aa r X i v : . [ phy s i c s . a pp - ph ] A p r International Journal of Microwave and Wireless Technologies , page 1 of 8. © Cambridge University Press and the European Microwave Association, 2016.doi:0000000000
RESEARCH PAPER
Radar for projectile impact on granular media
FELIX RECH AND KAI HUANG , From the prevention of natural disasters such as landslide and avalanches, to the enhancement of energy efficiencies inchemical and civil engineering industries, understanding the collective dynamics of granular materials is a fundamentalquestion that are closely related to our daily lives. Using a recently developed multi-static radar system operating at GHz (X-band), we explore the possibility of tracking a projectile moving inside a granular medium, focusing on possiblesources of uncertainties in the detection and reconstruction processes. On the one hand, particle tracking with continuouswave radar provides an extremely high temporal resolution. On the other hand, there are still challenges in obtaining tracertrajectories accurately. We show that some of the challenges can be resolved through a correction of the IQ mismatch in theraw signals obtained. Consequently, the tracer trajectories can be obtained with sub-millimeter spatial resolution. Suchan advance can not only shed light on radar particle tracking, but also on a wide range of scenarios where issues relevantto IQ mismatch arise.
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I. INTRODUCTION
As large agglomerations of macroscopic particles, gran-ular materials are ubiquitous in nature, industry and ourdaily lives [1, 2]. Despite of its importance, a fundamentalunderstanding of granular dynamics from the perspectiveof transitions from a solid- to a liquid-like state (e.g.,when and where does an avalanche start) is still far fromcomplete. One of the main challenges in deciphering thedynamics of granular materials arises from the fact thatmost granular particles are opaque. In the past decades,there have been substantial progresses in imaging granularparticles [3]. Optical means for imaging particles in threedimensions (3D), such as refractive index matching [4], arelimited to certain combinations of particles and interstitialliquids. X-ray tomography [5] and Magnetic ResonanceImaging [6] are also frequently used to identify the inter-nal structures of granular materials. However, the limitedtime resolution of scanning technique as well as the hugeamount of data to be processed hinder the investigationof granular dynamics, which is better resolved with suf-ficiently high temporal resolution. Note that the mobilityof single particles can influence dramatically the collectivebehavior, owing to its discrete nature as well as heteroge-neous distributions of force chains inside [7]. Therefore, it Experimentalphysik V, Universität Bayreuth, 95440 Bayreuth, Germany Division of Natural and Applied Sciences, Duke Kunshan University, No. 8 DukeAvenue, Kunshan, Jiangsu, China 215316
Corresponding author:
Kai HuangEmail: [email protected] is desirable to have a technique capable of tracking granularparticles with high temporal resolution.Since the beginning of last century, radar technology hasbeen continuously developed and benefiting us in many dif-ferent ways: From large scale surveillance radar systemsthat are crucial for aircraft safety and space exploration [8],to small scale systems for monitoring insects [9]. Consider-ing the capability of radar tracking technique, it is intuitiveto ask: How small can an object be accurately tracked bya radar system? Can it be as small as a tracer particle witha size comparable to a grain of sand? Recently, we intro-duced a small scale continuous-wave (CW) radar systemworking at X-band to track a spherical object with a sizedown to mm [10]. In comparison to other techniques,the continuous trajectory of a tracer particle obtained bythe radar system helps in deciphering granular dynam-ics greatly, owing to the high temporal resolution. Here,advantages and disadvantages of this technique, particu-larly how to handle the possible sources of uncertainty willbe discussed in details. II. PARTICLE TRACKING SET-UP ANDRECONSTRUCTION ALGORITHM
Figure 1 shows the experimental set-up that utilizes theradar system to track a free falling projectile into a gran-ular bed. The multi-static radar system operates at 10 GHz(X-band) with one transmission (Tx.) antenna pointing inthe direction of gravity (defined as − z direction) and threereceiving (Rx.) antennae mounted symmetrically aroundthe z axis. Polarized electromagnetic (EM) waves, after RADAR FOR PROJE CT IL E IMPACT
Fig. 1.: Schematics (upper panel) and a top-view pictureof the particle tracking system, showing the configurationof the (a) transmission (Tx.) and (b) receiving (Rx.) anten-nae, (c) granular sample, (d) tracer as well as the (e) tracerholding and releasing device.being scattered by the tracer particle, are captured by theRx. antennae.A metallic sphere with a diameter d =
10 mm is used asthe tracer. The cylindrical container has an inner diame-ter of cm and a height of cm. To avoid unnecessarymultiple scattering, the sample holder is constructed withmostly foamy materials as possible. The granular sam-ple (see Fig. 9 and relevant text for more details) is filledin the container till few centimeters below the rim andgently tapped until the initial packing density of . %is achieved. The tracer is initially held by a thin threadwrapped around and released by gently pulling the threadsuch that the initial velocity of the falling sphere is close to . This design enables a defined and reproducible initial condition for a comparison among various experimen-tal runs. The raw IQ signals from the AD converter (NIDAQPAD-6015) are recorded and further processed with aMatlab program to obtain the reconstructed trajectories.IQ-Mixers play an essential role in accurate ranging atarget, as it measures the phase shift (i.e., time delay) of thereceived signal with respect to the emitted one. Supposethe latter can be described as a cos(2 πf t ) and the formeras b cos(2 πf t + θ ) , where a and b are the magnitudes ofthe corresponding signals, f and f are the transmitted andreceived signal frequencies, the output signals of an IQ-Mixer is I = ab π ( f − f ) t − θ ] ,Q = ab π ( f − f ) t − θ ] . (1)Subsequently, the relative movement of the tracer isobtained from the phase shift of I + Qi in a complex plane,where I (in-phase) and Q (quadrature) correspond to thetwo outputs of a IQ mixer. With the help of an IQ mixer, thechange of the absolute traveling distance for the i th antenna L i = l + l i can be obtained, where l and l i are the dis-tance between Tx. antenna and the target and that from thetarget to the Rx. antenna, respectively. If L i varies by a dis-tance of one wavelength, the vector I + Qi rotates π . AsIQ mixers provide analogue signals representing the mobil-ity of the tracer, the time resolution of the radar system isonly limited by the analogue-digital (AD) converter. Thisis an advantage of using continuous wave radar systems forparticle tracking.Although distance measurements rely only on the phaseinformation, the sensitivity and accuracy of the systemdepend on IQ signal strength. In order to have a sufficientsignal to noise ratio, the directions of the horn antennae(Dorado GH-90-20) are adjusted with the help of a laseralignment and range meter (Umarex GmbH, Laserliner) toface the target area. The three Rx. antennae are arrangedsymmetrically about the axis starting from the Tx. antennapointing along the direction of gravity, so that the receivedsignals have similar signal-to-noise ratios. According to thespecification of the antenna, the main lobe of its radiationpattern has an opening angle of ∼ degrees. Thus, weestimate the field of ‘view’ of the radar system has a vol-ume of about × × , taking into accountthe average working distance of the antennae. Neverthe-less, as will be shown below, the field of view can beextended after a proper correction of the IQ mismatch. Thedistance between each antenna and the center of the coordi-nate system is also measured by the laser meter during theadjustment process. The polarization of the antennae areadjusted to maximize the raw I and Q signals. The wholesystem is covered with microwave absorbers (EccosorbAN-73) to reduce clutter and unwanted noises from thesurrounding. ADAR FOR PROJECTILE IMPACT From the measured distances ~L ≡ ( L , L , L ) , thereconstructed trajectory can be obtained with a coordinatetransformation xyz = ~r − ~L~T , (2)where the vector ~r is chosen to be as it contributesonly to a constant offset to the reconstructed trajectory, thetransformation matrix reads ~T ≡ sin θ cos φ sin θ sin φ θ sin θ cos φ sin θ sin φ θ sin θ cos φ sin θ sin φ θ (3)with θ i and φ i the tilt and azimuth angles of the i thantenna, respectively. The transformation matrix is deter-mined from a calibration process using the same tracerparticle moving in a given circular trajectory in the hor-izontal plane. More descriptions of the calibration andcoordinate transformation processes can be found in [10]. III. HOW TO ENHANCE SPATIALRESOLUTION?
Although extremely high temporal resolution can beachieved with the CW radar system, the spatial resolu-tion relies strongly on the adjustment of the system, aswell as the calibration and reconstruction algorithms. Thereare three main sources of uncertainty in the calibrationand reconstruction process: (i) Fitting error arising fromthe calibration process; (ii) Reflection and multiple scat-tering from surroundings; (iii) Mismatch between signalsobtained by I and Q channels. In the following part of thissession, details on how to handle various sources of uncer-tainty, particularly for the case of IQ mismatch, will bediscussed.First, the antennae parameters determined from the cali-bration process are essential for the accurate reconstructionof the tracer trajectories. Following the algorithm describedabove, circular motion of the tracer particle in the calibra-tion process leads to harmonic oscillations of L i . Basedon a first order approximation [10], the tilt and azimuthangle θ i and φ i of the Rx. antennae can be determined fromfitting. Note that although the antenna parameters can bedirectly measured by laser assisted alignment tools, the out-come can not only serve as a rough initial guess, since anaccurate determination of the exact location where the elec-tromagnetic waves are emitted is nontrivial. Thus, we needto apply the aforementioned fitting algorithm to a referencetrajectory. We choose a circular trajectory in the horizontalplane (defined as x − y plane) for the following reasons:(a) The center of the three dimensional Cartesian systemcan be defined as the center of rotation with the rotatingaxis pointing toward the + z direction, along which the Tx.antenna is aligned. In another word, the coordinate system Radius (mm) A ng l e o f R x . A n t. ( deg r ee ) Fig. 2.: The elevation angle of antenna 1 obtained from thecalibration process as a function of the radius of circulartrajectory. The red dashed line marks the averaged anglefrom Radius mm to mm. The error bars correspondto the uncertainty from the fitting algorithm.is defined by the calibration circle. (b) A circular trajec-tory with different radius R and rotation frequency f isimplemented with a Styrofoam tracer holder attached toa stepper motor. Styrofoam, which shares similar materialproperties as granular sample, is chosen as they are trans-parent to EM waves and rigid enough to support the tracers.Here the tracer is directly embedded into the rotating arm.Concerning the accuracy of determining antennae parame-ters, the circular trajectory has to be well constructed. Dueto the low rigidity of Styrofoam, sources of errors such aseccentricity of the trajectory due to the coupling with themotor shaft or the relative motion of the tracer with respectto the Styrofoam arm may occur and lead to higher rela-tive error in the radius of the reference circle, which weconsider to be one source of error. As shown in Fig. 2, thefitted outcome of tiling angle of Rx. antenna 1 deviates sys-tematically away from the expected value as R decreases.Note that the calibration outcome should not depend on theradius and angular frequency of the circular motion. Theabove comparison suggests that the radius has to be largerthan ≈ mm for a reliable determination of the antennaeparameters for the current configuration.Second, there always exist scattered signals from thesurrounding environment, thus it is necessary to have EMabsorbing materials to enhance the signal-to-noise ratio.In addition, microwave absorbers also play an importantrole in isolating the system from the surrounding environ-ment as the Rx. antennae may response to people walk-ing around. In practice, the most efficient way of signalenhancement is to record a background signal at the sameconfiguration of the experimental setup and subtract thebackground signal for the I and Q signals of all three chan-nels. As shown in [10], this step is essential for the casethat there are mechanical components other than the tracermoving periodically with time, as such kind of movementsmay lead to strong distortions to the signals from the tracer.Note that the smallest size of tracer that can be tracked is to RADAR FOR PROJE CT IL E IMPACT (a) (b)
Unrealistic oscillations
Fig. 3.: An illustration (a) showing the trajectory of thetracer falling freely into a granular bed with a coordinatedefinition. (b) One segment of the reconstructed trajectory(corresponding to 0.04 s). The unrealistic oscillations ofthe trajectories in both horizontal directions arise from IQmismatch.a certain extent associated with the signal-to-noise, there-fore special care has to be taken to remove the backgroundnoise for a better performance of the tracking system.The third and perhaps the most serious source of errorarises from the strong IQ mismatch, which is partly owingto the fact that the range of tracer movement (up to . m)is on the same order of magnitude as the working dis-tance (about . m), consequently the fluctuations of bothI and Q signals are relatively strong, leading to unrealisticfluctuations in the reconstructed trajectory. As an example,Figure 3(b) shows the reconstructed trajectory of a tracerfalling freely under gravity. The oscillations in the horizon-tal direction can sometimes approach the diameter of thetracer. One possible reason in connection with the abovedescription is the amplitude fluctuations in the IQ plane.The other possible reason is the the offset of IQ signals:The tracer movement corresponds to the phase shift in theIQ plane, which is determined by the corresponding tracerpath, (ideally it should be an arc). For either case, there willbe a systematic deviation of the measured phase angle withrespect to the ideal one.In order to demonstrate the above analysis, we intro-duce artificially the aforementioned two sources of errorinto the raw signal. As shown in Fig. 4(a), the raw signalof Q from the Rx. antenna 1 oscillates as a function oftime, representing the fact that the tracer is moving awayfrom the antennae when it falls down freely along the z direction. The oscillation amplitude may fluctuates as timeevolves, leading to one source of error. For the ideal case,one expects a constant amplitude (i.e., constant radius inthe IQ plane), as indicated by the red curve. Using the idealsignal for reconstruction, one obtains a constant x = 0 , i.e.,no unrealistic oscillations in the x direction. If we artifi-cially add a small offset to the I signal or multiple the Qsignal with a factor slightly larger than 1 (i.e., introduce aslight distortion to the circular trajectory in the IQ plane). R e c e i v ed s i gna l , U ( V ) Raw signalIdeal signal (a)
Time, t (s) Ideal (b)
Fig. 4.: (a) Real part of the raw signal from antenna 1 andone ideal case (without amplitude modulations) for com-parison. (b) Reconstructed trajectory for the free fallingcase shown in 2 for the ideal case (red line, without oscilla-tions) and two artificially generated IQ mismatched cases:One with offset (blue curve) and the other one with Q signalbeing scaled up by a certain factor. −1 −0.5 0 0.5 1−1−0.8−0.6−0.4−0.200.20.40.60.81
I (arb. unit) Q ( a r b . un it ) Corrected signals
Fig. 5.: Raw (continuous lines) and corrected (open sym-bols) signals representing a free-falling sphere from aheight of cm. Red (dark red), green (dark green) andblue (dark blue) curves (points) correspond to the resultsfrom channel 1, 2, and 3, respectively. For a better visibility,the offsets of the raw signals are removed.In either case, one observes clear oscillations in the x direc-tion, demonstrating how IQ mismatch leads to unrealisticfluctuations in the reconstructed trajectory.As Fig. 5 shows, the raw IQ signals are typically notideal in the sense that the IQ signals are not always orthogo-nal with each other. This mismatch may arise from the DCoffsets of either I or Q signal, gain and phase imbalance. ADAR FOR PROJECTILE IMPACT −0.0200.02 V r a w ( V ) −0.04−0.0200.02 V r a w − b i a s ( V ) Time t (s) V c o rr ec t e d ( V ) a)b)c) Fig. 6.: Process for IQ mismatch correction. (a) A repre-sentative raw signal with peaks and valleys marked withred and blue open circles. From an average of both splinefits for the peaks and valleys, the bias error (green line) forthe raw signal as a function of time is estimated. (b) Biascorrected signal time dependent rescaling factors (greenline) for the correction of gain error. (c) Corrected signalfor further analysis.How to correct such kind of errors has been extensively dis-cussed in, for instance [11] or [12], particularly along withthe development of telecommunication and non-invasivemotion detecting techniques [13]. The distortions are typ-ically attributed to device imperfections as well as clutter.However, for the system being used here, there are addi-tional errors arising from the mobility of the tracer itself,which can not be readily corrected with an additional cal-ibration of the hardware. Moreover, distortion may alsoarise from the interaction of the scattered signal from thetracer with that from objects not completely transparentto EM waves. In that case, the existence of ‘mirrored’particles may lead to additional uncertainty.Here, we use the following approach to correct IQ mis-match arising from multiple sources of errors. It worksbest when the object moves in a distance covering multiplewavelengths. As illustrated in Fig. 6, the correction processis composed of the following steps: First, we identify thetime segment of the raw data V raw that contains the move-ment of the tracer particle via finding the start and end ofthe fluctuations. Second, the peaks (red circles) and valleys(blue circles) of individual fluctuations are determined byfinding the local extreme values in the selected data. Third,the bias error V bias [green line in (a)] is estimated as themean value of the spline fits of peaks and valleys (dashedlines). In order to avoid unrealistic extrapolations, the biaserror starts to vary only from the first peak. Fourth, the biaserror is removed and the corrected signal V raw − bias is seg-mented by zero crossings. Finally, the data in individualsegments are rescaled by local maxim and minim to correctgain mismatch.As shown in Fig. 5, this approach can effectively findtime dependent correction factors due to tracer movement. Time t (s) A ng l e / π Time t (s) L ( c m ) Uncorrected angle Φ Phase angle φ Corrected angle Φ Fig. 7.: Arc-tangential demodulation process to obtain thetraveling distance from the Tx. to a Rx. antenna. The redopen symbols correspond to the outcome from the demod-ulation and the blue curve represents the continuous phaseshift that scales with the traveling distance of an EM wave.The gray curve corresponds to the Φ without correcting IQmismatch. Inset shows an example of the variation of L over a longer time.For the corrected data of channel 3 (dark blue circles), thereexists a slight deviation from a perfect circle, indicating theexistence of a small phase error. This arises presumablyfrom the fact that perfect polarization cannot be achievedfor all three Rx. antennae. Further investigations are neededto check whether this error can be avoided by using circu-lar polarized EM waves or by correcting the phase errorbetween I and Q signals in the Matlab program.After the correction of IQ mismatch, the correspondingphase angles are obtained by φ = arctan( Q/I ) . Because φ is a modulo of π , a further correction on the phasejump is needed to obtain the continuous phase shift Φ . Inthis step, a threshold is introduced to determine whethera phase jump occurs or not and in which direction thejump takes place. As the phase shift of the i th channel Φ i ∝ L i , the variation of Φ with time (see the blue curvein Fig. 7) indicates that the target object moves initiallyslow and accelerates while moving away from the anten-nae. As demonstrated by a comparison between corrected Φ and uncorrected Φ uncorr phase shift, the aforementionedcorrection method can effectively reduce unrealistic fluctu-ations (see also Fig.3(b)) in the reconstructed curves. Morequantitatively, the magnitude of oscillations enhances withthe speed of the projectile and it can reach ± . cm. Aftercorrection, it reduces to less than . mm. As shown in theinset of Fig. 7, the distance L obtained from Rx. antennarepresents exactly what is expected: The object falls freelywith a growing velocity and bounces back when reach-ing the container bottom, suggesting that the coefficientof restitution, which measures the relative rebound overimpact velocities, can be determined with the radar system. RADAR FOR PROJE CT IL E IMPACT t (s) z ( c m ) /2Falling height (cm) Fig. 8.: A comparison of reconstructed free-falling curvesat various initial falling heights. The solid line correspondsto the expected free-falling curve for the largest fallingheight. Note that the curves for various H are shifted tohave the initial falling position z = 0 cm, and only thetrajectories before the first bouncing with the container bot-tom are shown except for H = 22 . cm. For each curve,one over 15 data points are shown here for a better visibil-ity. The typical error bar ( ∼ mm) of the position data issmaller than the symbol size.In comparison to the standard high speed imaging tech-nique [14], the radar tracking technique requires less datacollection and processing efforts. IV. VALIDATION OF CORRECTIONALGORITHM
As the goal of this investigation is to explore the possibilityof obtaining an object moving inside a granular mediumusing microwave radar. We proceed with the following twosteps:First, we focus on a spherical projectile falling in freespace without the presence of granular materials. We com-pare the reconstructed trajectories of the object from dif-ferent initial falling heights with the expected paraboliccurve. As shown in Fig. 8, the falling curves agree withthe expected curve well, demonstrating that, after a propercorrection of IQ mismatch, the radar system can be usedfor particle tracking. In particular, the tracer falls undergravity over a distance up to cm, which is about / of the working distance. After a proper correction of thesignal fluctuations for both IQ channels, the correct infor-mation on the phase (i.e., distance) can be extracted toa satisfactory level. This outcome also suggests that theconfiguration built for releasing the tracer with minimizedinitial velocity and also for a better signal-to-noise ratioworks well.Second, we replace the lower part of the free spacewith a granular medium composed of the EPP particles(see Fig. refsetup), which are expected to be transparentto EM waves. Expanded polypropylene (EPP) particles(Neopolen, P9255) are used as the granular sample. As the P r obab ili t y Particle volume (mm ) Measured areaNormal distribution
Fig. 9.: A close view of expanded polypropylene (EPP)particles used as granular sample with the volume distribu-tion assuming the particles are prolate ellipsoids. In totalthe shapes of 241 particles are analyzed to generate thedistribution.particles are porous with % air trapped inside, its dielec-tric constant (relative to vacuum) is . , very close to air.Therefore, they are practically transparent to electromag-netic (EM) waves. As the snapshot in Fig.9 shows, the EPPparticles have an ellipsoidal shape with a length-to-widthratio of ≈ . and an average volume of . ± . mm,where the uncertainty corresponds to the standard deviationof the volume distribution. Here, the volume is estimatedassuming that the particles are of prolate spheroid shape(i.e., a = b < c with a , b and c semi-axes of an ellip-soid). The density of the particles is kg · m − , whichcan typically be tuned in the expansion process. Othermaterial properties include: average particle weight . mg,bulk density kg/m , tensile strength kPa, thermalconductivity . W/(mK).Two intruder shapes are used for the test experiment: Asphere with a diameter of . cm and a cylinder with adiameter . cm and height . cm, both made of Styro-foam with the tracer embedded. For each type of projectile,three free-falling experiments are conducted with the sameinitial falling heights. As shown in Fig. 10, both projectilesfollow the same trajectory before they touch the surfaceof the granular medium as expected. While penetratingthrough, cylindrical projectile experiences a slightly largergranular drag and consequently land at a relatively shal-low depth in comparison to the spherical one. Note that thesmoothness of the tracer trajectory while impacting on thegranular layer demonstrates that the EPP particles chosenhere are indeed transparent to EM waves and there is noinfluence from possible multiple scattering of EM wavesby granular particles. For the case of spherical projectile,the reconstructed trajectories of ten repetitions give rise tothe same parabola for the free falling region. This outcomevalidates the correction protocol introduced here. From theprojectile trajectory inside a granular medium, one canobtain the acceleration as well as total force acting on it. ADAR FOR PROJECTILE IMPACT Sphere in free space
Fig. 10.: Reconstructed trajectories of projectile impactinto a granular bed composed of EPP particles. The initialfalling height is fixed at cm with respect to the floor. Thegreen, red and blue data points represent the three scenar-ios: Free falling into the empty container without granularfilling, impact into a granular bed by a spherical tracerand by a cylindrical tracer particle. The typical error bar( ∼ mm) of the position data is smaller than the symbolsize. The vertical dashed line corresponds to the time whena projectile touches the surface of the granular medium.Note that mechanical properties of granular particles canbe determined experimentally or from the specificationsprovided by the producers. Subsequently those informa-tion can be used in numerical simulations using discreteelement methods to have a direct comparison with experi-mental results. Thus, radar tracking technique can be usedhere to explore the ‘microscopic’ origin of the drag forceinduced by granular particles in combination with numer-ical simulations. Interested readers may refer to [15] for arecent example. V. CONCLUSION
To summarize, this investigation suggests that advances inradar tracking technology can be helpful in the investiga-tion of granular dynamics. Using an X-band continuouswave radar system, we are able to track a centimeter sizedmetallic object in 3D, which enables, for instance, a mea-surement of the coefficient of restitution of the particle. Incomparison to other particle imaging techniques alreadybeing used for granular particles [3], continuous-waveradar tracking has the advantage of high time resolutionand low data collection and processing requirements. Withthe rapid development of radar technology, this approach isalso expected to be more cost effective and accurate.Moreover, we show that the accuracy of the radar track-ing technique depends strongly on a proper correction of IQmismatch, which arises predominately from the mobilityof the tracer itself. A practical approach has been pro-posed to correct the instantaneously changing bias as wellas gain errors in the raw IQ signals. Finally, we validate thisapproach through an analysis on the reconstructed trajecto-ries of projectiles falling under gravity in free space as well as impacting into a light granular medium. In comparisonto our previous investigation [10], this approach enablesmore quantitative studies of an object moving in a threedimensional granular medium.Further investigations will focus on particle trackingwith various types of granular materials, particularly howto deal with distorted signals arising from multiple scat-tering of the surrounding granular particles that are notcompletely transparent to EM waves. As the algorithm doesnot rely on the frequency band chosen, it would also beinteresting to employ radar systems working at a higherfrequency band to achieve better spatial resolution.
ACKNOWLEDGMENT
We acknowledge Felix Ott for his preliminary work onthe experimental set-up and Klaus Oetter for technicalsupport. Helpful discussions with Valentin Dichtl, SimeonVölkel and Ingo Rehberg are gratefully acknowledged.This work is partly supported by German Research Foun-dation through Grant No. HU1939/4-1.
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