XVIII IMEKO WORLD CONGRESS

Metrology for a Sustainable Development

September, 17–22, 2006, Rio de Janeiro, Brazil

ULTRASOUND MICROSCOPY TECHNIQUES TO DETECT DELAMINATIONIN STACKED LAYERS

Stefan Johann Rupitsch1, Bernhard Gunther Zagar2

1Institute for Measurement Technology, Linz, Austria, stefan.rupitsch@jku.at2Institute for Measurement Technology, Linz, Austria, bernhard.zagar@jku.at

Abstract: We present the theory and some applica-tions of the synthetic aperture focusing technique appliedto single transducer ultrasonic data sets. In this tech-nique a virtual source located at the geometrical focalpoint of the physical transducer is algorithmically gen-erated and thus allows for tighter focusing over a geo-metrically larger scan volume. We present results froma structural test phantom (two copper wires) and a de-laminated specimen.

Keywords: ultrasound, synthetic aperture focusingtechnique, virtual source, B–mode imaging, delamina-tion.

1. INTRODUCTION

Ultrasonic imaging is widely used in the material test-ing where different scanning schemes are employed. Themain disadvantage of common B–mode imaging lies inthe depth dependent lateral resolution in the image. Thesynthetic aperture focusing technique (SAFT) overcomesthis principle limitation [1, 2]. The SAFT treats thetransducer’s focal point as a virtual source generatingspherical waves over a certain aperture angle. WithSAFT a depth–independent resolution within certainlimits (actually diffraction limited) is achieved theoreti-cally.

In this paper we use a transducer with a fixed focus,that is laterally displaced to yield structural informationof an object. Subsequently an off line SAFT–algorithmis applied to the already recorded echo–signals for eachscan line resulting in an enhanced B–mode image.

Experiments with a pair of 180 µm copper wires areperformed to evaluate the imaging quality of the syn-thetic aperture focusing technique. The wires wereplaced in the positive and negative defocus regions. Wepresent the applicability of preliminary experimentaldata for the location of delamination in stacked mate-rial layers. As a test specimen two transparent Perspexplates are stuck together and the adhesive joint is inves-tigated.

2. THEORETICAL DERIVATIONS

2.1. Principle of synthetic aperture imaging

with a virtual source element

The synthetic aperture technique considers the trans-ducers focal point as a virtual source (Fig. 1), whichis assumed to produce a pressure wave. Its pressurewave is spherical within a certain angular extend 2Θ andpropagates in both the forward and backward directionwith respect to the transducer. Displacing of the trans-ducer in positive or negative x–direction by sufficientlysmall increments ∆x cause an overlapping field gener-ated by the virtual sources, where the synthetic aper-ture focusing can be performed. One can see, that thedesired focal point P in Fig. 1 is exposed to the virtualsource’s fields at the lateral position x0 and xi = x0+i∆x(i = ±1,±2 . . .).

With the aim of evaluating the synthetic aperture fora desired focal point P all transducer echo signals fromdifferent lateral position xi, which cause a field in P aresummed up coherently. Due to the different transducerpositions and therefore different distances from the vir-tual sources to the desired focal point P time delays ∆tioccur. Note that these time delays need to be calculatedto obtain coherent summation. The time delay ∆ti isgiven by

∆ti =2 (di − d0)

csgn {z − z0} , (1)

where xi − x0 = i∆x denotes the lateral transducer dis-placement, c is the propagation velocity of the acousticwave, z0 stands for the geometrical focal depth of the ul-trasonic transducer, z is depth of the desired focal pointP , di describes the distance from the virtual source toP at the lateral position xi and d0 = abs (z − z0) is theaxial distance from point P to the virtual source. di canbe expressed as

di =

√

d20

+ (i∆x)2

. (2)

Fig. 1: Schematic of the synthetic aperture imagingusing a virtual source element

The signum function in Eq. 1 is necessary to distin-guish desired focal points P in the positive defocus re-gion (z − z0) > 0 from points in the negative defocusregion (z − z0) < 0.

SΣ (P ), the coherently summed signal for the desiredfocal point P can be calculated as

SΣ (P ) =

N∑

i=−N

αiS (tp + ∆ti, i) , (3)

where S (t, i) (common B–mode image, shown for exam-ple in Fig. 7) stands for the received two–dimensionallysampled echo signal from the lateral transducer positionsxi. tp = (2z)/c is twice of the time–of–flight of theacoustic wave in the propagation medium for the axialdistance z. αi is an apodization weight [3, 4] to suppressside lobes and is normally a function of the lateral dis-tance. In this study a simple boxcar function is used toachieve best lateral resolution and therefore αi = 1 ∀i.N in Eq. 3 refers to the received echo signals from lat-eral transducer positions, which contribute to the sumand depends on the lateral spacing ∆x of the transducerpositions, the aperture angle 2Θ and the axial distanced0 from the virtual source to the desired focal point. Thehalf aperture angle Θ is defined by Eq. 4 where 2a is theelement size of the transducer (Fig 1).

Θ = arcsin

(

a

z0

)

(4)

2.2. Lateral resolution of a spherically fo-

cused transducer

Until now it was assumed that the transducer focus ispoint like but strictly speaking it is really a focal volume

with finite extent.

The normalized lateral acoustic pressure distributionin cylindrical coordinates of a spherically focused trans-ducer in the focal plane (z = z0) can be expressed as

∣

∣

∣

∣

p (r)

p0

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

∣

2J1

(

kraz0

)

(

kraz0

)

∣

∣

∣

∣

∣

∣

, (5)

with the acoustic pressure p0 in the focal point (r =0) (Fig. 1) and the wave number k. p(r) denotes theacoustic pressure at distance r from the focal point in thefocal plane. The operator J1 (·) in Eq. 5 is the Bessel–function of the first kind of order one [5, 6].

From Eq. 5 the −3 dB–lateral beam width bwlat fortransmit only, which is equal to the −6 dB–lateral beamwidth for the transmit–receive mode (used in this study)of the ultrasonic transducer in the geometrical focalplane can be calculated as

bwlat = 1.028

(

λz0

2a

)

, (6)

with λ the acoustic wavelength.

3. MEASUREMENT SET–UP

In Fig. 2 one can see a schematics of the measurementset–up. The specimens are placed in a tank filled withdistilled and degassed water. The transducer (Panamet-rics V390) is spherically focused with a focal length z0 of12.8 mm, an element size 2a of 6.35 mm and an apertureangle Θ of 28.72◦ (Eq. 4). With the center frequencyfc = 44.52 MHz of the transducer, an acoustic wave-length of 33.2 µm is obtained and the −6 dB beam widthresults in bwlat = 68.9 µm (Eq. 6). The transducer is ex-cited by a pulse train generated by a Pulser/Receiver(Panametrics PR–5900), which operates in pulse/echomode. Received signals are digitized by a 2 GSample/soscilloscope (Tektronix TDS 744 A). The transducer istraversed in three dimensions with a translation unitdriven by a motor controller (Linos x.act CommanderST3). The x– and y–positions outlined in later measure-ment results are always related to the reference–positionof the translation unit. The whole measurement set–upis controlled by a 3.0 GHz–PC.

4. MEASUREMENT RESULTS AND DIS-

CUSSION

The general goal of the signal processing lies in obtain-ing as precisely as possible the correct lateral and axialposition of the targets as well as their dimension and itmight also be of interest to resolve internal structures.

4.1. Structural Resolution Test Target

With the aim to determine the ultimate resolutionof the current measurement system an impulse function

Fig. 2: Block diagram of the measurement set–up

mimicking target was devised [1, 3, 5]. It consists of twocopper wires with 180 µm diameter tapering off to anintersection. So an effective and well determined lateralspacing between 0.2 mm and 2.0 mm can be selected totest spatial resolution as shown in Fig. 2 schematically.The wires were placed in both positive defocus regionz − z0 ≈ 4.2 mm (Fig. 3) and negative defocus regionz − z0 ≈ −5.5 mm (Fig. 4). The transducer was dis-placed in x–direction (lateral) and the spacing betweenscan lines ∆x was set to 20 µm. 176 scan lines wererecorded with a sampling rate of 2 GSamples/s with 1621samples each.

The images in Fig. 3 and Fig. 4 are displayed as mag-nitude of the complex envelope SH of the raw data andSAFT–processed data respectively [7].

SH = |H (SO)| (7)

The operator H (·) in Eq. 7 stands for Hilbert–transformation, |·| is the absolute value, SO is the origi-nal data set and SH denotes the magnitude of the com-plex enveloped original data.

In order to extend the dynamic range in the printedimages a dynamic compression is performed by applyinga square root function normalized to the peak value ofcomplex enveloped data.

The true lateral spacings of the wires were 0.2 mm(Fig. 3[a,b] and Fig. 4[a,b]), 0.5 mm (Fig. 3[c,d] andFig. 4[c,d]), 1.0 mm (Fig. 3[e,f] and Fig. 4[e,f]) and2.0 mm (Fig. 3[g,h] and Fig. 4[g,h]). One can observetypical hyperbolically echoes due to the lateral scanningof the transducer caused by the wires being located out-side the transducer’s focal point, which is in a depth ofz0 = 12.8 mm. Figures 3[b,d,f,h] and Figures 4[b,d,f,h]on the other hand are the SAFT–processed data cor-responding to the respective raw data shown on theleft. Using the SAFT–algorithm no hyperbolic reflected

echoes from the wires occur anymore, which facilitate theexact localization of the two wires.

The non–ideal transducer spatial impulse responsecause second order diffraction effects which are clearlyvisible in the box A in Fig. 3[c]. Beside artifacts theyare still visible due to the square root compression in thebox B in Fig. 3[d].

Another interesting fact is observable in the images.The rear reflections of the wires are positioned exactlywere they geometrically are expected even though thelongitudinal acoustic wave propagation velocity in cop-per (cCu = 5010 m/s) is more than three times largerthan in water. This is attributed to a consequence of theBabinetsches–principle [8].

Figure 4 shows similar results for negative defocus re-gion. It is interesting to note that artifacts are less pro-nounced and less visible here. Additionally the secondorder diffraction effects caused by the non–ideal trans-ducer spatial impulse response are not observable in theraw data (left panels of Fig. 4) as well as in the SAFT–processed data (right panels of Fig. 4).

Furthermore faint echoes can be observed in the cop-per filled region. Their exact cause is to be investigatedfurther on.

4.2. Delamination in stacked Perspex plates

With the intention to prove the efficacy of SAFT–algorithm for localization of delamination areas two op-tical transparent Perspex plates with a dimension of20 × 20 × 4.75 mm3 were stuck together with a plas-tic glue. Due to the usage of transparent Perspex platesthe glued region, which is less than 0.2 mm in thicknesscan be investigated both acoustically and optically.

Figure 5 is an optical image of the region of interestof the two adherent Perspex plates. An acoustic im-age (Fig. 6) consisting of 121 × 121 points in x– andy–direction was performed for the section indicated asA in Fig. 5. The grid spacing between two adjacentscan points was 25 µm in each direction. The maxi-mum of the magnitude of the complex envelope of anA–scan was recorded with the oscilloscope and stored.The inadequately glued regions (delaminations), whichare usually accompanied by trapped air bubbles cause ahigher output–voltage of the pulser/receiver due to thelarge acoustic mismatch of Perspex and air.

In order to investigate the size and localization of theinadequately glued region a B–mode image at the fixedy–position of 56.4 mm (see Fig. 5 and Fig. 6) was gen-erated. 251 scan lines with a lateral spacing betweentwo adjacent scan lines of 10 µm were recorded with asampling rate of 2 GSample/s with 541 samples each.Again the magnitude of the complex envelope (Eq. 7) isvisualized in Fig. 7 as a contour–plot.

Figure 8 shows the result of the SAFT–processed rawdata of Fig. 7. Note that it is of prime importance to

dept

h (m

m)

(a)16.7

17

17.3 dept

h (m

m)

(b)16.7

17

17.3

dept

h (m

m)

(c)

A16.7

17

17.3 dept

h (m

m)

(d)

B16.7

17

17.3

dept

h (m

m)

(e)16.7

17

17.3 dept

h (m

m)

(f)16.7

17

17.3

lateral position (mm)

dept

h (m

m)

(g)

8.5 9 10 11 12

16.7

17

17.3

lateral position (mm)de

pth

(mm

)

(h)

8.5 9 10 11 12

16.7

17

17.3

Fig. 3: The left panels show raw data dynamically compressed to visualize even weak echoes and Hilbert–transformedto get a depth averaged image of the two copper wires tapering off with a lateral spacing of 0.2 mm [(a)], 0.5 mm[(c)], 1.0 mm [(e)] and 2.0 mm [(g)] respectively. In the right panels the corresponding SAFT–processed data are

shown, again dynamically compressed and Hilbert–transformed. All the images are for the positive defocus region.

dept

h (m

m)

(a)7.2

7.5

7.8 dept

h (m

m)

(b)7.2

7.5

7.8

dept

h (m

m)

(c)7.2

7.5

7.8 dept

h (m

m)

(d)7.2

7.5

7.8

dept

h (m

m)

(e)7.2

7.5

7.8 dept

h (m

m)

(f)7.2

7.5

7.8

lateral position (mm)

dept

h (m

m)

(g)

8.5 9 10 11 12

7.2

7.5

7.8

lateral position (mm)

dept

h (m

m)

(h)

8.5 9 10 11 12

7.2

7.5

7.8

Fig. 4: The left panels show raw data dynamically compressed to visualize even weak echoes and Hilbert–transformedto get a depth averaged image of the two copper wires tapering off with a lateral spacing of 0.2 mm [(a)], 0.5 mm[(c)], 1.0 mm [(e)] and 2.0 mm [(g)] respectively. In the right panels the corresponding SAFT–processed data are

shown, again dynamically compressed and Hilbert–transformed. All the images are for the negative defocus region.

x (mm)

y (m

m)

A

B−Scan

54 55 56 57 58 59

16

17

18

19

20

21

Fig. 5: Optical front view image of the region of interestof the two glued Perspex plates

y (mm)

x (m

m)

Pulser−Receiver Output−Voltage (mV)

← B−Scan

55 55.5 56 56.5 57 57.5 58

17

17.5

18

18.5

19

19.5 5

10

15

20

25

30

Fig. 6: Acoustic image of the zone A from Fig. 5(121× 121 points)

lateral position (mm)

dept

h (m

m)

Pulser−Receiver Output−Voltage (mV)

17 17.5 18 18.5 19 19.5

13.15

13.2

13.25

13.3

5

10

15

20

25

Fig. 7: Common B–mode image at the fixed y–position56.4 mm)

lateral position (mm)

dept

h (m

m)

SAFT−processed Voltage (mV)

17 17.5 18 18.5 19 19.5

13.15

13.2

13.25

13.3

5

10

15

20

25

Fig. 8: B–mode image after SAFT–processing of the rawdata from Fig. 7

17 17.5 18 18.5 19 19.50

10

20

30

40

x (mm)

Vol

tage

(m

V)

Pulser−Receiver Output−Voltage (mV)SAFT−processed Voltage (mV)

Fig. 9: Common B–mode image compared toSAFT–processed data at the fixed depth of 13.22 mm

take the different acoustic wave propagation velocity ofwater (cw = 1480 m/s) and Perspex (cp = 2700 m/s)into account to obtain the correct SAFT results.

In Fig. 9 one can see the common B–mode image andSAFT–processed image at the fixed depth of 13.22 mm.This is done with a view of comparing the common B–mode image and SAFT–processed image to the opticalimage. For common B–mode imaging a −6 dB objectsize of 0.54 mm is achieved. In contrast 0.66 mm is−6 dB object size obtained from SAFT–processed data,which is in a close agreement with the result from theoptical image. Using the optical image the extension ofthe inadequately glued region is 0.70 mm.

5. CONCLUSIONS AND FUTURE WORK

An approach to locate layer delamination was developed.The principle of ultrasound synthetic aperture imagingusing a virtual source element was applied. Experimentalresults were shown for a pair of 180 µm copper wires andtwo glued Perspex plates with inadequately glued regionsto demonstrate the efficacy of the SAFT–algorithm.

Currently the presented SAFT–algorithm is applicableto material science problems like detection and locationof layer delamination of printed circuit boards.

ACKNOWLEDGEMENTS

The authors greatly acknowledge the partial support ofthe research presented in this paper by the Linz Centerof Competence in Mechatronics (LCM).

REFERENCES

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