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Implementation of Linear Array of Ultrasonic Transmitter-Receiver Transducers for detection of Non-Smooth Porous Surface
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Implementation of Linear Array of Ultrasonic Transmitter-Receiver Transducers for detection of Non-Smooth Porous Surface

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Level measurements, thickness measurement or remote surface detection using ultrasonic pulse transit method require that the target surface be at 90O to the incident beam so that reflected beam ...

Level measurements, thickness measurement or remote surface detection using ultrasonic pulse transit method require that the target surface be at 90O to the incident beam so that reflected beam comes back at 180O angel to effectively use this method. This is perfectly true in case of flat, solid surface at right angle to the incident beam. But surface irregularities of a porous, non-smooth, uneven material such as snow cause penetration of incident wave into the surface, absorption of the incident energy, scatter of energy in many directions and further attenuation of reflected signal making it difficult to detect the reflected echo. Such a received reflected echo is very low in amplitude and is heavily noise ridden. The successful surface detection with excellent repeatability and accuracy without any false measurement in this case requires combination of physical acoustic, mechanical, hardware and software techniques together. In this paper we discuss the suitable physical, mechanical, electronics design to physically implement the theory of Arrayed Ultrasonic transducers to shape up the directional response, beam width and avoid interference to improve the chances of proper and sufficient reflection from the non-smooth, highly porous, uneven, non-planar irregular surface.

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Implementation of Linear Array of Ultrasonic Transmitter-Receiver Transducers for detection of Non-Smooth Porous Surface Implementation of Linear Array of Ultrasonic Transmitter-Receiver Transducers for detection of Non-Smooth Porous Surface Document Transcript

  • R. Attri Instrumentation Design Series (Snow Hydrology), Paper No. 4, July 1999Implementation of Linear Array of Ultrasonic Transmitter-ReceiverTransducers for detection of Non-Smooth Porous SurfaceRAMAN K. ATTRI (Ex- Scientist, CSIO, Chandigarh India)SWARANJIT SINGH (Senior Technical Officer, CSIO, Chandigarh India)ABSTRACTLevel measurements, thickness measurement or remote surface detection using ultrasonic pulse transit method require thatthe target surface be at 90Oto the incident beam so that reflected beam comes back at 180Oangel to effectively use thismethod. This is perfectly true in case of flat, solid surface at right angle to the incident beam. But surface irregularities of aporous, non-smooth, uneven material such as snow cause penetration of incident wave into the surface, absorption of theincident energy, scatter of energy in many directions and further attenuation of reflected signal making it difficult todetect the reflected echo. Such a received reflected echo is very low in amplitude and is heavily noise ridden. The successfulsurface detection with excellent repeatability and accuracy without any false measurement in this case requires combinationof physical acoustic, mechanical, hardware and software techniques together. In this paper we discuss the suitable physical,mechanical, electronics design to physically implement the theory of Arrayed Ultrasonic transducers to shape up thedirectional response, beam width and avoid interference to improve the chances of proper and sufficient reflection from thenon-smooth, highly porous, uneven, non-planar irregular surface.1. INTRODUCTIONRemote Surface Detection using Ultrasonic Pulse Transit(Pulse-echo) method is one of the popular methods fordetecting the target surface, estimating its distanceaccurately and its 3-D imaging[1]. Such kind of RemoteSurface Detector (RSDs) have numerous applications inIndustrial, military and physical instrumentationenvironments. Mostly such methods are used for solid,smooth and possibly flat surface or a target havingsmooth surface. In such cases the chances of reflectedenergy back to the source are high and the target isdetected accurately.However the issues do not remain simple when samemethod of Ultrasonic Pulse transit is used for detectionof targets with non-smooth surfaces, level detectionwhere the surface is uneven and for detection on non-sold porous surfaces. Such detection of non-solid,porous, uneven, non-smooth, irregular surface requirelot many considerations in design of such RSDs. There arenumerous applications, where the non-smooth, uneven,porous, irregular surface detection or target detection isan important application. For example the Snow Surfacedetection is very important application of such RSDs todetermine the thickness of the snow layers by findinghow much the current surface level is above the groundlevel. This requires detection of snow surface detectiondistance from the sensor[2]. This information is used forhydrological studies such as forecasting model for snowavalanche release, river run off water, glacier sliding andrelated phenomenon in the mountain areas and planesnearby[3, 4]. The fresh snow is extremely porous non-smooth and irregular surface where using remotesensing of snow using ultrasonic beams have its ownproblems[3, 5].Another example is automated chemical plant whereeither liquid or some powder compounds are being filledin big tanks and upper surface level of the compoundw.r.t to base of the tank is detected by ultrasonic sensorso as to stop the filling jet at right time to avoid thespilling. Liquid or oil level in tank is one of suchapplication employing ultrasonic techniques to surfacelevel detection[6]. This application is typical case of non-smooth porous and continuously growing surface.Another application may be detection of porous surfaceof sand. In such applications, the ultrasonic pulse transitmethod is generally employed but the accuracyrequirements make it a critical application[1, 7].In this paper, we will discuss the theory behind thearrayed transducers in series and its physicalimplementation to produce improvement in detection ofsuch non-smooth irregular surface of a porous material(typically snow). This method of minimizing the effects oflosses in the material because of its irregularities andincreasing the reliability of the signal received will bediscussed keeping the electronics design and softwarealgorithm out of the scope of this paper. The scope hasbeen limited to issues and their solutions throughphysical, mechanical or electronics design only.2. PULSE TRANSIT (PULSE-ECHO) METHOD OF LEVELDETECTIONLevel detector is one special case of remote surfacedetector which inherently detects the surface of thematerial or liquid whose level w.r.t. base is to be foundout. The ultrasonic based level detectors are quitepopular in oil tank level determination applications[6].The concept used in level detectors or surface detectoror depth sensors is same. From Electronics point of view,this depth sensor system is a standalone systemconsisting of ultrasonic transmitting transducers,ultrasonic receiver transducers with signal conditionercircuit and software controlled hardware designedaround microprocessor. The level or the surface isdetected using pulse transit method[1]. A short burst ofultrasonic pulses is transmitted by the piezoelectric
  • R. Attri Instrumentation Design Series (Snow Hydrology), Paper No. 4, July 1999Copyright © 2001 Raman K. Attri Pg 2transducer transmitter, which is mounted on a pole withthe sensors facing vertically downward towards thesurface of interest. Refer to Fig [1]. The system is usuallyhaving separate or dual purpose ultrasonic transducersfitted in its hood, facing the surface. The transmittersection works under the control of microprocessor and isdriven by high voltage power transistor giving out pulsesin ultrasonic frequency range of 40 KHz at around 60V to100V amplitude. The frequency and voltage levels areapplication dependent and are dependent upon thenature of the surface being detected. Mechanical wavesgenerated by transmitting ultrasonic transducers travelstowards the target surface. The transmission is done as ashort burst of ultrasonic pulses.The transmitted beam strikes the surface of the target.Some of the energy get reflected back and is received bythe receiver. Receiver is a set of ultrasonic transducersmounted adjacent to transmitter transducers. In somecases, the same transducers act as transmitter as well asreceiver. The receiver converts the received mechanicalenergy in electrical signal forming a voltage echo signal inthe signal conditioner[1].The microprocessor reads the time lag betweentransmitted pulse stream and received pulse stream. Thetime of travel between the transmission and thereception of the reflected pulses (more precisely echo) iscomputed which gives the distance of upper surface fromthe sensor as per distance-velocity equation. Thisdistance is employed for determining distance of theobject remotely.Fig [1]: Remote Surface Detector Mounting ArrangementThe other use of this distance is finding the net thicknessof the material if the base distance (distance of sensorfrom the ground i.e. sensor installation height) is alreadyknown. By subtracting the measured surface distancefrom the installation height, the surface level or thedistance of the surface from the ground or base isobtained. This method is called Pulse Transit methodsince a short burst of pulses of ultrasonic energy istransmitted toward the surface and time of transitbetween transmission and reception is found[1]. Thismethod is also called Pulse-echo method which meanslistening the reflected echo of the transmitted beam[7].Pulse-transit method can be used with sound waves, lightwaves or radio waves. However ultrasonic is mostpopularly used due to nominal accuracy required in theseapplications.3. PROBLEMS DUE TO ENERGY LOSSES IN NON-SMOOTH POROUS MATERIALThe overall performance and reliability of the depthsensor based on this method depends upon the ability ofthe system to detect the reflected echo of thetransmitted signal[1]. Further the system performancecan be increased only if one can enhance the reflectedecho to a sufficiently detectable level.This simple method of finding the thickness, depth orlevel is not as simple when applied to the snow or anyother similar porous material surface detection. Thereare many factors like losses in the material andirregularities of surface which govern the range andreliability of the depth sensor[8, 9]. Some of the criticalproblems associated with Pulse-transit method whenused for non-smooth porous surface are as follows:3.1 Attenuation of received echo due to divergenceOne very first phenomenon that happens with Ultrasonicbeam in all the applications requiring the long range isthe divergence of the beam. Additional allowance has tobe made for reduction of amplitude due to thedivergence of beam[10]. Divergence of the beamdetermines the range in case of materials, which canreadily be penetrated. As the distance increases thebeam becomes less strong and at very long distance thebeam eventually dies out. The coefficient of attenuationis directly proportional to frequency. Attempts need tobe made to avoid attenuation due to distance by usinglower frequencies. However using lower frequency hasanother disadvantage of reduced accuracy in the rangedetermination of the surface. A suitable tradeoff is surelyrequired in this case.3.2 Scattering of energy at rough surface grainboundariesIn the specific application of depth measuring, the shapeand the roughness of the surface is of decisiveimportance. These factors often limit the sensitivity ofdepth sensor. If we take the example of snow surface, aroughness of more than 1/10 of wavelength impairs thecoupling markedly[4]. The rough surfaces make the
  • R. Attri Instrumentation Design Series (Snow Hydrology), Paper No. 4, July 1999Copyright © 2001 Raman K. Attri Pg 3ultrasonic beam to become diffused and scatter in alldirections, as shown in Fig [2].The major loss in reflected energy is the scattering of theenergy at the grain boundaries. For non-smooth surfacelike snow, the grains are not strictly homogeneous andcontain boundaries on which acoustic impedancechanges abruptly because of change in density[4]. Theaverage grain size of snow is 2 mm to 5 mm which iscoarse as compared to wavelength being used and as aresult, scatter will take place as splitting of incident waveinto various reflected and transmitted waves at theoblique boundary. This process keeps repeating at everygrain boundary. So scattering is a severe problem in caseof snow, which reduces the effective energy gettingreflected in the direction of the sensor, and hencereducing the amplitude of reflected echo. Porosity ofsnow, where crystallites of different structure andcomposition are present, is also one of the similar flaws.The worst of all is that sometime the reflected echo isnot received at all. The reflected beam reflects at suchangle that it completely misses the receiver sensors andsystem remains in wait mode.Fig [2]: Scatter and Absorption of Ultrasonic wave in anon-smooth porous surface3.3 Absorption of transmitted energy by the poroussurfaceThe porosity of the such surfaces such as snow causeslarge amount of ultrasonic energy to get absorbed in thesnow, so only a small part of it get reflected back. Thephenomenon is depicted in Fig [2]. This absorption isanother reason of weak reflected signal[10]. It isconversion of sound energy into heat due to oscillationof particles. The absorption increases as the frequency ofthe incident wave. To counteract this effect transmittervoltage and amplification has to be increased. Steppingup transmitter voltage or the amplification can notcounteract the much more awkward disturbances causedby scattering, which not only reduces the height of echofrom both the flaw and the back-wall but in additionproduces numerous echoes with different transit times,in which true echoes may get lost. Absorption andscattering both can be reduced by lowering thefrequency of the transmitted pulses, for which againthere is a limit[10]. The received echo is very weak whichneed considerable amount of amplification[12, 13]. Theworst of all is that the ultrasonic beam is striking the non-smooth surface, which causes the scatter, and themissing of reflected beam. As a result system has to bevery sensitive to detect the weak reflected echo as well.The reflected echo is around 0.1 mV in response totransmitted wave of 100 V.3.4 Inherent errors Associated with ultrasonic beamAlong with design constraints, some errors are alsoencountered in the system. It pertains to the near-fieldinterference and grating lobes caused by thisinterference[9, 14]. The reflected echo is received as resultof these grating lobes instead of the actual reflection,thereby causing effect of side-looking, implying as iftarget is lying in the immediate proximity of thetransducers[9, 15]. In the directional pattern, the sidelobes are shown in the figure [3]. These grating lobesinduce a signal in the nearest receiver situated on theside of these lobes; hence it is taken as reflected signalby the unit, thus giving wrong distance reading as if thetarget surface is very near to the sensor hood. Theseside lobes also depend upon transducer diameters andwavelength ratio[14, 15]. One obvious solution could be tomodify the dimensions of the transducer, which is notpossible as these sensors comes in pre-fabricated form.However, by changing the geometry of multipletransducers in an array could be one solution assuggested by array theory to reshape the directionalresponse and also some implementation in hardware toprovide such near-field compensation so that side lobe isnot detected at all.Fig [3]: Side lobes in the Directional Pattern of UltrasonicTransducers[14, 15]To sum up, such critically irregular and non-smoothporous surface (e.g. Snow surface) causes penetration ofwave of incident wave into the surface, absorption in thesurface and scattering around which results in eithermissed reflected wave or a very low amplitude highlynoise ridden reflected signal[16]. These have to takeninto consideration while designing the system. It hasbeen found that echo reflected from non-smoothirregular snow surface is of such small amplitude which is
  • R. Attri Instrumentation Design Series (Snow Hydrology), Paper No. 4, July 1999Copyright © 2001 Raman K. Attri Pg 4difficult to detect. The received echo is very weak whichneeds considerable amount of amplification. The worstof all is that the ultrasonic beam misses reaching thereceiver and system keep waiting for the reflected beam.4. DESIGN SOLUTIONSThe phenomenon of divergence, absorption andscattering should be dealt simultaneously throughunified design techniques. Three obvious options havebeen:i) increase the transmitted voltageii) Reduce the operating transmittedfrequency.iii) Increase the receiver amplificationExperimentally it has been found that increase intransmitted voltage amplitude do have someimprovement of results, but this improvement getsaturated after certain point and no amount of increasein transmitted voltage make any effect. The use of lowerfrequency does have some positive effects of increasingthe range and reducing the losses due to scatter andabsorption, but there is a limit on lower frequencyultrasonic transducers available. It further affects therange accuracy badly. Further the increase inamplification of received echo will only increase thenoise beyond the threshold level.So these obvious design approaches could not be usedbeyond a particular limit. However we optimized thetransmitter voltage by keeping the current consumptionlower and the response at maximum possible. Arelatively low frequency of 40 KHz was selected withoutsacrificing the accuracy much. A nominal gain andsuitable threshold was provided at receiver to limit thenoise within threshold limit so as not to give falsereading.However, all these solutions could improve the reliabilityof the system, but scattering, absorption and chances ofaltogether missed wave was still there. In addition tonormal electronics signal conditioning requirements, theoptimal design was required to fulfill followingrequirements:i) Broader surface area of receiverii) Broader beam widthiii) Higher range (min 4 meters)iv) Accuracy of + 1 cm in distance detectionv) Lesser absorption in the surfacevi) Increased amplitude of superimposed receivingpulsesvii) Effective compensation of the scatteringviii) Effective cancellation of side grating lobesWe found that the theory of planar array technique wasquite suitable to provide effective solution for most ofour requirements. In planar array technique number oftransducer elements are connected in series to form anarray and mounted in a plane[7]. The resultant directionalpattern of the array is a mathematical function ofdirectional pattern of the individual transducer. Thedesired pattern, which increases the range and thesensitivity, is obtained by controlling the factors likenumber of transducer elements, diameters oftransducers, frequency, geometry and inter-elementspacing etc[15, 17]. By using proper number of transducerelements, spacing and geometry, this array of transducerdirectional pattern could be made little broader toincrease the chances of reception after selecting thediameter of pre-fabricated transducer and selecting theoptimal frequency.5. PHYSICAL IMPLEMENTATION OF ULTRASONICTRANSDUCER ARRAYSAlthough the crystals used are reversible (can be used intransceiver mode), even then separate sensors fortransmitter as well as receiver are used. Further one-to-one ratio of transmitting and receiving sensor has notbeen found suitable in the present application. Separateset of transducers have been used in the transmitter andreceiver in the array mode. Different arrangement ofarrays has been used for receiver and transmitter. Thetransmitted ultrasonic beam directional pattern has beenmodified using this Ultrasonic Transducer arrayarrangement in order to deal with the non-smoothsurface of snow and to counteract the scattering effects.The shape of these individual elements, spacing betweenthe individual transmitting transducers in x-axis and y-axis, mounting geometry i.e. whether in rectangle,square or triangle etc. drastically shape up the directionalpattern, beam width and side lobes.[14, 15, 16, 17].To achieve the right kind of directional pattern we eitherneed extensive mathematical computations to find theoptimal geometry or to perform the extensiveexperiments to select the right mounting geometry. Inour case we performed the experiments keeping thetheory of array as the basis. The purpose in our case wasto make the beam pattern relatively broader with largefront zone area[17]. This design effort increases thepossibility of getting even the scattered beam from thenon-smooth surface of snow.On the basis of mathematically model of array theoryand experimentation on it, for transmitting array wechose 3 x 1 line geometry and for receiver array we chose3 x 3 square geometry, mounted on same plate in planarfashion with same inter-element spacing between theelements for transmitter and receiver array. It is shownin Fig [4].
  • R. Attri Instrumentation Design Series (Snow Hydrology), Paper No. 4, July 1999Copyright © 2001 Raman K. Attri Pg 5Fig [4]: Transmitter and Receiver array arrangementAs mentioned, the transmitter is a line geometry withtransmitting array of 3 x 1 (i.e. 3 transducers mounted ina row) having a spacing between them equal to little lessthan the half wavelength. Refer to Fig [5].Fig [5a]: Transmitting Transducer in series arrayAs mentioned above the transducers are connected inarray. There are two options of connecting the array: oneis putting elements in parallel and one is putting thearray in the series[13, 17]. In our case we have chosen thelater approach. It has given a big design advantage.Putting transmitter array in series, one shown in Fig [5a]ensured that each of the three transducers are activatedwith little delay in between, so result is transmission ofthree envelops of bursts. This short delay makes the rightsuperimposition at the rough surface and chances ofreflection, from any one of the envelops, is strengthened.The series connection at transmitter adds up thedirectional response of the three individual crystals andresultant transmitted beam pattern is wide anddirectional enough to gives a beam focused on non-smooth snow surface covering good some surface areaso that at least form one point out of the covered area,there is good possibility of reflected signal reaching inthe direction of the receiver array.The result was that the array gave sufficiently broaderbeam width with beam expansion of 60owhich is doublethe normal beam width. Refer to fig [11] which showsthe improved & wider directional response of the arraytransducers (explain in later section).[15, 17, 18]The power distribution of broader beam width wascompensated by increasing the power supply to thetransducers from 30V DC to 60V DC. With thisconfiguration, the beam width becomes broader, so ittravels as broader beam rather than a straight-line thinbeam towards the surface. Even if the surface is uneven,there are chances that out of a bunch of integratedbeams some of the components will surely be reflectedin the direction of the receiver. Optimum performancecan be achieved by varying the geometrical parametersfurther as well as frequency of transmission, if we havean option.The receiver array response was also optimized by usingthe rectangular geometry consisting of arrayconfiguration with total 9 transducers mounted in squarearray of 3 x 3 receiver array isolated mechanically as wellas electrically by a shield for proper decoupling ofinterference from transmitting array, as shown in Fig[4][17]. Wider receiver surface area gives the ampleopportunity that the reflected beams at some angle willalso get captured. The techniques really made the systemvery robust thus worked well with almost all kinds ofrough surfaces and particularly proved suitable on snowsurface.The transducer elements in this 3 x 3 receiver array areconnected in series, as shown in Fig [5b]. This gives a verybig advantage that the overall voltage received at thereceiver section is superimposition of the wave frontarriving at each of the receiver transducer. Thisstrengthens the receiver signal and even if only onetransducer element has received the wave front, it actsas right input signal. The resultant signal is sum of theentire signal received at individual piezoelectric crystals,giving better sensitivity on receiver end. The use of arrayensures that receiver has got better surface area and atleast one of the receiver transducer shall receive theenough amplitude of the returned echo to detect thesurface.Fig [5b]: Receiver transducer in series arrayThe receiver section in this case will receive the threeechoes since there were three transmitted envelops. Thisensure that even if we are transmitting one envelopconsisting of N number of pulses, the receiver wave frontwill be a superimposed wave front consisting of 3 x Nnumber of pulses. This increases the system
  • R. Attri Instrumentation Design Series (Snow Hydrology), Paper No. 4, July 1999Copyright © 2001 Raman K. Attri Pg 6responsiveness and lessens the chances of missing thereflection. This will be clearer from the Fig [6] whichshows the three transmitted envelops received at thereceiver.Fig [6]: Superimposed time shifted 3 transmitted wavefront envelops6. THEORY BEHIND THE PHYSICAL IMPLEMENTATIONOF TRANSDUCER ARRAYThe theory of array sources relies on mathematicalderivations of aperture and frequency response. Thetreatment here is kept quite simple without includingintricate derivation in order to relate it with the physicalimplementation of ultrasonic array. Interested readersare advised to refer to Martin E. Anderson & Gregg E.Trahey’s seminar[22]on ultrasound which covers arraytheory, 2-D Fourier transform, spatial frequencies,nctions and detailed computations.Here we will touch the theory of transmitter and receiverlinear array to highlight that the totol response of thearray is some mathematical function of all the individualtransducers. Further it will be highlighted how directionalpattern, beam width, dispersion, number of side lobesand combined array response is dependent upon thesize, spacing and geometry of the transducers. However,detailed derivations can be found in literature atreference [17, 20, 22].To brief-up, the ultrasonic array is dealt in analogy withthe optics. In optics, the Huygen-Fresnel principle statesthat wave fronts can be decomposed into a collection ofpoint sources, each the origin of a spherical, expanding,wave that can be represented as a free space Greensfunction. This concept underlies the derivation of animportant tool, the Fraunhofer Approximation. TheFraunhofer approximation (FA) plays a pivotal role in ourexploration of ultrasound k-space. In a nutshell, this well-known expression from the optics literature states thatthe far-field complex amplitude pattern produced by acomplex aperture amplitude function is approximatelyequal to 2-D Fourier transform of that function. Appliedto ultrasound, this approximation states that theultrasound beams pressure amplitude pattern can beestimated by taking the 2-D Fourier transform of thetransducer aperture. Naturally, this approximation isbased on several assumptions and requirements thatconstrain its application to the far field of an unfocusedtransducer or the focal plane of a focused transducer. Aslong as we dont violate the assumptions made informulating the FA, this powerful approximation allowsus to extend our intuition regarding linear systems to thestudy of ultrasound beam forming. Restricting thediscussion for a moment to the lateral and axialdimensions, the most obvious example of an aperturefunction is the rectangular aperture of a linear array lyingalong the lateral coordinate axis, emitting a singlefrequency of sound.[22]6.1 Frequency Response of Planar TransmitterarrayConsider a planar Transmitting piezoelectric array of oddnumber (M x N) of identical elements, as shown in figure[7]. In general number of elements in X and Y directionsare not same, i.e. array is usually made a rectangle[15, 16,20, 21]. Also spacing in elements of X direction is not sameas spacing of elements in Y direction. Also note that xand y are usually chosen to be less than one halfwavelength to avoid grating lobes, that is, extraneousmain lobes, under all condition of beam steering.Frequency response of one ultrasonic element is functionof frequency ‘f’ and location (x, y). Let Frequencyresponse of one ultrasonic element located at (x, y)operating at a frequency ‘f’ is r (f, x, y). When a numberof such elements are mounted in a plane then the entiresystem have a resultant total frequency responseindicated by A (f, x, y).Using the principle of superimposition, we can infer thatthe total frequency response of the array is thesummation of response of all the elements taken over allthe locations. This is expressed as under:M NA (f, x, y) =   cj k r (f, x- j x, y- k y) --- eq (1)J=0 k=0Wherej, k position count number of the element in x and y directionw.r.t. to 0thelementM is the total number of elements in X directionN is the total number of elements in Y directionf is the frequency in Hz
  • R. Attri Instrumentation Design Series (Snow Hydrology), Paper No. 4, July 1999Copyright © 2001 Raman K. Attri Pg 7x is the constant inter-element spacing in meters in X-axisy is the constant inter-element spacing along Y-axisAnd cjk is the complex weight associated with element (j,k). This complex weight of the individual responses or thecoefficient of individual response by a particular elementat a desired point is given by:cj k = ajk exp(+i.)Where ajk is the real amplitude weighting term is the Real phase weighting termFig [7]: Planar rectangular Array arrangement of M x N(odd) Transmitter elementsThe convolution theorem can be applied as under onterm r (f, x-j x, y- k y) to express it in form of shiftedimpulse response of point sources. If we take  (x) as theimpulse response of a point source / transducer elementlocated at x and  (y) as the impulse response of a pointsource / transducer element located at y, then:r (f, x-j x, y- k y) = r(f, x, y)** (x- j x). (y -k y)where ** implies the convolution.Putting this value in equation (1) we getM NA (f, x, y) =   cj k r (f, x, y) **  (x- j x).  (y- k y )J=0 k=0A (f, x, y) = s(x, y) ** r(f, x, y) --- eq (2)where termM Ns(x,y) =   cj k (x- j x). (y- k y)j=0 k=0is defined as frequency response of an equivalent planararray of M x N odd complex weighted point sources. Itcontains all information containing the array, such as thetotal no of elements, the complex weight, geometry ofarray, positioning of array in XY plane.6.2 Far Field Beam Pattern of Planar TransmitterArraysIn transmit mode far field beam pattern of this array is ameasure of the ability of the array to concentrate theacoustic power in the preferred direction. When used inreceive mode, the far field beam pattern is a measure ofthe ability of array to distinguish among several sourceslocated at different spatial locations[14, 16, 20].Let A (f, x, y) is the complex frequency response function(aperture function), as given by the equation (2).From aperture theory, complex aperture function andthe far field beam pattern form a spatial Fouriertransform pair as under:[22]D (f, , ) = F {A(f, x, y)} ---.eq (3)Where D is the far field directivity function or beampattern,  And  are the spherical angles as shown in Fig[8]Fig [8]: Spherical angles for far filed beam transmissionFrom equation (2) and equation (3), we getD (f, , ) = F{ s(x, y)** r(f, x, y)}
  • R. Attri Instrumentation Design Series (Snow Hydrology), Paper No. 4, July 1999Copyright © 2001 Raman K. Attri Pg 8Which impliesD(f, , ) = S( , ) R(f, , ) ---eq (4)Because convolution in spatial domain gives products inspatial frequency domain. Here R(f, , ) is the doubleFourier transform (DFT) of {r(f, x, y)} and S( , ) is thedouble Fourier transform of {s(x,y)}. In terms of spatialfrequencies above equation can be written as under:D( f, fx, fy) = S( fx, fy) R( f, fx, fy) --- eq (5)Where fx and fy are spatial frequencies in units of cyclesper meter, given asfx = u /  = (sin. Cos)/fy = v /  = (sin. sin)/Here ‘u’ and ‘v’ are direction cosine with respect to X andY axis.Eq (5) is referred as Product theorem for planar Arrays. Itstate that the far field directivity function of a planararray of identical elements is equal to the product ofthe far-field directivity function R(f, fx, fy) of one of theelements and the far field directivity function of anequivalent planar array of point sources.S (fx, fy) is in form of Discrete Spatial Fourier Transform(DSFT), i.e. transform in form of sines and cosines, alsocalled Wannier transform, of complex number. Real partof amplitude weight cjk controls the shape of the far fieldbeam pattern, i.e width of the main lobe and the level ofthe side lobes. The phase weight  allows the steering orthe tilting of the beam in the preferred direction.6.3 Frequency Response of Rectangular ReceiverarrayConsidering a case of a planar array of M x N (odd)identical, complex-weighted point sources lying in theX-Y plane as shown in Fig[9]. The array is being used inthe receiver mode. Based on output electrical signal fromthe individual element in array, it is desired to estimateboth the target’s direction and the frequency contents ofradiated acoustic field[17, 21].Assume that output electrical signal from element (m,n) of array is y(t, r) which can be written as y(t, m x, ny) also since element (m, n) is located at x = m x , y =n y as shown in figure [9]. Here m = -(M-1)/2,.....0,....+(M-1)/2 and n = -(N-1)/2,....0.....+(N-1)/2for M and N odd.Adding complex weight to above output, the output fromone elements becomesY(t, x, y) = Cmn. Y(t, m  x, ny)Outputs from all the elements isY (t, x, y) =   Cmn. Y (t, m  x, ny) --- eq (6)Fig [9]: Rectangular receiver array in 3 x 3 configurationA treatment on this equation similar to eq (1) will resultin Frequency and angular spectrum is given by:Y (, x, y) = Ft Fx Fy {y (t, x, y)} --- eq (7)This equation again shall give rise to equations of DSFTsimilar to as derived for the case of transmitter. From thedetailed computations of arrays, it can be inferred fromthe plot of the above frequency response equations thatArray has a region of maximum response to signalscentered at  =0 (broadside) This region of maximumresponse is usually called main lobe and the othermaxima is called side lobes. The response drops offrapidly as the signal is moved away from broadside[22,23, 24].In the resultant response of the entire array, to avoidgrating lobes (extraneous main lobes) under allconditions of beam steering, inter-element spacing xand y must satisfy nyquist condition:x and y < min / 2 --- eq (8)7. IMPLEMENTATION OF TRANSDUCER ARRAYIn the present case, design comprises of planar array of 3x 1 transmitter array and 3 x 3-receiver array ofultrasonic transducers. The characteristic frequency is 40kHz with a wavelength of 9-11 mm (varies with velocityof sound) and diameter of the element used is 12 mm.Inter-element spacing is calculated from equation (8) ismaximum 5 mm. However the inter-element spacing of 5mm is not possible when diameter of the transducers is13 mm. The diameter of the transducers can not be
  • R. Attri Instrumentation Design Series (Snow Hydrology), Paper No. 4, July 1999Copyright © 2001 Raman K. Attri Pg 9selected too less because the directional patterndepends upon D/ ratio. In the current case the D/ratio of 1.2 is associated with each of the transmittingelement. It can be seen from the Figure how D/ governsthe beam pattern of individual element. Too less a valueof D implies multiple grating lobes generated by eachelement which are not acceptable in this case.Fig [10]: Effect of Diameter to wavelength ratio of theradiator on the Directional pattern of the ultrasonic beam[14, 15, 16]So only way is to adjust the centre to centre inter-element spacing at an optimized value. We fixed itapproximately at . A nominal value of 13 mm inter-element spacing is good enough to tradeoff betweencombined resultant multiple-grating of the completearray and gratings of individual transducer element.Incidentally this is the minimum spacing allowed due tosize of the transducers. However our experimentsindicate that number of gratings increase as we increasethe spacing and hence the receiver gets triggered withwrong reflection and responds to the grating beam itself.The resultant directional characteristics for unidirectionalresponse of the combined array are shown in Fig [10] inform of plot of acoustic pressure vs angle vs distance atall the points around the radiators[15, 20]. The directivity issurely obtained, but the transmitting beams utilize largersurface area at the surface where it strikes and hence theprobability of considerable reflection even at large rangeis increased proportionately. Fig [11] shows the uni-directional response of transmitter array at 40 kHzhaving element diameter D= 1.2.Directional pattern of this array consists of two zones,namely near zone and far zone. The side lobes in thenear field zone do not get completely removed from thedirectional pattern as it should have been as ideallyshown in Fig [10] for D / =1.2.Fig [11]: Improved Directional response using arraytransducers with D/ =1.2, x=y=  (D is diameter ofone element and  is the wavelength, x & y inter-element spacing)[15, 17, 18]The number of maxima is D/, currently a numbergreater than 1. The D/ ratio not being exactly equal to1.2 and also since the inter-element spacing do notsatisfy nyquist condition, two maxima (side lobes) aroundthe main maxima are observed. In case of odd number, amaximum is obtained in the centre with double the meanacoustic pressure. The acoustic pressure along the axis ofthe oscillator fluctuates between zero and double meansvalue.To remove these side lobes, there could have beenfollowing three solutions:a) Use of lower frequencies could have resultedinto no side lobes, but that would have givennon directive response[8]. Optimum frequencyof 40 kHz has been used.b) Proper shielding of the transmitting transducerand receiving traducers so that near filed do nottrigger the receiver. Too long shielding wouldcreates severe interference at the sensor hooditselfc) The effects of near field side-lobes could beremoved through electronics design andsoftware implementation by not allowing thereceiver to “see” anything in the near field. Thiscould have impaired the near field detection.In our application, we used all the three solutions withproper tradeoffs. The 40 KHz frequency has beenoptimally chosen. The reasons for choosing thisfrequency are many. Fist reason being the availability oftransducers in 40 KHz frequency range with broaderdirectional pattern response. At 40 KHz ultrasonic haverelatively less absorption in the material surface and
  • R. Attri Instrumentation Design Series (Snow Hydrology), Paper No. 4, July 1999Copyright © 2001 Raman K. Attri Pg 10range is nominally good at around 4-5 meters. Furtherusing 40 KHz transducers do not sacrifice the accuracy.In case of transmitting-receiving operation thetransmitter and the receiver are fitted with couplingadapter and two probes are carefully shielded fromeach other both electrically and acoustically.Mechanically both probes have been combined in singleunit connected to the instruments by a twin cable.The far field is simpler as compared to the near field. Thesteep maximum at the end of the near field widens withincreasing distance. The figure [12] shows that patternopens at a definite angle, which is obtained for the firstzero point, by connecting it to the center of the radiatoralong the broken lines. The angle of one of these lineswith the axis of the radiator is the angle of divergence orbeam dispersion. The angle of divergence is o given bythe theory of diffraction:Sin o = 1.2  / DAbove formula is valid only for small value of  / D i.e.only small values of angles of divergence are obtainedcorrectly.Fig [12]: Beam Divergence in the far field with D/= 1.2The figure [12] shows the beam dispersion[20]. The aboveequation gives approximately a dispersion of around 60owith D= 12 mm and  = 9 mm, which is double ascompared to normal applications. This further increasesthe area of front exposure. The power attenuation due todispersion is compensated through greater voltageamplitude at transmitter for generation of ultrasonicpulses.8. CONSIDERATIONS FOR IMPROVEMENT OFDIRECTIONAL RESPONSEDirectional characteristics of array include the angle ofdivergence and beam width of the emitted signal. Themeasure of directional pattern are beam width anddirectivity factor or directivity index. When applying theecho method the sensitivity of array is also veryimportant than directional characteristic of the radiatedsound field. The sensitivity characteristics in echomethod are equal to the square of the directionalcharacteristics of the sound field. Directional responseand sensitivity of the transducer array is greatly affectedby Geometry, shape, diameter and area of the radiator.The magnitude of the acoustic pressure at a givendistance is determined by the ratio of area to thewavelength of the radiator. This in turn createsdependency on the diameter of the element. Shape toohas great effects on directional pattern. Conical surfaceradiator may have many side lobes while rectangularradiator is no longer axially symmetrical. It becomesbroad in the plane, which contains the axis and narrowside of rectangle, and vice versa. Circular disc radiatorhas more flattened and free from directional pattern asshown in the figures. At great distance, sound fieldfollows the distance law of spherical wave, i.e. theacoustic pressure decreases inversely with the distance.Out of this at design stage we can not control any of thefactor except wavelength i.e. frequency of thetransducer. The diameter of the transducer is prefixedhowever; the transducer with right diameter could beselected with right frequency.The governing factor is diameter to wavelength ratio. Asseen above the ratio of oscillator diameter D towavelength  determines the spread of interferencefield and number of maxima and minima. The characterof acoustic beam is determined by the ratio of D to . Bymaking this value large, we get a sharply defined and farextending beam, but number of gratings also increases.Beam becomes narrow if diameter of the radiator isincreased. With small diameters, angle of divergenceincreases for the same wavelength. Further if higherfrequencies of the order of 100 kHz (smaller wavelength)are used, more narrower beam pattern is obtained.For a radiating array, there can be dramatic effect inresponse by varying the amplifier gains for transmittingvoltages. Since three set of transducers in transmitterarray are used, pulses three times in number ascompared to transmitted pulses shall be received withdifferent amount of phase shifting[17,19]. The first pulsecrossing the threshold gives fair amount of accuracy ofdistance measurements. So the random phase shifts inreceived signal is not a problem.Occasionally focusing probes of special design are used
  • R. Attri Instrumentation Design Series (Snow Hydrology), Paper No. 4, July 1999Copyright © 2001 Raman K. Attri Pg 11to increase the sensitivity over a definite range[21]. Forthis purpose either a curved, ground, piezoelectric plateoff ceramic material is used, or a curved layer with lenseffect is cemented to the flat crystal plate[24]. The lattermethod greatly increases the sensitivity.9. CONCLUSIONSThe experimental results have been very favorable. With40 kHz ultrasonic transducers arranged in array fashion,considerable amount of reflected signal is receivedthrough arrayed receivers, which can be detected withthe help of the suitable electronics design. The surfacedistance more than 5 meters can be fairly detected inspite of the non-even, rough, porous snow surface whichnormally do gives problems of scattering and absorptionof energy in to the surface. However the range is purelydependent upon the independent transducerspecifications. If the transducers are combined in asuitable array the results are more encouraging andreliable. The directional patterns can be made broader tooffset the effects of non-smoothness of the surface.However the suitable tradeoff with ultrasonic power persquare centimeters should also be taken intoconsideration before shaping the beam width pattern.This non-contact remote measurement of level or depthcan be made very effective with above designmodifications incorporated in it.REFERENCES1. Gooberman G.L., Pulse Techniques, Ultrasonic Techniques inBiology and medicine, Illiffe books Ltd, London, 1967.2. Satish Kumar et al, Snow Depth Senor, Proceeding of nationalsymposium on Sensors and Transducers, 1996.3. Mellor, M., Engineering properties of snow, Journal ofGlaciology, volume 19, pg 15-66, 1977.4. Yamazaki, Kondo, T. J., Sakuraoka,T. and Nakamura, T., A onedimensional model of evolution of snow cover characteristics,Journal of Glaciology, Vol. 18, pg 22-26,1993,5. Hall, Derothy K., Remote sensing of Ice and Snow, London,Chapman and Hall Publications, 1985,6. Combs, Charles M.; Goodwin, Jr., Perry H., Adjustable ultrasoniclevel measurement device, United States Patent 4221004, Aug19787. M. Krause, et. Al. Comparison of Pulse-Echo-Methods for TestingConcrete, E-Journal of Non-destructive testing, Vol.1 No.10,October 1996,8. A.Hämäläinen1 and D. MacIsaac2, Using Ultrasonic SonarRangers: Some Practical Problems And How To Overcome Them,Phys. Teach. Vol 40, pp 39, 2002.9. Ilene Busch-Vishniac, Elmer Hixson, Acoustical Instrumentation,Encyclopedia of Applied Physics vol 1, VCH publishers, , pg 63-88,.199110. Heizfield K.K & Litovitz T.A Absorption & dispersion of Ultrasonicwave, 1959.11. Mason W.P, Properties of Gas, Liquids and Solids”, PhysicalAcoustics, vol 2, 196512. Balantine D.S et al, Acoustic Wave Sensors-theory, Design andphysico-chemical applications, Academic Press, 199713. Ensminger D, Ultrasonic – the low and high intensity applications,Marcel Decker Inc, New York, 197314. Busch I, Huxson E, Ultrasonic, Encyclopedia of applied Physics,VCH Publishers, vol 1, pp 63-88, 199115. Ultrasonic, Encyclopedia of Physical Science and Technology, Vol12, pp 662-664, Mcgraw Hill, 1982.16. Papadakis E.P., Physical acoustic principles and methods (W.P.Mason , ed.), vol 4 B, Academic, NY, 196817. Hudson J.E, Adaptive Array Principles, Peter Peregrinus , London198118. Piezoelectric Ceramic Sensor (Piezoliote), Cat-P19-E8, MurataManufacturing Co. Ltd, Japan,http://www.murata.com/catalog/p19e.pdf19. Harold Carey, Reducing Side lobes of SRF10, Robot Electronics, Inc.http://www.robot-electronics.co.uk/htm/reducing_sidelobes_of_srf10.htm20. John Szilard, “Ultrasonic”, Encyclopedia of Physical Science andTechnology”, vol 14, Academic, London , (1987), pg 191-209,21. Edmund J.Sullivan, Acoustic Signal Processing, Encyclopedia ofPhysical Science and Technology, Vlo1, Acedemic Press- Orlando,Florida, 1987.22. Martin E. Anderson and Gregg E. Trahey, A seminar on k-spaceapplied to medical ultrasound, Duke University, April 12, 2000,http://dukemil.egr.duke.edu/Ultrasound/k-space/bme265.htm23. Ziomek L.J., Underwater Acoustic, A linear systems theoryApproach, Academic Press- Orlando, Florida, 1985.24. Lawrence J. Ziomek, Underwater Acoustic, Encyclopedia ofPhysical Sciences and Technology, Vol 1, Acedemic Press- Orlando,pg 183-190, 1987.Further Readings Szilard J, Ultrasonic testing – non-conventional testing techniques,Willey, NY, 1982 Silk M.G., Ultrasonic transducers for non-destructive testing ,Adam hilger Ltd, Bristol, 1984 Hueter and Bolt, Sonics, Wiley, NY, 1955 Landee, R.W. et al, Electronics Designer’s handbook, Mcgraw Hill, 1957 P. Boltryk , M. Hill , A. Keary , B. Phillips , H. Robinson and P.White, An ultrasonic transducer array for velocity measurementin underwater vehicles, Ultrasonics, Volume 42, Issues 1-9, April2004, Pages 473-478 M. G. Maginness, J. D. Plummer, W. L. Beaver, and J. D. Meindl,State-of-the-art in two-dimensional ultrasonic transducer arraytechnology, Medical Physics, Volume 3, Issue 5, pp. 312-318,September 1976 Walter Patrick Kelly, Jr. , Rodney J Solomon, Two-dimensionalultrasound phased array transducer, United States Patent6894425, May 17, 2005 S. Smith et al, “2-D Array Transducers for Medical Ultrasound atDuke University: 1966”, ISAF 96 Proceedings of the 10th IEEE Intl.Symposium on Appl. of Ferroelectrics, vol. 1, Aug. 1996, pp. 5-11. T. Miyashita, T. Itaya and T. Matsumoto, "Reconstruction of Wide-Bandwidth Scattering Responses from Narrow-BandwidthUltrasound Echo in Air," Japanese Journal of Applied Physics,vol.38, pp.3135-3138 (1999). 10W. J. Hughes, W. Thompson, Jr., and R. D. Ingram, ‘‘Transducerarray scanning system,’’ United States Patent 3905009, Sept.1975. Susan Dumbacher et.al, Source Identification Using Acoustic ArrayTechniques, Proceedings of the SAE Noise and VibrationConference, Vol 2, pp 1023-1035, Traverse City, MI, May 1995 Charles W. Danforth, Acoustic Applications of Phased ArrayTechnology, 1998,http://casa.colorado.edu/~danforth/science/sonar/sonar1.html
  • R. Attri Instrumentation Design Series (Snow Hydrology), Paper No. 4, July 1999Copyright © 2001 Raman K. Attri Pg 12Aut hor Det a ils :Author is Global Learning and Training Consultantspecializing in the area of performance technology.His research and technical experience spans over16 years of project management, productdevelopment and scientific research at leadingMNC corporations. He holds MBA in OperationsManagement, Executive MBA, Master degree inTechnology and Bachelor degree in Technologywith specialization in Electronics andCommunication Engineering. He has earnednumerous international certification awards -Certified Management Consultant (MSI USA/ MRAUSA), Certified Six Sigma Black Belt (ER USA),Certified Quality Director (ACI USA), Certified Engineering Manager (SMEUSA), Certified Project Director (IAPPM USA), to name a few. In addition tothis, he has 60+ educational qualifications, credentials and certifications inhis name. His interests are in scientific product development, technicaltraining, management consulting and performance technology.E-mail: rkattri@rediffmail.comWebsite: http://sites.google.com/site/ramankumarattriLinkedIn: http://www.linkedin.com/in/rkattri/Copyright InformationCopyrights © 2001 Raman K. Attri. Paper can be cited withappropriate references and credits to author. Copying andreproduction without permission is not allowed.