubachi, N. (1985). Material characterization byline-focus-beam acoustic microscope. IEEE Trans. SU-32, 189-212. [68, 78, 133, 137, 146, 147, 189,... 

Kushibiki, J., Ohkubo, A., and Chubachi, N. (1982). Effect of leaky SAW parameters on V(z) curves obtained by acoustic microscopy. Electron. Lett. 18,668-70. [131] Kushibiki, J., Horii, K., and Chubachi, N. (1983). Velocity measurement of multiple leaky waves on germanium by line-focus-beam acoustic microscope using FFT. Electron. Lett. 19,404-5. [242]... 

---