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TH E 8‘ S SITY LIBRARIE lllllllllllll llLlll lllll‘ ll \lLlllll‘l W This is to certify that the thesis entitled ULTRASONIC MEASUREMENT FOR HIGHLY ATTENUATED MATERIAL presented by Mo Zhang has been accepted towards fulfillment of the requirements for MS degree in Electrical Engineering fl/flé/w/ fly;fl Major professor/ Date t/v/ 7% 0-7639 MS U is an Affirmative Action/Equal Opportunity Institution LIBRARY Michigan State mversity PLACE N RETURN BOX to romavothb chockomm your mould. TO AVOID FINES Mom on or More data duo. DATE DUE DATE DUE DATE DUE MSU Is An Afflrmntlvo Action/Equal Opportunlty Imam Wynn-9.1 ULTRASONIC MEASUREMENT FOR HIGHLY A1TENUATED MATERIAL By Mo Zhang A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Electrical Engineering 1994 ABSTRACT ULTRASONIC MEASUREMENT FOR HIGHLY ATTENUATED MATERIAL BY Mo Zhang This paper describes the design of an ultrasonic measurement system and the use of ultrasonic detection to analyze the data from highly attenuated materials.When a fruit tree is damaged by borer infestation, the properties of the boundary between the bark and the trunk of the cherry tree change, and if the borer damage is extensive, large spatial sep- aration occurs. The damaged areas contain a greater percentage of air space, feces, larvae or other low density substance. The boundary material property change inside the fruit tree can be detected by using ultrasonic measurements. As a result, when an ultrasonic pulse propagates through highly attenuated dam- aged layers, preferential attenuation of high-frequency components cause the pulse to change in shape continuously as it propagates through the medium. The center frequency appears to shift toward the low-frequency end of the pulse, with a decrease in intensity as well. The effective frequency shift allows feature identification. ACKNOWLEDGMENTS I would like to express my greatest gratitude to Dr. H. Roland Zapp and Dr. Bong Ho, my advisors, for their guidance on this thesis and for my education and I would like to thank Dr. C.L. Wey for his helpful sugges- dons Furthermore, I also would like to express my gratitude to my wife, Jingchun Xu, for her support and taking care of our daughter during these years of my graduate study. TABLE OF CONTENTS LIST OF TABLES ............................................................. v LIST OF FIGURE ............................................................. vi 1. INTRODUCTION ............................................................. l 2. THE MEASUREMENT SYSTEM AND EXPERIMENTAL METHODS ................................................... 5 2.1 Description of the System ................................................... 5 2.2 Experimental Procedures ................................................... 10 3. THEORETICAL BACKGROUND .............................................. 13 3.1 The Characteristic Acoustic Impedance ................................. 13 3.2 Reflection and Transmission at an Interface ........................... 14 3.3 Attenuation of an Ultrasonic Wave ......................................... 19 4. TIME AND FREQUENCY DOMAIN ANALYSIS .................... 22 4.1 Impulse Response ................................................... 22 4.2 Fourier Transform of Impulse Response ................................ 34 4.3 Gaussian-Shaped Signals ................................................... 42 5. EXPERIMENTAL RESULTS ................................................... 52 6. CONCLUSIONS ................................................... 55 LIST OF REFERENCES ................................................... 65 iv LIST OF TABLES TABLE Borer Damage Detection for Different Cherry Tree Diameters and Damage Levels ................................... 67 Figure 2.1 Figure 3.1 Figure 4.13 Figure 4.1b Figure 4.2a Figure 4.2b Figure 4.3 Figure 4.4 Figure 4.5a Figure 4.6b LIST OF FIGURES Page Schematic Diagram of the Experimental System ............... 7 Reflection at an Interface .................................................... 15 Non-Borer—Damaged Sample ............................................. 24 Impulse Response of Layered Structure for a Non-Borer-Damaged Sample ..................................... 25 Borer Damaged Sample ..................................................... 26 Impulse Response of Layered Structure for a Borer Damaged Sample ............................................. 27 The Reflected Signal from a Non-Borer-Damaged Sample ............................................. 30 The Reflected Signal from a Borer Damaged Sample ....... 31 The Reflected Signal from the Surface of a Wood Slab ..... 32 The Power Spectrum of the Reflected Signal from the Surface of a Wood Slab ................................................ 33 vi Figure 4.6 Figure 4.7 Figure 4.8 Figure 4.9a Figure 4.9b Figure 4.10a Figure 4.10b Figure 5.1 Figure 5.2 Figure 5.3 The Power Spectrum of the Reflected Signal form a Non-Borer-Damaged Sample ................................. 41 The Power Spectrum of the Reflected Signal from a Borer Damaged Sample .......................................... 42 Experimental Configuration ............................................... 44 Schematic Diagram Illustrating Reflections from a Non-Borer-Damaged Sample .......................................... 45 Illustration of Pulse Spectra Shifts due to Linear Attenuation of the Spectra of Reflected Pulses EA (co) and 53 ((0) .......................................................................... 46 Schematic Diagram Illustrating Reflections from a Borer Damaged Sample ................................................... 50 Illustration of Pulse Spectra Shifts due to Linear Attenuation in the Spectra of Reflected Pulses EA (co) 55(0)) and EC(0)) .............................................................. 51 Power Spectrum Comparing Reflected Signals ................. 56 The Overall Reflected Signal from a Borer Damaged Sample ................................................... 57 The First Reflection from a Borer Damaged Sample ......... 58 Figure 5.4 Figure 5.5 Figure 5.6 Figure 5.7 Figure 5.8 Figure 5.9 The Power Spectrum of the First Reflection from the Surface of a Borer Damaged Sample .......................... The Second Reflection from the Top of the Damaged Layer ......................................... The Power Spectrum of the Second Reflection from the Top of the Damaged Layer ................................. The Third Reflection from the Bottom of the Damaged Layer ................................... The Power Spectrum of the Third Reflection from the Bottom of the Damaged Layer ........................... The Power Spectra of All Reflections Superimposed Showing the Frequency Shift due to Linear Attenuation... viii .59 .60 .61 .62 .63 64 LINTRODUCTION Wood is an anisotropic (orthotropous) material and is highly attenuative. Conse- quently a significant component of ultrasonic research is concerned with determining the relationship between the physical and structural properties of wood and the propagation of the acoustic wave. The physical properties being investigated include the moisture con- tent, density, and temperatures of wood. Structural properties include propagation direc- tion(i.e., grain direction) and within ring growth pattern(i.e., diffuse) versus ring porous vessel distribution for hardwoods and abrupt versus gradual transition from early to late wood for softwood. Preliminary investigations indicated that attenuation was influenced by moisture content and propagation direction, but the trends were not consistent (Lemaster and Dom- fel 1987). In fact Lemaster and Domfeld (1987) reported that if the measurements made on the oven-dry specimens were removed from the analysis, the data showed virtually no relationship between moisture content and signal energy. The determination of wood properties using acoustic wave propagation has attracted considerable research interest. Miller, et a1. 1965, Shaw 1978, and Arita and Kuratani (1984) have used acoustically based nondestructive evaluation (NDE) devices to monitor the structural condition of wood utility poles subjected to the degradative efl'ects of decay and insect attack. Patton- Mallory et al.(1987) used multiple waveform characteristics to distinguish decayed wood from nondecayed wood under controlled conditions in the laboratory. More recently, ultra- sonic analysis has moved into a subsequent stage of multiparameter analysis of the trans- mitted waveform in both the time and frequency domain, Beall. (1988). The use of ultrasonic pulse-echoes to detect damage, such as borer infestation, in- side fruit trees has not previously been attempted. Therefore, the purpose of this thesis is to develop and evaluate an ultrasonic detection device for borer damage in Michigan cher- ry trees. When an incident pulse reaches a boundary between two different media, such as the cambium between the trunk and the bark of the cherry tree, the amount of wave energy which is reflected or refracted is dependent on the acoustic impedance at the boundary. The amplitude of the reflected signal provides information on the acoustic impedance of the target. A tree damaged by the borer will contain air, feces, and larvae in the damaged areas which results in a higher acoustic impedance mismatch relative to the normal inter- face between bark and the trunk of the fruit tree. Thus, at an interface between the bark and the damaged areas, the reflection coefficient approaches unity, and an incident pulse is essentially reflected with negligible energy transmitted through the damaged area. Mea- surement of the reflected or transmitted energy in the time domain can therefore be used to indicate the presence of borer damage to the fruit tree. The measurements in the time domain are conventional applications of ultrasonic nondestructive testing, when evaluation is based primarily upon amplitude and time infor- mation. The transducer is selected to satisfy a nominal test frequency that meets the re- quirements of the inspection task, but, in general, the relationship between the initial and received pulse spectrum is not recorded. The differences between borer and non-borer—damaged samples identified from re— flected signals are more readily quantified if the frequency content of reflected signals is determined. This is achieved by carrying out a Fourier transform of the reflected signal. At any time and for any component, the time and frequency-domain can be interchanged by Fourier or inverse Fourier transform. In the time-domain, the signal is sufficiently de- scribed by its amplitude while in the frequency domain both amplitude and phase are re- quired. This thesis discusses both techniques to characterize the borer-damage inside the cherry tree. The power spectrum of the reflected signal from a borer damaged and non- borer-damaged sample is compared to see their differences at different frequency compo- nents. This application will be illustrated by laboratory results obtained with a detection system now being used in a program aimed at evaluating the utility of spectral analysis in many different areas. The acoustic attenuation coefficient measured in dB/cm is known to increase lin- early with frequency for most highly attenuated material. The slope of this linear function is denoted by the symbol [3. The effect of this acoustic attenuation on an ultrasonic pulse having a Gaussian envelope is to translate the normalized power spectrum to lower fre- quencies by an amount, V f, proportional to [3 while maintaining the bandwidth. If the medium has a loss factor which can be described by H (r) = exp ( (-K|flp) x) , where r is the frequency and o S p S 2 (valid for tissues and other objects of interest), then the pulse retains its Gaussian shape, shifting only its center frequency (L. Ferrari, 1986). The difference between borer damaged and non-borer damaged samples is manifested in a fre- quency shift observed in the spectrum of the reflected pulses. In particular the power spec- trum of the reflected signal from the damaged layer is shift to lower frequency by an amount V f. Thus, analysis of the spectral composition or frequency shift at given fre- quencies provides the potential for distinguishing between borer and non-borer damaged samples. This capability is of major importance in helping to identify which cherry tree are borer infested and then need to be separated and removed. In this thesis, the ultrasonic detection system and experimental set up are de- scribed. The ultrasonic principles which are concerned with understanding the dynamics of the propagation of ultrasonic pulses in material, and the influence of boundary damage on the return signal are reviewed. It is hypothesized that the difference in signal return from borer and non-borer-damaged material could be exploited to image the damage dis- tribution inside tree trunks. A mathematical model is established using both time domain signal analysis and frequency-domain analysis. The experimental results are presented to show validity of the theoretical development and lead to the conclusions that the detection of borer-damage is indeed possible. Throughout this paper it is assumed that broad-band sources are used. 2.THE MEASUREMENT SYSTEM AND EXPERIMENTAL METHODS 2.1 Description of the System It is convenient, for purpose of description, to consider the ultrasonic detection system as two distinct part, the scanning system and the signal processing unit. In this sec- tion each part will be described individually. The function of the scanning system is to use ultrasonic techniques to collect and store information related to defects or damage from a given area of a specimen, so that the signal processing unit can use it to construct a visual representation of that specimen and of any defects present. The information collected is, therefore, concerned with the size and position of areas of ultrasonic reflectivity within a testing material. These areas are bound- aries between media of different acoustic impedances and the reflectivity is a measure of the mismatch in acoustic properties. The data are obtained by recording the data at equally spaced positions over the surface of the material to be examined. At each position the ul- trasonic waveform reflected from the specimen is digitized and information concerning the time and amplitude of echoes, along with the X and Y position co-ordinates, is stored. When ultrasonic techniques are used to detect defects, information is convention- ally collected and displayed in three basic ways, called A-, B- and C-Scans. Because the program for detecting borer-damage inside the fruit tree is just concerned with the A-Scan mode, only this will be described. An A-Scan shows the amplitude of echoes or reflections viewer with information concerning the depth and reflection of points of discontinuity in the material below the sample at one location. By keeping the sample and transducer un- der water a good acoustic coupling between the two is achieved. A three dimensional im- age can be generated by computer controlled stepper motors for X and Y positioning while the 2 position is obtained by A-Scan ranging. At each position the ultrasonic wave- form reflected from the sample is digitized and information concerning the time and am- plitude of echoes, along with the X and Y position co-ordinates, are stored. After the data is sampled, it is sent to the signal processing unit for further use. A schematic diagram of the experimental equipment used is shown in Figure 2.1. The detection system consisted of an IBM-P0486 Microcomputer, an Ultrasonic 5050 Pulser/Receiver Unit (P/R unit), a Waveform Acquisition and Arbitrary Generator (WAAGII) board, an Accuscan Immersion Transducer, and the MD-2 Dual Stepper Motor Driver System.The IBM-PC-486 Microcomputer is the core of the system. Each of the elements of the system are peripherals of the computer in that they are controlled by the signal initiated by the computer. It features a 64K high speed cache and 4Mb RAM. The microcomputer is used to both to control the scanning equipment and the signal process- ing system. The transmission and reception of the ultrasonic wave is achieved using a commercial ultrasonic transducer and pulserlreceiver unit. The Model 5050 is a broadband ultrasonic pulserl receiver unit that, when combined with appropriate transducer, provides a unique, low-cost ultrasonic measurement capability. The WAAGII board converts a pre- selected portion of a time varying analog waveform to digital (binary) data with maximum sample frequency for a single channel (40 MHz to acquire, display and store waveform as a function of time) which is equivalent to distance, if a value for the velocity of sound in the medium is known. oooooooooooooooooooooooooooooooooooo I PULSER I RCEIVERI ‘ " l STEPPER MOTOR] DISTILLED , g 5 WATER - IBM PC-486-25 MHz f f , MICROCOMPUTER MM DUAL IBMGRAPHICS f .................. 1*..z STEPPER MOTOR PRINTER 5 WAAGII BOARD INCLUDE. DRIVER SYSTEM ‘ AID CONVERTER WITH SAMPLING AT 40 MHZ AND THEN PUTING IT DATA INTO SIGNAL PROCESSING SYSTEM LOAD DOWN SAMPLED' OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO Figure 2.1 Schematic Diagram of the Experimental System The A-Scan presents the amplitude and period. The MD-2 Dual Stepper Motor Driver System consists of MD-2Dual Stepper Motor Controller, XY-l8 Positioning Table, and two Stepper Motors. Motors can be driven using the keyboard and position information can be saved to the disk of the microcomputer for complicated motion sequences. During scanning, both the specimen and transducer are kept under water in an im- mersion tank to ensure good acoustic coupling between the two. The transducer is held above the specimen, the exact height being determined by the focal length of the transduc- er. The transducer is moved parallel to the surface of the material by two stepper motors which control movements in the X and Y directions. Before scanning commences, the co-ordinate system is set up by the operator. Us- ing a keyboard to control its position the transducer is moved to an arbitrary location in the immersion tank, remote from the specimen, which is then defined as the co-ordinate ori- gin. The area of the specimen to be scanned or the one point of the specimen to be sampled (for our experiment) is then selected by moving the transducer to that location. The co-or- dinates of the scan area are defined in terms of numbers of pulses to the stepper motors. These units are related to conventional units by the step size of the motors, which is 0.1 mm/step. The operator also defines the spatial resolution by specifying the intervals at which measurements will be recorded, the minimum spacing being 0.1mm. Once the initial parameters have bee set, the sampling starts. A trigger pulse is sent to the FIR unit, which itself generates an electrical pulse to excite the ultrasonic transduc- er. This pulse is converted by the transducer into an ultrasonic wave packet, which propa- gates towards the specimen. The wave reflects from boundaries and discontinues within the material, returns to the transducer and is processed by the signal processing unit. Each time the P/R unit is triggered in this way, the resultant A-scan waveform is available at its signal output, after any required analog processing has been performed. The function of the data processing unit is to process the data stored during the scanning or sampling process and to display the results on a color monitor. The WAAGII board is used to digitize this signal. It measures the amplitude of the signal at equally spaced sample points in time using an 8 bit analog-to-digital converter. This provides a digital equivalent of the input voltage as one of 256 amplitudes at each sample time. The WAAGII board is inserted into PC-mother board and is externally controlled by the PC- 486 microcomputer. The WAAGII board starts recording and digitizing a waveform only after it has re- ceived a trigger pulse. This pulse is produced by the P/R unit when it sends the excitation pulse to the transducer, and hence is synchronized with the ultrasonic waveform. Howev- er, there is relatively long delay between the transducer excitation pulse and the first re- flected echo from the specimen surface due to the time taken for ultrasound to travel through the water. Since the transient WAAGII board will only record a finite number of samples, a variable delay is introduced between the trigger output of the P/R unit and the trigger input of the transient WAAGGII board. This time delay is adjusted before scanning or sampling, so that the trigger anives at the transient WAAGII board to start it recording just before the signal corresponding to the first reflected echo arrives at the signal input. The waveform to be digitized comprises a peak due to the main electrical pulse from the FIR unit, a specimen front surface echo, and possibly other echoes representing the back surface and defects within the material. Once the waveform has been digitized, the amplitude of each sample point is stored in the computer. To reduce the effects of ran- dom noise a number of waveforms can be averaged. This is done by digitizing a Specified 10 number of A-scan waveforms and adding their amplitude values at corresponding sample times. These summed values are then used in the subsequent processing. The software compares the amplitude of each sample with preceding values and detects any peaks. Once a peak has been found approximately its position is then comput- ed accurately, and its amplitude determined. The amplitude is then divided by the number of A-scan waveforms summed together to complete the averaging operation and the infor- mation stored. Any further peaks are found in the same way. When the A-scan information from the first measurement point on the specimen’s surface has been stored, the computer sends out a series of pulses to advance the stepper motor of the transducer transport mechanism to the next data point. The P/R unit is nig- gered to initiate the next ultrasonic pulse so that the whole process can start once again. 2.2 Experimental Procedures Conventional ultrasonic pulse-echo system are widely used to detect the defects inside materials. These systems transmit short bursts of radio frequency ultrasound into the test object and display the echoes reflected from inhomogeneities on a microcomputer. The time of occurrence and amplitude of these echoes can be related respectively to the location and magnitude of the ultrasound reflectors.To avoid range ambiguities in systems that transmit the same waveform in each burst, it is necessary to wait until the echo from the most distance target has returned before another burst can be transmitted. Therefore, the repetition period T of the rf bursts is limited by T2 (2R )/c (2-1) max 11 where c is the velocity of ultrasound and Rm ax the maximum range from which echoes can be detected. The testing signal was generated from a 2.25MHz, 1.5 cm diameter ultrasonic transducer with a 5 cm focal length. The panametrics 5050 Pulser/Receiver was employed to provide the pulse signal to the transducer and to receive the reflected signals. The ultra- sonic reflected waveform was sarnpled by the WAAGII board with a high sampling rate of 40MHz. The sampled data were sent to an IBM-PC486-25MHz microcomputer for signal processing. After recording the reflected signal from the non-borer-damaged sample, the target was replaced with a borer-damaged sample and the measurements repeated. The impulse response, and its frequency spectrum, of the reflected signals from borer damaged samples are compared with that of the impulse response and spectrum, with the same distance between the transducer and the surface of the sample. For the target that is known to be non-borer-damaged data are stored in the computer can be used to car- ry out the comparison to non-damaged targets in order to give an immediate indication of the damage level. There were 11 cherry tree samples used in our tests which were obtained from op— erating fruit farms in Northwest Michigan. To evaluate whether a difference exists be- tween damaged and non-borer-damaged samples, we cut two similar diameter (12 cm diameter) fruit tree 20 cm bolts, one borer-damaged and the other non-borer-damaged. In order to minimize the scattering of the ultrasound signal from the non-uniform bark and to provide a perpendicular signal, we scrapped the bark to provide a flat surface. The pulse-echo technique generally uses a single transducer capable of sending and receiving a pulse of ultrasound. The delay between pulses and the geometry of the transducer ensure that reverberations from the transmitting crystal have died away before 12 the echoes are received. Provided the pulses are short enough the individual echoes from each interface can be resolved, their position and amplitude being used to detect the pres- ence of borer-damaged areas. A large proportion of ultrasound will be reflected at a borer- damage area owing to its large reflection coefficient. Echoes from discontinues behind the borer-damaged area will be reduced and usually disappear. Due to the severe impedance mismatch between solid material and air, it is diffi- cult to propagate ultrasound from a transducer through air to the testing sample surface. It is therefore vital that there be a satisfactory coupling agent between the transducer and the test samples. This was achieved by immersing the test samples and the transducer in a wa- ter tank. The transducer can be independently positioned along three dimensions. The dis- tance between the transducer and the surface of the sample was adjusted by a sliding transducer-holder. The borer-damaged area usually occurs just below the boundary between the bark and the trunk, and forms a very thin damaged layer, as the larvae forms tunnels through the soft cambium layer. A borer-damaged sample, with its borer-damaged layer perpendic- ular to the incident signal, was selected for testing and a non-damaged sample of similar shape and size was used for comparison. 3.THEORETICAL BACKGROUND Propagation of ultrasound in wood material depends on the ultrasound propagation velocity, the acoustic impedance, the attenuation in the wood and scattering of ultrasound by the inhomogeneities in the wood structure. It is obvious that there is a considerable amount of information contained in an ultrasonic wave propagated through wood. Thus, in order to extract the information about variation of acoustic impedance along the path of propagation, the object is modelled as consisting of parallel layers of different impedanc- es. Some basic properties of ultrasound propagation are employed for this purpose. 3.1 The Characteristic Acoustic Impedance The ratio of the acoustic pressure to the particle velocity in a medium is defined as the specific acoustic impedance for that medium. For plane wave in free field conditions it can be show that this quantity is equal to the product of the density of the medium (p) and the velocity of sound (c) in the medium, which is known as the characteristic acoustic im- pedance for that medium (Z), or Z = pc (3.1) The extent to which ultrasonic energy is transmitted or reflected at an interface separating two continuous isotropic media is determined by the characteristic impedance. The relationship between pressure and particle speed for the forward wave is x+kl x+kl Pl(- c )=ZUl(t— c J (3.2a) 13 l4 and for the backward wave x-l-k2 x+k2 P2 (t+ c J: -ZU2 (t+ c ) (3.2b) where U1 and U2 represent forward and backward traveling waves, respectively, propa- gating at velocity c and 1‘l , k2 are real constants and P1, P2 represent the acoustic pres- sure. 3.2 Reflection and Thansmission at an Interface When an ultrasonic plane wave meets a boundary between two different media it may be partially reflected. The ratio of the characteristic impedance of the two media de- termines the magnitude of the reflection coefficient at the interface. The reflected wave is returned in the negative direction through the incident medium at the same velocity with which it approached the boundary. The transmitted wave continues to move in a positive direction, but at a velocity corresponding to the propagation velocity in the new medium. Just as optics, Snell’s law for reflection applies, and the angles of incidence and reflection are equal when the wavelength of the ultrasound is small compared to the dimensions and roughness of the reflector as illustrated in Figure 3.1 In Figure 3.1 the subscripts i, r and t refer to the incident reflected and transmitted waves respectively and 1 and 2 to the first and second media that the ultrasound encoun- ters. “6th the ultrasonic plane wave traveling in the direction 0i relative to the Z-axis, a distance S in the direction of propagation may be related to its X and Z components by S = xsin0i+ zcosfli (3.3) 15 p 1c1 Medium.l. W» X p2c2 Medium. 2. Figure 3.1 Reflection at an Interface Therefore, the incident pressure plane wave in complex notation becomes xsinfli + zcosfli P. (t, x, z) = A exp {jm[t- ]} (3.4a) 1 1 (:1 Similarly, the reflected and transmitted pressure waves are xsinOr + zcosflr Pr(t, x,z) = Blexp {jw[t- ]} (3.4b) c1 xsinOt + zcosflt Pt (I, x, z) = Azexp {jm[t - :l} (3.4c) c2 16 At the medium boundary, the pressure must be continuous. Thus Pi + Pr = Pt (at z=0) (3.5a) 01' -j (ox sinfli -j (ox sinflr -j tux sin 0t Alexp (——-—c-1—-—) + B lexp (T) = A2exp (T) (3.5b) Two results from Optics are helpful in defining the relationships among the inci- dent, reflected and transmitted waves at the boundary between two media. First, the angle of reflection is equal to the angle of incidence, that is 9 = 0. (3.6) Second, Snell’s law relates theIangles of incidence and transmission in terms of the speed of sound in the two media. For the angles as defined in Figure 3.1 Snell’s law requires that - = — (3.7) Applying these relationships to (3.5b), we see that 17 __£=_=__ (3.8) with the result that all exponents in (3.5.b) are equal. Therefore, we again obtain A1+B1 = A2 (3.9) As an additional boundary condition, we require that the particle velocity in the z- direction be continuous. This results in the relationship Uicosei-t-Urcosflr = Utcoslit (3.10) .53 u where "1 C‘. II " C.‘ II N|>leNl> Nady—thir— N sing equations (3.6) and (3.9) in (3.10), we obtain: (Ui - Ur) c056i = Utsinflt (3.11) The amplitude of the reflected and transmitted pulses are dependent on the reflection coef- ficient of the interface, which may be calculated by solving for the ratio of reflected to the incident amplitude 18 Pr _ B1 - chosfli-Zlcoset (312) [TI - KI - Z 0 Z 6 . 2cos i+ 1cose 1' The ratio of the transmitted to incident pressure amplitude gives the following result 5 = 2 - 2Z2cosfli (313) P A1 _ chosfli-t-Zlcosflt ' For normal incidence, (3.14) GD ll GD II CD II C Thus from equations (3.12) and (3.13), the reflection coefficient R12 for normal incidence is: P Z -Z r 2 1 R = — = —— (3.15) 12 Pi Z2-t-Z1 and the transmission coefficient is P 22 r — —‘ = 2 (3.16) 12 - P. 22+Z1 19 According to equations (3.14) and (3.15), no phase shift occurs between the incident wave and the transmitted wave either in the displacement or in the stress, regardless of which medium has the higher acoustic impedance. However, when the acoustic impedance of medium 2 is greater than that of medium 1, the displacement of the reflected wave is 180U out of phase with that of the incident wave, but the stresses are in phase. The reverse is true if the acoustic impedance of medium 2 is less than that of medium 1. In practice, the actual situations are often considerably more complicated than the ideal conditions described here. Reflections and refraction at interfaces between media en- ter into every aspect of the applications of ultrasonic energy. 3.3 Attenuation of an Ultrasonic Wave The intensity of a plane progressive ultrasound field can be reduced by interaction with the transmitting medium. Two important sources of attenuation are scat-tering and absorption. The interface of each discontinuity within a medium serves as a reflecting sur- face, the size of which (in relation to the wavelength) determines its effect as scatterer. Most of this scattered energy no longer moves only in the original direction of propagation and thus the total amount of energy transmitted is reduced. When scattering occurs, the amplitude of the scattered signal is proportional to fn where f is the frequency of the ultra- sound signal and n is greater than or equal to 1. Thus greater scattering occur at higher fre- quencies.The other significant source of attenuation is absorption, which occurs primarily at the macromolecular level for logitudinal waves (Carstensen, 1979; Edmonds, 1981). The attenuation coefficient is always larger than the absorption coefficient because absorp- tion is only one of the means by which the ultrasound field is attenuated. 20 Attenuation refers to the diminishing of intensity of a waveform as it progresses through a medium. The effect of attenuation on a periodic wave is demonstrated by the equation: P = Poe- ax +j((ot-kX) (3.17) where PO is the pressure amplitude of the wave as it leaves the source, k = (0/0 , is the propagation constant and a is amplitude attenuation coefficient of the medium for a given frequency. Two important source of attenuation coefficient a are scattering and absorp- tion. It can be expressed by a = “a + as , where a“ is absorption coefficient and a, is scattering coefficient (Chivers, 1980). Upon encountering an infinite plane surface that is parallel to the front, part of the energy is reflected, depending on the relationship between acoustic impedances of the two media. During the reflection process, the wave also may undergo a 1800 shift in phase. If the distance between the source and the reflecting surface is L, the pressure amplitude of the incident wave at L is -ctL Pi = Poe (3.18) The pressure amplitude of the reflected wave at L is -aL-2aO-2jB P =Pe r o (3.19) where do accounts for the loss of energy on reflection and B is the phase shift due to reflection.( B can be 0 or 90°). It is a measure of the rate at which an ultrasonic wave decreases in intensity by other than 21 geometric means as a function of distance it propagates through a medium. Since acoustic intensity is proportional to the square of acoustic pressure, this can also be expressed in terms of intensity I as: -2a 1x = IOe " (3.20) where x is the distance traveled, and or is the amplitude attenuation coefficient. Ultrasonic attenuation in a medium generally increases with increasing frequency in a manner that can be expressed approximately (over a limited frequency range) in the form: a = cor“ (3.21) where at is the amplitude attenuation coefficient of the medium at frequency f and a0 is the attenuation coefficient of the medium at the reference frequency f o . 4.TIME AND FREQUENCY DOMAIN ANALYSIS 4.1 Impulse Response Determination of the difference between the borer-damaged and non-borer-dam- aged cherry tree depends on distinguishing the different acoustic impedances in the time domain. Ultrasonic impediography is based on the time domain characterization of the object in terms of an impulse response. This approach utilizes the incident and reflected signals to obtain the object impulse response which is then summed to give the impedance variation along the path of propagation. In the sampled data system, a signal can be described by a succession of impulse responses obtained by the reflections from various boundaries. The amplitude of reflected signal is an indication of the intensity of energy present in the reflected signal. However, the reflected intensity is a complicated function of many other interface parameters such as: 1. Amount of attenuation in the path between the transducer and interface. 2. Angle that the axis of the ultrasound beam makes with the reflection interface. 3. Acoustical properties of the medium forming interface. 4.Curvature of the interface 5. Scattering properties of the interface. 22 23 This paper will assume that the attenuation can be accounted for by an exponential factor, although there are still four other factors that affect the intensity of the reflection. Approximating the discontinuity to be a smooth semi-infinite plane reduces the number of significant parameters of the reflection coefficient and of the angle of incident, which is define angle between the axis of the ultrasound beam and the normal to the incident. The response of the detection system depends on the acoustic impedance of the testing material. A non-borer-damaged sample shows high stiffness relative to the borer- damaged one and thus damps the vibrations of the active transducer throughout the active band of frequencies. Any borer-damaged area in the cherry tree affects its impedance, which is reflected in the response of reflected signal from the interface between bark and trunk. Even voids, inclusions, and other perhaps non-serious defects cause changes in the spectrum that are identifiable. The curved boundaries inside the cherry tree between the bark and trunk can be minimized by using narrow ultrasonic beams which insure that the curvature displacements are much smaller that the illumination wavelengths. Spectral analysis of echoes from these boundaries can establish relative acoustic impedance differ- ences and absorptivity as a function of frequency. Although the cherry tree structures are acoustically complex, they can be thought of as a homogeneous material for a small thickness such as bark or multiple layers consist- ing of bark, damage area and trunk or just bark and trunk for non-damaged trees. The extent of the lateral area covered by the ultrasonic beam can be reduced by beam focus- sing. Hence the models shown in Figure 4.1a, Figure 4. lb, Figure 4.2a and Figure 4.2b can be used to represent the borer and non—borer—damaged cherry tree structures. 25 R[l] R [2] Interface Between Interface Between Water and Bark Bark and Trunk Figure 4.1b Impulse Response of Layered Structure for a Non-Borer-Damaged Sample 26 Borer-Damaged-Layer Bark of Fruit Tr - Trunk of Fruit Tree Figure 4.2a Borer Damaged Sample 27 R[l] y R12] R [3] Interface Between Interface Between Interface At Water and Bark Bark and Trunk Damaged Layer Figure 4.2b Impulse Response of Layered Structure for a Borer Damaged Sample 28 If the reflected signal is represented by R [k] , and the impulse response by h [n] , then: h [n] = R [k] 5 (n - k) (4.1) k=1 where R[l] = R1 R[2] = (1+R1)R2(1-R1) R[3] = (1+R1) (1+R2)R3(l-Rl) (1_R2) n-l R[k] = HRnU—Riz) , (4.2) i=1 where Rn is the reflection coefficient from the nth layer and the is the 5 (n) is the dirac delta function (Lighthill.1958). First, we consider the case of normal or perpendicular beam incidence on the non- borer-damaged cherry tree sample (Figure 4.1a and Figure 4.1b). By placing the sample in a water medium, most of the incident wave energy is reflected from the first boundary due to the large acoustic impedance mismatch between the cherry tree and the water interface. This should produce a negative reflection coefficient. The second much smaller 29 reflection R [2] comes from the interface between the bark and the trunk with intact cam- bium which should produce a positive echo. Since the signal is highly attenuated in the bark medium the resultant amplitude response is lower than anticipated. The impulse re- sponse from a non-borer—damaged sample is given by: h[n] = R[l]6(n- 1) +R[2]6(n-2) = R1+R2(l -R§) (4.3) The experimental reflection results from non-borer damaged cherry tree sample are shown in Figure 4.3. When the cherry tree is damaged by borer infestation, the borer-damaged areas are just under the bark in the cambium area. The borer-damaged areas are actually voids formed by the feeding consumption of cambium (see models shown in Figure 4.2a and 4.2b). Because of this, the acoustic impedance mismatch at the borer-damaged interface is much larger causing most of the wave energy to be reflected. As a result, the signal from the borer-damaged samples contains an additional reflection R [3] , from the bottom of the borer-damaged layer as shown in Figure 4.4. For the borer-damaged sample, the impulse response is represented by: h(n) = R[1]6(n—1)+R[2]8(n—2)+R[3]6(n—3)= R1+R2(l-R%) +1?3 (1 -Rf) (1 —R§) (4.4) Accurate determination of the impulse response function plays a critical role in ul- trasonic detection systems. The impulse response is determined and the frequency re- sponse is computed with aid of a digital microcomputer which allows noise reduction and appropriate signal processing. 1.5 plitude (Volts) .0 OI Relative Am .6 or 30 O ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo I 0 3 Pi ......’.......... } C i i i 0.5 1 1.5 2 2.5 3 3.5 4 Time (Sec.) Figure 4.3 The Reflected Signal from a Non-Borer-Damaged Sample 31 1.5 .0 or Relative Amplitude (Volts) .0 or O oooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo ........... Time (Sec.) Figure 4.4 The Reflected Signal from a Borer Damaged Sample 32 15° ! f ! ! I 100 8 Relative Amplitude (dB) 0 $ ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo .100- ............... t.-.u.u.u.ng ................ ;.H.H.-.H.”§ .......... -150 3 ' o 0.5 1 1 5 2 2.5 3 Time (Sec.) x 10-5 Figure 4.5a The Reflected Signal from the Surface of a Wood Slab 33 4 x 10 3.5 I I l I I I I 3 .. ............................................................................................... —. 2.5 .. .................................................................................................. .— =§ 2 .. .............................................................................................. - i“ o : .2 : 5 1.5 .. ........................................................... .................................. _. O . a: S 1 _. ........................................................... .................................. - 0.5 )- ............................................................ . ................................... q o l l l I L l 1 2 3 4 5 6 7 8 9 Frequency (MHz) Figure 4.5b The Power Spectrum of the Reflected Signal from the Surface of a Wood Slab 34 Consider the response of a linear time-invariant system to an input signal of a unit impulse, or more generally to a sequence of impulses given by: N X(t) = 2 and (t - tn) (4.5) n = 1 The output signal is, therefore, N y (t) = 2 anh (t- tn) (4.6) n = l where h (t) is the system impulse response. The impulse response of a reflected signal from the flat wood surface and its Fourier spectrum are shown in Figure 4.5a.and 4.5b. 4.2 Fourier Tiansform of Impulse Response Assuming the Fourier transform of s (t) is S (to) or more generally, -]0)t0 F{s(t-t0)} = e 8(a)) (4.7) and applying this to two pulses separated in time by 2 ‘0 we obtain display shown on a spectrum analyzer of: I jam0 -jcot = e 8(a)) +e |F{s(t+t0) +s(t-t0)}| 08(0))l = |2coscot0||S((u)| (4.8) 35 Two pulses may result from two boundaries in the cherry tree. From Equation (4.8) the spectrum is now that Of a single pulse modulated by |2cos and In Other words, the enve- lope Of the resulting spectrum is the same as that Obtained for a single pulse, but the spec- trum now has maxima and minima that depend on to . Approximating the maxima Of Equation (4.8) by the maxima Of lcostotol yields tut0 = nrt , n = 0,1, 2 ,..., (4.9) Of fn = n/ (2t0) n/ (At) (4.10) where the fn are the frequencies Of the maxima and At is the total time delay between the two pulses. Suppose now that the two incident signals are identical, except that the second has been shifted in phase by a constant amount (1) with respect to the first. The spectrum, using Equation (4.7), becomes jmt - -ja)t F{s(t+t0)+s(t—toitp)} = Ie o+eiJIpe DI|s((1))| = |2cos (cot0=F(p/2)||s ((1))l (4.11) The resulting spectrum is thus identical tO that expressed by Equation (4.8), except for a frequency shift equal to half the phase shift between the two incident signals. Equa- tion(4.10) predicts that the maxima are separated by 1/ (V t) and occur at multiples Of 36 l/ (V t) Equation (4.11) predicts that the maxima are still separated by f", but that they no longer occur at multiples Of 1/ (V r) but rather by: :l: / 2 rn=“ IA”), n=o.1.2..... ‘ (4.12) Thus, one can easily determine the phase shift between the two signals by first measuring 1/ (V t) and then solving for (p in Equation (4.12). The present result also explains the experimentally Observed fact that the spectral maxima do not project back to zero frequen- cy. The differences in the time domain signal are exhibited by a difference in the spec- tral characteristics Of the two signals. For a single frequency at a fixed spectral reference in a lossless, isotrOpic and homogeneous medium, the reflected signals from various bound- aries are expressed as: r(t) = 2 Akcos(t00t+cpk) (4-13) k=l where (pk is the phase shift due to the respective time delay. A shift in the time domain by Q) (1]) positive corresponding to a time advance and (p negative to a time delay) corre- sponds in the frequency domain to multiplication Of the Fourier transform by the linear phase factor e.” (Oppenheim and Schafer 1989).'Iherefore, the spectrum Of the signal reflected from the first boundary is identical to the spectrum Of the incident signal except 37 for a phase shift and amplitude reduction. Thus, the Fourier transform for the first reflected signal yields: “’1 ‘ZIIPI R(a)) = A11: e 8((0-(00) +e 8(m+a)0) (4.14) j“’1 'jq’r . . The term e and e represent the phase shrft due to the location of the re- flecting surface. For a non-borer-damaged sample, the reflected signal is: rn (t) = Alcos(a)0t+tp1) +A2cos((oot+(p2) (4.15) where q>l = time delay from the first boundary, (p2 = time delay from the bark-trunk interface, A1 = amplitude Of the signal reflected from the first boundary, and A2 = amplitude of the signal received from the bark-trunk interface. The spectrum of a signal reflected from the non-borer-damaged sample consists Of two terms, the reflection from the surface Of the cherry tree and from the bark-trunk boundary. This results in a sum of two signals with spectrum given by: 38 .I‘pl 'j(p1 Rn((o) =A11r e 6(m-(o0)+e 5(a)+m0) + . . (4.16) [ 1‘92 “III’Z :l A21: e 8(m—m0)+e 6(m+co0) The Fourier transform of the reflected signal from non-borer-damaged sample is shown in Figure 4.6. Similarly for a borer-damaged sample, the reflected signal consists Of three terms: the reflection R [ 1] from the surface Of the cherry tree, the reflection R [2] from the top Of the damaged layer and the reflection R [3] from the bottom Of the damaged layer. This results in a sum Of three signals: rd(t) = Aldcos(coot+(p1d)+A2dcos(coot+(p2d) +A3dcos(a)0t+(p3d) (4.17) with spectrum given by: _ N do N do Azd“[e 2d8(w-wo) +e 2d8((o+coo)] + (4.18) N -J°€P A3d’t[e 3d5((1)--r1)0)~t-e 3d8(m+mo)] where 39 (p1 d = time delay from the outer boundary, on = time delay from the tOp Of the borer-damaged layer, (93 d = time delay from the bottom Of the borer—damaged layer, A1d = amplitude Of the wave energy received from the first boundary, A2d = amplitude of the signal received from the top of the borer-damaged layer and, A3 (I = amplitude of the signal received from the bottom Of the borer-damaged layer. The Fourier transform Of the reflected signal from the borer damaged is shown in Figure 4.7. The above results apply to a single frequency. The same procedure can be applied tO a range of frequencies tO compose an arbitrary broadband signal. In Figure 4.7 it is noted that the spectrum has well defined periodic spectral nulls. It is believed these due to frequencies interact with damage layer. Research is on going in this area and shows considerable promise. For example, the two main dips occurring ap- proximately at frequency 1.5 and 2.2 megahertz in Figure 4.7 arise from the standing wave resonances Of the boundaries to the damaged layer. They each appear as two main split dip because the damaged layer couple the standing wave in borer damaged sample to create an 4o up-shifted and a down-shifted resonance depending on whether the reflected signals from the bark surface and the bottom Of the damaged layer are moving in-phase or out-Of-phase. When the reflected signal is in phase case, the detected interface simply add some inertia tO the motion and lower the frequency and its frequency spectrum in signal power com- pare with out Of phase case. This phenomenon may be correlated signal from the interface between the bark and the trunk. When the reflected signal is out Of phase case, the detected interface is stretched and compressed so that it adds stiffness to the motion and increases the frequency and its frequency spectrum decrease in the signal power.This phenomenon may be correlated to the reflected signal from damaged layer. In either case, the interface of sample are subjected to the stresses and can be expected to influence the numerical val- ues at different frequencies. Therefore, this approach to detecting a borer damage is to compare numerical values of frequencies and its signal power. -‘ N 01 I0 01 Relative Magnitude (dB) d 0.5 41 Frequency (MHz) Figure 4.6 The Power Spectrum Of the Reflected Signal from a Non-Borer Damaged Sample 42 _ ................................................................................. f ............... a .......................... .- A 3 CD : 3 . .............. .. ° : 'O . 3 : a: . c . a: , .............. _. “3 : 2 : o : .5 : g oooooooooooooooooooooooooooooooooooooo : IIIIIIIIIIIIIII - O I a: : ,_ ............................................................................. f ............... .. .............................................................................. 5.....noccuauco-q l l A 3 4 5 6 Frequency (MHz) Figure 4.7 The Power Spectrum Of the Reflected Signal from a Borer Damaged Sample 43 4.3 Gaussian-shaped Signals One experimental technique commonly used by researchers is to measure the acoustic attenuation for highly attenuated materials using a Gaussian-shaped pulse. The effect of acoustic attenuation on an ultrasonic pulse having a Gaussian envelop is to trans- late the normalized power spectrum tO lower frequencies by an amount V f, proportional to the attenuation a while maintaining the bandwidth. By applying this technique to iden- tify the difference between borer and non-borer-damaged cherry tree have been Obtained a good result. The borer damaged layer contains highly attenuated material relative to non- borer-damaged ones thus amplifying the spectrum translation. The attention coefficient or of a damaged layer can be estimated from the measured frequency translation experienced by the pulse power spectrum shift due to the propagation through the damaged layer.The difference between the borer and non-borer—darnaged layer can be distinguished by com- paring the amplitudes Of the power spectra or the frequency shifts relative to their center frequencies. The experimental configuration for this measurement is shown in Figure 4.8. The Transducer TIR transmits a wideband acoustic pulse into a water coupling me- dium and signal return is received by the same transducer. The output Of the transducer is connected tO a spectrum analyzer which computes the power spectrum Of the received sig- nal. The experiment is first performed with non-borer-damaged samples and then repeated with borer damaged samples. The schematic diagram illustrating reflections from this ex- periment and for the output spectrum as shown on a spectrum analyzer are provided in Figure 4.9a and in Figure 4.9b. TIR Transducer Sample Holder \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ Transducer Slide Bar \ Testing Sample“ WWW/”WWW .4", L tram . \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ ‘LJ Spectrum Analyzer FFI‘ \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\‘ ‘ /////////////// ///////////////// ’///////////////////////////////////////////////////////////// V Figure 4.8 Experimental Configuration “““““““‘““““““““““““““““‘““ ““““““““““““““““““ 45 Transducer A B r- LAB _‘ _J ea“) ‘—/ eb(t)"_/ Figure 4.9a Schematic Diagram Illustrating Reflections from a Non-Borer-Damaged Sample 46 Relative Amplitude (dB) 9 P P .0 .° .° .° 9 t 2: e :* °.° ‘9 .° N l _L I Figure 4.9b Illustration Of Pulse Spectra Shifts due to Linear Attenuation of the -1 .5 -1 -0.5 O 0.5 Frequency (MHz) Spectra Of Reflected Pulses EA (to) and E B (to) . 47 The theoretical model is described as follows: The attenuation versus frequency characteristic, H (f) , Of a frequency linear atten- uating medium has the form H0) = exp (-x|flx) , where K is a medium constant, f denotes frequency and x denotes the propagation distance. The Fourier transform Of the output pulse, Y (f) , is Y (f) = X (f) H (f) , where X (f) is the Fourier transform Of the input pulse. The center frequency shift Of a Gaussian modulated pulse experienced by propagation through a distance x is determined as follows. The Fourier transform Of the incident Gaussian modulated signal is given by: X (f) = (it/(26)) >< [exp {—(nz/O'Z) (r-r0)2} +exp { (-(1r2/02)) (f+f0)2}] (419) The output Fourier transform Y (f) is then: Y (r) = exp (-Kxf) exp {- (1:2/02) (r- to) 2} (4.20) + exp (-Kxf) exp { (413/02) ) (H to) 2} Completing the squares, a closed-form expression for Y (f) can be written in terms Of ’62 = 02 (4.21) and V r = i0 - to (4.22) 48 where f0 represents a shift downward in mean frequency Of the pulse Fourier transform, f0 is the center frequency and o is the standard deviation Of the Gaussian-shaped enve- lope. Applying the above equations tO damaged and non-damaged samples allow us to evaluate the attenuation corresponding to the center frequency shift Of a Gaussian modu- lated pulse and thus to distinguish between the borer-damaged and non-borer-damaged samples. Figure 4.9a illustrates the reflections from non-borer-damaged samples. The spectrum, EA ((1)) , Of the echo from the first surface is: E A ((1)) = p AP (0)) (4.23) where a) is temporal frequency in radians and p A is the pressure reflection coefficient and P (0)) denotes the spectrum Of the pulse received from the surface Of the cherry tree. P (0)) includes the effects of frequency dependent attenuation in coupling medium as well as transducer and transfer function. This function defines the frequency range over which valid data can be Obtained. For small values Of p A’ the spectrum Of the echo from the boundary between the bark and trunk is (420:1) /Ce(-JZO)I) / B ((1)) = pBP (0)) e (4.24) where pH is the reflection coefficient, 1 is the bark thickness, aand c are the absorptivity, nepers ( (us) '1, and propagation velocity, respectively. The ratio, H (0)) , Of the two spec- tra define in Equation (4.23) and (4.24) enable the desired parameters to be determined since P (to) is removed from consideration: 49 -2a't' 42(1) 8 (m) = (pB/pA)e (4.25) whereT = l/c In most case, Ot is linearly proportional to (1) and the ratio pz/pl can be evaluated by interpolation to zero frequency. The phase Of H ((1)) specifies the phase relation between the two reflections which is ordinarily a linear function Of frequency with a slope propor- tional to 1/ c. Therefore this function has the same form of H (j) = exp (-x|f| x) . By applying the same arithmetic methods, the borer damaged sample can be evaluated by the same procedures. The schematic diagram illustrating reflections for this experiment and the output Of the spectrum analyzer using a borer-damaged specimen are shown in Figure 4.10a and 4.10b. 50 __] _J ea“) ._/ chew—J Figure 4.10a Schematic Diagram Illustrating Reflections From a Borer Damaged Sample 51 o to {TI > 3 O a) I 5:}- Z 1 I ' l l .o .0 (II 0 l I .0 h I Relative Amplitude (dB) 9 0) I p N I P .5 I \ l I l 1 92 -1.5 -1 -0.5 0 0.5 1 1.5 2 Frequency (MHz) Figure 4.10b Illustration Of Pulse Spectra Shifts due to Linear Attenuation in the Spectra Of Reflected Pulses EA ((1)) , EB((1)) and 126(0)) . 5. EXPERINIENTAL RESULTS The research reported here summarizes the results Of using ultrasonic pulse-echoes to detect the borer damage inside cherry trees known to have been infested with borers. As the transducer is moved from non-borer-damaged to borer-damaged areas, the acoustic impedance decreases. The reflected signal R [1] from the non-borer-damaged samples (Figure 4.2.2a) had a higher acoustic impedance mismatch causing most of the energy to be reflected at the first boundary. In addition to the initial reflection, there were some low amplitude reflections caused by scattering from the surface roughness and wood anisotro- py. The second reflection R [2] had a very low amplitude due to the highly attenuated bark and small acoustic impedance mismatch at the cambium between the bark and the undamaged trunk. The reflected signal R [2] from a borer-damaged sample (Figure 4.2.3a),showed a high amplitude reflection at the interface between the bark and the borer—damaged layer caused by the high acoustic impedance mismatch at the interface. The amplitude Of the third reflection, R [3] , was very small and overlapped with the reflection R [2] due to the very thin borer-damaged cambium layer. The differences between the received signals are more readily quantified if the frequency content Of the reflected signals is determined. This is achieved by carrying out a Fourier transform Of the reflected signal. The theoretical reflec- tion amplitude versus frequency was Obtained by programming the computer to calculate the frequency dependent reflection coefficient of a multilayer consisting of water, bark, damaged layer, trunk and water. The spectra Of the reflected signals for non-borer-dam- aged and borer-damaged as shown in Figure 4.3 and 4.4 are combined in Figure 5.1. The 52 53 ultrasonic detection system can be used reliably tO locate the borer-damaged areas when the frequency shifts between the non-borer-damaged and the borer-damaged samples are significanLIt can also be used to find the extent Of borer-damage by comparing the mea- sured frequency shifts with those Of sample containing known damage. The borer-dam- aged area has more energy in the returned pulse at low frequencies, but the energy content falls off rapidly with increasing frequency. The non-borer—damaged sample returned signal has a lower rate of decrease Of energy with frequency. This means that the damaged area, consisting Of feces, larvae and voids in the interface makes it is hard to pass the higher fre- quencies in the ultrasonic pulse. The acoustic impedance difference between borer-damaged and non-borer-dam— aged samples from cherry trees caused a reflection coefficient difference. A comparison Of the reflected signals from the two sample types showed that the acoustic impedance mis- match for the borer-damaged sample was larger than the acoustic impedance mismatch for the non-borer-damaged sample. Thus we essentially have identified a discriminant for bor- er damage detection. Table 1 summarizes the results Of tests on 11 cherry tree samples which contained 5 borer-damaged and 6 non-borer-damaged samples. Comparison was done using time domain analysis and power spectral estimation. The results indicate that an extensive borer-damaged cherry tree sample can be identified by Observing the first two reflected signals. The interference caused by the superposition Of two signals of the same frequency with very little time delay. The phase difference causes a partial cancellation of the combined effects Of reflected signal and determines which frequencies are out Of phase and in phase. As a result, when the frequencies are out Of phase, the frequency spectrum would exhibit a decrease in signal power at those frequencies and when the frequencies are in phase, the frequency spectrum could exhibit an increase in signal power at those fre- quencies. Thus, analysis Of the spectrum composition or power at a given frequency pro— 54 vides the potential for distinguishing between borer-damaged and non-borer-damaged samples. The experimental configuration is used to determine the central frequency shift as described in the previous section, except that rather than Observing the signal reflected from different boundaries, the data is collected and analyzed automatically by an IBM-PC microcomputer.The entire reflected signal is divided into reflections from the sample sur- face, interface between bark and trunk and the damaged layer by locating the maxima in the reflected signal envelope and multiplying the reflected signals by an appropriate time window centered about the envelope maximum position. The power spectrum Of each re- sulting section was calculated and frequency locations of the spectral maximum were not- ed. The frequency locations Of power spectral maxima from the borer damaged sample are plotted in Figures 5.2 to 5.9 as a function of penetration depth into the cherry tree. In this data set the random variation Of the spectral maxima locations due to boundary irregulari- ties and the downward trend in the frequencies Of spectrum due to attenuation can be Ob- served. For example, when a 5.2 cm bark width and 1.42 cm layer borer-damaged width are introduced into the acoustic path, the normalized received pulse power spectrum from the interface between the bark and trunk is shift downward by an amount V f = 0.06 MHz from the central frequency Of the pulse reflected only from surface Of the cherry tree. The pulse spectrum from the damaged layer is shift downward an additional amount V f = 0.18 MHz relative tO the central frequency Of the pulse from interface between the bark and the trunk. Thus their result shows that the application Of these techniques to other insect damaged trees is highly promising. 6.CONCLUSIONS The measurement Of distinguishable features between borer-damaged and non- borer damaged cherry tree samples is still a difficult problem, but the results Obtained demonstrate that there are characteristics in the ultrasonic signal, reflected by a borer-dam- aged structure, that provide information On the very thin damage layer at the interface be- tween the bark and the trunk. The measurement Of these features and their use in making predictions of the borer damage requires quantitative analysis Of the signal and an excel- lent data base Of signal returns from borer damaged and non-borer-damaged samples. This will allow reliable prediction of damage when comparison tO the data base Of borer dam- aged reference signals are made. Excellent analysis and predictions on damage characteristics were possible using time domain and frequency domain techniques. The extension Of frequency analysis tO in- clude the fine spectral details such as the periodic frequency dips referred to in the text would provide available additional material feature specification. This efl‘ort should be pursued 55 56 x104 as 832%: peace x106 Frequency (Hz) Figure 5.1 Power Spectrum Comparing Reflected Signals 57 8° I I I I 60 .. .............................................................................................. .- 40 1- ............................................................................................ . N O Relative Amplitude (Volts) O -20 .40 .. .................. .................... . t ................. .................... .................. .. '60 - .................. t ..................................... .................... .................. . 0 0.5 1 1.5 2 2 5 Time (Sec.) x 10.5 Figure 5.2 The Overall Reflected Signal from a Bore Damaged Sample 58 3° 1 I 2 t ,0 _ .............................................................................................. . 40 ...................................................... - 20 ....................................................... - Relative Amplitude (Volts) C) -20 ,40. ............................................................................................. q -60' ............................................................................................... - ’80 l 1 I l 0 O 5 1 1.5 2 2.5 Time (Sec.) x 10-5 Figure 5.3 The First Reflection from a Borer Damaged Sample Relative Magnitude (dB) 0 .0 a) on P a 0.2 59 Frequency (MHz) Figure 5.4 The Power SPeCtrum of the First Reflection from the Surface Of a Borer Damaged Sample Relative Amplitude (Volts) 6O 8° 1 ! E : so . . ............................................................................................... - 4o _ ............................................................................................... _ 20 . ............................................................................................... - o . -2o .40 t ................................................................................................ _ -,,_ .................. ................... .................... .................... .................. - '800 0E5 1P 155 2 2.5 Time (Sec.) x 1045 Figure 5.5 The Second Reflection from the Top Of the Damaged Layer 61 Relative Magnitude (dB) 0 P O) on ' ‘. j .0 h I 0.2 - ooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo Illuocoooono-Otoool'ooo-uuno...0.!OIOIIII-v-oOIOOQODIJO'IOIIIo-OIIQOOIIOOIOIOIOOIOI- oooooooooooooo COCOIIOIOIOIIO ......IOOOOOIacoupon-......ICODnil-Ono- uuuuuuuuuuuuuu Frequency (MHz) Figure 5.6 The Power Spectrum Of the Second Reflection from the Top Of the Damaged Layer 62 ao . . , j 60 - ................................................................................................ .1 40 .. ................................................................................................ -1 M O Relative Amplitude (Volts) O -20 -40 -60' ................... .................... .................... .................. .1 0 0.5 1 1.5 2.5 Time(Sec.) x106 Figure 5.7 The Third Reflection from the Bottom of the Damaged Layer Relative Magnitude (dB) 0 .0 a) a) P A 63 o I o - ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo ‘ p oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo d p oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo ‘ — oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo ‘ Frequency (MHz) Figure 5.8 The Power Spectrum Of the Third Reflection from the Bottom Of the Damaged Layer .0 a) Relative Magnitude (dB) 0 6) .0 A 0.2 ' 3 Frequency (MHz) Figure 5.9 The Power Spectra Of All Reflections Superimposed Showing the Frequency Shift due to Linear Attenuation LIST OF REFERENCES 65 LIST OF REFERENCES Alan V. Oppenheirn, and Ronald W. Schafer. 1989. Discrete-Tune Signal Processing, Prentice-Hall, Inc. A Division Of Simon and Schuster Englewood Clifl's, NJ 07632. Arita, K., and Kuratani, K. 1984.WOOden Pole Tester: For Determining the Strength Of Decayed Poles, Japan Tele communications Review, Nippon Telegraph and Telephone Public Corp., Tokyo, Japan, pp 167-173 July,1984. Carstensen, EL. 1979. Absorption Of Sound in Tissues, Ultrasound Tissue Characteriza- tion II. M. Linzer (Ed). National Bureau Of Standards, Spec Pub 525. Chivers, RC. 1980. Tissue characterization. Ultrasound in Medicine and Biology. D.W. Hill, P. N. Well, and John P. Woodcock. 1977. Computers In Ultrasonic Diagnostics, Medical Computing Series. Vol, pp 35. Edmonds, J. L. 1981. The Molecular Basis Of Ultrasonic Absorption by Proteins. Ultra- sound Med Biol. F. C. Beall. 1988. Nondestructive Testing and Evaluation for Wood Products, Nondestruc- tive Testing and Evaluation for Manufacturing and Construction. PP. 127-136. Hayt, W. H. 1974. Engineering Electromagnets. McGraw-Hill Book CO., New York, New York. 66 Kuc, R., Schwartz, M., Von Micsky, L., Parametric estimation Of the attenuation coeffi- cient for soft tissue, Ultrasonic Symposium Proceedings, 1976. L.Ferrari, J. P. Jones and Gonzalez, V. M. 1986. In vivo Measurement Of Attenuation, IEEE Ultrasonics pp 66-71. Lmaster, R. L., and Domfeld, D. A. 1987. Preliminary Investigation Of the Feasibility Of Using AcoustO-Ultrsonics tO Measure Defects in Lumber. J. Acoust. Emiss. 6 (3): 157- 165, 1987. Miller, B. D., Taylor, F. L. and Popeck, R. A. 1965. A Sonic Method for Detecting Decay in Wood Poles, American Wood Preserves Association, From NO. 1351. M. J. Lighthill. 1958. Fourier Analysis and Generalized Functions, New York: Cambridge University Press. Oppenheirn, AV. and AS. Willsky. 1983. Signals and System. Prentice-Hall, Inc., Engle- wood Cliffs, New Jersey Patton-Mallory, M., Anderson, K. D, and DeGrOOt, R. C. 1987. An AcoustO-Ultrasonic Method for Evaluating Decayed Wood, Proceedings Of Sixth Nondestructive Testing Of Wood Symposium, Washington State University, Pullman, WA, pp. 167-189. R. E. Edwards. 1967. Fourier Series: A Modern Introduction, Now York: Holt Rineheat and Winston, Inc. Shaw, D. A. 1978. Bandpass Filter Comparator for Confirming the Absence of Serious In- ternal Voids in Wood Poles, IEEE Trans. Instrum. Meas. IM-27 (31). 67 Sample Dia. Damage Extent Reflected Signals Which are Detected 7 cm Engrsligziamage R I 1] R [2] R [3] 9 cm His?) 5233“ R [1] R [2] R [3] 10cm ngiegiggjgcfl R[1] R [2] R [311 12cm 13;,mfnaggeafezsd. R111 R121 (NONEZ 14 cm zzbljtgfizmgeafiemqb R [1] R [2] (NONE) 2 7 cm Non-Borer-Damage R [ l] R [2] (—)3 9 cm Non-Borer-Damage R [1] R [2] (_) 3 10 cm Non-Borer-Damage R [ 1] R [2] (—) 3 12 cm Non-Borer-Damage R [1] R [2] (—)3 14 cm Non-Borer-Damage R [ l] R [2] (—)3 16 cm Non-Borer-Damage R [1] R [2] ( —)3 Table Borer Damage Detection for Different Cherry Tree Diameters and Damage Levels. 1. The reflected signal R [3] from the moderate damaged sample is very small and 0' t with R [2] . It is very hard to detect 2. The reflected signal R [3] from the a little damaged sample can not be detected du y small borer tunneling. 3. NO reflected signal R [3] in the Non-Borer-Damaged Samples. nICHIan STATE UNIV. LIBRARIES lllllllllllll11111111lllllllllllllllllllllll 31293010222614