96 M.T. Huber et al. variations cause a change in optical path length along the laser’s path [5]. The time varying modulation of the laser is detected by the vibrometer, just as it would Doppler shift on the light reflected from a vibrating surface. The vibrometer is thus able to interpret the modulating laser to detect passage of acoustic waves. By repeatedly emitting pulses from a transducer and measuring the time of arrival at acoustic waves at a large number of laser scan points, the vibrometer software can reconstruct an image of a traveling wavefront. Schlieren photography is a comparable non-invasive technique that can be used for sound field characterization [7]. Schlieren systems, like refracto-vibrometry setups, observe density variations in fluids. In Schlieren systems the density variations create enough of a disturbance in the fluid that sound can be directly imaged using a camera if the fluid is properly illuminated. To produce images of traveling wavefronts, a Schlieren system will sequentially record video frames with successively longer delays between the emission of an ultrasound pulse and a short-duration, very high intensity light flash [8]. While a finely tuned Schlieren system can produce images similar to those produced by a vibrometer, there are several distinct advantages to using a vibrometer. First, vibrometer systems produce easily quantifiable results. The output at each scan point for a vibrometer is a voltage reading that can directly be interpreted in the context of the system being analyzed. With a Schlieren system, quantifying the image produced requires some secondary analysis of variations in intensity recorded in the video pixels. In addition, for refracto-vibrometry the cross-sectional area of the laser beam is the size of the area being observed. This means minute sections can be studied individually, and the beam can be placed wherever a measurement needs to be taken. In Schlieren systems pixels from the video must be picked and chosen for analysis, and this analysis is limited by the resolution of the camera used. Refracto-vibrometry also enables very high time resolution; for example, the system used for the current experiment had a sampling rate of 100 MegaSamples/s.It is clear that refracto-vibrometry is a fundamentally different type of imaging modality compared to conventional techniques. The current study demonstrates two applications of this unique technique: the capability to image traveling wavefronts as they pass through and are reflected from different samples, and the ability to use these detected wavefronts to measure the speed of the sound waves. 9.2 Theory 9.2.1 Refracto-Vibrometry A vibrometer measures Doppler shift through interferometric techniques. A modulated laser in a Mach-Zehnder interferometer is split into a reference beam that is recombined with a beam that has been reflected from the target [9]. The time variations of the interference pattern are normally due to a Doppler shift of the reflected beam; however, in the case of refracto-vibrometry, the retroreflected target is motionless so the time variations are due to changes in the optical path length between the vibrometer and target. The optical path length, ¿, is defined as the integral of the index of refraction n(s) along the path the light travels [10] ¿DZ path n.s/ ds: (9.1) When a portion of a wavefront with higher density, thus larger index of refraction, passes through the vibrometer laser, it will increase slightly the optical path length and thus the time the laser takes to travel from the vibrometer to the surface and back. Similarly, a lower density region with lower index of refraction will result in a shorter optical path length and thus shorter light travel time. These alterations in optical path length show up as time variations in the interference between the reference and measurement beam. A noteworthy feature of refracto-vibrometry is that it samples the line integral of density variations along the laser’s path. This is different than most conventional ultrasound transducers and needle hydrophones that measure the surface integral of the waves that strike the surface of the detector. 9.2.2 Speed of Sound Measurement The standard approach to speed of ultrasound measurements involves sending an ultrasound pulse from one transducer to another with no blocking materials. Then, by placing an intervening sample of known thickness, L, in between the transducers, the time-of-flight difference can be used to find the speed of the sound wave through the sample, cs, given the speed of sound in water, cw [11]
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