Page 22 - Winter 2008

Fig. 4. Block diagram of a complete RUS system using synchronous digitization.
is to bond the specimen to a “buffer rod,” and then measure the time difference between the first echo from the buffer rod/specimen interface and the first echo from the far face of the sample, as shown in Fig. 2a. In this case, the buffer rod was a SiC anvil used in a high-pressure cell. As is clear, the sound pulse consists of a tone burst modulated by an enve- lope. In the simplest and least precise measurements, one measures the time difference just by looking at electronical- ly-smoothed (detected) envelope onsets. This has poor preci- sion because both the envelope amplitude and shape vary from pulse to pulse, and so any attempt to pick a signal level as the timing marker is doomed to produce some scatter in the result. A better approach is to retain the tone burst and “overlap” (meaning electronically multiply) it with a second
echo, and then average the result over many pulses. By regis- tering the sinusoidal signal under the envelope of one echo, with the delayed sinusoidal signal of the second echo, much greater precision can be obtained. Registration can be achieved by adjusting the pulse repetition period to equal the time delay between echoes. The time of flight is then just the time between successive pulses. Getting this overlap correct is the issue. Without going into the many ways to electroni- cally indicate overlap, note that as the signal strength decreases, and noise increases, it becomes increasingly diffi- cult to determine exactly which cycle in the sinusoidal signal from the buffer rod should match with which cycle in the sample echo. If one is off by even one cycle, the answer is wrong, while all the electronics blindly report happiness. Precision is still maintained, and at low temperature and for very good signals, one can resolve variation in sound speed
8
with temperature of 1 part in 10 . However, to get the
absolute sound speed right, one must be certain of getting the overlap right. It turns out that a simple digital process can make the overlap unambiguous.
The trick is to use the correlation function and the fre- quency dependence of the overlap-determined time delay to label exactly which cycle in the sine wave is the exact right one. This process, described in detail by Pantea,5 begins with a very simple electronics setup. An arbitrary waveform gen- erator is used to produce a tone burst to drive the transduc- er. A digital oscilloscope (A/D) captures one buffer rod echo and the one subsequent specimen echo with 8-bit/1Gs/s res- olution, but with several different tone-burst frequencies. Because the A/D has a precision time base, all timing infor- mation is recorded. No further measurements are needed
Fig. 5. A resonance acquired with the SD RUS system. The Q is 109,000.
20 Acoustics Today, January 2008