Fraunhofer
Diffraction :
A form of diffraction in which the light source and the receiving
screen are in effect at infinite distances from the diffracting
object, so the the wave fronts can be treated as planar rather
than spherical.
Piezoelectric:
Electricity produced by mechanical pressure on a crystal with
low symmetric atomic structure.
Transducer
Beam Spread
As discussed on the previous page, round transducers are often
referred to as piston source transducers because the sound field
resembles a cylindrical mass in front of the transducer. However,
the energy in the beam does not remain in a cylinder, but instead
spreads out as it propagates through the material. The phenomenon
is usually referred to as beam spread but is sometimes also referred to as
beam divergence or ultrasonic diffraction. It should be noted that there is actually a difference between beam spread and beam divergence. Beam spread is a measure of the whole angle from side to side of the main lobe of the sound beam in the far field. Beam divergence is a measure of the angle from one side of the sound beam to the central axis of the beam in the far field. Therefore, beam spread is twice the beam divergence.
Although beam spread
must be considered when performing an ultrasonic inspection, it
is important to note that in the far field, or Fraunhofer zone, the maximum sound pressure is always found along the acoustic
axis (centerline) of the transducer. Therefore, the strongest
reflections are likely to come from the area directly in front
of the transducer.
Beam spread occurs because the vibrating particle of the material
(through which the wave is traveling) do not always transfer all
of their energy in the direction of wave propagation. Recall that
waves propagate through the transfer of energy from one particle
to another in the medium. If the particles are not directly aligned
in the direction of wave propagation, some of the energy will
get transferred off at an angle. (Picture what happens when one
ball hits another ball slightly off center). In the near
field, constructive and destructive wave interference fill the
sound field with fluctuation. At the start of the far field, however,
the beam strength is always greatest at the center of the beam
and diminishes as it spreads outward.
As shown in the applet below, beam spread is largely determined
by the frequency and diameter of the transducer. Beam spread is
greater when using a low frequency transducer than when using
a high frequency transducer. As the diameter of the transducer
increases, the beam spread will be reduced.
Beam angle is an important consideration in transducer selection
for a couple of reasons. First, beam spread lowers the amplitude
of reflections since sound fields are less concentrated and, thereby
weaker. Second, beam spread may result in more difficulty in interpreting signals due to reflections from the lateral sides of the test
object or other features outside of the inspection area. Characterization
of the sound field generated by a transducer is a prerequisite
to understanding observed signals.
Numerous codes exist that can be used to standardize the method
used for the characterization of beam spread. American Society
for Testing and Materials ASTM E-1065, addresses
methods for ascertaining beam shapes in Section A6, Measurement
of Sound Field Parameters. However, these measurements are limited
to immersion probes. In fact, the methods described in E-1065
are primarily concerned with the measurement of beam characteristics
in water, and as such are limited to measurements of the compression
mode only. Techniques described in E-1065 include pulse-echo using
a ball target and hydrophone receiver, which allows the sound
field of the probe to be assessed for the entire volume in front
of the probe.
For a flat piston source transducer, an approximation of the
beam spread may be calculated as a function of the transducer diameter (D),
frequency (F), and the sound velocity (V) in the liquid or solid
medium. The applet below allows the beam divergence angle (1/2 the beam spread angle)
to be calculated. This angle represents a measure from the center of the acoustic axis to the point where the sound pressure
has decreased by one half (-6 dB) to the side of the acoustic axis in the far field.
Note: This applet uses the equation:
Where:
θ = Beam divergence angle from centerline to point where signal is at half strength.
V = Sound velocity in the material. (inch/sec or cm/sec)1
a = Radius of the transducer. (inch or cm)1
F = Frequency of the transducer. (cycles/second)
Note 1: Units must be consistent throughout calculation (i.e. inch or cm but not both)
An equal, but perhaps more common version of the formula is:
Where:
θ = Beam divergence angle from centerline to point where signal is at half strength.
V = Sound velocity in the material. (inch/sec or cm/sec)
As discussed on the previous page, round transducers are often
referred to as piston source transducers because the sound field
resembles a cylindrical mass in front of the transducer. However,
the energy in the beam does not remain in a cylinder, but instead
spreads out as it propagates through the material. The phenomenon
is usually referred to as beam spread but is sometimes also referred to as
beam divergence or ultrasonic diffraction. It should be noted that there is actually a difference between beam spread and beam divergence. Beam spread is a measure of the whole angle from side to side of the main lobe of the sound beam in the far field. Beam divergence is a measure of the angle from one side of the sound beam to the central axis of the beam in the far field. Therefore, beam spread is twice the beam divergence. 
