Air-coupled ultrasound: operating principle and applications

Corinna Sander, 05.03.2015

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Air-coupled ultrasound is a non-destructive testing method. This method allows for testing material properties such as density, Young’s modulus and for testing homogeneity and flaws. Such results help to determine the component’s quality and its fitness for purpose. An ultrasound system generally consists of a receiver and a transmitter. A special quality of “air-coupled ultrasound” is the use of the surrounding air as a couplant between the specimen and transmitter or between specimen and receiver and not the typical ultrasound gel or water. ^[1]

What is air-coupled ultrasound

Ultrasound is a non-contact measurement method, which was developed in the field of biomimetics. The transmitted sound wavelengths are above the audible frequency range of humans by about 16 Hz – 20,000 Hz. ^[2]

Sound can be reflected, scattered or transmitted from the specimen. In the most straightforward case, a transmitter generates sound waves, which are collected by a receiver head and converted into electrical signals. The collected data can be depicted as A, B, C and D scans. ^[3]

In the past few years, new broadband ultrasonic transducers have been developed that are also able to generate and receive wave transmissions between air and solid transducer media. ^[4] Indoor air can be used as couplant between transmitter and receiver objects for air-coupled ultrasound. In this case, using air-coupled ultrasound is of great advantage: The complex coupling techniques of common ultrasound tests can be avoided using air-coupled ultrasound, as the measurement can be carried out independently of the surface nature and any electric conductivity of the body. Additionally, it can be helpful that a measurement requires only a few centimetres distance to the object. Coupling problems often occur in the case of a rough surface or if the penetration of liquid couplant should be avoided. When difficult to access components are tested, it is of great use that measurement with air-coupled ultrasound is also possible from only one side. ^[1]

With air-coupled ultrasound it is possible to detect material flaws and errors in homogeneity. Furthermore, using the travel through time, a quantitative statement about the thickness of the specimen can be made.

This method is mainly used for quality testing of individual components, yet also with special uses in industrial batch production to gain economic advantage.

Physical fundamentals of the method

The main difference of the acoustic resistances Z (impendance = alternating current resistance / property of electromagnetic wave propagation) of the air as couplant for the piezo-ceramics of the transmitter/receiver presents a difficulty, to transfer the same approaches of fluid-based ultrasound methods to air-coupled ultrasound. The sensitivity of the specimen can be described by the ratio between the transmitting voltage and receiving voltage in the air. The usable spectrum of the frequency range is limited by the impedance of the air. ^[5]

For convergence, the following formula is used to determine the velocity of sound in a fluid (a substance that is limitlessly deformable and that responds to any small force acting upon it ^[6]) derived from the hydrodynamic equation: ^[5]

$//<![CDATA[ \begin{array}{l}v_{ph} = c = \sqrt{\frac{\delta p}{\delta \rho}}\end{array} //]]>$ (1. Formula: sound velocity fluid)

• $//<![CDATA[ \begin{array}{l}v_{ph}\end{array} //]]>$ = phase velocity [m/s]

• $//<![CDATA[ \begin{array}{l}c\end{array} //]]>$ = velocity of light within the medium [m/s]

• $//<![CDATA[ \begin{array}{l}\dfrac {\delta p} {\delta \rho}\end{array} //]]>$ = partial derivation of pressure according to density

The formula altered to apply to a gas instead of a fluid is: ^[5]

$//<![CDATA[ \begin{array}{l}v_{ph} = \sqrt{\gamma \dfrac{p}{\rho}}\end{array} //]]>$ (2. Formula: Sound velocity gas)

• $//<![CDATA[ \begin{array}{l}\nu_{ph}\end{array} //]]>$ = phase velocity [m/s]

• $//<![CDATA[ \begin{array}{l}\gamma = \dfrac{C_p}{C_\rho}\end{array} //]]>$ = adiabatic index, the ratio of the heat capacity at constant pressure and volume

• $//<![CDATA[ \begin{array}{l}p\end{array} //]]>$ = sound pressure [Pa]

• $//<![CDATA[ \begin{array}{l}\rho\end{array} //]]>$ = density [kg/m³]

Taking into consideration the temperature, the following applies: ^[5]

$//<![CDATA[ \begin{array}{l}v_a = 331 \dfrac{m}{s} \cdot \sqrt{1 + \dfrac{T_c}{273 °C}}\end{array} //]]>$ (3. Formula: Dependent relationship velocity - temperature)

• $//<![CDATA[ \begin{array}{l}v_a\end{array} //]]>$ = sound velocity [m/s]

• $//<![CDATA[ \begin{array}{l}T_c\end{array} //]]>$ = temperature [°C]

Under constant laboratory conditions (20 °C and 1013 hPa) the following formula shows the sound velocity $//<![CDATA[ \begin{array}{l}v_a\end{array} //]]>$ and the acoustic impedance $//<![CDATA[ \begin{array}{l}Z_a\end{array} //]]>$ of air: ^[5]

$//<![CDATA[ \begin{array}{l}v_a = 343 \dfrac{m}{s}\end{array} //]]>$ (4. Formula: sound velocity)

$//<![CDATA[ \begin{array}{l}Z_a = \rho v = 413 \dfrac{kg}{m^2s}\end{array} //]]>$ (5. Formula: acoustic impedance of air)

Sound waves do not travel infinitely. Obstacles reflect, transmit or sometimes absorb them. Analysis of the absorption, reflection or transmission can determine the properties of the objects. With mass transfers of different impedance (e.g. air - solid or steel - concrete) the arriving sound waves are reflected differently. The larger the difference, the stronger the reflection. ^[7]

To describe the reflection $//<![CDATA[ \begin{array}{l}R\end{array} //]]>$, ^[5] the transmission $//<![CDATA[ \begin{array}{l}T\end{array} //]]>$^[5] or the level of absorption $//<![CDATA[ \begin{array}{l}\mu\end{array} //]]>$^[8] at an interface, the following formula applies:

$//<![CDATA[ \begin{array}{l}R = \dfrac{Z_1 - Z_2}{Z_1 + Z_2}\end{array} //]]>$ (5. Formula: level of reflection)

$//<![CDATA[ \begin{array}{l}T = \dfrac{2Z_1}{Z_1 + Z_2}\end{array} //]]>$ (6. Formula: level of transmission)

$//<![CDATA[ \begin{array}{l}\mu = 1 \dfrac{dB}{MHz \cdot cm}\end{array} //]]>$ (7. Formula: level of absorption)

• $//<![CDATA[ \begin{array}{l}Z\end{array} //]]>$ = impedance [Rayl]

• $//<![CDATA[ \begin{array}{l}dB\end{array} //]]>$ = sound pressure level

• $//<![CDATA[ \begin{array}{l}MHz\end{array} //]]>$ = megahertz, physical size of the frequency $//<![CDATA[ \begin{array}{l}[MHz = 10^6 \dfrac{1}{s}]\end{array} //]]>$

If the thickness of a plate is much smaller than the pulse duration $//<![CDATA[ \begin{array}{l}(D < < \lambda)\end{array} //]]>$, the wave travels without hindrance through the medium. Thus interfaces cannot be seen as separated in this case. With perpendicular wave incidence and considering all of the factors of the reflections and transmissions, the following formula applies: ^[5]

$//<![CDATA[ \begin{array}{l}T_{Platte} = \left [1 + \dfrac{1}{4} \left (m - \dfrac{1}{m} \right )^2 \cdot \sin^2 \left ( D \dfrac{2 \pi}{\lambda} \right) \right]^{-1}\end{array} //]]>$ (8. Formula: wavelength in plate)

• $//<![CDATA[ \begin{array}{l}T_{Platte}\end{array} //]]>$ = transmission through a plate

• $//<![CDATA[ \begin{array}{l}m = \dfrac{Z_1}{Z_2}\end{array} //]]>$

• $//<![CDATA[ \begin{array}{l}D\end{array} //]]>$ = plate thickness [m]

• $//<![CDATA[ \begin{array}{l}\lambda\end{array} //]]>$ = longitudinal wavelength in a plate [m]

Gravitational forces cannot be transmitted in liquids and gases, thus only longitudinal waves are propagated. As with air-coupled ultrasound where the test object is surrounded by air, only these physical pressure waves exclusively can be applied. Where a sound wave hits the surface at a specific angle, it is partially transmitted inside the object. ^[5]

• $//<![CDATA[ \begin{array}{l}\rho \cdot v\end{array} //]]>$ = density ⋅ wave velocity

• $//<![CDATA[ \begin{array}{l}\phi\end{array} //]]>$ = incidence angle/reflection angle

• $//<![CDATA[ \begin{array}{l}\gamma\end{array} //]]>$ = angle of the transversal wave

Sound waves can only be deflected by moving air and often at an angle $//<![CDATA[ \begin{array}{l}\phi\end{array} //]]>$ to the object. Often a conducted wave $//<![CDATA[ \begin{array}{l}g\end{array} //]]>$ already exists on the surface and this influences the arriving velocity of air waves $//<![CDATA[ \begin{array}{l}v_a\end{array} //]]>$. This is known as the coincidence condition: ^[5]

$//<![CDATA[ \begin{array}{l}\sin \theta = \dfrac{v_a}{v_g}\end{array} //]]>$ (9. Formula: Resonant Coupling)

Measurement principle

The air-coupled ultrasound system is only slightly different to a conventional ultrasound system. Simply, the surrounding air serves as couplant instead of a specially applied paste, gel or water. In the case of high testing frequencies, the smallest of deviations in perpendicular incidence angle lead to measurement errors, thus the best method here is stationary normal transmission. ^[5]

The transmitter generates a wave and the receiver collects it after time delay or attenuation. The measured propagation time and sound amplitudes are converted into digital electric signals by an A/D converter and visualised with a computer. ^[5]

There are three kinds of measurement:

Normal through-transmission ^[5]

With normal through-transmission the sound waves of the transmitter hit the surface vertically. The receiver collects the transmitted waves on the opposite side. The incident waves generally depend on the test frequency and the properties of the material.

Shear transmission ^[5]

In this method, the sound wave hits the object at a known angle and is reflected at the same angle. The receiver collects the transmitted waves at the same angle. The waves react more sensitively to flaws and the elasticity of the specimen with shear transmission.

One-sided measurement ^[5]

With some objects it is not possible to place the transmitter and receiver on two different sides. Thus, with the third measurement method, the medium can be measured from one side. However, in this method it is not the transmitted wave that is measured but the reflected. To only receive waves that ran through the medium, a sound barrier has to be placed between transmitter and receiver to shield unwanted and deviated sound waves.

Use and application

Using ultrasound, many different factors can be measured and therefore the fields of application are numerous.

By the means of ultrasound testing for example, the following information can be collected: ^[1]

• Thickness or change of thickness (quality control) ^[3]
• Flaws, cracks (quality control)
• Material density/homogeneity (quality control)
• Flexibility (determination of material)
• Detection (quality control, placing of objects)

The broad field of air-coupled ultrasound testing stretches from quality control for economic production to geological trenching by means of depth measurement.

Additional applications: ^[5]

• Anisotropy measurement (material characterisation)
• Depth profiling (material characterisation)
• Optimised crack-detection (non-destructive testing - imaging air-coupled ultrasound)
• Drying processes on sheet (process tracking)
• Polyurethane foaming (process tracking)

The origin of ultrasound

The conventional ultrasound was originally developed form a combination of biology and physics. ^[9] In nature some animals have already made use of it.

Bats for example use the system of echo-orientation to find their way without problem in the dark without visual indicatorss. Bats form 3D images using the reflected echoes. ^{[1] [10]} Dolphins use echo to precisely track and hunt down their prey. In the animal kingdom, not only are sound waves used for the detection of objects, but mice and rats also communicate using different ultrasounds. ^[11]

Even plants emit ultrasounds. When trees suffer a lack of water, they sigh in ultrasound frequencies. These sounds are generated when vessel walls are set in oscillation and water threads tear. ^[12]

Literature

1. Hasenstab, A.; Krause, M.; Hillger, W.; Bühlung, L.; Ilse, D.; Hillemeier, B.; Rieck, C.: Luftultraschall und Ultraschall-Echo-Technik an Holz. DGZfP-Berichtsband 94, Plakat 54, DGZfP-Jahrestagung 2005. Rostock, 2005.
2. Ringel, C.M.: Materialien: Wellen, Wellenlänge und Frequenz. Fakultät für Mathematik, Universität Bielefeld. 28.02.2015.
3. Hillger, W.; Bühlung, L.; Ilse, D.: USPC 4000 AIRTech – ein neues, bildgebendes Ultraschallprüfsystem für Ankopplung über Luft. DGfZP-Jahrestagung (2004) Salzburg, www.NDT.net, 27.11.2014.
4. Lerch, R.; Sessler, G.; Wolf, D.: Technische Akustik: Grundlagen und Anwendung. Springer, S. 573, 2009.
5. Döring, D.: Luftgekoppelter Ultraschall und geführte Wellen für die Anwendung in der Zerstörungsfreien Werkstoffprüfung. Institut für Kunststofftechnik Stuttgart, Dissertation 2011.
6. Herwig, H.: Strömungsmechanik A-Z. Vieweg Praxiswissen, 1. Auflage (August 2004), S. 110.
7. Block, B.: Der Sono-Trainer: Schritt-für-Schritt-Anleitungen für die Oberbauchsonografie. Georg Thieme Verlag, 5. Ausgabe, April 2014.
8. Bildgebende Verfahren in der Medizin und medizinische Bildverarbeitung, Ultraschall (Skript). TUD Graphische-Interaktive Systeme, 14.11.2007.
9. Frentzel-Beyme B.: Die Geschichte der Ultraschalldiagnostik. Berlin, 28.02.2015.
10. Ehret, G.: Akustische Kommunikation. Universtität Ulm, 16.12.2014.
11. Kranz, B.: Pfeifende Ratten: Verständigung per Ultraschall. 28.02.2015.
12. Ultraschall-Laute, Bäume „seufzen“, wenn ihnen Wasser fehlt. Focus (23.07.2014). 16.12.2014.