Filtering is used within this project to remove noise. Time-gating is applied to remove any waves that arrive after the last possible single scattering event (such as multiple scatters which this project does not consider), and any signals detected before the fastest wave could have travelled directly from emitter to receiver. The entire capture is also time-shifted to allow the assumption that the centre of the pulse originated at the zero time point. Each A-scan has its median subtracted, to remove DC offsets, assuming the DC offset does not drift significantly during any single A-scan. The median assesses the zero level quite well, as it is only very weakly affected by outliers, such as those caused by the signal from the ultrasound waves, as long as there is a much longer period without significant signal energy present.
3.7.1
Plasma noise
When using a laser-EMAT system (laser generation and EMAT reception) with both generation and reception on the same surface, a wave can be observed due to the EMAT directly detecting the plasma generated when the laser ablates the surface of the sample [139], which a piezoelectric transducer will not detect. The wave can be significantly attenuated by a thin layer of plastic (1mm was tested) placed between the generation point and the EMAT, ensuring no gap is left between the obstruction and the surface.
The wave speed was measured using a B-Scan with the laser generation static and the EMAT moving. By measuring the gradient of the arrival time of the wave, the speed was found to be approximately (373±4)m/s; this is the same order of magnitude as has been measured in other
Figure 3.14: Passive analogue low-pass 3-section filter using the Cauer topology.
studies [133], when the plasma has travelled a greater distance, and represents an average speed (the instantaneous speed slowing with distance travelled). However, this method also provided an inter- cept, as the wave appears before it is expected in absolute terms. The intercept is (19.2±0.4)mm, close to 50μs, which is approximately when the wave reaches the EMAT casing, allowing it to be
detected through electrical conduction.
Filtering of the plasma signal is only necessary if ultrasound waves arriving at very late times are required, or if the EMAT receiver and laser ultrasound source are close together, and this is not generally the case. For most cases, the plasma wave can be removed from the signal using simple time-gating. Due to the low frequency of the wave, it is not possible to filter out the wave with a conventional frequency filter, as it would also remove significant parts of the signal of interest.
3.7.2
Low-pass passive analogue filters
The signals received by the EMATs used in this project have frequency domain representations that extend from DC upwards, and hence low-pass filtering is appropriate. Low-pass passive analogue filters ideally contain no resistance, and therefore use mismatch to reflect power outside the pass- band away from the load. Within the pass-band, the low-pass filter matches the load and the source (this approximation is improved for higher section filters). Such filters can be specified by a 3dB point,f0[145]. A n-section low pass filter has n=capacitors+inductors. An example of a 3-
section filter prototype filter (cut-off frequencyf0= 1/2πradians and source impedanceR= 1Ω)
is shown in figure 3.14 with normalised values for resistance, R1,2 = 1Ω, inductance, L = 2H,
and capacitance, C1,2= 1F. To scale this, resistors become the required load (R0), inductors are
multiplied by the required load and divided by the cut-off angular frequency (L0 =LR0/ω), and
capacitors are divided by the required load and the cut-off angular frequency (C0 =C/R0ω). More
sections can be included by adding inductors and capacitors to either end (the filter can start with a capacitor and finish with an inductor, or vice versa, or start and finish with a capacitor or inductor) [145].
3.7.3
Band-pass FFT filters
After digitisation, additional finite impulse response (FIR) filtering in software can provide an improved SNR. A band-pass filter is a combination of a low-pass filter and a high-pass filter. If data can be buffered and operated on in segments (these segments are A-scans in this project), it is possible to implement an FIR filter using a standard FFT based technique. The advantage of such a filter is both its mathematical simplicity, and that it can be as complicated as necessary in the frequency domain without any change in the computational complexity. The actual filter
implemented is very simple, and is just a rectangle in the frequency domain that starts at the lowest frequency to pass (typically 0Hz) and ends at the highest frequency to pass (typically 5MHz). For a signalf(t)being filtered betweenf1and f2:
F(ω) = ˆ ∞ −∞ f(t)e−jωtdt (3.21) f0(t) = 1 2π ˆ f2 f1 F(ω)ejωtdω (3.22)
The filter must symmetrically cover the positive and negative frequencies if the signal is to remain real; many FFT implementations can optionally just examine the positive frequencies and assume the negative frequencies fulfil the required symmetry. Alternatively, this can be combined with taking the analytic signal by multiplying the inverse fast Fourier transform (IFFT) stage by 2 (except for the DC frequency). Care must be taken to not filter significantly any useful frequency components in the signal, as such filtering will adversely affect the time domain representation.
A matched filter was also tried, as an alternative to the band-pass filter; this will detect the signal to which it is matched with the optimum signal-to-noise ratio when the noise can be con- sidered white (the noise must be white if it is to remain uncorrelated after passing through the matched filter) [146]. The measured improvement over the band-pass filter was not sufficient to warrant its use.
3.8
Use in development of TOFDI
This chapter has demonstrated how a TOFDI system can be constructed, and the major consid- erations when doing so. In particular, the choice of transducers, the properties they must have, and how they are arranged, has been decided for the rest of this work. The B-scan configura- tion offers advantages over the D-scan configuration when scanning samples that are continuously moved along, as is the case for the prototypical application, and hence has been chosen for this work. Some aspects of this section would not be carried over to the prototypical configuration, such as the linear slide controlled by stepper motors. However, an alternative method for tracking the sample is available, and is discussed in chapter 4. The performance of an 8bit digitiser relative to a 16bit digitiser has been considered, comparing averaged and single shot cases. At the sort of noise levels experienced within this work, there is little advantage to a more expensive 16bit digitiser over an 8bit equivalent, in either averaged or single shot cases. Consequently, the 8bit digitiser is used within this work, and would most likely also be the choice if using TOFDI outside of the laboratory. Finally in this chapter, it has been shown how the signal is filtered, and then made complex using the Hilbert transform described, to improve the imaging process later. It has been shown that the Hilbert transform produces the analytic signal with sufficient accuracy.
Chapter 4
Non-contact position tracking using
phase correlation
This chapter has been published [147] in a modified form in a peer-reviewed journal.
This chapter describes a method for tracking a moving sample, that does not require expensive equipment, complicated processing, or any contact with the sample surface. As a primary use of TOFDI will involve a relatively fast moving sample, that may be rough and hot, non-contact tracking may eventually be required.
4.1
Introduction
There are various ways to track the relative position of sample and transducer. The use of a stepper motor to control a linear slide tackles the problem by precisely controlling the sample position, hence tracking the relative position if the transducer is held stationary. A linear or rotary encoder is also commonly employed, sometimes in conjunction with a stepper motor based system [5]. In the same way that some NDT work requires non-contact transducers, these applications and many others could benefit from non-contact position tracking. This chapter considers the use of a basic low-resolution digital camera, in conjunction with the phase correlation technique [148], to remotely track the two dimensional movement and rotation of a sample as it is conveyed.
Phase (as depicted in figure 4.4) is known to be more important than amplitude when consider- ing the intelligibility of an image (figure 4.1). Matched filters that use only the phase information have (for some conditions) been shown to be superior in terms of peak sharpness to those that use phase and amplitude information, although using phase and amplitude typically provides a better SNR in the correlation output, and using just the amplitude information is not viable [149]. However, if only using phase information, the input cannot have a narrow bandwidth if reasonable performance is to be achieved.
Phase correlation can be simply extended to include scale [148], or indeed any other image change that can be converted to a simple shift by means of a coordinate transform [150]. Scale has not been included in this demonstration since checking for changes in scale would not detect changes in height of the sample surface. This is because a change in height is not a change of scale of part of the existing image, but a new part of the image appearing as the sample moves. Therefore, knowing the scale change is not useful when the transducer and sample base are at fixed
(a)
(b)
(c)
Figure 4.1: Three versions of the same image of a retort clamp. From left, with phase and amplitude (a), with only phase (b), and with only amplitude (c). Due to (b) and (c) having a few very high magnitudes, the greyscale axis was rescaled for these images to improve clarity. Most of the image information appears to be contained in the phase.
heights relative to each other, as was the case for the experimental testing done here. Knowing the rotation is useful, hence it is included in this demonstration. When examining in the frequency domain the cross-correlation of an image with its rotated form, the cross-correlation is only changed from the auto-correlation by a linear phase factor and a rotation equivalent to the angle between the two forms of the image [151,152].
There are alternatives to phase correlation, such as normalised cross-correlation [153,154], but phase correlation works well, and can handle both the translation and rotation that could occur, whilst being simple to implement. Such techniques are part of the broader field of image regis- tration, and phase correlation, as used here, is considered an area based method of multitemporal analysis for motion tracking, and is known to be robust to noise [155].