TABLE OF CONTENTS

Abstract Introduction to Technology Theory of operation Methodology Results Depth of field Beam spot Beam Divergence Signal-to-noise Ratio(SNR) Conclusion References

Abstract

Recent developments in Phased Array hardware developed by R/D TECH for nondestructive testing now allow dynamic focusing on reception. This new option, borrowed from medical technology, enables a programmable, real-time array response on reception by modifying the delay line, the gain, and the activation of each element as a function of time. This technology is presented as a new powerful tool which can extend the depth-of-field, reduce the beam spread and increase the overall signal-to-noise ratio. Implementation of dynamic focusing in Phased Array systems will present many advantages such as an increase of the Pulse Rate Frequency (PRF). The technology implies a lot of significant possibilities, but also an extensive beam characterization. Some results are presented to quantify the advantages and drawbacks of the technique in comparison with standard phased array zone focusing and conventional UT. Results are clearly demonstrating the effect of dynamic focusing on the depth- of-field, the beam spread, the signal-to-noise ratio, and the acquisition rate, both with linear and annular arrays. Therefore this technique is suitable for applications where long soundpaths and small beam divergence are required as boresonic, billet, and blade root inspections

Introduction to the Technology

Ultrasonic testing is, by definition, highly dependent of the transducer involved. The ultrasonic beam generated by the transducer is reponsible for the A-scan obtained. As the A-scan representation is the parent of all other representations (i.e. B-scans, C-scans, and S-scans), the ultrasound community has invested efforts to maximize the reliability of A-scans and to increase the fidelity of the inspections. Two parameters are indeed very important and related: divergence and amplitude of the acoustical beam as a function of depth in material. To obtain the maximum spatial resolution or defect definition, the beam divergence should be small, known, and in accordance with the application. Same thing for the distance-amplitude curve (DAC) which can be corrected with simple amplification. So, the more linear is the DAC, and smaller is the beam and its divergence, the better is the definition of the inspection, and easier the analysis. The power of standard Phased Array system resides in its ability to electronically focus an acoustical beam at some specific point. This advantage induces a side effect because the region of interest is most of the time larger than the focal area. It means that the pulse-echo sensitivity will tend to ignore off-focus reflectors. To stretch the beam by applying a more divergent focal law is somehow a solution, but the beam width will increase. Another solution would be to have multiple foci with subsequent firing (multi-zone inspection). However, this technique slows the PRF and increases the amount of data storage. Then as applications as boresonic, billet and bladeroot inspections require large depth coverage, high speed acquisitions, and low storage requirements, a problem occurs. Dynamic focusing on reception, or Dynamic Depth-Focusing (DDF), is then an interesting solution.

Theory of Operation

Based on the delay-and-sum model for synthetic apertures, Standard Phased Array Focusing (SPAF) is the simplest beamforming technique possible. For that technique, the two influent parameters for focusing an array are the delays and the apodization (gain) of each element of the array. The set of delays is called « delay law », and the set of gains is called « amplitude law ». Those two laws are often grouped as a single « focal law ». Standard Phased Array Focusing allows one focal law for transmission and one for reception. The delay law has, most of the time, an hyperbolic shape as calculated by raytracing from the elements to the common focal point. SPAF is also known as multi-zones focusing. Figure 1 demonstrates the principle of SPAF.

Fig 1: Standard Phased Array Focusing (SPAF) : a single focal law is applied both on transmission and reception, forming a small pulse-echo focal spot.

Fig 2: Dynamic Depth-Focusing (DDF) : a single focal law is applied at transmission, but multiple subsequent delay laws are applied on reception, forming a long and thin pulse-echo focal spot.

Dynamic Depth-Focusing is also a beamforming technique, but it is more versatile from an application point of view. It allows while the reception to change the spatial response of the array, by changing the reception focal laws. In other words, it allows to move the focal spot off the probe as a function of acquisition time on reception. It is the main difference in comparison to Standard Phased Array Focusing. This beamforming technique is actually hardware implemented as variable delay laws as a function of time. So a single focal law is used for transmission, and many subsequent delay laws are used for reception. The following table presents the main differences between conventional UT, Standard Phased Array, and Dynamic Depth-Focusing on reception.

Topics	Conventional	SPAF	DDF
Beamforming technique	no	yes	yes
Possibility of electronic focusing	no	yes	yes
Possibility of electronic scanning	no	yes	yes
Number of TX focal laws	-	1	1
Number of RX focal laws while receiving	-	1	MULTIPLE delay laws 1 amplitude law
Variable TX aperture	no	yes	yes
Variable RX aperture while receiving	no	no	yes**
Table 1 : Principle and performance comparison between conventional UT, Standard Phased Array Focusing (SPAF), and Dynamic Depth-Focusing (DDF).

**Projected in next R/D Tech hardware

In the Dynamic Depth-Focusing approach, the transmission aperture response acts as a limiter within the convolution. Indeed, the emitted acoustical beam should be optimized to maximize the insonification of the region of interest and to minimize the resulting pulse-echo beam width and divergence. It can also be shown easily that the minimum beam size and maximum amplitude are obtained with SPAF at the specified depth. Dynamic Depth-Focusing should then be seen as a good compromise between linear amplitude response, minimum beam width and divergence, and highest PRF.

Methodology

To determine the proper delays to apply on reception (RX), we used the Fermat raytracing technique from the center of the elements to the focal point. This technique produces the so-called « hyperbolic » delay laws. It is the method which offers the maximum spatial rejection (the smallest focal spot). We used such a technique for all the delay laws applied on reception, with SPAF or DDF. On transmission (TX), we used the Fermat technique, but also another one generating triangular delay laws for linear arrays only. The concept of triangular delay laws is to split the probe into two probes. From the first element to the center element, a constant delay variation is applied which deflects the beam. This delay patch is then copied and reversed to the remaining elements. The resulting pattern gives a pyramidal shape centered on the middle element. Many other techniques exist to optimize the radiation patterns of phased arrays like sparsed arrays[] and vernier arrays[].

The methodology to achieve a Dynamic Depth-Focusing scan is the following :

1. Determination of the depth coverage and the angle of the beam
2. Calculation of the transmission focal law
   Attention should be paid on the delay law. The calculation technique may be one of the previously proposed. The amplitude law may be adjusted to correct the material attenuation.
3. Calculation of the reception focal laws
   The number of delay laws will depend on the desired resolution of the depth coverage. The time elapsed between to subsequently applied delay laws should be also programmed.

We tested two DDF configurations to depict its power and to isolate the effects of important parameters on the DDF performances. The first test was a zero degree, wedged LW scan achieved with the probe A on the block #1. The second one was an annular array (probe B) on the block #2 with a waterpath. The probes are featured in Table 2 and the characterization blocks are described in Table 3.

Results

Depth-of-field


Fig 3: Performance comparison between Standard Phased Array Focusing(SPAF) and Dynamic Depth-Focusing (DDF) on the depth-of-field. From the left to the right, SPAF at FTX/RX=35 mm depth and DDF at FTX=35 mm depth respectively.

Fig 5: DDF small beam width and divergence seems to offer the best Standard Phased Array Focusing beam width over the depth.

Fig 6: Beam measurement of a DDF scan achieved with an annular array with FTX= 200 mm. Comparison with SPAF at different depths denotes the advatage of using DDF.

Fig 7: Beam measurement comparison between DDF hyperbolic laws and DDF triangular laws.

Fig 8: Signal-to-Noise Ratio comparison between DDF and SPAF.

The effect of the Standard Phased Array Focusing (SPAF) on the depth-of-field, or working range, is illustrated in Figure 3. The SPAF technique generates a limited working range nearby the focal point. The beam spot is small nearby the focused position, but very large out of this range. The effect of the Dynamic-Depth Focusing is also shown in Figure 3. This figure presents a comparison of the results for a Standard Phased Array Focusing and Dynamic Depth-Focusing. The effect of dynamic focusing on reception is clearly shown. The results are longer depth-of-field and smaller beam spread. We optimized the transmission field by applying a triangular delay law. Figure 4 and subsequent DDF results presents optimized DDF triangular delay law.

Fig 4: Depth-of-field comparison between DDF with hyperbolic laws, DDF with triangular laws, and SPAF.

Beam spot
The DDF technique reduces considerably the variation of the beam dimension over a long soundpath range as shown by the next figure. The beam dimension variations are very high for Standard Phased Array Focusing. A minimum is obtained at the focal position. In opposition to this, the dynamic depth focusing beam is uniform over a large soundpath. Two very important points should be denoted.

1. The beam spot produced by the DDF is always as small as the one produced by standard phased-array.
2. The DDF diminishes the beam spread without jeopardizing the dimension of the beam obtained with the standard phased array.

An annular array was also tried to verify that observation. Figure 6 denotes that DDF offers the smallest beam size and divergence over the depth coverage (56 mm up to 252 mm in aluminum billets). Beam measurements were performed with hyperbolic and triangular types of focal laws using DDF. For all the emission focal laws used, the beam size is always less than 5 mm large. The use of the triangular focal law with F=32 mm gets the beam smaller than 3 mm for all the studied range.

Beam divergence
The next table shows the very low half-angles (-6 dB) obtained with the linear and annular arrays.

Technique	Half-angle (-6 db) degree(s)
Linear array, Triangular focal law, FTX=32 mm	0,30
Annular array, Hyperbolic focal law, FTX=200 mm	0,14
Table 5 : Half-angle performance report for the linear and annular arrays, both used with DDF.

Signal-to-Noise Ratio (SNR)
Figure 8 presents the improvement of the signal-to-noise ratio with the DDF technique. For the considered ultrasound path, the obtained SNR with the DDF is always higher than the one obtained with the SPAF.

Conclusions

The DDF technique as developed by RDTECH gives some improvement in regards with the standard phased-array focusing. The main advantages are:
1. The depth-of-field generated by an optimized DDF is improved by a factor 4 in regards to the SPAF ;
2. The beam spot produced by the DDF is always as small as the one produced by SPAF ;
3. The use of DDF creates very small beam spread. Half-angles as small as 0,30 and 0,14 degree were obtained with linear and annular arrays ;
4. The DDF diminishes the beam spread without jeopardizing the dimension of the beam obtained with the standard phased array.
5. The obtained SNR with the DDF is always higher than the one obtained with the SPAF ;
6. File size is greatly reduced because only one A-scan is recorded at one mechanical position.
7. PRF is increased because only one A-scan is needed to cover a long soundpath.
All those properties make the use of DDF suitable for applications as boresonic, billet and bladeroot inspections.

References

1. "Optimizing the Radiation Pattern of Sparse Periodic Linear Arrays", Lockwood, Li, O'Donnell, Foster, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 43, n°1, January 1996
2. "Ultrasound Synthetic Aperture Imaging : Monostatic Approach", Ylitalo, Ermert, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 41, n°3, May 1994
3. "Review of practical applications of Ultrasonic phased-array in NDT", Lamarre A., Mainguy F., Q-NDE Conference, Snowbird, Utah, July 1998