This report describes an optical phase contrast imaging technique for the measurement of wide bandwidth ultrasound fields in water. In this method, a collimated optical wavefront ( l = 810 nm) impinges on a wide bandwidth ultrasound pulse. The method requires that refractive index perturbations induced by the ultrasound field be sufficiently small. Specifically, on exit from the acoustic field, the phase of the optical wavefront must be proportional to the ray sum of local density taken in the direction of propagation of the incident optical wave. A similar restriction is placed on the dimensions of the ultrasound pulse. Repeated measurement of this phase as the ultrasound field is rotated through 180 about an axis normal to the direction of propagation of the incident optical wave generates the Radon transform of the ultrasonically induced refractive index perturbation. Standard tomographic reconstruction techniques are used to reconstruct the full three-dimensional refractive index perturbation. A simple two-lens imaging system and an optical signal processing element from phase contrast microscopy provide a method of directly measuring an affine function of the desired optical phase for small optical phase shifts. The piezo-and elasto-optic coefficients (the first partial derivatives of refractive index with respect to density and pressure) relate refractive index to density and pressure via a linear model. The optical measurement method described in this paper provides a direct, quantitative measurement of the piezoand elasto-optic coefficients (from the density or pressure fields).

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-microm needle hydrophone shows excellent agreement.

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I am very grateful to my advisor, Dr. James F. Greenleaf, for his support and insight. I greatly appreciate the assistance of Randall R. Kinnick and Tom Kinter in the experimental and computer administrative aspects of the research. To the fellow students who endured numerous conversations on topics related to this research, I offer my thanks as well. I am particularly grateful for the unflagging patience and encouragement of my wife Emily and our four children through the many years of graduate school.