Phased Array Leseprobe

element diameter in Equation 2-5 with the dimension of each side. This yields one short near field
and long near field distance. The actual near field length of a rectangular virtual probe aperture is
somewhere between these two values.
Near field length of a circular element:
Figure 2-7: Diagram of sound field
zones
N = D 2 * F/4C Equation 2-5
N = Near-field length
D = Element Diameter
F = Frequency
C = Material Velocity
When considering the propagation of sound through a medium, some assumptions are made.
Assumptions are necessary to predict the direction and velocity of propagation as well as the
intensity of sound at any point in the medium and how it interacts with discontinuities. A short
discussion about these assumptions is presented here before the more general discussion on sound
beam characteristics.
Ray tracing is a standard method of modeling the way sound propagates through isotropic media,
which involves first order approximations to determine the sound field characteristics. These
assumptions are reasonable in the far field when considering isotropic materials. Within this
assumption, the sound is treated as a ray that is reflected or refracted by the interfaces it
encounters. The grain structure is considered isotropic and does not affect the sound beam. The
sound is also assumed to have no intensity variation across the pressure front. There is no
distinction between the near field and the far field within this assumption.
In reality, the propagation of sound is far more complex, and includes diffraction and nonlinear
effects. Sound beams are better approximated by Gaussian equations, which have far different
behavior in the near field (or Fresnel zone) than in the far field (or Fraunhofer zone). They also
have a nonlinear intensity profile in a direction perpendicular to the direction of beam travel.
Using beam mapping, one can determine the area of maximum amplitude, which is typically
within the centre of the beam. Amplitude decreases as the perimeter of the beam is approached,
but the function is not linear as assumed in many ultrasonic applications. At any particular cross
section within the beam, energy density is not constant. This is seen in Figure 2-8 where the
intensity of a sound beam is shown as colour. In the top series of figures, the cross section of the
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