Self-focusing transducers

Acoustic waves emitted by ultrasonics transducer crystals exhibit a property known as self-focusing (or "natural focusing"). Note that this is distinct from the electronically controlled focusing employed in diagnostic ultrasound devices which employ arrays of transducers. The self-focusing effect exists even for a single crystal.

Self-focusing refers to the narrowing of the ultrasonic beam in the near-field. The near-field extends from the crystal face out to $D\; =\; frac\{d^2\}\{4\; lambda\}$ where $d\; =$crystal diameter and $lambda\; =$wavelength of emitted wave. At the edge of the near-field, where the focusing reaches its maximum, the beam width reaches $frac\{d\}\{2\}$.

The self-focusing effect occurs because the ultrasound wave is "coherent" and because the vibration mode of the crystal at the emitting surface generates wavelets that constructively interfere in a narrowing region from the surface out to a distance $D$. [cite journal|title=Investigations of compact self focusing transducers using stacked piezoelectric elements for strong sound pulses in therapy|author=Dreyer, T.; Krauss, W.; Bauer, E.; & Riedlinger, R.E.|location=Ultrasonics Symposium, 2000|publisher=IEEE|volume=2|date=October 2000|page=1239-1242|url=http://ieeexplore.ieee.org/Xplore/login.jsp?url=/iel5/7345/19924/00921547.pdf?tp=&isnumber=&arnumber=921547/|accessdate=2008-05-06]

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