1. Abstract

There are a number of models for sound field calculations. They include analytical, partly analytical [1] and numerical methods [2]. As far as they refer to sound fields of pulsed sources, their results are often given in so called snapshots, i.e. images of sound field values at a fixed time (see [2] for an example). An other word for that type of mapping, used here as a synonym, is stroboscopic imaging. These images are helpful for understanding the physics of sound field propagation and the interaction of sound fields with defects.

Only a few experimental methods are known which generate these ultrasound wave images but they are either limited in its applicability or very expensive. The aim of this paper is therefore twofold: Firstly existing methods of experimental production of sound field images will be reviewed. Secondly new and rather inexpensive method for sampling of stroposcopic pictures is given. Our considerations are limeted to sound fields in solids and on their surfaces.

The article provides a demonstration of a movie-file "rayleigh.mpg". The file can be viewed with any MPEG viewer.
The movie shows a 10 second length of a 2 Mhz Rayleigh wave hidden between two notches on a AL-plate. The movie file can be downloaded from the SWRI South West Research Institute server - URL: ftp://ftp.nde.swri.edu/pub/nde/ultrasonic_fields/rayleigh.mpg
You can download it now also => Download rayleigh.mpg movie 750KB

Content
1. Abstract
2. METHODS OF VISUALISATION OF SOUND FIELDS
3. PRINCIPLE OF STROBOSCOPIC MEASUREMENTS
4. EXAMPLES OF APPLICATIONS
5. SUMMARY
6. Literatur

2. METHODS OF VISUALISATION OF SOUND FIELDS

The simplest and most common way for tracing sound fields in solids is launching a sound wave into a solid and measuring the sound intensity on the opposite side of the specimen. In Fig. 1 an appropriate experimental arrangement is given. A probe is excited to transmit ultrasonic waves into a test specimen. That ultrasound propagates through the specimen and its intensity is scanned for by a small aperture probe at the opposite surface. The amplitude or intensity values are collected by a computer which also controls the manipulator. The corresponding plots are called C-scans. Complete different methods are sound field mappings by optical means. One possible experimental arrangement is schematically given in Fig. 2 (see [3]). Here the light of a stroboscopic source travels via two mirrors through an optically transparent sample. Two additional polarisers are crossed so that elastic waves in the sample are mapped as a brightness picture. In this way wave phenomena can be studied as for example in Fig. 3 where a wave hitting a cylindrical inclusion in water is mapped. Here also a lot of caustics (one indicated by an arrow) are visible. 22k Fig. 3 Stroboscopic image of a longitudinal wave in a water bath hitting an Al-cylinder. However, the method described above is only applicable for optically transparent solids. To visualise waves on surfaces of solids an other optical method, the double pulse laser interferometry [4] has been proposed (Fig. 4). Here the surface is illuminated by two pulses of coherent light shifted nearly 180 degree in phase. If the surface is motionless, the two images cancel out nearly. If they are taken at time points separated by halve a period of the ultrasonic wave, points of maximum deflection are mapped bright whereas the points of zero displacement difference appear dark due to the mentioned light cancellation. In Fig. 5 an example is given where a probe transmits Rayleigh waves into the surface of a coated sample containing bonding flaws. The primary waves are clearly visible together with the bonding flaws mapped as disturbances of that plane waves. The two flaws are of a size of 6 mm and 14 mm. These two optical methods have the advantage to map the wavefront of the ultrasound at a fixed time whereas the conventional intensity method does not provide this information. But they have the disadvantages of either being limited to transparent solids (polarizing optics or schlieren method) or being very expensive. So a further method is proposed based on conventional scanners, which are available in most ultrasonic laboratories, to visualise sound fields much less expensive but with all the necessary information to characterize materials and defect states at surfaces of opaque solids. 13k Fig. 5 Rayleigh waves (f= 500 kHz) on a coated (0.8 mm thickness) sample surface with two bonding flaws

Fig. 1 System for conventional (intensity) sound field measurements Fig. 2 Polarizing optics for mapping ultrasonic fields in transparent solids Fig. 4 Experimental arrangement for double pulse laser holography

3. PRINCIPLE OF STROBOSCOPIC MEASUREMENTS

The basic idea is indicated in Fig. 6. A probe (not shown) sets up pulses of ultrasonic waves. As they travel to the surface (or over it) the (say) surface displacement u is measured by a point transducer, digitised and stored. From this time signal only the value for the time f0 is taken and stored together with the position co-ordinates x1, y1. For a next position with co-ordinates x2, y2 we repeat the measurement, storing again displacement for the time t0 and so on. So a complete map of u(x,y,t0) can be sampled e.a. a snapshot. This is rather simple and it can be done using existing scanners and modifying only the software. In fact we used in our experiments the scanning system shown in Fig. 1.Of course, the displacement data for various time points can be stored in parallel to generate a series of snapshots out of the same scan. In this way a movie of the wave prapagation can be generated in the same time which is necessary for conventional scanning to produce intensity images. The type of point transducers can be varied. Piezoelectric pin transducers, electrodynamic probes and laser interferometer are possible receivers. A necessary condition to apply a transducer is aperture is small compared to the trace wavelength. The measurement e.g. the sensor contact should not affect the sound propagation. Of course, different sensors measure different physical quantities.The above discussion the surface displacement u should be replaced e.g. by particle velocity in normal direction or in some tangential direction (in plane motion) for various types of electrodynamic probes.

Fig. 6 Principle of collecting snapshots by sampling

4. EXAMPLES OF APPLICATIONS

Flat bottom holes have been drilled in an AL-plate from the rear. They end 0.5 mm below the surface. Transient surface waves of 2 MHz where transmitted by a piezoelectric transducer and the sound field has been recorded as anintensity map and stroboscopic map. The two holes are clearly visible as centres of spherical waves in the snapshots (Fig. 7b). Contrary to this, in the intensity map (Fig. 7a) the incident wave covers up the structure of the scattered wave completely and the holes can only be sensed.

30k	Fig. 7 plate containing two flat bottom holes of 5 mm and 3 mm drilled from the rear
a) intensity map b) stroboscopic map

An other interesting example is shown in Fig. 8. Here out of a time series of snapshots three interesting images are selected. The localisation of the artificial flaw is indicated by the dark bar. It is a notch of width 2 mm and ending 1 mm below the surface. The "tip diffraction" appears as a spherical ringing and later a transmitted and a refracted waveis visible. There are some locations where the wavefronts are not continuous (arrow). We interpret this by a lower sound velocity of the wave in the 0.5 mm thick and 2 mm wide area above the notch where some kind of plate wave occurs.

27k

Fig. 8 Snapshots of the sound field on an Al-plate surface; incident Rayleigh waves of 2 MHz; a notch machined from the rear is aligned 45° to the sound propagation direction with a width of 2 mm, ending 1 mm below the surface

15k

Fig. 9 Snapshot of a Rayleigh wave field prapagationg along the left border of the plate striking a flat bottom hole of 1 mm diameter

Fig. 9. reveals an other interesting effect. Here we have a Rayleigh wave striking a flat bottom hole of 1 mm diameter. But the hole is near the side edge of the plate, so the bundle of Rayleigh wave reaches the plate edge. Apparently a wave pattern occurs starting from the edge. Because the boundary condition - the normal projection of the stress tensor is zero for a free surface - is not fulfilled for Rayleigh waves at the edge they cannot exist exactly. Nevertheless the true kind of wave coming from the edge is not clear. Images like the shown provide help to discover such waveforms and may give hints to explain them.

5. SUMMARY

A simple method to visualize sound fields by stroboscopic images (snapshots) was demonstrated. This method is especially situated for tracing images of Rayleigh waves travelling along surfaces with flaws. In this way sub-surface flaws in low depth can be recorded, which are otherwise difficult to detect and characterized by ultrasonic methods. That has been shown for some artificial flaws. Flaw characterisation and sizing is improved by evaluating these images.

6. LITERATUR

1. B. Köhler, Sound Fields of Ultrasonic Circumferential Arrays - Case of an Array for Steam Generator Heat Exchanger Tubes, 21st International Symposium on Acoustical Imaging, 28.-30. March, Laguna Beach, CA, USA
2. F. Fellinger, K.J. Langenberg, Numerical Techniques for Elastic Wave Propagation and Scattering, in: Elastic Waves and Ultrasonic Nondestructive Evaluation, Ed. by S.K. Datta et al.; North Holland 1990, p. 81-86
3. R.D.Andrews, Study of Waveforms in Acoustic Diffraction Patterns Using a Stroboscopic Schlieren Technique, SPIE Vol. 248, International Congress on High Speed Photography and Photonics, San Diego, 1982
4. K. J. Pohl, H. A. Crostack, E. H. Meyer, Holographic Visualization of Laser Induced Ultrasonic Rayleigh Waves, International Conference on Hologram Interferometrie and Specle Metrology, Nov. 5.-8. 1990 Baltimore USA,
5. E. Neumann, u.a., Ultraschallprüfung von austenitischen Plattierungen und austenitischen Schweißnähten, Berlin 1995

Author