Air-coupled Ultrasound Transducers

Eric Eschler, 10.07.2016

The air-coupled ultrasound technique offers the advantage that ambient air can be used as couplant between transducer and test specimen, which is why it’s an interesting method for numerous applications of non-destructive testing, for example in case of materials that are sensitive to contact with water (corrosive materials) or when rapid scanning is required. Accordingly, the field of air-coupled ultrasound transducers has become an important research topic during the last decades and will be introduced in this article. ^[1]

Problem description

A major problem for the design of air-coupled ultrasound transducers is the high impedance mismatch at the boundary between transducer and air. This causes a very low transmission coefficient T compared to the use of water as a couplant between transducer and component, according to the formula: ^[2]

$//<![CDATA[ \begin{array}{l}T_{12} = \frac{4 \cdot Z_{1}Z_{2}}{(Z_{1} + Z_{1})^2}\end{array} //]]>$

• $//<![CDATA[ \begin{array}{l}{T}\end{array} //]]>$: transmission coefficient [-]

• $//<![CDATA[ \begin{array}{l}Z\end{array} //]]>$: acoustic impedance [$//<![CDATA[ \begin{array}{l}Ns/m^3\end{array} //]]>$]

Furthermore, ultrasonic waves lose energy by scattering and absorption while travelling through media, which leads to the loss of amplitude and thereby makes the signal harder to evaluate. The sound pressure of a plane wave attenuates over distance exponentially as follows: ^[2]

$//<![CDATA[ \begin{array}{l}p = p_{0} \cdot e^{-\alpha s}\end{array} //]]>$

• $//<![CDATA[ \begin{array}{l}p_{0}\end{array} //]]>$: initial sound pressure [$//<![CDATA[ \begin{array}{l}Pa\end{array} //]]>$]

• $//<![CDATA[ \begin{array}{l}\alpha\end{array} //]]>$: sound attenuation coefficient [$//<![CDATA[ \begin{array}{l}dB/(MHz \cdot cm)\end{array} //]]>$]

• $//<![CDATA[ \begin{array}{l}{s}\end{array} //]]>$: distance travelled [$//<![CDATA[ \begin{array}{l}{m}\end{array} //]]>$]

The attenuation coefficient increases amongst others with the frequency of the ultrasonic wave, for which reason the frequencies for air-coupled ultrasound testing are typically limited to below 2 MHz roughly [3]. On the other hand, the frequency which is used for testing should not be too low to assure reliable identification of defects. The attenuation coefficient for air ($//<![CDATA[ \begin{array}{l}α_{Air} = 1,64 \frac{dB}{MHz \cdot cm}\end{array} //]]>$) is many times higher than the coefficient for other couplants such as water ($//<![CDATA[ \begin{array}{l}\alpha_{Water} = 0,0022 \frac{dB}{MHz \cdot cm}\end{array} //]]>$), which is why the distance travelled in air should be minimized. ^[3]

Solution Approach

Due to the high sound pressure losses, conventional ultrasound transducers cannot be used for air-coupled ultrasound systems. Besides, an increase in transmission is usually not sufficient, because this also leads to an increase of background noise, which complicates the signal analysis. ^[3] A basic approach to match the acoustic impedance of the transducer elements to that of air is by reducing the impedance of the piezoelectric material or by using a matching layer between device and air with an impedance value between the two mentioned materials, as described below. The transmission coefficient $//<![CDATA[ \begin{array}{l}T_{13}\end{array} //]]>$ of an ultrasonic wave, which passes two interfaces within a short distance, can be calculated with the following formula: ^[4]

$//<![CDATA[ \begin{array}{l}T_{13} = \frac{4 \cdot Z_{Piezo}/Z_{Air}}{ \left (\frac{Z_{Air}}{Z_{Piezo}} + 1 \right )^2- \left( \left (\frac{Z_{Air}}{Z_{ML}} \right )^2 - 1 \right ) \left ( \left (\frac{Z_{ML}}{Z_{Piezo}} \right )^2 - 1 \right ) \cdot sin^2 \left (\frac{2 \pi}{\lambda_{ML}} \cdot d_{ML} \right )}\end{array} //]]>$

• $//<![CDATA[ \begin{array}{l}\lambda_{ML}\end{array} //]]>$: wavelength inside matching layer [$//<![CDATA[ \begin{array}{l}{m}\end{array} //]]>$]

• $//<![CDATA[ \begin{array}{l}d_{ML}\end{array} //]]>$: thickness of matching layer [$//<![CDATA[ \begin{array}{l}{m}\end{array} //]]>$]

This formula describes the general case and depends on the impedance of the two materials, the impedance of air, the wavelength of the ultrasonic wave in the matching layer $//<![CDATA[ \begin{array}{l}\lambda_{ML}\end{array} //]]>$ and the thickness of the matching layer $//<![CDATA[ \begin{array}{l}d_{ML}\end{array} //]]>$. The goal is to maximize the transmission coefficient, which can be achieved by appropriate selection of materials and thickness of the matching layer. The formula includes a sinus-term which reaches its periodic maximum for the following thickness:

$//<![CDATA[ \begin{array}{l}d_{ML,opt} = \frac{\lambda_{ML}}{4} \cdot (2n + 1)\end{array} //]]>$

• $//<![CDATA[ \begin{array}{l}n \in N\end{array} //]]>$

Accordingly, a matching layer with the thickness of one quarter of the wavelength in the material is required to maximize the transmission factor. In this case $//<![CDATA[ \begin{array}{l}T_{13}\end{array} //]]>$ can be calculated in the following way:

$//<![CDATA[ \begin{array}{l}T_{13} = \frac{4 \cdot Z_{Piezo}/Z_{Air}}{Z_{ML}^2 \left (1 + \frac{Z_{Piezo}Z_{Air}}{Z_{ML}^2} \right )^2}\end{array} //]]>$

This expression equals one if the impedance of the matching layer reaches the geometric mean value of piezo-material and air:

$//<![CDATA[ \begin{array}{l}Z_{ML,opt} = \sqrt{Z_{Piezo} \cdot Z_{Air}}\end{array} //]]>$

In conclusion, the ideal matching layer for the use in air-coupled ultrasound transducers has a thickness of one quarter of the wavelength and an acoustic impedance thats calculated as shown above. Hence, the matching layer is only effective for one test frequency.

Buildup of real Air-coupled Ultrasound Transducers

A difficulty of the buildup of such a transducer is finding the appropriate material for the matching layer, because solid materials usually have a higher impedance compared to the mathematical optimum. A possible solution to this challenge are silicone materials with a high percentage of small air bubbles, which reduce the overall impedance. ^[5] Bubbles of the wrong size can however lead to problematic scattering effects. Given that, the matching layer is most effective for a certain frequency, since a $//<![CDATA[ \begin{array}{l}\lambda/4\end{array} //]]>$-matching layer acts as a frequency filter, which only a narrow band of frequencies is able to pass without significant losses. ^[6] In order to further increase the transmission coefficient, it is possible to use multiple matching layers in series using the same principle. Currently there are some other promising approaches for the buildup of air-coupled ultrasound transducers under development which are introduced below.

Piezocomposites

Besides common piezoceramic plates, piezocomposites represent an effective method for ultrasound generation. Piezocomposites are composed of parallel-aligned piezoelectric rods, which are positioned orthogonally to the transducers’ active surface and a passive polymer matrix surrounding the rods (see graphic). ^[7] These structures can be manufactured using the “dice and fill” process, in which a piezoceramic plate is sawed with orthogonal cuts up to a depth of 80 % of the material thickness. The space between the rods is subsequently filled with a polymer matrix. Finally, both sides are provided with an electro conductive layer, which serve as electrodes for the excitation of the piezo rods. ^[8] Due to the low impedance of the matrix, the overall impedance of the piezocomposite can be reduced to approximately one fourth of that of the piezoceramic itself. ^[8] Hence, the matching to air is significantly better and can be further improved by using a matching layer.

Capacitive Transducer

A capacitive transducer is an element to stimulate ultrasonic waves without using a piezoelectric material. It consists of two electrodes, which are separated by an insulating polymeric membrane and an air gap. The lower electrode (backplate) is rigid and the upper one is flexible and able to oscillate with the membrane, in order to generate an ultrasonic wave in air. ^[9] The membrane is usually only a few micrometers thick and metallized on the upper side, in order to create the upper electrode. During reception, the membrane is set into motion due to fluctuations of the air pressure, which causes the distance between the electrodes to change and thereby alters the capacitance of the two separated electrons. During transmission an alternating voltage is applied that causes a charge difference between the electrodes, which modifies the electrostatic forces that appear between the plates as shown by the following formula: ^[9]

$//<![CDATA[ \begin{array}{l}\Delta Q = -\frac{\epsilon_{0} \cdot A \cdot \Delta x}{d^2} \cdot U\end{array} //]]>$

• $//<![CDATA[ \begin{array}{l}\Delta Q\end{array} //]]>$: charge change [$//<![CDATA[ \begin{array}{l}{C}\end{array} //]]>$]

• $//<![CDATA[ \begin{array}{l}\epsilon_{0}\end{array} //]]>$: permittivity of free space [$//<![CDATA[ \begin{array}{l}F/m\end{array} //]]>$]

• $//<![CDATA[ \begin{array}{l}A\end{array} //]]>$: surface area [$//<![CDATA[ \begin{array}{l}m^2\end{array} //]]>$]

• $//<![CDATA[ \begin{array}{l}\Delta x\end{array} //]]>$: change in distance between plates [$//<![CDATA[ \begin{array}{l}{m}\end{array} //]]>$]

• $//<![CDATA[ \begin{array}{l}d\end{array} //]]>$: thickness of air gap [$//<![CDATA[ \begin{array}{l}{m}\end{array} //]]>$]

• $//<![CDATA[ \begin{array}{l}U\end{array} //]]>$: voltage [$//<![CDATA[ \begin{array}{l}V\end{array} //]]>$]

Capacitive Transducers feature a good impedance matching with air and have a high bandwidth, in contrast to piezoelectric transducers which use a matching layer. The properties in terms of frequency and bandwidth of a capacitive transducer are heavily dependent on the membrane thickness and surface texture of the backplate. The latter is currently an important research topic, in which roughened, grooved and micromachined surfaces are examined. ^[9]

Thermoacoustic Transmitters

Thermoacoustic transmitters use a simple physical principle and basically only consist of electrically conducting films or wires, with or without a solid substrate for stabilization. When electric power is applied, heat is transferred from the conductor to the surrounding gas, thus a sound wave emerges. When the power is turned off, the temperature of conductor and gas drops quickly. If an alternating voltage is applied, it’s possible to create ultrasound with high frequencies. ^[10]

Among the considerable advantages of thermoacoustic transmitters are, that no post-ringing occurs when the power is turned off and that no matching layer or the like affect the broadband frequency spectrum. On the other hand, the technique is only applicable for ultrasound transmission and has to be combined with a receiver, which, for example, is based on the piezoelectric effect. Alternatively, an optical microphone as shown by Guruschkin can be used as receiver. ^[3]

Literature

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3. Guruschkin, E.: Berührungslose Prüfung von Faserverbundwerkstoffen mit Luftultraschall. Masters Thesis. Technical University Munich. Munich, 2015.
4. Sutilov, V. A.: Physik des Ultraschalls. Springer-Verlag. Vienna, 1984.
5. Hillger, W.; Gebhardt, W.: Bildgebende Ultraschallprüfung an CFK-Probekörpern mit Ankopplung über Luft. DGZfP annual meeting. Celle, 1999.
6. Hillger, W.; et al.: Ultraschallprüfung mit Ankopplung über Luft: Prüfsystem, Praxiseinsatz und Forschungsbedarf. DGZfP annual meeting. Dresden, 2013.
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8. Stößel, R.: Air-Coupled Ultrasound Inspection as a New Non-Destructive Testing Tool for Quality Assurance. Dissertation. University Stuttgart. Stuttgart, 2003.
9. Hutchins, D. A.; Neild, A.: Airborne ultrasound transducers. Woodhead Publishing Limited. Oxford, Cambridge, Philadelphia, New Delhi, 2012.
10. Gaal, M.; et al.: Novel air-coupled ultrasonic transducer combining the thermoacoustic with the piezoelectric effect. 19th WCNDT. Munich, 2016.