Fundamentals of Ultrasonic Phased Arrays by Lester W. Schmerr Jr

Author:Lester W. Schmerr Jr.
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Fig. 8.6 a Geometry for beam steering, through a planar interface in three dimensions.b A side view, looking down the axes

(8.7)

where the location of the centroids of the elements are again given by Eq. (8.2) and is the wave speed in the medium adjacent to the array. From Snell’s law we have

(8.8)

where is the wave speed of the transmitted wave in the second medium. From the geometry of Fig. 8.6 it is easy to show that in the coordinates on the interface we have

(8.9)

with being unit vectors along the coordinates, respectively. These unit vectors can be written in terms of the unit vectors along the axes:

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