Acoustical Scattering
Low-Coherence Reflectometry
The experimental arrangement for implementing a low-coherence reflectometry experiment using an acoustic radiation field is shown. Major components include two signal generators, two mixers (x) that provide sum and difference frequency outputs, a temporal delay circuit, and T1, T2 broadband transducers.
A low-coherence (i.e. broadband) acoustic signal is generated by a signal generator. The versatile signal generator has the capability to produce an arbitrary waveform and broadband white noise. This instrument, coupled with the programmable dual filter, will give us the ability to vary the coherence length of the acoustic signal and to optimize the center frequency to match the frequency response of the acoustic transducers to be utilized. The acoustic signal will then be split, with one portion producing a sound wave in the disordered medium. The transducers to be used in this work will be plastic PVDF or electrostatic due to the lower Q of their frequency response characteristics, which is necessary to reproduce broadband signals. In both cases, the transducers’ response will be completely characterized using a FFT spectrum analyzer. The sound wave will be scattered by the disordered medium (e.g. steel spheres suspended in a gelatin matrix) and by the object to be imaged. This scattered signal will be received by the signal detector and mixed with the signal from the reference arm of the acoustic interferometer.
Some of the audio signal produced by the signal generator will traverse the reference arm. In the reference arm, its frequency will be mixed with a sine wave whose frequency is within the lock-in’s detection range. This mixed reference arm signal (the frequency sum) will be temporally delayed and mixed with the output of the signal detector. A beat, at the lock-in reference frequency, will be produced only by that part of the detected signal that is coherent with the signal from the reference arm. That is, only scattering paths that match the "length" of the reference arm to within the coherence length of the audio signal will produce a stable beat detectable by the lock-in. Thus, by varying the delay in the reference arm, differing sample depths can be probed. A PC will be used to collect and analyze the data.
This acoustic technique will be used to conduct studies of fundamental and practical importance. The impact of scattering coefficient and source coherence length on the system’s resolution (the ability to distinguish adjacent objects) and the point spread function (the impulse response of the imaging system) will be investigated. This complete and quantitative investigation will be of great value and may lead to direct applications in medical imaging or remote sensing in geology.
Phonon Correlation Spectroscopy
Experimental configuration to be used in the phonon time-resolved correlation spectroscopy experiment is similar to that shown for the optical analog. Acoustic pulses are focused to a small volume within the highly scattering sample. The scattered sound is collimated, temporally gated, and averaged. Temporal intensity distributions are illustrated.
The acoustic correlation spectroscopy experiment will enable the investigation of scatterers that are significantly larger than those used in the optical domain, due to the difference in the wavelength of the respective radiation fields. Additionally, experiments can be done in a somewhat more controlled manner, by driving the scatterers with low-frequency acoustic waves to simulate the Brownian motion observed optically. Rather than adjusting temperature and viscosity, the experimenter can control the motion electronically, allowing a study of a broader range of motions. Another important aspect of phonon correlation spectroscopy is that optically opaque samples may be used, as ultrasound is currently used to image the human body. It should then be possible to study the motion of particles in a turbid liquid that is moving or calm. These studies would augment laser Doppler measurements which provide essentially one-dimensional velocity information. Other possible applications include the study of a large number of particles undergoing turbulent hydrodynamic flow.
Pulse Transmission Time-of-flight
Schematic diagram of the time-resolved pulse transmission experiment. Narrow radiation pulses are injected at various injection to exit window distances (s) and the much broader transmitted pulse shape is recorded. The sample thickness (L) and cell diameter are typically much larger than s.
This time-resolved pulsed transmission experiment consists of injecting acoustical pulses into a random medium and recording the transmitted intensity profiles which are then fit to a suitable diffusion model to obtain the transport mean-free-path length. In the optical experiment, light pulses are launched into a single mode optical fiber and subsequently injected into the colloidal suspension under study, while in the acoustic analog the signal producing transducer is imbedded in the scattering medium. This procedure is schematically illustrated in Fig. 4. The distance s, indicated in Fig. 4, is the straight line distance from the injection point to the exit window. As shown, a narrow radiation pulse is injected at reference time 
and the intensity that is detected at a later time is temporally more diffuse. Intensity profiles are gathered over a wide range of injection to exit window distances for each sample studied. The wide distribution of photon/phonon exit times results because the photon/phonon executes a random walk within the medium.
The diffusion model that is fit (with the system response function convolved as necessary) to the temporal intensity profiles contains two physically significant parameters: the transport mean-free-path length and a characteristic absorption length16. These parameters will allow for a complete characterization of the scattering samples used in the first two studies, and the addition of angular resolution to the temporal time-of-flight experiments may enable the determination of mean scatterer size and/or anisotropy.