Vector Theory of Ultrasonic Imaging [chapter]

W. S. Gan
2008 Acoustical Imaging  
Sofar works on ultrasonic diffraction imaging are based on scalar theory of sound wave. This is not correct as sound has vector nature. When sound propagates in fluids it can be approximated as a scalar wave as there is no polarization. But when sound propagates in solids, its vector nature has to be considered as polarization occurs and transverse wave as well as longitudinal wave will appear. Vector theory is especially needed when the obstacle size is smaller than the wavelength. We use the
more » ... length. We use the Smythe-Kirchhoff approach for the vector theory of diffraction.Comparing the result with the scalar Kirchhoff approximation, we find that both contain the same diffraction distribution factor and the same dependence on wave number. But the scalar result has no azimuthal dependence whereas the vector expression does. The azimuthal dependence variation comes from the polarization properties of the field and must be absent in a scalar approximation. We use the analogy of the sound velocity as equivalent to the magnetic field and the acoustic stress field as equivalent to the electric field to convert our result from the electromagnetic case to the acoustic case. We then derive the image formation theory based on the vector diffraction theory. We use the angular spectrum approach. We found the existence of the components of the angular spectrum known as evanescent waves. These waves are more properly treated in a vectorial approach. We then discuss the effect of polarization on acoustical imaging.
doi:10.1007/978-1-4020-8823-0_53 fatcat:hzb57otombcy5panm6ujej5axu