Variation with coil size for surface waves

The set-up depicted in figure 5.13 was used, with the laser line source acting ablatively; an A-scan was collected for each coil. Only the temporal region containing the Rayleigh wave was captured, using signals averaged from 16 collections. Results were collected for the EMATs described in table 5.1.

The response of the EMATs was modelled as previously described for a plane wave front; this is acceptable due to the use of a line source that is longer than the length of the EMAT coil being used as a receiver. Setting the angle to zero in equations 5.10 and 5.11:

F(ω) = 2Rv ω sin |s|ω 2v (5.15) F(0) =R|s| (5.16)

The EMATs were modelled using the parameters in table 5.1 and a wave speed of 2987m/s. Only Rayleigh waves were modelled, as the experimental results for compression waves were not of a sufficient standard to form a meaningful comparison with simulated results. The frequency domain transfer function due to the size of the EMAT was calculated and can be seen in figure 5.14a. At each trough, a phase shift that is some multiple of 180° is expected. To test this, the experimental A-scans were converted to the frequency domain using an FFT, and the phase extracted. The phase was then unwrapped, and the linear trend removed, such that large jumps in phase could easily be seen (figure 5.14b). The phase jumps are in approximately the correct place

(a) 0 0.5 1 1.5 2 2.5 3 3.5 0 0.2 0.4 0.6 0.8 1 Frequency (MHz) Magnitude (arbitrary) 10 20 30 40 (b) 0 0.5 1 1.5 2 2.5 3 3.5 −600 −400 −200 0 200 400 600 Frequency (MHz) Phase (degrees) 10 20 30 40

Figure 5.14: The simulated frequency spectrum magnitude (a) and experimentally measured phase at each frequency (b) for a series of linear EMAT coils, with 10, 20, 30, and 40 turns (as noted in the legend), operating on a mild steel sample. The frequency spectrum magnitude has been scaled such that the maximum magnitude is one. Where the simulated frequency spectrum magnitude nulls are found (a), a large change in phase is observed in the experimental data (b), which is consistent with a null being present in the experimental frequency spectrum magnitude. Considering the phase is the clearest way of observing these nulls in the experimental data.

in terms of frequency, and approximately a multiple of 180°, although unfortunately the results cannot be claimed to be particularly clear.

It is necessary to check the transforms calculated due to the EMAT coil spatial width are accurate. The A-scans were converted to the frequency domain using an FFT, and the magnitude taken. These magnitudes are scaled such that for a given coil, the maximum magnitude was one and the minimum zero (no offset was added, zero was simply left as zero), forming figure 5.15a. To compare with the calculated transforms, the experimentally measured frequency domain form for the coil with 10 turns was divided by the calculated response for a 10 turn EMAT (such as the response shown in figure 5.14a). The result of this operation was then multiplied by the calculated transforms (figure 5.14a) for EMAT coils of the other number of turns that are under test, to produce an expected frequency domain response for each coil, 5.15b. The output of the transform was set to zero for any frequencies above the first trough for each calculated response. Directly comparing figures 5.15a and 5.15b, it can be seen that the frequency of the first trough has good agreement between the experimental and simulated data. This would strongly suggest that the model used was valid for this purpose.

The model can be used to calculate the upper useful frequency for any linear EMAT coil used. However, it cannot predict the form of the signal received, nor the peak-to-peak amplitude, and hence its application is limited.

5.5

Conclusions

Any transducer has a finite size for both generation and detection, and the affect of non-zero size on frequency response must be considered. Models were constructed for both far-field and near-field cases. Simulated data was found to agree with experimental tests when considering nulls in the frequency response. The models were too narrow in scope to fully describe the impact of changing coil configuration on the frequency response; for example, they do not include frequency changes due to changes in mutual and self inductance. However, it is beneficial to explore the change just due to transducer size, and that is what this work has achieved. It could potentially be combined

(a) 0 0.5 1 1.5 2 2.5 3 3.5 0 0.2 0.4 0.6 Frequency (MHz) Magnitude (arbitrary) (b) 0 0.5 1 1.5 2 2.5 3 3.5 0 0.2 0.4 0.6 Frequency (MHz) Magnitude (arbitrary)

Figure 5.15: The experimentally measured (a) and simulated (b) frequency spectrum for a series of linear EMAT coils, with 10, 20, 30, and 40 turns (as noted in the legend), operating on a mild steel sample. The simulated results were obtained by dividing the frequency domain form for the EMAT coil with 10 turns by the calculated response for a 10 turn EMAT coil, and then multiplying by the calculated transforms for EMAT coils of the other number of turns that are under test. The output of the transform was scaled such that the maximum magnitude is one, and set to zero for any frequencies above the first trough for each calculated response.

with models of the other factors impacting on EMAT response in future work.

5.6

Use in development of TOFDI

This chapter has compared a simple model of how the spatial impulse response of a linear EMAT coil is related to coil width, against experimental data. Although insufficient factors have been included to provide a matching waveform, the model is sufficiently quantitative to correctly predict the troughs in the frequency domain, and the variation in the trough position as the ultrasound angle of incidence changes. This information can be used to choose a linear coil that is most suitable for use in TOFDI, as implemented within this work. From the model and the experimental data, it can be seen that the EMATs retain sufficient frequency bandwidth (80% of peak amplitude up to 1MHz at 80°, this frequency range containing most of the signal energy) at coil widths equivalent to 30 turns. This makes 10, 20, and 30 turn coils viable. Although not presented here, data on peak-to-peak amplitude variation with angle, and data on peak-to-peak amplitude variation with lift-off, have been collected. The 30 turn coil did not have sufficient peak-to-peak amplitude relative to the 10 and 20 turn coils, and thus has been disregarded. The 10 turn coil can offer superior performance if there is zero lift-off, but above this, it drops to the same level as a 20 turn coil. Since the drop is so much less for a 20 turn coil (although it is still a significant drop in peak-to-peak amplitude with lift-off), it was chosen instead of the 10 turn coil, as it is expected that the lift-off will vary when performing a TOFDI scan, if TOFDI is being used for the prototypical application. Less variation in peak-to-peak amplitude due to lift-off, leads to a more consistent signal, which then requires less signal processing stages.

Chapter 6

Removing direct and reflected waves

This chapter has been published [165] in a modified form in a peer-reviewed journal.

This chapter describes a method for removing ultrasonic waves from B-scans, that have either travelled directly from the emitter over the surface to the receiver, or that have been reflected from the back-wall, or that have gone from the emitter, along the surface to the sample edge, and back to the receiver. These waves do not contain useful information on bulk defects, but they can obscure bulk waves scattered by defects, and they can also make examining the B-scan more difficult, as their presence means that much of the dynamic range of the B-scan is occupied with these very strong directly received or reflected waves, rather than the weaker scattered waves. As the cross-sectional imaging stage of TOFDI requires the defect indications to not be heavily obscured by coherent interference, and B-scans are also shown as part of TOFDI, a technique to remove these lines is required.

6.1

Introduction

The Hough transform (HT) [166] is an effective method to detect straight lines or other paramet- erisable shapes [167], and is known to be robust to noise [168]. The HT is used in areas including machine vision [169], electron back-scatter diffraction (EBSD) analysis [170–172], and feature loc- ation in geoscientific images [173]. In NDT, it can locate parabolas in B-scans [17,18,34], although such work often uses an inverse Hough transform (IHT) [174] and genetic algorithms to solve the consequent parameter optimisation problem [18, 34].

Due to image discretisation, lines in the image space can be split into “thick” (figure 6.1a) and “thin” (figure 6.1b) lines [175, 176], where a thick line is split into a series of vertical or horizontal segments. It is clear from this that a thin line can only exist at 45°(in either direction), and that the extremes of thick lines are found at 0°and 90°. However, the issue of “sparse” lines does not appear to have been considered previously.