Sensors and Actuators A 186 (2012) 118–124
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Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
2D phononic crystal sensor with normal incidence of sound M. Zubtsov a , R. Lucklum a,∗ , M. Ke a,b , A. Oseev a , R. Grundmann a , B. Henning c , U. Hempel d a
Institute of Micro and Sensor Systems (IMOS), Otto-von-Guericke-University Magdeburg, Germany Department of Physics, Wuhan University, Wuhan, PR China c Faculty of Electrical Engineering, Computer Science and Mathematics, University of Paderborn, Germany d Institute for Automation and Communication (ifak), Magdeburg, Germany b
a r t i c l e
i n f o
Article history: Received 3 October 2011 Received in revised form 7 March 2012 Accepted 8 March 2012 Available online 28 March 2012 Keywords: Phononic crystal sensor Ultrasonic sensor Liquid sensor
a b s t r a c t The contribution presents the sensor application of a resonance-induced extraordinary transmission through a regular phononic crystal consisting of a metal plate with a periodic arrangement of holes in a square lattice at normal incidence of sound. The characteristic transmission peak has been found to strongly depend on sound velocity of the liquid the plate is immersed in. The respective peak maximum frequency can serve as measure for the concentration of a component in the liquid mixture, if a beneﬁcial relation to the speed of sound of the liquid exists. Experimental veriﬁcation has been performed with mixtures of water and propanol as model system. Here we especially pay attention to numerical calculations based on EFIT and COMSOL which reveal more insides to the wave propagation characteristics. Experimental investigations with Schlieren method and laser interferometry support the theoretical ﬁndings. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Phononic crystals (PnCs) which are, in a broad sense, periodic composites designed to control, direct and manipulate sound, have recently been introduced as a new sensor platform exploiting modal phenomena in resonating acoustic structures at ultrasonic frequencies . Typically a 2D PnC consists of a matrix material, a slab or plate, with periodically arranged inclusions of another material with acoustic properties different to the surrounding homogeneous matrix. Fig. 1 schematically depicts a typical PnC. The inclusions of equal size, for example cylinders having a diameter d, which act as scatters, are periodically arranged in a two dimensional lattice, where the lattice constant, a, is the measure of the spatial modulation of material properties. There are two basic orientations for the exposure of the PnC to ultrasound: in-plane and normal acoustic wave incidence. In the original arrangement ultrasound propagates in-plane. Acoustic waves propagate through the body of the PnC undergoing multiple sequential scattering from periodically arranged inclusions. This results in constructive as well as destructive interferences of waves, which causes the most important feature of PnCs, frequency bands, so-called stop bands within which sound cannot propagate through the structure . They are therefore also called band gap
∗ Corresponding author. Tel.: +49 391 671 8310; fax: +49 391 671 2609. E-mail address: [email protected]
(R. Lucklum). 0924-4247/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2012.03.017
materials. In the following years a large variety of structures and different kinds of acoustic waves have been studied, mainly directed to achieve large absolute band gaps, e.g. [3–14]. Since the lattice constant determines the acoustic wavelength in the stop band, PnCs can be designed in a wide range of characteristic dimensions of geometry by adjusting the probing frequency. The transmission characteristics are one key design parameter. Structural resonances are, in turn, considered as primary source of required properties determining desired transmission features. Usually the material properties of the constituents of phononic crystals are regarded only in the sense of optimising the band gap. Only recently the shift in the band gap edge frequencies has been suggested as measure of thin layers covering the surface of holes drilled into the solid matrix . The basic idea behind our phononic crystal sensors is the dependence of structural resonances, and consequently the dependence of speciﬁc transmission features on the material properties of particular constituents of periodic composites. It is worth to note that those transmission properties of periodic composites signiﬁcantly differ from transmittance through randomly structured composites. The randomly placed inclusions do not provide requisite sharp and discrete features in their transmission spectra. They are diffusive by nature and therefore we do not take them into account as an appropriate subject in this study. We consider a transmission peak inside the band gap, more speciﬁcally the frequency of maximum transmission, or a transmission dip outside as the most appropriate signal for phononic crystal sensor applications. A set of those peaks appears for example when liquid-ﬁlled holes act as scatters in a solid matrix .
M. Zubtsov et al. / Sensors and Actuators A 186 (2012) 118–124
Fig. 1. Scheme of a regular phononic crystal.
Symmetry reduction by changing the arrangement of the inclusions , incorporation of a defect  or replacing material in one or several inclusions  give rise to a well separated narrow pass band or peak inside the stop band. The acoustic band gap crystals with their speciﬁc dispersion properties represent only one of the possible applications of PnCs. In the case of the normal incidence setup the waves passing the PnC propagate through the matrix body of the PnC and through the inclusions in a parallel fashion. The same structure, the same periodic composite also demonstrates a profound dependence of transmission characteristics on structural resonances, and hence, dependence on material properties of their components. We therefore keep the name phononic crystal sensor since plate with apertures or alike is less illustrative. However, the physics behind this phenomenon signiﬁcantly differs from the physics behind the band gap crystals. There are speciﬁcally neither evidences of the creation of band-gap-like features (acoustic waves/phonons do not scatter sequentially) in the normal incidence setup nor suggestions considering the band structure as relevant to the speciﬁc feature of this setup: extraordinary transmission and shielding. Here we apply extraordinary transmission through a regularly perforated plate at normal incidence of sound to a 2D PnC sensor. The nature of the underlying phenomena will be discussed in . In this sensor arrangement the PnC is placed in the liquid of interest and the inclusions are holes ﬁlled with the same liquid. Pressure waves coming from the liquid undergo multiple conversions when passing in parallel through the periodically arranged holes of the PnC. These conversions result in complex interaction phenomena where a number of different mechanisms, speciﬁcally cutoff-free waveguiding through the holes , acoustically induced interaction among holes, and coherent direct transmission through the matrix material are assumed to be responsible for some unusual phenomena like extraordinary transmission [22,23] or extraordinary
shielding . The extraordinary transmission is usually considered as interplay between two basic mechanisms: the coupling of the incident wave with cavity resonances located inside the apertures and excitation of periodic structure-speciﬁc compositions of coupled surface waves [21–24]. Similar to frequency stop and pass bands formed in the case of in-plane propagation, extraordinary acoustic transmission or shielding is also characterized by a sharp resonance-like peak at a well-deﬁned frequency. This frequency primarily depends on the PnC lattice constants and plate thickness, therefore, the frequency of extraordinary transmission can also be properly set by adjusting these parameters. More importantly for the sensor application we have demonstrated that the extraordinary acoustic transmission peak frequency in the normal incidence setup is sensitive to the speed of sound of the liquid. Therefore the resonant frequency can be used as a measure of speed of sound and related properties, like concentration of a component in the liquid mixture. The latter of course requires a beneﬁcial relation between speed of sound of the liquid and its composition. Further details speciﬁcally dealing with the measurement and systematic differences between theoretical predictions and experiment can be found in . In order to get more insights to the sensor transduction phenomenon we examine some speciﬁc aspects of the resonant wave propagation through PnC in the normal incidence setup and their relevance to the sensor applications. 2. Experimental 2.1. Demonstrator We employ a thin steel plate ( = 7600 kg m−3 , vl = 6010 m s−1 , vt = 3230 m s−1 ) as demonstrator whose thickness (t = 0.5 mm) is smaller than the half wavelength in the scanned frequency range with respect to steel (thin plate limit) and compares to the half wavelength in water at the upper frequencies. Holes having a diameter of 0.5 mm are arranged in square array (x,y) having a lattice constant of 1.5 mm. A picture of the sample (Sossna, Germany) is shown in Fig. 2a. This sample facilitates the study of all propagation features mentioned above. 2.2. Measurement setups The PnC sample has been placed in a tank, together with immersion ultrasonic transducers (Panametrics V302-SU) in some distance to the PnC plate to avoid near ﬁeld effects. The components are always carefully aligned with adjustment stages (Newport), see Fig. 2b. The transmission curves have been obtained using a network analyser (Agilent 4395A) together with an S-parameter test set (Agilent 87511A). Transmission S21 has been measured with
Fig. 2. Photos of the phononic crystal sensor demonstrator (a) and the experimental setup (b) with 1 being the adjustment stages, 2 the ultrasonic transducers and 3 the sample shown in (a).
M. Zubtsov et al. / Sensors and Actuators A 186 (2012) 118–124
Fig. 3. Scheme of the experimental setup for Schlieren visualization. DMD is a digital micromirror, L1–L3 are lenses.
and without sample in place, respectively. The transmission amplitude has been obtained by normalizing with the amplitude of the equivalent setup without the sample. The principle of Schlieren visualization of ultrasound wave ﬁelds is shown in Fig. 3. A digital micromirror device (DMD) is used as a variable ﬁlter for the signals in the Fourier plane. Sequential application of different ﬁlters together with methods of information fusion improves the quality of the sound ﬁeld visualization in comparison with the classical Schlieren method . The phononic crystal plate is adjusted that the x-direction is parallel to the laser beam. Note further that the laser beam penetrates the whole width of the sound ﬁeld above and below the PnC-plate; the image therefore delivers integral information. Measurements have been performed sequentially in a wide frequency range. The ultrasonic signal has been generated by a V303 (Panametrics). Home-made software records the data and creates the image for each frequency. A scanning laser Doppler vibrometer provides information about out-of-plane vibrations of a solid surface. The laser beam is directed at the surface of the demonstrator. Scattered light from the sample is collected and interferes with light of a reference beam. Vibration of the reﬂecting surface causes a Doppler shift which appears as modulation frequency in the received signal. The measurement scheme is shown in Fig. 4. Measurements have been performed sequentially for a set of frequencies selected from the transmission spectra. A computer controls the generation of an ultrasonic burst in the transducer behind the sample and records the vibration amplitudes. A motordriven x–y table moves the sample after each measurement. A typical scanning range is 4 mm × 4 mm, the resolution can be as low as 20 m. Home made software provides several data processing tools, including Fourier transform, averaging, ﬁltering, and visualization of amplitudes at a certain (acoustic) phase. 2.3. Sample analytes Different liquid properties are obtained by gradually changing the liquid in the holes and the surrounding from pure DI-water to pure 1-propanol via a series of liquid mixture with different molar ratios x2 of 1-propanol. Density and sound velocity of pure DI-water, pure 1-propanol and mixtures thereof have been taken
Fig. 5. Transmission through regular phononic crystal at normal incidence of sound for DI-water (blue, ), 1-propanol (red, ) and a mixture thereof with molar ratio of 0.056 (magenta, ).
from . Before applying a new mixture, tank and sample have been carefully cleaned. 2.4. Design The design of the demonstrator is based on calculations using the three-dimensional ﬁnite-difference time-domain (FDTD) method [27–29]. A computational cell with dimension 30 × 30 × 300 grid points has been used. The faces of the computational domain which are normal to in-plane directions have been chosen to have periodic boundary conditions, while the faces normal to incidence wave propagation have been set to Mur’s absorbing boundary conditions. The transmission coefﬁcient has been calculated by dividing the transmitted energy ﬂux by the energy ﬂux of the incident plane wave. Fig. 5 exemplarily shows the results for pure DI-water, pure 1-propanol and the mixture thereof having the highest speed of sound (x2 = 0.056) . 3. Results Fig. 6 compares the experimentally determined peak frequency with data extracted from FDTD simulation as function of molar ratio x2 of 1-propanol in the water–propanol mixture . The inset shows the dependence of density and speed of sound on x2 . As one can see, speed of sound governs the frequency of extraordinary transmission which, in turn, can be exploited to determine the composition of the mixture. The sensitivity f/x2 in the concentration range between x2 = 0.0.035 is about 1370 kHz. The systematic deviation of the experimental data from simulation must be attributed to a small deviation in the lattice constant of the real sample rather than in the hole diameter . The experimental data obtained with an improved experimental setup have conﬁrmed earlier results
Fig. 4. Scheme of the experimental setup for scanning laser Doppler vibrometer visualization.
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4. Resonance-induced effects
Fig. 6. Dependence of extraordinary transmission peak frequency on 1-propanol ). molar ratio extracted from FDTD simulations (black, 䊉) and experiment (red, The inset shows that speed of sound dependence (green, ) has a maximum whereas density (blue, ) decreases monotonously with x2 .
with respect to the transmission peak frequency maximum; however the unexpected decrease in the transmission peak amplitude with increasing propanol concentration reported in  could be overcome .
Besides the apparent evidence that the peak maximum frequency of extraordinary transmission through a phononic crystal can serve as measure for liquid analysis, the obtained results also demonstrate the existence of interesting features of second order (with respect to transmission amplitude) at frequencies above the extraordinary transmission peak. FDTD as well as ultrasonic wave transmission measurements through the PnC cannot provide all details on internal mechanisms involved in both extraordinary transmission and perturbations at higher frequencies. Therefore, further investigations have been performed for better understanding of the interaction between pressure waves in the surrounding liquid and the PnC structure consisting of both solid and liquid components. Elastodynamic Finite Integration Technique (EFIT) and COMSOL MultiphysicsTM simulations have been exploited for analysis of those phenomena. In contrast to FDTD technique, the EFIT starts with the governing elastodynamic equations in integral form and simulates the ultrasonic wave ﬁeld without any approximations. Using unique discretisation of the basic ﬁeld equations on a staggered grid, the method permits implementation of a pertinent code for widely arbitrary inhomogeneous structures. The underlying governing equations in integral form are discretized on the same dual grid in space and time which yields the so-called discrete grid
Fig. 7. Simulation results of Cauchy tensor components T33 (a), T13 (b) (EFIT) and displacement (d) (COMSOL).
Fig. 8. Comparison between COMSOL simulation of out-of-plane displacement component (a) and laser vibrometer out-of-plane displacement measurement (b) of the phononic crystal at an excitation frequency of 881 kHz, the frequency of an eigenmode close the frequency of extraordinary transmission.
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Fig. 9. Comparison between COMSOL (a), Schlieren experiment (b and c) at the frequency close to maximum transmission (a: 854 kHz; b: 842 kHz; c: 853 kHz) and above (d and e: 1.1 MHz) as well as Schlieren visualization of the sound ﬁeld without sample (f).
equations. Another advantage of this approach is that the resulting discrete matrix equations represent a consistent one-to-one translation of the underlying ﬁeld equations. Basic EFIT simulations that we have been performed in the time domain visualize all kinds of interactions between propagating wave and PnC structure which are typical for an acoustic wave–structure interaction rather than for wave propagation through an ideal solid. Some results are illustrated in Fig. 7a and b. The time-domain snapshot of a time-harmonic acoustic plane wave impinging on a hole and its close vicinity in an inﬁnite PnC plate demonstrate propagation of both pressure waves and pressure disturbances through the liquid and elastic perturbations through the solid part of the PnC. Both waves and perturbations are presented as longitudinal T33 and shear T13 components of the Cauchy tensor. This uniform presentation reveals details of simultaneous and consistent propagation of all four kinds of waves and disturbances. Piston-like formation of pressure perturbations within the hole and Poisson-effect induced mode conversion, which gives rise to shear waves inside the solid as well as out-of-plane vibrations, have been revealed as the most prominent effects in the extraordinary transmission resonance by this method. COMSOL simulations have been concentrating on frequency domain analysis of coupled element vibrations: liquid conﬁned in the holes, a periodic set of areas of the plate circumscribed by the adjacent holes and a regular set of holes with adjacent portions of the plate. The simulations show that each of these elements has its own set of modes and each of these modes can support either transmission or reﬂection. Fig. 7c displays distinct pressure resonance pattern inside the hole which is accompanied by mechanical plate vibration. Fig. 8 shows the out-of-plane displacement pattern of the phononic crystal at an eigenmode close to the frequency of maximum transmission in experiment, taken at maximum displacement. COMSOL calculations, Fig. 8a and experiment, Fig. 8b, are very consistent. The rim of the hole and the surrounding area
has circular displacement pattern. Note that this circular symmetry gets lost at a distance of about 1/20 with respect to the bulk velocity of longitudinal waves in steel. The maximum displacement in opposite direction can be found in the middle between two neighbouring holes diagonal with respect to the lattice. The distance to the rim of the hole in the centre of the picture is less than 1/10. In this experiment the hole itself does not give any optical signal, since there is no boundary the laser beam can be scattered at. It is important to note that the results demonstrate neither the involvement of bulk nor of surface elastic waves in the plate in extraordinary transmission. COMSOL simulations and the Schlieren method have been further used for visualization of ultrasound wave propagation. They provide some more details about internal mechanisms involved in extraordinary transmission and modal phenomena at higher frequencies. Fig. 9 presents a comparison of COMSOL simulations and their experimental veriﬁcation with the Schlieren method at a frequency very close to extraordinary transmission and at a frequency of a speciﬁc tiny peak above the so-called Wood’s anomaly (the minimum in the transmission curve) at 1.1 MHz. We ﬁrstly note a strong acoustic ﬁeld below the phononic crystal plate in Fig. 9a and b. The transmitted signal in Fig. 9d and e is much weaker; however, the low-frequency modulation of the reﬂected (simulation) and transmitted signals (simulation and experiment) is obvious. Closer inspection of the Schlieren experiments secondly reveals three side ‘lobes’ in Fig. 9b. These lobes appear outside the illuminated area only above the phononic crystal and only at certain frequencies. Their existence could be conﬁrmed also with laser vibrometer measurements. They do not exist behind the plate. Position, number and shape strongly depend on frequency. Note, that the arrangement is symmetric; we therefore attribute the different intensity at the right and left hand side to an imperfect alignment. Thirdly, the illuminated area seems to be broader in Fig. 9e. For comparison we have added a Schlieren picture without sample in Fig. 9f. The sample position would be at the bottom of this picture.
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Moreover, we note two dark lines within this region and another ‘lobe’ outside. We must conclude that the intensity proﬁle of the acoustic wave, which is the result of interference of the incoming wave and the back propagating wave above the sample, is strongly inﬂuenced by the latter. The back propagating wave cannot be reduced to that of a wave reﬂected off an unperforated plate. There must be contributions from plate vibrations. Fourthly, the intensity across the plate diameter is not constant in the near ﬁeld of the phononic crystal. We have added a near ﬁeld detail at a frequency slightly higher (853 kHz instead of 842 kHz) in Fig. 9c. This distribution is a direct consequence of the phenomena discussed above. We ﬁnally have to note that the incoming wave is not plane across the whole illuminated area. Although we recognize the angle dependence of transmission through and reﬂection off a solid plate, we assume that these effects play a minor role here. 5. Conclusions The Schlieren method for ultrasonic ﬁeld distribution measurements in liquids and laser vibrometer measurements of the PnC plate have been successfully applied for deeper insights to the phenomenon of extraordinary transmission. The experimental results apparently support results of EFIT and COMSOL simulations indicating that interactions between propagating ultrasonic pressure wave and the PnC structure are similar to the acoustic wave–structure interaction which involves plate vibrations rather than wave propagation through an ideal solid. It is important to note that all kinds of interactions between propagating wave and vibrating periodic structure must be taken into account to understand extraordinary acoustic transmission phenomenon and its relevance to material property determination of the liquid. Volumetric liquid oscillations, not just restricted to the liquid column formed by the PnC plate holes, supported by plate vibrations govern the frequency of extraordinary transmission and hence give access to material properties of the liquid in the holes of the plate and the adjacent liquid. Since the sample acts as compound resonator adjustment of the respective frequencies and coupling conditions are a key issue for the design of the sensor. We expect that the large band width of the extraordinary transmission peak, the major drawback of this sensor arrangement compared to others exploiting phononic crystals [16,18], can be optimized. Band width has been taken as measure for the peak frequency resolution achievable in an experiment. A large band width decreases the reduced sensitivity Sr = S/(f0 fHBW ) = f/(xf0 fHBW ), where f is the extraordinary peak frequency shift, x is the change of some input parameter, S = f/x is the sensor sensitivity and f0 and fHBW are the probing frequency and half value band width, respectively . Acknowledgements The work has been supported by a grant of the German Research Foundation (Lu 606/12-1) and the European Commission Seventh Framework Program (233883, TAILPHOX) which is gratefully acknowledged. The authors also want to thank Hendrik Arndt (ifak) as well as Bernhard Penzlin and Carsten Kralapp (OvGU) for technical assistance and fruitful discussions. References  R. Lucklum, Phononic crystal sensor, Proc. IEEE Freq. Control Symp. (2008) 85–90.  M.M. Sigalas, E.N. Economou, Elastic and acoustic wave band structure, J. Sound Vibr. 158 (1992) 377–382.  F.R. Montero de Espinosa, E. Jimenez, M. Torres, Ultrasonic band gap in a periodic two-dimensional composite, Phys. Rev. Lett. 80 (1998) 1208–1211.  Y. Lai, Z.-Q. Zhang, Large band gaps in elastic phononic crystals with air inclusions, Appl. Phys. Lett. 83 (2003) 3900–3902.
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Biographies Mikhail Zubtsov has been employed as research associate at the Otto-vonGuericke-University Magdeburg, Institute for Micro and Sensor Systems since 2010. He received his diploma degree in physics, with specialization on electron–phonon interaction in disordered alloys, from Moscow State University in 1979 and the Ph.D. degree in physics of magnetic phenomena, with specialization on the quantum theory of non-local and non-linear exchange interactions in metals, from the same university in 1985. He currently works on phononic crystal sensors. Ralf Lucklum studied physics at the Technical College Leuna-Merseburg, Germany. In 1983 he received his Ph.D. degree. His thesis work belongs to the area of polymer physics. Since 1986 he has been employed at the Otto-von-Guericke-University as a senior lecturer at the Department of Electrical Engineering. In 2003 he habilitated and is now private lecture at the Institute of Micro and Sensor Systems, Department of Electrical Engineering and Information Technology and currently chairing the Sensor and Measurement Science group. His present research activities include the development of ultrasonic sensor systems for process monitoring in
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ﬂuidic systems based on phononic crystals, acoustic microsensors for chemical analysis and material science as well as application orientated sensor projects. Manzhu Ke is an associated professor in Department of Physics, Wuhan University (China). She received her Ph.D. degree from Wuhan University in 2006. In 2010–2011 she was a visiting scientist at the Otto-von-Guericke-University Magdeburg for one year. During this period she worked on design and experiment of phononic crystal sensors. Her research ﬁeld mainly focuses on artiﬁcial-structure material and phononic crystals. Alexandr Oseev has master degree in microelectronic and solid state electronic in 2008, Faculty of Electronic in Saint-Petersburg Electrotechnical University, Russia. Present employment: researcher in Otto-von-Guericke-University Magdeburg, Germany. Scientiﬁc interest: acoustoelectronic devices for sensing application. Current work concentrated on liquid sensors and phononic structures for sensor applications. Ralf Grundmann was born in Leipzig, Germany, in 1982. He received his diploma in electrical engineering from the Otto-von-Guericke University of Magdeburg in 2011. Within the scope of his diploma thesis he delved into the topic of simulation of acoustic wave propagation through phononic crystals. He is currently working toward the Ph.D. degree at the Otto-von-Guericke University Magdeburg within this subject area.
Bernd Henning was graduated in 1986 in electrical engineering and received his Ph.D. in 1991 from Otto-von-Guericke-University Magdeburg, Germany. From 1986 to 1993, he worked at the Department of Electrical Engineering of the Otto-von-Guericke-University Magdeburg and from 1993 to 2001 at the Institute for Automation and Communication, Magdeburg. His research activities included chemical sensors based on mechanical resonant structures and ultrasonic sensors. In October 2001, he has been appointed as professor of electrical measuring techniques at the University Paderborn, Germany. His current research interests are development and application of acoustic sensor systems for liquid analysis, material characterisation, ﬂow and level monitoring as well as optical sensors and biomedical measuring systems. Ulrike Hempel graduated as industrial engineer at the Otto-von-GuerickeUniversity, Magdeburg in 2002 and received her Dipl.-Ing. degree in information technology. From 2002 to 2008 she worked as research assistant at the Institute of Micro and Sensor Systems in the Sensors and Measurement Group and she obtained her doctoral degree in the ﬁeld of resonant acoustic sensors. Since 2008 she works at the Institute for Automation and Communication (ifak) e.V. Magdeburg. She joined the Department of Mechatronic Systems as research assistant; since 2009 she is technical manager of the research group measurement and analyser systems. Her research activities include sensors for process and liquid analysis.