The Plane Wave Spectrum in Acousto-Optic Imaging of Ultrasonic Fields.

This thesis takes an in-depth look at two major areas of acousto-optics: Bragg diffraction imaging and Schlieren imaging. Both of these methods relate to the imaging of ultrasonic sound fields. The latter method is particularly relevant as it forms the basis for many practical signal processing schemes. A review of the angular plane wave spectrum concept is followed by an outline of a three-dimensional acousto -optic interaction formalism. This formalism forms the basis for the wave-theory analyses of Bragg diffraction and Schlieren imaging which are undertaken in later chapters. A ray tracing method, applicable to acousto-optic scattering, is also developed and justified on the basis of eikonal theory. Bragg diffraction imaging is analyzed by means of both ray tracing and wave theory methods, and the results are shown to be in mutual agreement. Also discussed are the development and results of a computer program which generates three-dimensional ray tracings that depict various Bragg diffraction imaging configurations. Experimental results are presented that support our theoretical findings. Schlieren imaging is analyzed in chapter 4. The classical Raman-Nath model (and its limitations) is first discussed. We then proceed to analyze Schlieren imaging by means of wave theory. We find that the Schlieren image of a monophonic sound field possesses an extremely large depth of focus (i.e. it is almost diffraction free). We proceed to show that the Raman-Nath interpretation can be extended to high frequency (Bragg) regimes, provided certain constraints are met. Finally, we examine wideband Schlieren imaging using optical heterodyning, which is of great practical importance in signal processing schemes. Several key results are obtained. We first present an illustrative example of a Schlieren signal processing scheme employing optical heterodyning. Although this scheme is not new per se, we present experimental results of a working experiment in which we correlate a pulse modulated sound signal with a correlation mask. We then proceed to present other novel experimental results in an attempt to support our theoretical findings.