McKee, J. G., Wilcox, P. D., & Malkin, R. E. (2019). Effect of surfacecompensation for imaging through doubly-curved surfaces using a 2Dphased array. In S. Laflamme, S. Holland, & L. J. Bond (Eds.), 45thAnnual Review of Progress in Quantitative Nondestructive Evaluation,Volume 38 (38 ed., Vol. 2102). [100008] American Institute of Physics(AIP). https://doi.org/10.1063/1.5099836

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Effect of surface compensation for imagingthrough doubly-curved surfaces using a 2Dphased arrayCite as: AIP Conference Proceedings 2102, 100008 (2019); https://doi.org/10.1063/1.5099836Published Online: 08 May 2019

Jessica G. McKee, Paul D. Wilcox, and Robert E. Malkin

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Effect of Surface Compensation for Imaging Through Doubly-curved Surfaces using a 2D Phased Array

Jessica G. McKee1, Paul D. Wilcox1,a) and Robert E. Malkin1

1 Department of Mechanical Engineering, University of Bristol, Bristol, BS8 1TR, UK

a)Corresponding author: p.wilcox@bristol.ac.uk

Abstract. In order to characterise and size defects located beneath complex surface geometries in components when using ultrasonic non-destructive testing methods, correct surface compensation is of critical importance when generating images. The effect of the accuracy of surface compensation when generating Total Focusing Method (TFM) images through a doubly-curved surface with a 128-element sparse 2D phased array has been investigated. An aluminium test specimen was created with an axi-symmetric surface with a Gaussian profile in order to create a surface that curves in multiple directions. By determining the resolution of a defect for different assumed surface profiles, it has been shown that an extracted surface works best when compared to a planar surface parallel to the array and a 2D fitted planar surface. The results show that, even for surfaces that are curved very slightly, incorrect surface compensation can lead to significant image de-focusing.

INTRODUCTION

One of the most commonly used methods in NDT involves the use of ultrasound, whereby high-frequency (generally > 1 MHz) ultrasonic energy is transmitted into a component and the reflected signals from the defects are processed to generate an image. This technique is widely used in many industrial sectors such as nuclear [1], power generation [2] and transport [3].

Traditionally, single-element transducers have been used in ultrasonic testing methods, however in recent years 1D linear phased arrays have become more widespread. As ultrasonic phased arrays are essentially composed of many single-element transducers, they have the ability to speed up ultrasonic inspections dramatically and improve defect image resolution [4]. This is due to the fact that phased arrays have the added benefits of electronic beam steering, focusing and scanning [5] which are made possible by applying delay laws to individually addressable elements. However, phased array technology can be extended further with the inclusion of another dimension, and so by implementing the use of 2D phased arrays, it is possible to better characterise and size defects within components [6].This ability is important for inspections, as defects are 3D in reality and so can appear in arbitrary orientations.

Volumetric inspections using a 1D phased array have traditionally involved placing the array at multiple locations and stitching the resulting images together to reconstruct a 3D volume from a series of 2D slices [7], [8], or simply by probing the defect from different angles using a single-element transducer [9]. This makes for a challenging and time-consuming process with many limitations. These include the inability to focus in multiple dimensions, no ability to capture scattering in the reconstructed dimension, and the consequent potential for missing defects that are in unexpected positions or orientations. When using a 1D phased array, the orientation of the defect to the incident beam is crucial to defect detection. In some inspections the orientation of potential defects can be predicted, but in many cases the defect orientation cannot be anticipated and so multiple inspections at different orientations must be carried out. Data sets taken in full matrix capture (FMC) [10] format using 2D phased arrays excludes the need to align the incident beam to the defect as every point in the imaging region can be probed from any angle in post-processing.Using a 2D phased array also guarantees complete coverage of the imaging region (as long as the array and surface orientations are favourable) by steering and focusing the ultrasound beam throughout the 3D volume without moving the array, thus allowing a more detailed inspection [11]. 2D phased arrays have been taken up in medical ultrasound imaging [12], [13], but they have been slower to take off in industry, due in part to the cost and computational power required.

Imaging through doubly-curved surfaces, such as those found in pipework branches or nozzles, can be challenging when using a 1D phased array, due to the inability of this type of array to accommodate a surface that is curved in more than one direction. This is due to the element layout only permitting a single plane of elements to transmit and receive signals; however, due to the element layout of 2D phased arrays, beam steering is not limited to a single plane

45th Annual Review of Progress in Quantitative Nondestructive Evaluation, Volume 38AIP Conf. Proc. 2102, 100008-1–100008-9; https://doi.org/10.1063/1.5099836

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and so this type of phased array has the unique ability to focus through doubly-curved surfaces. It is important to correctly account for non-planar surfaces in order to maintain a high image quality [14]. There exist multiple methods to achieve ultrasonic coupling to the component when surfaces of this nature need to be inspected, such as using a wedge fitted to a specific surface profile [15], using a membrane-coupled device that moulds to the surface [16] orsubmersing the component in water and experimentally extracting the surface using an imaging algorithm [17].

In this paper, we investigate the effect of compensating for a doubly-curved surface on the ability to image and determine the ability to resolve a defect using a 2D phased array in immersion. The first crucial step in the imaging process is to correctly compensate for the surface profile. To investigate the effect of correct surface compensation on the resulting defect image, three different surfaces are compared: a fitted 2D planar surface, a planar surface parallel to the array and an experimentally extracted surface. The three surface compensation strategies are examined by using the Total Focusing Method (TFM) [10] to image a bottom-drilled hole (BDH) that is located directly below the surface of the specimen, which in turn is located directly underneath the array.

TEST SPECIMEN AND EXPERIMENTAL PROCEDURE

A sparse array with elements arranged in a Poisson disk formation has been demonstrated to outperform a matrix array with the same number of elements, as the non-periodic element layout prevents the formation of grating lobes, while still maintaining a high level of imaging resolution [6], and thus this type of 2D phased array is used. A description of the 3 MHz 128-element sparse 2D phased array used in this paper is given in Table 1. The longitudinalwavelength of ultrasound specific for this array and test specimen material, , is 2.1 mm, using an acoustic velocity of 6300 m/s and an array centre frequency of 3 MHz.

TABLE 1. 2D sparse array parameters.

Array Parameter ValueElement Count 128Element Shape Circular

Element Diameter 1.7 mmElement Pitch mm

Element Spacing 0.2 mmCenter Frequency 3 MHz

Bandwidth 5 MHz

To represent a doubly-curved surface geometry, an aluminium test specimen was manufactured with an axi-symmetric surface with a Gaussian profile, as shown in the side view in Figure 1(a). The test specimen has 4 electron discharge machining (EDM) notches at different depths and 21 BDHs of 3 mm diameter as shown in Figure 1(b).Each radial arm of BDHs is at a different depth below the surface. The maximum inclined region of the surface is at 45° to the horizontal. A picture of the test specimen and the 2D phased array used is shown in Figure 1(c).

As highlighted previously, the reason for choosing the surface of the test specimen was to represent a doubly-curved surface geometry. The only region imaged in this paper is highlighted by the yellow box in Figure 1(c). In order to image through the surface, the array is mounted above the surface of the test specimen which is directly above the defect highlighted in Figure 1(b), and then aligned parallel to the back wall of the specimen. This defect was chosen as it is below a portion of the surface with moderate curvature, which was found during preliminary testing to be at the upper limit of inclination which could be measured with the array in this configuration. The A-scan data iscaptured in FMC format with 20 averages then filtered and Hilbert transformed using a Gaussian window function centered at the array centre frequency using -40 dB at a half bandwidth equal to the array center frequency.

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(a) (b)

(c)

FIGURE 1. Illustrations of test specimen and defects with doubly-curved surface profile. (a) shows the side profile and defects, (b) shows the view of the base, and (c) shows a picture taken of the specimen next to the 2D phased array used and a 30 cm ruler

and a £1 coin for scale. Length and diameter dimensions are given in mm.

IMAGE PROCESSING METHODS

As different methods have been used to generate volumetric images, it is worth clarifying that a ‘true 3D’ method is described and implemented, in which one FMC dataset is obtained and a single 3D TFM image is produced without stacking or stitching 2D planes. It is important to note that a 2D array has been used to generate 3D TFM images in a previous study, however in this case the test specimen had a planar surface and there was no mention of a surface extraction method [18].

One of the paths used to calculate the minimum time of flight (ToF) between points , and in three dimensions is shown in Figure 2(a). The ray path follows an ultrasonic pulse emitted from element before being transmitted through the surface at position and travelling to point , where the signal is reflected and crosses the surface again at point before being received by element . Due to the different acoustic velocities in each medium, points and are found according to Fermat’s principle of least time.

TFM through an arbitrary surface in three dimensions using an immersion setup is achieved using a two-stage process detailed below.

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(a) (b)

FIGURE 2. Illustration of (a) single ray tracing using a 2D phased array in an immersion setup and (b) and planes through point . The velocity of sound in water is and the velocity of sound in the component is .

Stage 1: Surface Extraction

The method used here involves extracting the surface profile experimentally, so that corrections can be made when calculating the minimum ToF from each element to a point of interest in the component. One such ray path corresponding to a minimum ToF is shown in Figure 2(a). The first step to experimentally extract a surface is implementing a contact TFM algorithm using only the velocity of sound in water, . The intensity, ( ), at an arbitrary point in the imaging grid for each transmit-receive element combination is calculated using:( ) = , (1)

where the summation is over all transmitter, , and receiver, , combinations and , and are the position vectors of the transmitter, receiver and image point. , is the time-domain signal corresponding to transmitting from element and receiving on element . Linear interpretation of , ( ) is required as it is discrete at the sampling times. denotes the Euclidean norm of a vector and is the velocity of sound in water.

At this point, there is no reference made to the component under inspection and the strongest response in the TFM image is assumed to correspond to the location of the surface. Each ( , ) surface coordinate in the TFM image is examined and the maximum amplitudes that are above a specified threshold in each dimension are extracted and considered as surface reflections. The result is then an extracted surface composed of a finely discretised mesh of distances below the array.

Stage 2: Interior Imaging

Once the surface has been extracted successfully, a second set of ToFs are then calculated while compensating for the surface. For the case of the transmit ray, this is achieved by calculating the ToF from to all extracted surface points, and then calculating the ToF from all extracted surface points to point . The two ToFs corresponding to each individual surface point are then summed and the surface point corresponding to the shortest summed ToF is found, which represents the true ray path. The same logic applies to finding on the receive path. This is to ensure that each time-domain signal in the FMC is being queried at the correct position to contribute to the interior TFM image. By using this result, the intensity of the image, ( ), at any point in the imaging grid is calculated by summing over all

and combination: ( ) = , + + + (2)

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where and are the position vectors of surface-crossing locations, is the velocity of sound in aluminium and the remaining symbols are defined previously.

Due to the large amount of computationally-intensive calculations required in this process and the independent nature of ToF and TFM calculations, the parallel computing platform CUDA was used to provide speedup on the GPU. Once the 3D TFM image of the interior of the component has been obtained, 2D TFM images in the and planes at the maximum defect amplitude location can be obtained, as illustrated in Figure 2(b) for point , in order to determine the resolution of the defect.

SURFACE TYPES

A short description of how each of the three surface types are generated is given here. The surface points obtained in all cases create the assumed surface that ToF values are calculated through in Stage 2 of the imaging process described in the previous section.

1. Fitted 2D planar surface Surface points are extracted from the surface 3D TFM image and a linear regression is applied to the points to create a fitted 2D plane.

2. Surface parallel to the array The front wall standoff from the array is found from the pulse-echo A-scan from the central element in the array. All surface points are then assumed to have this constant value.

3. Experimentally extracted surface Surface points are extracted from the surface 3D TFM image with no assumption of the surface and no interpolation between points.

EXPERIMENTAL RESULTS

Throughout these results, we define resolution in a 2D plane as the half amplitude (6 dB drop) [19] measurement of the maximum amplitude of a defect. In all cases, the resolution of the surface grid is 0.4 mm (0.19 ) and theresolution of the interior imaging grid is 0.5 mm (0.24 ). The first surface case examined is the case of a fitted 2D planar surface. An isosurface of the extracted surface TFM is shown in Figure 3(a) in grey, with the black dots representing the assumed surface points. After focusing through these surface points, the resulting interior TFM isosurface is shown in Figure 3(d). For both the and imaging planes, the 2D TFM images are shown in Figure4(a)i and (a)ii, where the horizontal dashed white line represents the -location of the maximum defect amplitude and the colour bar is in dB. Figure 4(a)iii and (a)iv shows the amplitude variation along the dashed white line, with a –6dB drop from the maximum amplitude shown by the horizontal red line. The resolution is then taken as the difference in values corresponding to the length of the horizontal red line. The resolution of the defect for this surface case is 2.69 mm and 5.95 mm in the and planes respectively.

The next surface case considered is a surface parallel to the array, i.e. it is assumed there is no curvature or inclination of the front wall of the specimen relative to the array. The surface TFM image is shown in Figure 3(b) in grey and the assumed surface profile locations are shown by the black dots. The associated interior TFM image obtained from using this profile is shown in Figure 3(e). As in the last case, the and 2D TFM images are shown in Figure 4(b)i and (b)ii. The associated amplitude plots for each plane are then displayed in Figure 4 (b)iii and (b)iv, which show that the resolution of the defect is 2.77 mm and 4.47 mm in the and planes respectively.

The final surface considered is an experimentally extracted surface using the method described in the image processing section. The surface TFM image is shown in Figure 3(c) in grey and the assumed surface profile locations are shown by the black dots. For this case, the assumed surface is in the exact same location as the surface isosurface. The associated interior TFM image obtained from using this profile is shown in Figure 3(f), with the and 2DTFM images shown in Figure 4(c)i and 4(c)ii. From Figure 4(c)iii and (c)iv, the resolution of the defect is 2.70 mm and 2.70 mm in the and planes respectively.

In order to compare the resolutions obtained in each plane for all surface cases, Figure 5 is generated. The right -axis shows the resolution in terms of the wavelength of sound in aluminium, .

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(1)

Fitte

d 2D

pla

nar s

urfa

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(a) (d)

(2)

Surf

ace

para

llel t

o th

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ray

(b) (e)

(3)

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ext

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rface

(c) (f)

FIGURE 3. Results of the two-stage process used to image through an arbitrary surface in three dimensions. (a)-(c) are the results from Stage 1 where the TFM image of the surface is shown by the grey isosurface plotted at -12 dB relative to the

maximum amplitude in the surface. The black dots represent the mesh of surface point locations that are used in ToF calculations. (d)-(f) are the results from Stage 2, plotted as isosurfaces at -30 dB relative to the back wall, with the front wall shown in blue,

the defect in green and the back wall in yellow. (a) and (d) are the results obtained in the case of using a fitted 2D planar surface. (b) and (e) are the results obtained for the case using a surface parallel to the array, and (c) and (f) are the results obtained in the

case using an experimentally extracted surface.

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(1)

Fitte

d 2D

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(a)

(2)

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(b)

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FIGURE 4. Defect resolution analysis for the case of (a) a fitted 2D planar surface, (b) a surface parallel to the array and (c) an experimentally extracted surface. (i) and (ii) are 2D TFM slices in the and planes respectively where the horizontal dashed

white line represents the -location of the maximum defect amplitude and the colour bar is in dB. (iii) and (iv) show the amplitude variation along the dashed white line and the horizonal red line correspond to –6 dB below the maximum amplitude of

the defect. The resolution in each plane for each case is labelled in the top right corner.

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FIGURE 5. Comparison plot of the defect resolution obtained in each imaging plane along with the resolution in terms of .

DISCUSSION

Considering the 3D TFM images presented in Figure 3, it is clear that using an experimentally extracted surface produces the best results, as evidenced by the well-focused image of the BDH in the interior TFM image for this case, see Figure 3(f). For the remaining two surface cases, the defect is elongated due to de-focusing as a result of incorrect surface points used in the ToF calculations, but it is unclear which of these two surfaces produces the most unfocused image. There is not a high degree of surface curvature at this specific location, as evidenced by the surface TFM images in Figure 3 showing a distance of 4 mm in the -axis. The resolution of the defect in all cases is needed to quantitatively support these findings.

The 2D TFM images and resolution results for each case indicate that, in the plane, the extracted surface outperforms all other surfaces, as shown by the smallest resolution value obtained of the defect. The surface case with the next best resolution is obtained when the surface is assumed parallel to the array, as evident by a resolution value about 1.6 times larger in this plane than the extracted surface case. The surface that results in the worst resolution, and hence produces the most de-focused defect image out of the three surface cases in the plane, is the surface as a fitted 2D plane. For this case, the resolution is more than double that obtained in the extracted surface case.

The defect resolution in the plane, however, produces slightly different results from the plane. The case that results in the best resolution is when the surface is assumed to be a fitted 2D plane, and the surface that is assumed parallel to the array produces the worst resolution. From Figure 5, all resolutions in the plane are comparable and so overall in both planes, the extracted surface produced the smallest resolution results. Another feature evident when comparing surfaces is that the resolution in the plane remained relatively constant across all surfaces. This is due to the low surface curvature in this plane, whereas there was a much higher degree of curvature in the plane, as is reflected in the results.

Across all surface cases, it was expected that the fitted planar surface would perform second-best as this surface includes some inclination, but as this surface resulted in the worst overall resolution, it is implied that the defect must be located under the region of low inclination where the surface was predominately flat. These results confirm that using an extracted surface produces a well-focused defect image compared to the other surface types.

CONCLUSION

The challenge of imaging through a doubly-curved surface has been introduced and, in an attempt to accurately focus through a surface of this nature, a sparse 2D phased array was used to capture the data in FMC format and TFM was used as an imaging process. After considering three surface profiles, it has been found that an extracted surface outperforms other surface profiles and that incorrect surface compensation for these types of surfaces can lead to the

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de-focusing of a defect, which in this case was a BDH. As the surface location considered on the test specimen throughout this paper does not have a high degree of inclination in the and axis, it further reinforces the need for accurate surface compensation, as even a small surface inconsistency can lead to de-focused defect images.

Preliminary results suggest that compensation for a doubly-curved surface under inspection is an important factor in accurate defect imaging and sizing. Future work will address different defect types and assess the impact of surface compensation accuracy on imaging.

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