A practical ultrasound axicon for non-destructive testing

A practical ultrasound axicon for non-destructive testing S. NAGAI

and K. IIZUKA

A practical water-coupled ultrasound axicon has been developed, which is realized by a combination of an annular PZT and a conical plexiglass wedge bonded to it. The acoustic beam from the PZT is refracted by the wedge and focused over a certain range in the axial direction. Two kinds of axicon are prepared for flaw examination of metals or ceramics. Suppression of the surface echo and sidelobes is discussed. Some examples which show the abilities of the axicons are also presented. KEYWORDS:

ultrasonic

testing, axicons,

flaw characterization

Introduction With the development of new structure materials, an improvement of nondestructive testing, for which ultrasound is an important tool, is urgently required. Accurate methods are necessary to provide quantitative information about the size, shape and location of defects. The critical flaw sizes which lead to failure during service depend on the fracture toughness of the material. According to Tittmanni the critical sizes range, for example, from 1 to 27.5 mm for steel and from 0.02 to 0.05 mm for siliconnitride.

N

One problem associated with an ordinary ultrasonic transducer is its poor lateral resolution. This is due to its nonfocusing properties. Lateral resolution is improved by means of a focused transducer but this, unfortunately, gives a small depth of focus - only near the focal point is the acoustic beam convergent. However, an axicon focuses the acoustic beam over a certain range of depth? An ultrasound axicon was realized by Burckhardt3.’ but the device proposed by him is complicated and not to be easily applied to NDT'. In this paper we present a practical axicon transducer compatible with standard ultrasonic NDT equipment, with which a quantitative evaluation of the size, shape and location of small flaws is enabled. The capabilities of the developed axicon are shown by some preliminary experiments. Design of the ultrasound

\

axicon

\

The principle of a water-coupled axicon is illustrated schematically in Fig. 1. The acoustic ray from any zone of

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f \\‘I’

The authors are at the Mechanical Metrology Division, National Research Laboratory of Metrology, Sakura-Mura, lbaraki 305, Japan. Paper received 8 October 1981.

0041-624X/82/060265-06/$03.00

Test object

0 1982

I

Fig. 1

Schematic

Butterworth

view of an ultrasound

& Co. (Publishers)

axicon

Ltd 265

constant radius in a conical transducer intersects the axis in phase. Over a certain range in the axial direction one thus observes a high-intensity line. In addition to a large depth of focus, the developed axicon has several features. One is related to the spatial resolution. A shear wave is employed to improve the resolution, which increases by approximately a factor of 2 compared to a longitudinal wave. Accordingly an incident angle (Yfor test objects is chosen just above the critical angle for the longitudinal wave. It is well known that at this angle the echo signal reaches a maximum value, provided the acoustic beam is reflected completely along its incident path in the material.6 Another feature is a decrease of the effects of the reflected wave at the surface. As evident in Fig. 1, the reflected wave passes through a central hole region, making the inspection of near-surface flaws possible.

where a cylindrical coordinate system @,f3, z) is introduced with its origin at the centre of the transducer. The z-axis is chosen so as to coincide with the line of focus. The distance from the origin to the observation plane, where another

The detailed construction of the actual axicon is shown in Fig. 2. Since a conical transducer is not easily obtainable, we adopted an alternative fabrication method. The axicon consists of an annular PZT ceramic and a conical wedge machined from plexiglass. The acoustic wave from the PZT is refracted by the wedge and radiated into water. The greater part of the reflected wave at the surface of test objects is absorbed with glass fibre reinforced plastics placed at the centre of the transducer. Two kinds of transducer were prepared. One is used for the inspection of metals such as steel or aluminium, another is for siliconnitride. Characteristic values of the axicons are listed in Table 1. We shall hereafter call these axicons A and B for brevity. The axial beam pattern measured in water is presented in Fig. 3. The rounded tip of a 0.3 mm diameter steel rod was used as a reflector. Axicons A and B give adequate focusing over a range of 15 to 30 mm or 40 to 100 mm, respectively. These values are in good accordance with geometrical ray tracing. The beam pattern p(r) is written in a Fresnel approximation as7 (Fig. 4) Electrical connector

-

Fig.3 Beam Pattern of the axicons. The distance is measured from the case surface toward water: a - axicon A; b - axicon 6. P,@)

Case

-Insulator

1

f

Fig. 2

266

Axicon

structure

-

Backtng

-

PZT ceramic

-

ConIcal wedge

Axlcon

\

Geometry for beam pattern calculation. An axicon centred Fig. 4 at the origin of a cylindrical coordinate produces the acoustic field at the observation plane, A hatched area shows the first Fresnel zone

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Table 1.

Characteristic values of the axicons

Transducer code

Frequency

A

10

[MHz1

5

B

inner and outer radius of PZT [mm]

Incident angle [degrees]

Focusing range* [mm1

Test object and its lonaitudinal critical angle

5 10

17

15

Steel (15’) Aluminium

187

IO

60

Silicon nitride (7’)

(14O)

*values in water

I

b W _

0.1

t I

01 10

I

I

20

a

Dlstonce

I

I

30 [mm]

e r 0.4 m t Q w 0.1

a

r [mm]

F

1

0111111

40

b 6 dB beamwidth Fig. 6 b - axicon B.

60 Distance

as a function

80 [mm1

100

of the distance: a - axicon A;

radial coordinate (r, x) is adopted, is L. .I,, expresses the Bessel function of the first kind. The incident angle (Yis assumed to be small. In (1) the main contribution to the integral comes from the vicinity where the phase is stationary. The stationary points are the ones which satisfy the relation p = CYL,which we put as PF. If the acoustic ray radiated from the ring with a radius PF alone contributes to image formation, (1) reduces to P(r) = C’J,(c&r)

(2)

The experimental and theoretical beam patterns are shown in Fig. 5. The measured main lobes correlate well with theory. The 6 dB width & is derived from (2) as Ar = 2

b

?

r [mm]

Fig. 5 Comparison of the experimental and theoretical beam patterns. The solid lines indicateexperimental curves, the dotted lines the theoretical curves: a - axicon A, curve measured at 24 mm; b - axicon B, curve measured at 75 mm

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(3)

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Equation (3) indicates that the beam width is constant regardless of distance, which is confirmed in Fig. 6, though axicon B shows a slight increase. The measured width of axicon A is broader than expected from (3). This is attributed to the fact that the diameter of the rod is close to the

267

width. The lateral resolution Ax and depth of focus AZ for a focused transducer are written as

tral bandwidth, sidelobes whose positions are dependent on the wavelength are smeared out. Experimentally the pulse duration is 0.3 PS for axicon A and 1.5 PS for axicon B. The reason for different pulse durations is as yet unknown. Thus the pulsed nature of the acoustic wave effectively decreases the sidelobes of both the axicons. These two effects explain smaller sidelobes than (2) predicts.

(4) where F is the focal length and D the diameter of the transducer. In consequence, a resolution of 0.2 mm at 10 MHz is accomplished at the expense of a severely limited 0.5 mm depth of focus.

Application

Examination of Figs 3 and 5 revea& that, with the developed axicons, the sidelobe level is generally smaller than (2) predicts by up to about 20 dB. As the ultrasound axicon has a larger wavelength than the optical axicon, the first Fresnel zone centred on the radius &? has a finite area and its contribution should be taken into account for image formation. From numerical analysis of(l), sidelobe suppression for axicon A is expected to be 2 dB and for axicon B, 6 dB. Another effect arises from the fact that a pulsed wave is used. Since the pulsed wave has some spec-

An experimental set-up is a conventional pulse-echo C-scan apparatus, as shown in Fig. 7. In automatic data acquisition mode, a two-dimensional map of a test object is obtained. The axicon is scanned in an x-y raster by means of two stepping motors. The step size is 0.2 mm in each direction and the total scan is 200 x 200 points. The peak value of the gated echo signal is 8 bits, after analogue-to-digital conversion, which is stored in a microcomputer. Final results are displayed on an x-y plotter.

x Input Pulse repetltton

clock

x-y Scan controller

l

y Input

z Input

Experimental

Dsplay

c

slgnal

set-up fer C-scan

3

4

5

6 Depth

Fig. 8 Flaw echoes from 1 mm diameter holes in an aluminium and the top of the holes. The peak value is normalized to unity

260

l

bath

0 2

b Micro-computer

Echo

Fig. 7

*

I

1

Water

of the axicon

/

[mm 1

plate with axicon A. The depth indicates the distance between the surface

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Figure 8 shows the flaw echoes from 1 mmdiameter holes drilled from the bottom in an aluminium plate. The halfwidth of the echoes remains about 1 mm over a depth change of 9 mm. The hole 1 mm deep is also discernible, though it is obscured by the surface echo. Figure 9 is a two-dimensional image of 0.3 mm slots in an aluminium plate. This and the images shown hereafter are displayed after the smoothing process which consists of taking an appropriately weighted average of adjacent 5 x 5 picture elements to reduce the effects of the sidelobes. The flaw size can be estimated from the half-width instead of the echo amplitude.

Conclusions Practical ultrasound axicons have been developed which may be used to detect and characterize small flaws in slabs. Their abilities are analysed in terms of lateral resolution, sidelobe level and range of focusing. A good agreement has been found between experimental results and theoretical predictions. The axicons have been applied to flaw characterization of artificial cracks, solid inclusions and laminar flaws. The experimental results show that ultimate resolution to about 0.1 mm can be attained.

Figure 10 presents an image of artificial solid inclusions in a silicon-nitride plate. Though rather obscure, a 0.09 mmdiameter aluminium wire is detected. Figure 11 is a C-scan image of laminar flaws in 3-ply plexiglass. Each layer is 10 mm in thickness. Two interplies contain some laminar flaws. These flaws are clearly detected on account of large depth of focus. The obtained images agree well with a visual check of the test object.

8

7

0.09 mm drometer wrre

0jmm drameter

wire

43 mm

/

/ \ 0.09 mm drameter wire

1

2

3

4

5

6

Fig. 9 Isometric image of 0.3 mm-wide plate with axicon A

7

8

9

slots in an aluminium

a

Fig. 10 Isometric image of solid inclusions in a silicon-nitride plate with axicon B. Aluminium wires of diameter 0.09 and 0.3 mm are embedded. Undulated features are due to scattering of the acoustic beam at the edges of the sample

b

Fig. 11 C-mode image of laminar flaws in 391~ plexiglass with axicon B. In this case the longitudinal A range gate selects; a -two interply echoes; b - upper ones; c - lower ones

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wave travels through

the material.

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Axicon: a Device for Focusing over a Large Depth,J. Acoust.

Acknowledgement The authors are indebted to Dr H. Iwasaki of the Toshiba Corp. for kindly supplying the samples of silicon nitride.

Sot. Am. 54 (1973) 1628-1630

4 5

References 1 2 3

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Tittmann, B.R. Imaging in NDE Acoustical Imaging, ed. Wang, K.Y. 9 (Plenum Press, 1980) 315-340 _ _ McLoad. J.H. The Axicon: a new type of Optical Element, J. Opt. ioc. Am. 40 (1950) 592-597 Burckhardt, C.B., Hoffman, H., Grandchamp, P.A. Ultrasou Ind

6

7

Bnrckhardt, C.B., Grandchamp, PA., Hoffman, H. Methods for Increasing the Lateral Resolution of B-scan Acoustical Holography, ed. Green, PG. 5 (Plenum Press, 1974) 391-413 Burckhardt, C.B., Grandchamp, P.A., Hoffman, H. Focussing Ultrasound over a Large Depth with an Annular Transducer .a;:;ernatke method IEEE Trans. Son. Ult. SU-22 (1975) Krautkrainer, J., Krautkr&ner, H. Ultrasonic Testing of Materials (Springer Verlag, 1969) Fujiwara, S. Optical Properties of Conic Surfaces J. Opt. Sot. Am. 52 (1962) 287-292

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