Elfgard Kühnicke

Measurement of the sound velocity in fluids using the echo signals from scattering particles.

With conventional methods the sound velocity c in fluids can be determined using the back wall echo. This paper proposes a novel technique, in which the signals reflected by scattering particles suspended in a fluid are analysed instead. The basic idea is that the particles generate the strongest echo signal when being located in the sound field maximum. Therefore the position of the echo signal maximum is a measure for the propagation time to the sound field maximum. Provided that calibration data or sound field simulations for the ultrasonic transducer are available, this propagation time suffices to determine both sound velocity and the location of the sound field maximum. The feasibility of the new approach is demonstrated by different kinds of experiments: (i) Measurements of the sound velocity c in four fluids covering the wide range between 1116 and 2740m/s. The results show good agreement with values published elsewhere. (ii) Using the dependence of the sound velocity on temperature, it is possible to vary c over the comparatively small range between 1431 and 1555m/s with increments of less than 10m/s. The measured statistical variation of 1.4m/s corresponds to a relative uncertainty not worse than 0.1%. (iii) The focus position, i.e. the distance of the maximum of the sound field from the transducer, was varied by time-shifted superposition of the receive signals belonging to the different elements of an annular array. The results indicate that the novel method is even capable of measuring profiles of the sound velocity along the ultrasonic beam non-invasively.

Directional Field of a Point Source for Calculation of Three-Dimensional Harmonic Waves in Layered Media

The description of the propagation of elastic waves emitted by a transducer in a solid is of fundamental importance in many applications of ultrasonics. Since there exist many problems with two kinds of geometric dimensions — dimensions much larger than the wavelength and dimensions in the range of the wavelength — the application of the geometric ray theory and the finite element method, resp., is difficult. That’s why semianalytical methods are a good alternative for such problems with a mixed geometry. For a 2-dimensional geometry, such as a half-space, a plate with parallel surfaces or a horizontally layered medium solutions exist in form of Green’s functions1,2. In 3 the displacement in the interior of a test object for a disk-shaped single-element transducer is obtained by spatial convolution of the solution for a point force with the amplitude distribution of the point sources. This approach, however, is restricted to axisymmetrical sources.

Simulation Calculations for Monofrequent Sound Fields in Layered Media

As to optimize the ultrasonic transducer parameters and to interpret the measured results, knowledge about the sound field is required. That is relevant both in the fields of non-destructive testing (NDT) and of ultrasonic diagnostics in medicine. In many cases, the sound wave transmitted by the transducer passes layers of different impedances until it reaches the object to be tested and examined, resp. As the active element of the transducer has a finite aperture, which mainly is located not parallel to the surface of the specimen, and as the occuring interfaces are partly curved, the calculation of the sound field for such three-dimensional elastodynamic problems is not possible in the form of a closed solution.

Non-invasive measurement of sound velocity profiles

In ultrasonics, the time of flight to the object interfaces is often the only information that is considered. From this information, one can either determine distances or sound velocities if the other value is known. A combined determination of the sound velocity and the distance of the scattering particles to the transducer makes it possible to measure sound velocity profiles. To determine distance and sound velocity simultaneously, we use the focus position as a second piece of information beside the ultrasonic time of flight. The focus position can be determined, because the echo becomes strongest when the scattering particle is located within the maximum of the sound field. Thus the position of the averaged echo signal amplitude indicates the time of flight to the focus. In previous measurements with a strongly focusing transducer with lens an accuracy of 99.9% was achieved with this method. The current presentation deals with first steps toward the measurement of sound velocity profiles. To measure a velocity profile, the focus position, i. e. the distance of the sound field maximum from the transducer, is varied by beam forming with an annular array. By using adequate calibration curves, the sound velocity on different points along the acoustic axis can be determined in dependence of the chosen set of time lags used for focusing and the time of flight corresponding to the maximum of the averaged echo signal amplitude. The measurement of the locally resolved sound velocity in media with constant sound velocity yields information about the accuracy that can be reached for varying focus distances.

Calculation of three-dimensional harmonic waves in layered media

In ultrasonics, a separation approach in connection with integral transform and point source synthesis is a powerful tool to calculate the transducer generated sound field in layered media with curved interfaces. The equations to calculate the displacement, the normal stress and the directivity patterns of the point sources are derived. Calculated sound fields are presented.

Non-scanning measurement of local curvature with an ultrasound annular array

The paper studies a novel approach for measuring local object curvature radii without scanning. Instead of scanning, an ultrasound annular array is used, and the phase and amplitude differences on the different receiver rings, which contain the curvature information, are used to determine the object curvature radius. Two evaluation methods are compared: One method is based on changing the focus of the transducer, whereas the other one is based on measuring phase differences between several receiving channels.

Modelling of sound propagation in media with continuously changing properties towards a locally resolved measurement of sound velocity

A new method to measure sound velocity and distance in homogeneous media simultaneously had been developed. It works with only one transducer and needs no additional reflectors at known positions. Instead the echoes of moving scattering particles are analyzed to determine the focus position as a second piece of information. An annular array allows to move the focus along the acoustic axis of the transducer and so to measure locally resolved. To reach also high accuracy for media with continuously changing properties, the sound field of the transducer has to be calculated within these media. A first approach for simulation by using Fermats principle is presented and compared to measurement results. It can be shown, that this model is not sufficient and that the wave equation with additional terms has to be derived and solved.

The limitations of Snell’s law for the refraction of finite beams

Abstract Because the refracted sound field of a finite beam extremely depends on the size and on the frequency of the generating element, Snell’s law in many cases is not applicable to calculate the refraction angle of a finite beam. Approaches using plane reflection and transmission coefficients in connection with a discretization of the source into elementary point sources are more exact. This paper demonstrates that the application of plane reflection and transmission coefficients requires a point to point distance smaller than a half wavelength in order to obtain an accurate sound field of the refracted beam.

Semianalytical method to calculate acoustic waves in layered elastic media

To optimize the ultrasonic transducer parameters and to interpret the measured results, knowledge about the sound field is required. In ultrasonic testing, the transducer generated sound field often has to pass different layers until it reaches the object to be tested. The interfaces of these layers may be curved and the active element of the transducer has a finite aperture. This paper gives an approach for such three-dimensional elastodynamic problems. The transducer-specimen module is decomposed into different layers and the wave propagation is calculated separately in each layer by a point source synthesis. A factor is derived to determine the transmitted transient wave from the normal-stress distribution on the interface.

Improvement of the resolution limit caused by the width of the sound beam

Determining of size and shape of reflector with ultrasound imaging is subjected to several limitations. Beside the wavelength, the sound beam width is a second known constraint. However, the resolution can also be restricted by the analysed reflector itself by its shape, alignment, surface roughness and material. Furthermore, different reflectors can be displayed identically with a simple c-scan, so that no differentiation is possible. In this work two different basic reflectors, balls and circular disks, were analysed. An easy method to distinguish between them will be introduced. In addition, several approaches for estimating the size of balls with ultrasound will be presented.