Introduction
Ultrasonic testing has been in use for many years. Scanning techniques using both contact and immersion methods are often used during manufacturing and also during periodic in-service inspection programs to determine component quality. But because of a variety of component configurations and potential flaw geometries it is often necessary to perform several inspections, each with a different probe configuration, to assure adequate defect delectability. It is possible that a properly designed phased array probe can perform several different inspections without changing hardware thereby reducing inspection times. This presentation reviews the design and operation of ultrasonic phased array transducers and the necessary features to achieve the desired performance. An example situations in which these probes have already been implemented effectively is also discussed.
Single-element Monochromatic Ultrasound Transducers
Before designing a phased array transducer for a specific application, it is helpful to understand the sound field radiated by a single-element transducer. The sound field characteristics of a single-element transducer can be calculated knowing:
- The size and shape of the radiating element
- The emitted pulse characteristics
- The characteristics of the propagating medium
Nearfield of a Transducer
Let's consider a circular transducer radiating a monochromatic signal. If a small reflector is moved throughout the halfspace so that the signal at each point is reflected back to the transducer, the echo can be detected and recorded. The resultant field plot is found to be a cylindrical volume immediately in front of the source followed by a diverging conical section as shown in Figure 1. The cylindrical section is a region of large amplitude variations caused by the interference of the signal from various locations on the source. This region is called the Nearfield. The length of the Nearfield (N) can be calculated:
where
D is the diameter of the source
l is the wavelength of the radiated signal
Fig 1: Sound Field Emitted by a Transducer |
In many situations, the diameter of the source is larger that the radiated wavelength , therefore l2 can be neglected when compared to D2 and the Nearfield length can be approximated
The conical region beyond the near field is less turbulent because the path lengths differences to any point on the source are less than l and, therefore, there can be little destructive interference. This region is called the Farfield of the transducer and extends from the end of the nearfield to infinity.
Sound Field Divergence
The rate at which the energy in this region diverges is also a function of the source diameter (D) and the radiated wavelength (l). The highest amplitude signal occurs on the axis of the transducer and signal amplitude decreases as the angular displacement n from the axis is increased as shown in Figure 2.
Fig 2: Effect of l/D Ratio on Sound Field Divergence |
Although the signal is radiated into the entire half-space, most energy is included in this conical farfield region. We arbitrarily define the lateral limits of this cone as the angle at which the signal amplitude is reduced by 6 dB relative to the axial amplitude. Other reduction levels could be used but -6 dB is an accepted guideline.
The angle at which the signal amplitude is reduced by 6 dB (g) can be calculated
It can be seen that in situations in which l is large compared to D, the divergence angle can be large. This makes location of the reflector more difficult because the sound field is large. For this reason, most inspection codes specify ultrasound transducers having small divergence angles so that the reflector can be located more precisely. This can be accomplished using at least two techniques. First, the divergence angle can be reduced by reducing the l/D ratio in equation 3 above. Higher frequencies producing smaller wavelengths, and/or larger diameters will accomplish this objective. The second technique is focusing the ultrasound source itself.
Focused Transducers
As indicated earlier, the sound field characteristics are the result of phase interference of signals from all points on the source. The equations and discussions above assume that the source is circular and flat. Changing the curvature of the source, however, changes the relative phase of contributions from points on the source and, hence, changes the field pattern. As the degree of concavity of the source is increased, the nearfield changes from a cylindrical region to a converging conical region and the nearfield length is reduced. Focusing permits very small beamwidths to be achieved but only in the region of the focal point as shown in Figure 3. Unfortunately, the divergence angle beyond the focal point of a focused transducer increases often making reflector detection or location difficult.
Fig 3: Schematic Sound Field of a Focused Transducer |
Because the nearfield length is diffraction limited, it is not possible to focus beyond the nearfield length of the source.
Transducer Design for Specific Applications
The purpose of the discussion so far is to convey the idea that, given a particular test situation, one can choose an appropriate transducer size, frequency, and focal characteristic such that good reflector detectability exists in a region where the reflector is expected. Reflectors far from this region may be difficult to detect and a second transducer design may be necessary to interrogate the second region. This concept of using multiple transducers in an inspection is often used. Several transducers, each having different sound field characteristics and orientations are used to interrogate various regions of the testpiece and the results of these scans are assembled into an over evaluation.
If there are several different testpieces to be inspected, many different sets of transducers may be required. Furthermore, this hardware change, along with the calibration verification is likely to be time consuming.
Phased Arrays Are More Versatile
A phased array transducer is a 1-D rectangular group of individual elements, each having its own pulser and receiver circuitry. All elements are connected to, and controlled by, a computerized ultrasound system. The system is able to activate each element independently. By timing, or phasing the individual elements appropriately, a cylindrically converging wavefront can be created as shown in Figure 4. This is analogous to the phase delays caused by the mechanical lens placed on the front of a single-element transducer discussed above. Using a different phase pattern, a different focal point can be achieved. It is for this reason that phased arrays are sometimes called "electronic lenses".
Fig 4: Electronic Phasing Used to Generate a Focused Sound Field |
Additionally, a linear phase pattern will cause an unfocused beam to be steered off the axis of the transducer as shown in Figure 5. Naturally, these patterns can be combined to steer and focus simultaneously.
Fig 5: Electronic Phasing Used to Steer a Sound Field |
Phased Array Limitations
Are there limits on this control? Can the beam be steered or focused anywhere?
Let's assume that the aperture of our 1-D phased array is square and contains 16 elements. The sound field emitted by a square aperture, for the purposes of this discussion, is similar to that of a circular disk about the same size. We start the design process by selecting the frequency most suitable for detection of the reflector type we expect to encounter. This is identical to the frequency selection process used for single-element systems.
Now, let's consider beam steering. As shown in Figure 5, steering is caused by the constructive interference of wavefronts emitted by the 16 elements at different times. In Figure 5, the wavefronts from each element are shown being circular and uniform in amplitude. This is not the case. Remember that the energy is concentrated on the axis of each element - as the angular deviation from the element axis increases, the amplitude decreases. We also said that the rate at which this occurs is greater for large elements than for small elements (at constant frequency). Therefore as a phased array is steered off axis, the amplitude will decrease at the same rate as the individual elements making up the array. To steer to large angles, small individual elements are necessary. This is the second design criteria in phased arrays - determine the maximum necessary steering angle and set the individual element width so that at that angle the beam amplitude from the individual element is reduced by no more than 6 dB.
Finally, the number of elements in the group must be determined. This is dependent on the necessary focal requirements. For example, assume the region to be interrogated is 50 mm thick. Therefore, we want to be able to focus at depths as great as 50 mm in the testpiece. The soundfield of a phased array element group is approximately equal to that of a single element having the same size and frequency as the group. We know from our discussion above that we can only focus within the nearfield length. We must include a sufficient number of elements in the phased array group that the nearfield extends at lease to 50 mm.
Electronic Scanning
We have presented phased array design techniques capable of beam steering and beam focusing under electronic control. Our original scenario included scanning transducers over the test piece and there may be some situations in which electronic beam steering is not able to access some locations withis the testpiece. In such situations, electronic scanning can be used to increase coverage. In Figure 6, it is desired to inspect a 100 degree sector of a metal tube. A 5 MHz signal incident to the tube wall at 15 degrees is necessary to detect tube wall cracks. A sixteen element aperture, 13 mm square, is sufficient to achieve the requires steering and focusing. Due to the circular geometry of the tube, it is not possible to steer the beam to a different angular location without changing the angle of incidence, which is unacceptable. Electronic scanning, as shown in Figure 6, provides the solution.
Fig 6: Phased Steering, Focusing, and Scanning Combined in One System |
The original 16-element array is replaced with a 128-element array using the original element size resulting in an array 8 times the length of the original. With the addition of a multiplexing circuit in the array, any contiguous 16 elements can be phased. Additionally, the array can be formed in a circular arc concentric with the testpiece so that the sound field of any 16-element group using tha same phase pattern will impinge the tube at the same angle but a different location.
Additionally, electronic scanning is faster because no physical probe motion is required. If desired, the beam could initially operate at one end of the array, and then jump to the other end of the array with no lost time.
Summary
We have presented an overview of the factors affecting the sound field of single-element ultrasonic transducers. We have used this information as a guide to design phased array transducers that offer greater versatiltiy in testing thereby reducing test time as well as system reconfiguration for new testpiece geometries.
