Three-Dimensional Wave Theory of Optical Image Formation from Scattered Sound*

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Abstract
A three-dimensional wave theory for the scattering of light by sound waves in a fluid is presented that clearly indicates the formation of optical images of objects immersed in the sound field. This technique, introduced by Korpel, allows real-time visualization of internal structure in opaque objects. In this paper, a scattering theory due to Wolf [ Opt. Commun. 1, 153 ( 1969)] is adapted to this problem and a general three-dimensional theory is developed in which both the sound and the light fields are represented by expansion into angular spectra of plane waves. This new theory describes the imaging phenomena without the use of Bragg’s law or similar additional physical assumptions and yields important image information, such as sufficiency conditions for image formation and a description of the location and character of the image.