98 M.T. Huber et al. the samples could fit between the transducers without needing to vary the distances. Behind this vertical transducer/sample arrangement a piece of 3 mm thickness aluminum covered in retroreflective tape was placed to reflect the vibrometer laser. To avoid reflections of the laser from the water tank glass, the enclosure was placed at an angle of approximately 15ı from being normal to the laser. Signals for the ultrasound transducers were produced and processed using a Panametrics 5055P pulser [12]. The signal for the emitting transducer was a single, narrow negative voltage pulse. Ultrasound signals that arrived at the receiving transducer were amplified by the pulser to produce an analog output signal. Coincident with the emission of the ultrasound pulse, the pulser output a TTL trigger pulse. A Polytec PSV-400 scanning laser vibrometer [6] was used for optical detection of the ultrasound wavefronts. The laser was emitted from the vibrometer, passed through the glass face of the tank into the water filled region of the tank, was reflected off a retro-reflective surface, and then returned to the vibrometer along the same path. The mirrors in the vibrometer allowed the laser to be positioned to measure the optical path length variation at many different scan points. The vibrometer velocity decoder was set to a scale that allowed detection of the modulation of the laser signal at frequencies up to 1.5 MHz. For each ultrasound pulse, the TTL trigger from the pulser was used as a trigger for the PSV-400 data acquisition system. The acquisition system digitized, sampling at a rate of 102.4 MSamples/s, a brief pre-trigger interval along with time-domain output of the vibrometer typically for a total of about 80 s. The vibrometer acquisition system simultaneously can digitize a reference signal; in the current experiment, the reference signal used was the analog output of the pulser that was proportional to the signal measured by the receiving ultrasound transducer. To suppress random noise, the acquisition system averaged between 50 and 1000 individual ultrasound pulses at each laser scan point. By performing these measurements for many separate laser vibrometer scan points, this refracto-vibrometry technique allowed determination of the time-varying acoustic wavefronts. 9.3.1 Optical Detection of 1 MHz Acoustic Wave and Its Reflections A 1 MHz wave was emitted by the transducer with a 5.9 mm thick lead block placed on the sample tray. The vibrometer scanned through the ultrasound field and measured the signal intensity in the time domain. By compiling all the data points in a two-dimensional grid, the sound field, composed of an emitted wave and all the reflections and transmissions occurring at the sample, could be characterized. This was repeated without a sample in the tray. By observing the wave traveling from the transmitting transducer to the receiver without interruption, a measurement of the speed of an unattenuated ultrasound wave through water was performed. This was done by finding the distance of wave travel and dividing it by the time of flight from wave emission to reception. By relating the distance of wave travel in an image of the setup to the size of a known object, the actual distance was found. Combining this with the time of flight as measured by the two transducers, the velocity of the wave was determined. 9.3.2 Speed of Sound Measurement Through Lead and Bone In order to calculate speed of sound through both lead and fabricated bone, different thicknesses of each were used. For speed of sound measurements through lead, four different lead thicknesses were used. For the fabricated bone, five different thicknesses of Sawbones 15 PCF Open Cell bone [13] were cut. The samples were placed underwater in a vacuum chamber for 10 min to remove air pockets from their pores. Time-of-flight measurements were taken for each of the different thicknesses and for the setup with no sample. Time of flight was determined as being from the time the ultrasound pulse was emitted, to the first major zero-cross time on the received signal; a representative time trace is shown in Fig. 9.2. Frame a of this figure displays the entire signal reading for the vibrometer and transducer. The output signal is seen in the red trace from the transducer several microseconds into the graph. There was a 2.38 s pre-trigger time period before the pulse emission. The time of flight was measured from the beginning of the sampling period until the zero-cross as marked in frame b of the exploded view of the wave reception portion of the graph. The zero-cross time was chosen as the measurement feature because it is easy to identify and there is a low margin of error in choosing the proper spot. By combining the previously calculated speed of sound in water with the time-of-flight time for the various thicknesses through Eq. 9.3, it was possible to determine the speed of sound through the different media.
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