Ultrasonics 48 (2008) 636–642

Contents lists available at ScienceDirect

Ultrasonics

journal homepage: www.elsevier .com/locate /ul t ras

Advanced post-processing for scanned ultrasonic arrays: Application to defectdetection and classification in non-destructive evaluation

Caroline Holmes, Bruce W. Drinkwater *, Paul D. WilcoxDepartment of Mechanical Engineering, University of Bristol, University Walk, Bristol, UK

a r t i c l e i n f o

Article history:Available online 20 August 2008

Keywords:Phased arrayNon-destructive evaluationPost-processingUltrasonic imagingScanning

0041-624X/$ - see front matter � 2008 Elsevier B.V.doi:10.1016/j.ultras.2008.07.019

* Corresponding author. Tel.: +44 117 9289749; faxE-mail address: b.drinkwater@bristol.ac.uk (B.W. D

a b s t r a c t

This paper describes a number of array post-processing methods developed for scanning applications innon-destructive evaluation. The approach is to capture and process the full matrix of all transmit–receivetime-domain signals from the array. Post-processing the data in this way enables a multitude of imagingmodalities to be implemented, including many that could not feasibly be achieved using conventionalparallel firing techniques. The authors have previously published work on imaging algorithms forimproving the characterisation of defects in solids by post-processing the data from a static linear ultra-sonic array. These algorithms are extended and applied to data from a scanned array. This allows theeffective aperture and range of probing angles to be increased, hence improving imaging and defect char-acterisation performance. Practical implementation issues such as scanning speed and data transfer arediscussed.

� 2008 Elsevier B.V. All rights reserved.

1. Background

Ultrasonic arrays for non-destructive evaluation (NDE) are nowroutinely used in industry due to the flexibility that they provide[1–5]. However, they are often simply used as a replacement forone or more conventional monolithic transducers with their set-up and operation designed to emulate an existing testing proce-dure. Current array controller systems are designed with this inmind and are set-up to fire multiple elements with programmabletime-delays between them so that the physical wavefront injectedinto the test-piece is equivalent to that from a monolithic transmit-ter. The received signals from elements in the array are typicallyrecorded in parallel and then summed with appropriate time-de-lays to emulate the operation of an appropriate monolithic recei-ver. However, there is an increasing amount of work beingcarried out to investigate the improved use of arrays for non-destructive evaluation applications using, for example, inversewave field extrapolation from the seismic field [6], synthetic aper-ture focusing from the sonar and medical fields [7,8] and super-resolution techniques developed for radar [9].

The majority of arrays currently used for NDE are one-dimen-sional (1-D) and consist of a row of rectangular elements as shownin Fig. 1. Throughout this paper the Cartesian co-ordinate systemshown in this figure will be used. Here the array lies in the x–yplane and the normal or axial direction is parallel to the z-axisand a two-dimensional (2-D) image is produced in the x–z plane.

All rights reserved.

: +44 117 9294423.rinkwater).

The elements are relatively long in the y-direction, behavingapproximately as infinitely long strip sources. 2-D arrays are alsoavailable [10,11] but although they have found use in medicalapplications, have yet to be fully exploited for NDE. These arraystend to have square elements in a grid pattern and are used to im-age in three dimensions. As an alternative, 1.5-D arrays have beenused in NDE to reduce the numbers of elements relative to a fullypopulated 2-D array [12].

There has also been significant development of ultrasonic arraymaterials over the last 10 years. Recent developments have seenhave seen an increase in the use of piezocomposite materials[13], which are particularly useful in the manufacture of flexiblearrays [14,15] to allow testing of components with complex geom-etries [16].

In a static position a 1-D array can be used to produce linearswept B-scans or angular sweeps (Sector-scans) by firing a subsetof elements, termed the aperture. By mechanically scanning the ar-ray in the y-direction, it is therefore possible to produce 3-D volu-metric images of a component or C-scan images with a single pass.This type of array C-scanning is used in the aerospace industry[17], where there is a need to inspect large areas and in whichthe array offers a significant reduction in inspection time.

The work in this paper is focused on the use of 1-D arrays toscan parallel to the x-axis to increase the effective aperture andrange of probing angles of the array. Section 2 of the paper de-scribes an alternative to the standard method of array operation[1], which is based on obtaining raw time-domain signals fromall permutations of transmitter and receiver elements in the arrayand performing beam forming in post-processing. Section 3

Fig. 3. Schematic diagram illustrating vector notation.

Fig. 1. Definition of array geometry for 1-D array.

C. Holmes et al. / Ultrasonics 48 (2008) 636–642 637

describes the implementation of the algorithms for scanned arraysand finally Section 4 shows a number experimental results ob-tained and discusses the practical limitations of the FMC approach.

2. Full matrix capture and post-processing methods

In order to maximise the flexibility of array signal processing, asmuch information as possible should be extracted from an array.The complete data set from an n element array has a finite sizeand is an n � n matrix of time-domain signals from every possibletransmitter–receiver element combination. This is referred to asthe full matrix and the procedure for obtaining it is referred to asfull matrix capture (FMC). In fact, it is possible to capture onlyn=2ðnþ 1Þ time-domain signals due to the reciprocity of pitch–catch signals and this is termed the half matrix. All possible pro-cessing algorithms, including those obtainable via conventional ar-ray operation may be implemented by post-processing the fullmatrix, together with an almost unlimited host of others. If theperformance of FMC is compared to that of parallel transmission,it has been shown that although the signal to coherent noise ratiois identical, in the case of incoherent noise (e.g. electrical noise,ambient acoustic noise) the signal to noise performance of FMCis worse by a factor of

ffiffiffinp

[18]. This is a potential drawback ofFMC but it should be noted that it is rare for signal to incoherentnoise to be a limiting factor in NDE, as it can be improved as re-quired by averaging.

A schematic diagram of the data acquisition system is shown inFig. 2. The system comprises a commercial array controller (man-ufactured by Peak NDT Ltd., UK) which contains 64 parallel trans-mission channels and is capable of FMC using 16-bit digitisation. Adata acquisition interface written for Matlab (The Mathworks Inc.,USA) is used to control the system and capture data using a100baseT Ethernet connection. For the purposes of mechanical

Fig. 2. Schematic of data

scanning, a rotary encoder is used to measure the position of thearray and trigger the firing of the elements. The position of the ar-ray can be controlled manually or automatically with an xyz scan-ning frame.

A 32 element linear array with 5 MHz centre frequency (manu-factured by Imasonic, France) was used with element dimensions15 � 0.53 mm and the spacing between elements was 0.1 mmresulting in an element pitch of 0.63 mm. At the centre frequencyof 5 MHz the wavelength of bulk longitudinal waves in aluminiumis 1.26 mm, hence the element pitch is half the wavelength andgrating lobes are suppressed.

2.1. Total focusing method (TFM)

One possible imaging algorithm that can only be performedpractically by using FMC and post-processing is the total focusingmethod (TFM). This is a post-processing technique which uses allelements in the array to focus at every point in the image. TheTFM yields a scalar image, in which the array is focused in trans-mission and reception at every point in the field of view. A detaileddescription of the method can be found in Ref. [1] so only the finalequations are shown here. Consider a data set, g(i)j(t), of analytictime-domain signals (i.e. Hilbert transforms of the experimentallyobtained time-domain signals containing real and imaginary com-ponents in quadrature) from one or more array positions on thesame test-piece. The subscripts i and j refer to the indices of thetransmitter and receiver locations, respectively (for the specificcase of a data set from an array at one fixed position, these indicescorrespond to element indices in the array). Note that parenthesesaround a subscript indicate that the subscript is referring to atransmitter. The vector notation describing spatial positions isshown schematically in Fig. 3 for a 1-D linear array. The geometryis generalised such that the same imaging equations emerge forboth static and scanned arrays. Let r denote the position vectorof a point in the output image, e(i) be the position vector of theith transmitter and ej be the position vector of the jth receiver.

acquisition system.

638 C. Holmes et al. / Ultrasonics 48 (2008) 636–642

The uncorrected TFM image, I0(r,a), for data from a set of elements,a, that could be either the whole array or a sub-set of the whole ar-ray (i.e. an aperture) is [1,2]

I0ðr; aÞ ¼Xi;j2a

gðiÞ;j t ¼ 1cðjdðiÞj þ jdjjÞ

� �� ����������� ð1Þ

where d(i) = r �e(i) and dj = r �ej are vectors from the transmitterand receiver to the image point and c is the ultrasonic velocity inthe test-piece. In some cases, it is desirable for the TFM algorithmto be corrected so that reflectors of the same type (shape and size)will appear with the same amplitude regardless of their position inthe image. The corrected TFM image, Ic(r,a), is therefore defined as:

Icðr; aÞ ¼I0ðr; aÞCðr; aÞ ð2Þ

where C(r,a) is a correction factor can be calculated from the direc-tivity functions of each element, the beam spread and attenuation.At each point in the image C(r,a) represents the amplitude of signalthat would be expected in I0(r,a) if a point reflector existed at thatpoint. The element directivity functions can be obtained eitherexperimentally or by using appropriate models [19].

This post-processing algorithm has been quantitatively shownby the authors [1] to provide superior resolution and image qualityto any standard imaging approach. The TFM is also sometimes re-ferred to as the ‘‘gold standard” [20]. This is particularly the case inmedical imaging where FMC results in an unacceptably slow framerate due to the requirement to transmit on all elements separately.However, in medical imaging the TFM image is used as the bench-mark of image quality to which other algorithms containing fewertransmission cycles are compared. A number of experimentalresults obtained using FMC and TFM on a variety of engineeringspecimens of different materials, containing both real and artificialdefects have been published by the authors [21]. Recent work hasalso been carried out [22] to investigate the use of TFM to measurestrain in steel and composite structures using the correlation ofhigh resolution ultrasonic speckle images. Initial results haveshown that micron level displacements can be measured with anaxial resolution of the order of a few millimetres.

The TFM produces the optimal image of reflector intensity, butit does not provide further information on the nature of reflectors.The TFM is a linear imaging algorithm (i.e. image pixel intensity isa linear combination of contributions from transmitter–receiverpairs) and as such the resolution is diffraction limited. This meansthat the detail of small reflectors with wavelength order dimen-sions cannot be resolved. An enhancement to the TFM that ad-dresses this issue is described in the next section.

2.2. Vector total focusing method (VTFM)

The concept of the algorithm described in this section is thatvector rather then scalar images are generated. The underlying

Fig. 4. Schematic diagram indicating the o

procedure is therefore referred to as the vector total focusingmethod (VTFM). A detailed description of the VTFM can be foundin Refs. [2,17] so only a basic description will be given here. Theoperation of the VTFM can be described as follows with referenceto Fig. 4. An image area consisting of a finite grid of points is de-fined in front of the array. The array (static or scanned) is then sub-divided into N equi-sized sub-arrays (these may be overlapped)that act as different apertures. For the kth aperture and an imagepoint, r, a vector, v(k)(r), is calculated that has the direction point-ing from the image point to the centre of the aperture and the mag-nitude of the TFM image obtained from the aperture. These vectorsare then summed to generate a single vector, O(r) at each point:

OðrÞ ¼XN

k¼1

fvðkÞðrÞga( )1

a

ð3Þ

where a is a weighting parameter introduced to skew the sum to-wards the dominant vector. The notation {x}y is used to indicatethat the magnitude of vector x is raised to the power y while pre-serving the orientation of x. If a = 1 then Eq. (3) represents simplevector summation of v(k)(r) while if a =1 then Eq. (3) is equivalentto taking the vector from v(k)(r) with the maximum magnitude. Fi-nally the vector V(r) is forced to have an magnitude equal to theTFM image at that point:

VðrÞ ¼ OðrÞjOðrÞj I0ðrÞ ðif jOðrÞj > 0Þ ð4Þ

In this way the computation of the VTFM vector fields is a subset ofthe overall TFM computation for the whole array. Therefore, otherthan increased data storage, the VTFM does not require significantadditional computational resource beyond that required to performthe TFM. In the results presented in this paper, a sub-array size of 16elements and a step size of four elements were used.

3. Implementation of algorithms for scanned arrays

The motivation for applying the imaging algorithms to scannedarrays is either to increase the coverage, resolution or the defectcharacterisation performance of the inspection. In this case, the ar-ray is mechanically scanned in the x-direction and the FMC datacaptured at a predetermined scan pitch. This produces more datathan for a fixed array but can still be carried out at reasonablespeeds as shown in the following sections. It is also possible touse FMC in conjunction with the more common scanning tech-nique in which the array is moved parallel to the y-axis, in orderto produce high resolution, volumetric images of a target, but thatmethod is not described here.

There are two potential methods for capturing FMC data withlinear scanned arrays. The first option, referred to subsequentlyas Method 1, is to scan parallel to the x-axis setting an arbitraryscan pitch as shown in Fig. 5a. In this case, the array is moved by

peration of the basic VTFM algorithm.

Fig. 5. (a) Possible array positions and (b) time-domain matrices obtained for the matrix for a Method 1 scan with an arbitrary pitch. (c) Possible array positions and (d) time-domain matrix for a Method 2 scan with pitch equal to element pitch.

C. Holmes et al. / Ultrasonics 48 (2008) 636–642 639

a fixed distance and at each step the full (or half) matrix is capturedfor processing. This concept is shown schematically in Fig. 5b. Thisapproach generates a large amount of data; for example, a 32 ele-ment array scanned over 50 mm using a 1 mm pitch generates26,400 time-domain signals. Also, because the scan pitch and arrayelement pitch are independent, it is not immediately clear howbest to process the data from the multiple separate half-matricesthat are generated. For example, the TFM could be applied to thedata from all the matrices and modifying the element locationsaccording to the scan position. However, it should be noted thatthe effective element pitch in the extended array may not be uni-form due to the overlapping contributions from different scan posi-tions of the original array.

An alternative approach, referred to subsequently as Method 2,is to set the scan pitch to be equal to the array element pitch asshown in Fig. 5c. This automatically enables a single matrix of datato be generated for the complete scan, which is referred to as theeffective matrix. In this case, at the start of the scan, the half matrixis captured from the first array position and used to populate ann � n region in the top left corner of the effective matrix. At thenext (and each subsequent) step, only the end element in the arrayis fired, but the n time-domain signals from all receivers are re-corded. This provides the data necessary to populate the n + 1thcolumn from row 2 to row n + 1 (and by symmetry the same ele-ments in the n + 1th row) in the effective matrix as shown sche-matically in Fig. 5d. Method 2 generates an order of n fewertime-domain signals than Method 1. For example, a 32 element ar-ray with 0.63 mm element pitch scanned over 50 mm, with a scanpitch equal to the element pitch produces 3024 time traces. Thisshould be compared with 26,400 time-traces with Method 1 and

Fig. 6. Photograph of steel specimen wit

it should also be noted that the scan pitch in Method 2 is actuallyfiner. Thus, to summarize, Method 2 produces significantly fewertime traces with a finer scan path compared to Method 1.

The second advantage of Method 2 is that the data in the effec-tive matrix can be processed exactly as if it was the data from a sin-gle array, and there is no longer the potential problem of unevenelement distributions associated with Method 1. However, itshould be stressed that the scanned array does not offer the sameresolution as one large array spanning the scan length, althoughthe effective matrix for the former is the same size as the full ma-trix for the latter. Elements more than n elements from the leadingdiagonal are missing in the effective matrix for the scanned array,because it is not possible to have a transmitter and receiver pairseparated by more than the physical array length. This can be seenin Fig. 5d.

4. Experimental results

A steel block, shown in Fig. 6 (courtesy of RWE npower, UK)with 5 mm diameter side drilled holes was used to compare theimage quality of both a fixed and mechanically scanned array.Fig. 7a shows an 80 mm by 100 mm TFM image obtained by fixingthe array at the centre of the block as shown and capturing the fullmatrix of time-domain data at a sampling frequency of 25 MHz(the system minimum) with 16 averages to improve the signal tonoise ratio. This image was produced (including data capture andprocessing) in 65 s with a standard desktop PC. It is possible toachieve much faster processing times with 64 bit or parallelprocessing systems. It is clearly possible to distinguish each ofthe side drilled holes in the image, although there is some blurring

h 5 mm diameter side drilled holes.

Fig. 7. TFM images (40 dB scale) from steel test specimen using 32 element array. (a) Fixed array with 16 averages and (b) scanned array a distance of 100 mm acrossspecimen. Imaged area is 100 mm � 80 mm in both cases.

Fig. 9. VTFM results from (a) fixed array (b) array scanned 50 mm across surface.

640 C. Holmes et al. / Ultrasonics 48 (2008) 636–642

at higher steering angles. It can also be seen that the back face ofthe block is not visible in the image outside the width of the array.This is due to the fact that at large steering angles, no paths existbetween array elements for reflections from the back face.

For comparison, Fig. 7b shows the TFM image obtained by scan-ning the same array 100 mm across the surface of the specimenusing Method 2 and taking 400 s to complete. It can be seen thatthe holes are now clearly distinguishable from one another andthe back face signal is extended throughout. It can also be notedthat the relative amplitude of the holes to the back face has in-creased. In both this and the previous image, some ghost artefactscan be seen just behind the main through hole images which arethought to be due to secondary reflections from between neigh-bouring holes.

Scanning experiments (50 mm scan using Method 2) were alsocarried out on a 50 mm deep aluminium test block with a numberof 1 mm � 0.25 mm angular slots as shown in Fig. 8. The slots are20 mm from the array surface. This specimen was used to demon-strate the VTFM method in a different publication [18]. Fig. 9shows the VTFM images obtained from three of the slots angled0�, 15� and 30�, respectively. The TFM image of the slots is alsoplotted. It can be seen that in each case, the slot orientation is de-tected by the VTFM vectors.

4.1. Practical implementation issues

The maximum scan speed that can ever be achieved is ulti-mately limited by the maximum physical pulse repetition fre-quency (PRF), fmax, that can be used in the object under test,before reverberations from one pulse interfere with the signal fromthe next one. This limits the rate at which successive transmissioncycles can be performed. If scanning using Method 1 at a pitch, p(1),the number of transmission cycles required per scan point is nsince each element in the array must be fired separately at each

Fig. 8. Aluminium specimen with a number of angled defects introduced usingEDM machining.

scan point. The maximum scan speed, sð1Þmax, in this case is thereforegiven by

sð1Þmax ¼fmaxpð1Þ

n: ð5Þ

For a Method 2 scan only one transmission cycle is needed at eachscan position (after the initial position) and the maximum scanspeed, sð2Þmax, for an array element pitch p(2) is given by

sð2Þmax ¼ fmaxpð2Þ: ð6Þ

The PRFs used in conventional ultrasonic testing are typically1–20 kHz. Using the array and scan parameters from the experi-mental examples presented earlier and with a low PRF of 1 kHz im-plies maximum scan speeds of 31 mm s�1 and 630 mm s�1 forMethods 1 and 2, respectively. In the case of Method 2 this is 1–2orders of magnitude faster than that which can be achieved exper-imentally. The reason why the experimental scan speed is currentlyso much lower than the theoretical maximum is due to limitationson the rate of data transfer, both within the array controller itselfand between array controller and PC. For this reason it is instructiveto examine the amount of data generated during FMC and the effectof a restricted data transfer rate on both the static FMC frame rateand the FMC scanning speed.

4.2. Static array

The number of bytes, D, of data in a single frame of FMC data is

D ¼ Nbn2; ð7Þ

C. Holmes et al. / Ultrasonics 48 (2008) 636–642 641

where N is the number of points per time trace and b is the numberof bytes per point (i.e. 1 bytes for 8 bit data and generally 2 bytes for8 + to 16 bit data). As noted previously, reciprocity can be used toreduce the amount of data by a factor of almost two if half matrixcapture is performed in which case:

D ¼ 12

Nbnðnþ 1Þ: ð8Þ

To give some idea of the numbers involved, a 32 element array pro-ducing 2000 point time-traces sampled using a 16 bit digitiser willgenerate 2.112 Mbytes of data per frame of half matrix data.

If the data transfer rate is limited to dmax bytes per second thenthe maximum achievable frame rate, Fmax, is given by

Fmax ¼dmax

D: ð9Þ

Since both full and half matrix capture require n transmission cy-cles, an effective maximum PRF, feff, can be calculated:

feff ¼ Fmaxn: ð10Þ

In the experimental system used here, the connection between ar-ray controller and PC is via a 100baseT Ethernet connection witha maximum transfer rate of 100 Mbits per second (or 12.5 Mbytesper second), implying a maximum frame rate of 5.92 Hz and aneffective maximum PRF of 189 Hz. This is around an order of mag-nitude lower than the typical physical limit on maximum PRF dis-cussed earlier. Nonetheless, if an imaging frame rate of 5.92 Hzcould actually be achieved it would be satisfactory for many manualinspection purposes as it permits a reasonable degree of interactionbetween an operator manipulating an array and the image pro-duced. Currently this has not been achieved for two reasons. Firstly,the actual data transfer rate obtained is somewhat lower than the100 Mbits s�1 implied by the 100baseT connection due to over-heads in the data transfer protocol and limitations in the Matlabinterface to the connection. Much more importantly, the currentimplementation of the TFM in the Matlab environment is not opti-mised in any way, and takes around 60 s to produce one imageframe. Work is ongoing to improve this.

4.3. Scanned array

When scanning with Method 2, the amount of data in bytes, D,required at each incremental scan position (i.e. excluding the firstwhere FMC must be performed) is

D ¼ Nbn: ð11Þ

Following the same procedure as described previously indicates aneffective maximum PRF of 98 Hz and a scan speed of 62 mm s�1.

Fig. 10. (a) Range-Doppler image of aluminium block shown in Fig. 8 (

This is now a similar order of magnitude but still considerably high-er than the 10 mm s�1 achieved experimentally and indicates thedegree of extra constraints on data transfer somewhere in thesystem.

4.4. Alternative acquisition and processing strategies

Within the limitations of the current system, it is possible tospeed up the imaging process but at the cost of some resolution.For example, a single transmission, multiple reception version ofthe TFM in which focusing is only applied in reception can beimplemented. This increases speed dramatically at the cost of sig-nal to coherent noise ratio as focussing is only carried out in recep-tion. Alternatively the pulse-echo data (i.e. the diagonal terms ofthe full matrix) can be processed using methods adopted for syn-thetic aperture sonar (SAS). One typical SAS approach is theRange–Doppler algorithm [23] which operates on pulse-echo data,denoted g(i)i(x,t) using the following steps:

hðiÞiðkx; tÞ ¼ FFT½gðiÞiðx; tÞ�; ð12Þ

h0ðiÞiðkx; zÞ ¼ hðiÞi kx;ct2

2� 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� ðkx=2kÞ2

q0B@

1CA

0B@

1CA; ð13Þ

Iðx; zÞ ¼ FFT�1½Qðkx; zÞ:h0ðiÞiðkx; zÞ�; ð14Þ

where FFT and FFT�1 are forward and inverse spatial Fast FourierTransforms (i.e. converting between x and the spatial wavenumber,kx) and the function Q is given by

Qðkx; zÞ ¼ exp izðffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4k2 � k2

x

q� 2kÞ

� �; ð15Þ

where k = x/c and i=ffiffiffiffiffiffiffi�1p

It can be seen from Eqs. (12)–(15) that theRange–Doppler algorithm is a manipulation in the spatial wave-number domain. This approach was implemented for a 64 elementarray with the same frequency, element pitch and width as de-scribed previously on the specimen shown in Fig. 8. Fig. 10 showsthe result of the Range–Doppler algorithm compared to a TFM im-age (using the full matrix of data). It is interesting to note that bothalgorithms produce similar images. However, the processing timetaken to produce the Range–Doppler image was 0.6 s as opposedto 45 s for the TFM image indicating that the post-processing timeis an area in which significant speed improvements are achievable.For this example the extra data used in the TFM image does not sig-nificantly improve the scalar imaging performance meaning thatprocessing speed can be dramatically improved with little loss inresolution. However, the VTFM approach, by definition, requires

40 dB scale) and (b) TFM image of aluminium block (40 dB scale).

642 C. Holmes et al. / Ultrasonics 48 (2008) 636–642

that the defect is illuminated from a range of angles and so thisnecessitates the use of the full matrix of data.

5. Conclusions

A number of post-processing techniques which exploit the fullmatrix of time-domain signals from an array have been discussedand implemented using a commercial array controller. A completeMatlab interface for data acquisition has been developed andexperimental results from a static and mechanically scanned arrayhave been compared and discussed. Although static dataacquisition (FMC) can be performed fairly rapidly at around 1 sper frame, the limitation of the system has been shown to be inthe speed of the post-processing (currently around 60 s). Forscanned arrays, the current data acquisition rate results in amaximum scanning speed of 10 mm s�1, which is acceptable foracademic and industrial research use. The TFM as currently imple-mented cannot be performed in real time, which prevents its use inan interactive manual mode. One option under investigation toincrease the speed of the TFM processing is to implement the algo-rithms in the array controller internal architecture, although thisrequires a significant amount of further work.

It has been shown that the TFM image using a scanned arraygives significant improvement in resolution outside the lateralrange of the array and therefore potentially improves the probabil-ity of detecting defects in these locations. It is also clear that usinga scanned array effectively increases the range of angles overwhich each point in the image is probed and therefore improvesresults for the VTFM approach. To date these algorithms have beenused to produce visual images of test-pieces but the long-term goalis to use the data to classify and size defects automatically. This‘automatic’ defect classification forms the basis for future workon FMC and the TFM processing technique.

Acknowledgements

The authors would like to acknowledge Prof. Peter Gough,Department of Electrical Engineering, University of Canterbury,New Zealand, for his help with the implementation of theRange–Doppler algorithm. This work was supported throughEPSRC Grants GP/C534824/1 and GR/S09388/01.

References

[1] C. Holmes, B.W. Drinkwater, P.D. Wilcox, Post-processing of the full matrix ofultrasonic transmit–receive array data for non-destructive evaluation, NDTand E International 38 (8) (2005) 701–711.

[2] P.D. Wilcox, C. Holmes, B.W. Drinkwater, Advanced reflector characterisationwith ultrasonic phased arrays in NDE applications, IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control 54 (4) (2007) 1541–1550.

[3] S. Mahaut, O. Roy, C. Beroni, B. Rotter, Development of phased array techniquesto improve characterisation of defect located in a component of complexgeometry, Ultrasonics 40 (8) (2002) 165–169.

[4] S.J. Song, H.J. Shin, Y.H. Jang, Development of an ultra sonic phased arraysystem for nondestructive tests of nuclear power plant components, NuclearEngineering and Design 214 (1–2) (2002) 151–161.

[5] P. Crowther, Practical experience of phased array technology for power stationapplications, Insight 46 (9) (2004) 525–528.

[6] N. Portzgen, D. Gisolf, G. Blacquiere, Inverse wave field extrapolation: adifferent NDI approach to imaging defects, IEEE Transactions on UltrasonicsFerroelectrics and Frequency Control 54 (1) (2007) 118–127.

[7] L. Von Bernus, A. Bulavinov, M. Dalichow, D. Joneit, M. Kroning, K.M. Reddy,Sampling phased array – a new technique for signal processing and ultrasonicimaging, Insight 48 (9) (2006) 545–549.

[8] J. Davies, P. Cawley, The application of synthetically focused imagingtechniques for high resolution guided wave pipe inspection, in: D.O.Thompson, D.E. Chimenti (Eds.), Review of Progress in Quantitative Non-destructive Evaluation, vol. 26, American Institute of Physics, Portland Oregon,USA, 2007, pp. 681–688.

[9] F. Simonetti, Localization of pointlike scatterers in solids with subwavelengthresolution, Applied Physics Letters 89 (2006) 094105.

[10] Y. Mendelsohn, E. Wiener-Avnear, Simulations of circular 2-D phase-arrayultrasonic imaging transducers, Ultrasonics 39 (9) (2002) 657–666.

[11] O. Martinez, M. Akhnak, L.G. Ullate, F. Montero De Espinosa, A small 2-Dultrasonic array for NDT applications, NDT and E International 36 (1) (2003)57–63.

[12] D.G. Wildes, R.Y. Chiao, C.M.W. Daft, K.W. Rigby, L.S. Smith, K.E. Thomenius,Elevation performance of 12.5-D and 1.5-D transducer arrays, IEEETransactions on Ultrasonics Ferroelectrics and Frequency Control 44 (5)(1997) 1027–1037.

[13] S. Gebhardt, A. Schönecher, R. Steinhausen, W. Seifert, H. Beige, Quasistatic anddynamic properties of 1–3 composites made by soft molding, Journal of theEuropean Ceramic Society 23 (1) (2003) 153–159.

[14] D.J. Powell, G. Hayward, Flexible ultrasonic transducer arrays fornondestructive evaluation applications. 2. Performance assessment ofdifferent array configurations, IEEE Transactions on Ultrasonics Ferroelectricsand Frequency Control 43 (3) (1996) 393–402.

[15] S. Chatillon, G. Cattiaux, M. Serre, O. Roy, Ultrasonic non-destructive testing ofpieces of complex geometry with a flexible phased array transducer,Ultrasonics 38 (1–8) (2000) 131–134.

[16] M. Spies, Efficient optimization of single and multiple element transducers forthe inspection of complex-shaped components, NDT and E International 37 (6)(2004) 455–459.

[17] R.J. Freemantle, N. Hankinson, C.J. Brotherhood, Rapid phased array ultrasonicimaging of large area composite aerospace structures, Insight 47 (3) (2005)129–132.

[18] P.D. Wilcox, C. Holmes, B.W. Drinkwater, Exploiting the full data set fromultrasonic arrays by post-processing, in: D.O. Thompson, D.E. Chimenti (Eds.),Review of Progress in Quantitative Non-destructive Evaluation, vol. 25,American Institute of Physics, Brunswick, Maine, USA, 2005, pp. 845–852.

[19] G.F. Miller, H. Pursey, The field and radiation impedance of mechanicalradiators on the free surface of a semi-infinite isotropic solid, Proceedings ofthe Royal Society of London Series A—Mathematical and Physical Sciences 223(1155) (1954) 521–541.

[20] O. Oralkan, S. Ergun, J.A. Johnson, M. Karaman, U. Demirci, K. Kaviani, T.H. Lee,B.T. Khuri-Yakub, Capacitive micromachined ultrasonic transducers: next-generation arrays for acoustic imaging?, IEEE Transactions on Ultrasonics,Ferroelectrics, and Frequency Control 49 (11) (2002) 1596–1610.

[21] C. Holmes, B.W. Drinkwater, P.D. Wilcox, The post-processing of ultrasonicarray data using the total focusing method, Insight 46 (11) (2004) 677–680.

[22] A.I. Bowler, B. Drinkwater, P. Wilcox, Feasibility of using ultrasonic arrayimages for mapping strain in engineering components, in: D.O. Thompson,D.E. Chimenti (Eds.), Review of Progress in Quantitative Non-destructiveEvaluation, vol. 27, American Institute of Physics, Golden Colorado, USA, 2007,pp. 648–655.

[23] P.T. Gough, D.W. Hawkins, Unified framework for modern synthetic apertureimaging algorithms, International Journal of Imaging Systems and Technology8 (4) (1997) 343–358.