Future work

The next sensible step is to examine the accumulated error in the shift over a large number of image pairs (analogous to accumulated slip in a mechanical system), and if this can be mitigated to some extent by not just comparing consecutive images, but also image pairs representing larger jumps. For example, comparing images 1 and 2, 2 and 3, and 3 and 4, could provide excellent local accuracy, and comparing images 1 and 4 could limit the error due to accumulated errors from comparing consecutive pairs. Changes of scale have not been investigated here, but can be

checked for as well [148], and the accuracy of the technique for scale changes for non-destructive testing applications may be of interest. An example is if the technique was sufficiently accurate to monitor lift-off of an EMAT, moving with the camera in the vertical and horizontal directions, from a top-down view of the sample. Finally, the importance of image resolution should be investigated for a range of surfaces with differing amounts of surface variation and motion blur (which reduces spatial frequency bandwidth). Samples move at significant speed in certain non-destructive testing applications, and it would be of interest to examine how robust the phase correlation technique is to motion blur, or if a very rapid shutter speed, and strong lighting to provide good SNR, would be necessary in these cases.

4.6

Conclusions

There are many applications in NDT which require precise knowledge of the relative position between transducer and surface. This can be done by precisely controlling position changes, using a stepper motor or a servo, but if this is not viable or sufficient, position must be measured using a device such as a linear/rotary encoder, usually requiring contact or very near-contact to operate. An alternative has been demonstrated here, which can be remote from the sample, using a phase correlation tracking technique and a basic camera.

The phase correlation technique is simple to implement, using the FFT for computational speed, and as shown within this work, is able to detect translation in two dimensions and (optionally) rotation, despite the presence of significant noise. It has been extended to sub-pixel precision by conventional FFT up-sampling, and filtering of spatial frequencies outside of those representing real image components reduces the impact of AWGN.

The algorithm has been tested within TOFDI project [142, 143, 163], using only a basic low resolution camera (640×480, fixed focus), tracking a TOFD style transducer configuration [1] as it scanned over a sample surface. Linear sample movement has been determined to sub-pixel precision on experimental data gathered this way, confirmed manually as a median accuracy of 0.01mm of linear movement (0.06 of a pixel) in this case, despite uneven illumination. The performance as noise increased was assessed, and for simulated noise with a standard deviation a fifth of the mean signal level, injected into the experimental data, the median accuracy was 0.02mm of linear movement (0.13 of a pixel) in this case, with some variation in the results due to the random nature of the noise introduced. Rotation was determined to 0.1°on simulated data, but the limits of resolution and noise tolerance were not explored to the same extent as for translational motion. Future work aims to reduce accumulated error, assess changes of scale, check the importance of image resolution with respect to the spatial frequency bandwidth of the sample surface, and examine the difficulties introduced by motion blur.

4.7

Use in development of TOFDI

This chapter has provided a method for tracking a moving sample, that only requires a basic cam- era, and relatively simple processing using the phase correlation technique. It is a method that could easily and effectively be used in the prototype application for TOFDI, providing accurate information on the transducer position relative to the sample. The accuracy of 0.01mm is accept- able; a compression wave moving at approximately 6000m/s will take under 2ns to travel that distance. Therefore, in the worse case scenario, the time of flight will be wrong by this much. The

than 0.3%. As the worst case change in amplitude is so small, the resultant error in the TOFDI cross-sectional imaging process will negligible. In addition, it is possible that with a better camera and lighting, that greater positional accuracy could be achieved.

Chapter 5

Effect of transducer width on

received signal

This chapter describes how the width of a linear coil EMAT changes the frequency response with respect to the receiving angle. Any transducer (piezoelectric, EMAT, or laser) has a finite size for both generation and detection. In certain cases, the size can be considered to be zero (the ideal point emitter/receiver), but in other cases the affect of non-zero size on frequency response must be considered. If a linear coil has more turns, a larger area of the sample will contribute to the ultrasound signal detected, but the larger coil will also lead to increased impedance, and also less sensitivity to higher frequencies. It is important to pick a linear coil with the optimum response for TOFDI, in order to improve the SNR where possible.

5.1

Introduction

There are many factors which result in a change in the frequency response of the EMAT, such as the magnet shape and strength, and the coil configuration (shape and number of turns being important factors). In particular, the latter can easily lead to a change in impedance, which is dependent on frequency, as is inductance [109, 141], which would also change.

A linear coil has been chosen for this TOFDI implementation, because that coil configuration can detect bulk ultrasound waves (compression and shear) over a relatively wide range of angles. In terms of bulk wave EMATs, the coil configurations used are usually either linear, spiral, or meander line. The meander line coil can be used to focus SV waves onto a focal line, which is not appropriate for the TOFDI application. The spiral coil usually has good performance close to (but not at) normal incidence, and is very useful for pulse-echo work, but has much poorer performance further away from normal incidence. In addition, the spiral and meander coil may not effectively detect plane waves that extend over a significant portion of the coil, due to the symmetry of the coil causing the plane wave to cancel itself; if equivalent motion is detected in two opposing parts of the coil, these parts will cancel and the sum will be zero or very small, depending on the exact scenario. A linear coil does not suffer from this limitation, and is therefore the choice for detecting bulk waves in the prototypical TOFDI application. Once a linear coil (such as in figure 2.5) has been selected, the magnetic field should be one that is strong and relatively consistent over the area of the coil, with the field direction dictating which oscillation direction is detected. As it is

(a)

v

s

wavefront

θ

wavefront

v

s

θ

Figure 5.1: The plane wavefront (a) represents the far-field approximation. The circular wavefront (b) represents the near-field approximation. The plane wavefront form is a good approximation in many cases where the deviation in time of flight and amplitude can be considered negligible for the section of the wavefront received by the transducer. The wavefront polarisation is perpendicular to the direction of propagation for shear waves, and parallel to the direction of propagation for compression waves. If the transducer is sensitive to the small variation in polarisation over the wavefront, the circular wavefront form may need to be considered even at distances that might normally be considered the far-field.

far easier to create a strong magnetic field perpendicular to the sample, that direction was chosen for this work (figure 2.7), although there are deviations due to the magnet not having an infinite extent (edge effects).

Having chosen the other key EMAT configuration parameters, coil width must be considered. For a series of different linear coil widths, each corresponding to a different number of turns of wire, this chapter explores the sensitivity of each coil to different signal frequencies with respect to angle of incidence of the ultrasound, and checks that it approximately correlates with a simple model.