Nonlinear ultrasonic propagation through aberrating and nonaberrating media

This dissertation examines the physics underlying the use of nonlinearly generated second harmonic signals to create images for medical diagnosis. The harmonic images are known to demonstrate better image quality than fundamental images. One of the proposed reasons for the improved image quality is a reduction of the effects of aberration. In this dissertation the spatial coherence of backscatter for the fundamental and second harmonic were measured. The spatial coherence provides a measure of the extent of aberration and provides an indication of the success of phase aberration correction routines. The measured spatial coherence for the second harmonic was significantly different from the spatial coherence for the fundamental. We found that the spatial coherence of the second harmonic was independent of transducer array type, frequency, F-number, aperture size, attenuation within the propagation medium, and focal distance. In addition to the direct spatial coherence measurements, we obtained indirect measurements of spatial coherence based on the concept of effective apodization. The effective apodization at 2f was measured for specific transmit apertures, where we defined the effective apodization at 2f as the linear back-propagation to the transmit aperture position of the second harmonic values measured within a plane positioned transverse to the nonlinear propagation of the ultrasound. Using the effective apodization at 2f, we were able to extend the Van Cittert-Zernike theorem to nonlinear propagation. Using Riesz, rectangular, and trapezoidal transmit apodizations we obtained the effective apodization at 2f. In each case, the effective apodization at 2f was narrower than the transmit apodization. Our results demonstrated that the effective apodization at 2f derived from measurements of the ultrasonic field within the focal zone provided a reasonable estimation of the second harmonic beam that is independent of frequency, aperture size, F-number, and focal distance. Our measurements of time shifts for phase aberration correction with porcine abdomen aberrators indicated that the second harmonic signals may provide a better measure of time shifts than the fundamental signals for certain propagation media. The results contained within this dissertation provide some insight into the physics of harmonic imaging for aberrating and nonaberrating propagation media.