Pitts, Todd A.

It has previously been shown that acoustic ray paths in range-dependent ocean models exhibit chaotic behavior. Most of the investigations into the ray chaos phenomenon have been primarily numerical in nature. The objective of this report is to study theoretically the existence of ray chaos in a parabolic ray system with an analytically prescribed sound-speed model consisting of a double-channel profile perturbed by a typical periodic range-dependent disturbance. The perturbed Hamiltonian ray system is studied analytically via Melnikov’s method. It is shown that, under certain conditions, ray trajectories in some regions of the Poincaré section are equivalent to trajectories of the horseshoe map no matter how small the corresponding perturbation is. These conditions are sufficient for ray chaos and easily satisfied, thus explaining why double-channel propagation is very likely to exhibit chaotic behavior. [Work supported by CA43920 NIH.]

Local perturbations in material density induced in a material by a compressional wave give rise to local perturbations in refractive index. Accurate, high-resolution, three-dimensional, optical measurements of an instantaneous refractive index perturbation in a homogeneous, optically transparent medium may be obtained from measurements of scattered optical intensity alone. The method of generalized projections allows incorporation of optical intensity measurements into an iterative algorithm for computing the phase of the interrogating optical pulse as the solution of a fixed point equation. The complex optical field amplitude, computed in this manner, is unique up to a constant unit magnitude complex coefficient. The three-dimensional refractive index distribution may be computed via the Fourier slice reconstruction algorithm from the optical phase data under the assumption of weak optical scattering. The refractive index perturbation is related to local instantaneous pressure under a linear, small-displacement model for the mechanical wave. A numerical simulation of the measurement experiment, phase recovery, and reconstruction process for a plane piston ultrasound transducer with a semicircular aperture and center frequency of 1.5 MHz is described and corresponds very well with experiment. Experimental data obtained using an 810-nm laser source are used to reconstruct the three-dimensional pressure field from two elements of a 2.5-MHz linear array. Comparison with a measurement obtained via a 500-μm needle hydrophone shows excellent agreement.

It has been shown that acoustic ray paths in range-dependent ocean models exhibit chaotic behavior. Most of the investigations into the ray chaos phenomenon have been primarily numerical in nature. Analytical derivation of sufficient conditions for chaos in acoustic systems has been restricted to inherently discrete problems. This article reports a theoretical study of the existence of ray chaos in a class of continuous parabolic ray systems. This class of ray systems is indexed by a family of analytically prescribed double-channel sound-speed profiles perturbed by periodic range-dependent disturbances. The perturbed Hamiltonian ray systems are studied analytically via the Melnikov method. It is shown that, under certain conditions, ray trajectories of the systems are equivalent to trajectories of a classic chaotic system known as the horseshoe map when the perturbation is periodic and small. These conditions are sufficient for ray chaos and easily satisfied, thus explaining why double-channel propagation is very likely to exhibit chaotic behavior.

A technique for measuring instantaneous three-dimensional pressure in a wideband ultrasound pulse is presented. A collimated laser pulse impinges on the ultrasound field, and the optical intensity in a diffraction plane subsequent to this scattering event is imaged onto a CCD camera and stored. Timing is controlled precisely, allowing the acousto-optic interaction to occur at the same point in the temporal evolution of the sound field each time the experiment is performed. After interaction with the ultrasound pulse, the optical phase is approximately proportional to the ray sum of instantaneous pressure in the pulse (taken in the direction of optical propagation). Optical phase immediately subsequent to passage through the ultrasound pulse is computed from recorded optical intensity via a phase retrieval algorithm. The experiment is performed at several angles as the ultrasound transducer is rotated about an axis normal to the optical axis of the imaging system. Tomographic reconstruction algorithms are applied to the retrieved optical phase data, computing pressure at all points in the ultrasound pulse. The resulting pulse may be propagated forward or backward in time under a source-free model. Reconstructions of the field from a 2.5-MHz array transducer compare well with hydrophone measurements.