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M30, p.45”, Date 4 //7/ {/7 0-7639 MS U is an Afi‘irmative Action/Equal Opportunity Institution 4 \gh‘fi 1 MSU LlBRARlES .—.:I—— RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES will be charged if book is returned after the date stamped below. 3139 109 11:97" L861 99mins maisfis pun Supaauifiug [nomoalg JO Juaunmdaq HDNEIIDS :10 HELLSVW aarfiap 9m 10} smamannbar sq) JO 111911119an [cured or melanin 91819 “831mm 01 pammqng SISEIHJ. V 37 811011327 58 sanomnoal omosvumn A8 .LNEIW’ERIIISVEIW Mouvnnauv ATTENUATION MEASUREMENT BY ULTRASONIC TECHNIQUES By Leenong Li A THESIS Submitted to Michigan State University in partial fulfilment of the requirements for the degree MASTER OF SCIENCE Department of Electrical Engineering and System Science 1987 ABSTRACT ATTENUATION MEASUREMENT BY ULTRASONIC TECHNIQUES By Leenong Li This thesis presents ultrasonic measurement techniques for attenuation imaging. The object to be imaged is modeled as consisting of parallel layers of different impedance. Two methods for determining attenuation coefficients are presented. One is to use the impulse response functions. The other is to utilize the ratio of the reflected signals. The theoretical development is verified experimentally by three different measurement configurations. The results of the experiments Show that the technique utilizing the ratio of the reflected Signals is more accurate than the impulse response technique. Acknowledgments I would like to express my sincere appreciation to Dr. Bong Ho and Dr. H. Roland Zapp, my advisors, for their guidance and support. I want. to thank Mr. N. T. Wang for offering his FFI' program and for many helpful suggestions. I would also like to thank Mr. Tao-shinn Chen for his constant help and encouragement. Table of Contents List of Tables List of Figures Chapter 1 Introduction Chapter 2 Theoretical Considerations 2.1 Review of Basic Ultrasound Principles _- 2.2 Ultrasound Reflection from a Layered Model 2.3 Determination of Attenuation Coefficient from Impulse Response 2.4 Determination of Attenuation Coefficient from Reflected Signals Chapter 3 Experimental Procedures 3.1 Experimental Configurations 3.2 Data Processing 3.3 Experimental Results Chapter 4 Analysis of Experimental Results 4.1 Tradeoffs for Finding the Impulse Response Function 4.2 Discussion 4.3 Conclusion and Suggestion for Future Study Bibliography ...... . -- iv 12 Is 18 28 28 32 50 64 -70 -75 78 Table 2.1.1 Table 2.1.2 Table 3.3.1 Table 3.3.2 Table 3.3.3 Table 3.3.4 Table 3.3.5 Table 4.2.1 Table 4.2.2 List of Tables Aplproximate values of ultrasonic ve ocrtres of various media ' Characteristic acoustic impedance of various me 1a Result for test object 1 using the impulse response function Result for test object 1 usrng the Signal peak value - -_ ..... Result for test object 1 using the signal magnitude sum Result for test object 2 Result for test object 3 Ratios for simulation data 1 ...... Ratios for simulation data 2 10 -63 63 63 -63 74 74 Figure 2.1.1 Figure 2.2.1 Figure 2.2.2 Figure 2.3.1 Figure 2.4.1 Figure 2.4.2 Figure 3.1.1 Figure 3.1.2 Figure 3.1.3 Figure 3.1.4 Figure 3.1.5 Figure 3.2.1 Figure 3.2.2 Figure 3.2.3 Figure 3.2.4 Figure 3.3.1 Figure 3.3.2 Figure 3.3.3 List of Figures Transmission and reflection at an interface ............................... 7 A one dimensional layered structure ............................................. 13 First and second order reflection from a layered structure 14 Bi-directional ultrasonic interrogation ......... 15 Bi-directional ultrasonic interrogation 19 A reflected signal waveform - 21 Incident signal processing I - 30 Incident signal recording 11 31 Reflected signal processing I - ------- 33 Reflected signal processing 11 - - 34 Reflected signal processing III 35 A single layered object. for uni-directional attenuation determination 44 Acoustic transmission and reflection in the smgle layered object 44 Samge 1 for the attenuation measurement wr out knowrng the mcrdent Signal - 48 Samglle 2 for the attenuation measurement wr out knowrng the Incrdent signal 48 Test object 1 for the bi-directional attenuation measurement 51 Incident signal for test object 1 51 Frequency spectrum of the incident signal 51 vi Figure 3.3.4 Reflected signal from test object 1 - ..... 52 Figure 3.3.5 Frequency spectrum of the reflected signal .............................. 52 Figure 3.3.6 Impulse response function in test 1 ............................................... 53 Figure 3.3.7 Test object 2 for the uni-directional attenuation measurement 1 -- ............................... 55 Figure 3.3.8 Incident signal for test object 2 ................... 55 Figure 3.3.9 Frequency spectrum of the incident signal - - 55 Figure 3.3.10 Impulse response of the incident signal ................................... 56 Figure 3.3.11 Reflected signal from the plexi glass/air interface ....... 56 Figure 3.3.12 Frequency spectrum of the reflected signal - 57 Figure 3.3.13 Impulse response in test 2 -------- . 57 Figure 3.3.14 Test object 3 for the attenuation measurement wrthout knowing the mcrdent Signal 60 Figure 3.3.15 Incident signal for test 3 - 60 Figure 3.3.16 Frequency spectnrm of the incident Signal ....... 60 Figure 3.3.17 Reflected signal in sample 1 ........................................ 61 Figure 3.3.18 Frequency spectrum of the reflected signal In sample 1 ............................... 61 Figure 3.3.19 Impulse response in sample 1 ......... 61 Figure 3.3.20 Reflected signal from sample 2 ....... 62 Figure 3.3.21 Frequency spectrum of the reflected signal In sample 2 _ - ................... 62 Figure 3.3.22 Impulse response for sample 2 _ - 62 Figure 4.1.1 Simulation result for comparison of the impulse response function ............................. 66 Figure 4.1.2 Figure 4.1.3 Figure 4.1.4 Figure 4.1.5 Figure 4.1.6 Figure 4.1.7 Figure 4.2.1 Figure 4.2.2 Measured result for comparison of the impulse response function Simulation result without interpolation ....... Simulation result with interpolation Measured result without interpolation Measured result with interpolation Measured result using correlation -_ Simulation data 1 Simulation data 2 -66 68 68 -69 69 71 73 ' 73 Chapter 1 Introduction The interaction between ultrasound and even simple biological tissue structures is a complex process. Major factors which describe the propa- gation of ultrasound in biological material include the density of the material, the sound velocity in the material, the acoustic impedance and the attenuation in the material. By contrast, the propagation of X-rays in tissue is determined solely by the density of the material. Thus, in princi- ple, a considerable amount of information could be extracted from the analysis of the interaction of sound with tissue. This coupled with the noninvasive nature of ultrasound has been its main attraction to biomedi- cal application. 7 A biomedical ultrasonic imaging system, in general, transmits an acoustic pulse through a test object and receives an echo waveform result- ing from the interaction with the object. In transmission systems, the received signal is the deformed pulse resulting from the incident pulse propagating through the object. In reflection systems, the received signal is the waveform resulting from reflections of the incident pulse at the discontinuities inside the object. 2 Most current ultrasound systems are based on energy detection(or envelope detection) methods and use only the echo amplitude information. A conventional A-scan system displays the amplitude of the echo waveform as a function of acoustic travel time. A conventional B-3can system produces an ultrasonic mapping in which the spot intensity is pro- portional to the echo intensity. Recently, research has been conducted on how frequency and phase information of the received signal can be used for imaging and tissue characterization. The result produced ultrasonic impediography which allows determination of acoustic impedance along the path of propagation. This thesis investigates the measurement techniques which can extract the information on acoustic attenuation in addition to acoustical reflection along the path of ultrasound propagation. Attenuation is important from several viewpoints. First, it determines the amount of acoustic energy which can reach structures of interest at various depths in a medium. For example, knowing the attenuation between the surface of a mother’s abdo- men and the uterine cavity determines the amount of energy reaching the fetus. Second, it is important because part of the propagating energy is permanently converted. Third, attenuation by scattering canresult in ultra- sonic energy reaching structures not intended to be probed or in produc- tion of standing waves, creating peaks and nodes in the spatial distribution of the ultrasonic energy. This thesis is organized as follows. First, the basic properties of ultrasound propagation will be briefly reviewed. Second, the basic princi- ples of ultrasonic impediography will be outlined. Third, it will be shown that information sufficient to find out the variation of attenuation along the path of propagation can be extracted by transmitting two ultrasound sig- nals from opposite sides of the test object. For this purpose, the test object is modeled as consisting of parallel layers of different impedances. Fourth, two measurement techniques for determining attenuation variation and impedance profiles will be investigated. Finally, experimental results are presented to show the validity of the theoretical development. The system limitations and suggestion for future study will also be discussed. Chapter 2 Theoretical Consideration This chapter provides the necessary theoretical background for the proposed techniques of attenuation and impedance measurement. In the first section, some related ultrasound principles are reviewed. It is fol- lowed by the analysis of acoustic reflection from a layered model. With this background we are able to derive a method to determine the acoustic attenuation and impedance profile as will be shown in section 2.3. We propose a simpler and more accurate method in section 2.4. 2.1 Review of Basic Ultrasound Principles Ultrasonic ,enggy_is transported by mechanicaLthratMat frequen- cies above the.upper_limit_of human audibility. The ultrasound consists of a propagating periodic disturbance in the elastic medium, causing the par- I ticles of the medium to vibrate about their rest(equilibrium) positions. The vibratory motion of the particles is Wmaganngme transmission through the medium is strongly dependent on the ultrasound frequency and the state of the medium- gas, liquid, or solid. Table 2.1.1 illustrates that the values of the velocities of longitudinal sound waves in solids are the highest, those in liquids and biological soft tissues lower, and those in gases still lower. 5 Table 2.1.1 Approximate values of ultrasonic velocities of various media.* Medium Sound Velocity(m/s) Dry air(20°C) 343.6 Water(37°C) ' 1524 Amniotic fluid 1530 Brain 1525 Fat 1485 Liver 1570 Muscle 1590 Tendon 1750 Skull bone 3360 Uterus 1625 *From H .F .Stewart&M .E .Stratmeyer8 In this section, some related properties of ultrasound propagation are reviewed as following. Sound Velocity The speed at which ultrasonic vibrations are transmitted through a medium is inversely proportional to the square root of the product of the density and the adiabatic compressibility of the material. The speed of C :3 J? 8: 5'1?an (MoMn/us) 6 sound(c), along with frequencyU) determine the wavelengthOt) , from the relationship i=3. (2.1.1) f . Knowledge of the speed at which ultrasound is transmitted through a medium is used in the conversion of echo-return time into depth of material being imaged. Sfurl Reflection and Transmission at Interfaces 76 (/W #1]? M Z 3 / 4/ ”0...: 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 waves in free field conditions it can be shown that this quantity is equal to the product of the density of the medium(p) and the velocity of sound(c) in the medium. Thus the medium characteristic acoustic impedance is: Z=pc (2.1.2) When an ultrasonic plane wave meets a boundary between two different media, it may be partially reflected. The ratio of the characteris- tic impedances of the two media determines 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 7 move in a positive direction, but at a velocity corresponding to the propa- gation velocity in the new medium. Just as in 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 dimen- sions and roughness of the reflector as illustrated in Figure 2.1. In Figure 2.1 the subscripts i, r and I refer to the incident, reflected and transmitted waves respectively and 1 and 2 to the first and second media that the ultrasound encounters. Medium 1 /- / 159mm /. /' // Figure 2.1.1 Transmission and reflection at an interface 1 The relationship between 9,- and 6, as given by Snell’s law is: 8 Czsin91=Clsinet (2.1.3) The equations relating the ratios of the transmitted intensity([,) to the incident intensity(I,-) and the reflected intensity(I,) to the incident intensity(I,-), respectively, are given in the following expressions: 1, (4ZZZ1coszei) -= 2 (2.1.4) 1; (chosefizlcosep and I, chose,—-Zlcos9, 2 2 1 5 1,.- choseft-Zlcoset ( ° ° ) where Z land Zzare the characteristic acoustic impedances of the media on either side of the interface, 9,. is the angle between the normal to the reflecting surface and the direction of the incident ultrasound, and 0, is the angle between the normal to the reflecting surface and the direction of the transmitted ultrasound. For normal incidence, the angle of incidence(9,-) and the angle of transmission(0,) both equal zero and the previous equations become: .1_,: 42221 (216) 1.- (22+zl)2 and Ir_ 22—21 2 7‘.“- [Zz-l-Zl ] (2.1.7) 9 These relations can also be expressed in terms of transmitted, reflected, and incident pressures (P,, P,, and Pi, respectiveIY), since 1 P2 I: — — 2.1.8 (2)(pc) ’ ( ) where P is the pressure amplitude we get: P —’= 222 (2.1.9) P,- (Zz-I-Zl) and P (2 —Z —'-= 2 1) (2.1.10) P,- (Z2+Z1) The reflectivity, or the reflection coefficient, r, is defined as the ratio of pressure reflected to the pressure incident alike the transmissivity, or the transmission coefficient, 1, as the ratio of pressure transmitted to the pressure of the incident wave. Therefore we have the following relation- ships: P r 22.21 ——= 2.1.11 7—Pi 22+zl ( ) and P _—’-= 22 (2.1.12) Pi 22+Zr From equations (2.1.11) and (2.1.12), we can see t1+r (2.1.13) 10 Table 2.1.2 lists the characteristic impedances of some biological materials. Analysis of the reflections from a layered model will be dis- cussed in section 2.2. Table 2.1.2 Characteristic Acoustic Impedances of Various Media.* Medium Acoustic Impedance 103kg/(sm2) Dry air(205C) 0.45 Water(37°C) 1524 Amniotic fluid 1510 Brain 1571 Fat 1366 Liver 1570 Muscle 1685 Tendon 2100 Skull bone 7392 Uterus 1706 *From H .F .Stewart&M .E .Stratmeyer8 Attenuation and Absorption The intensity of a plane progressive ultrasound field can be reduced by interaction with the transmitting medium. Two important sources of 11 attenuation are scattering and absorption. The interface of each discon- tinuity within a medium serves as a reflecting surface, the size of which ( in relation to the wavelength) determines its effects as a scatterer. Most of the scattered energy diverges from the original direction of propagation and thus the total amount of energy transmitted is reduced. When spatter- 11: 0 or s 1‘ 211-117 0 ‘- .. 11‘1"- wve i 91'000111131 0, wigrej is the frequency of the ultrasound and n is greater than 1. Thus greater scattering occurs at higher frequencies. The other significant source of attenuation is absorption, which occurs primarily at the macromolecular leveL for longitudinal waves. The attenuation due to absorption causes the acoustical energy to be converted to some other form of energy, typically heat. The acoustic pressure amplitude PX of a plane progressive ultrasound wave of initial acoustic pressure amplitude Po and intensity Io at a dis- tance x in any uniform attenuating medium, is described by the relation- ship: Px=Poe-°“ (2.1.14) where e is the base for natural logarithms and a is the amplitude attenua- tion coefficient of the medium for a given frequency. Since acoustic inten- sity is proportional to the square of acoustic pressure, this can also be expressed in terms of intensity (I): 12 I =10e-2w‘ (2.1.15) x Ultrasonic attenuation in a medium generally increases with increas- ing frequency in a manner that can be expressed approximately ( over a limited frequency range ) in the form azaof" (2.1.16) where or is the amplitude attenuation coefficient of the medium at a fre- quency f and a0 is the attenuation coefficient of the medium at the refer- ence frequency f0. For many human tissues and other materials of interest, n has a value between 1 and 2. In sections 2.3 and 2.4, the measurement techniques of attenuation coefficients will be considered in detail. 2.2 Ultrasound Reflections from a Layered Model The structures of biological tissues and composite materials allow to construct a multilayered model for the purpose of acoustic imaging. The model is shown in Figure 2.2.1. In the rest of this chapter, the following assumptions are made: 1. Reflections of Ware Qné'g‘ligible. This assump- tion is valid for biological tissues and composite materials in general, since the ' ' ce variation across media boundaries is Got 1 large. \ 211017“; N111 be 1201 13 2. Each layer is homogeneous in acoustical properties (i.e. constant impedance within each layer). 3. In; man of the boundaries between layers is small compareg to the acoustic wavelength. 0 1 2 i i+1 N—l N 20 Z1 Z2 Zr Z1.“ ZN_1 20 0‘0 0‘1 0'2 0‘1 “1+1 “Iv-1 0Lo To 11 1:2 t,- tm tN_1 To r1 r2 ’1' rm 7111.1 Y N Figure 2.2.1 A one-dimensional layered model where: Zi=Acoustic impedance of the ith layer a1=Attenuation coefficient of the ith layer in Np/s 1:,=Time taken for acoustic wave to propagate through the ith layer ri=Reflection coefficient at the boundary between (i-1)st and ith layers The impulse response, h(t), of such a structure consists of N 14 V «516.5135: 3 8 sum"— . .N 2 N N Hahn— was com 98 3.5 o: co.— .— 92. a . a E omn— 3.. 3% 830 v Elect: N «L V 3.313951 V 3.51881 38:1 X x5: N wait: a N v 29.5 13.31 C :3 XTI N- .1315? \\ u aviary u g 3..er 15 impulses, one for each boundary. N h(t)=Za,5(t-—ti) (2.2.1) i=1 where a,- and t,- are the amplitude and delay corresponding to the reflection at the ith interface. Figure 2.2.2 shows the amplitude relationships at each boundary. In Figure 2.2.2, i—l t1: 2 21k (2.2.2) 1:0 2 1k: round trip delay in kth layer _ i-l =e( “01°1r11'1(1—r2)e‘2°‘*‘*’ (2.2.3) Zi-Zi-l r‘_ 2,421.1 (2.2.4) x(:) 410) —-> «n— Test object ‘—— Y1“) 2’20) Figure 2.3.1 Bi-directional ultrasonic interrogation 2.3 Determination of Attenuation Coefficients from Impulse . Response 16 The impulse response in equation(2.2.1) contains information on the attenuation coefficient of each layer as well as the reflection coefficient of each boundary. In order to extract the attenuation information, the target is interrogated from the opposite directions as shown in Figure 2.3.1, using an acoustic signal resulting in two impulse response functions. Let the corresponding impulse response functions be h1(t) and h2(t). Using the results of section 2.2 and refening to Figure 2.2.2, 11,0) and h2(t) can be written as N .- h1(t)=2a,6(t-ti) (2.3.1) i=1 where /1 D t: 221,1 (2.3.2) @ -1 =e"( 2‘10“) ”h(1—2 —rk )e"( zaktk) (2.3.3) Zi—Zi—l '1'" 21+ 2M (2.3.4) Similarly, N h2(t)=2b15(t-tj) (2.3.5) j=l where 539;,- (2.3.6) 1%? 17 -2a -2 bF—e e( Mrj [I (1 -r ,‘e-2)( am) (2.3.7) k=j+l The in equation (2.3.7) is due to the fact that the reflection efficient changes its sign when the incident wave is from the . The values for a,- and bi (i,j=1,2,...,N) can be read directly from the impulse response functions h1(t) and h2(t). Using equations (2.3.3) and (2.3.7), we have a b r- r- £21.: 2‘ (—2a¢,-) 1:1 (4014;) (2'3'8) “M I rm(l-r,- )e ’ r,(l—ri+1 )e ’ Hence the attenuation coefficient or,- can be determined by: 1 a'b+l at-ELn n[— '1; b (l—r 2)(1— [+15] (2.3.9) where a1, b,- and t,- are known. The reflection coefficient r,- can be found as follows: First, thwousticalJmpmieLof me first and thummm are W. This normally is the case because the object is immersed in water. Thus, r1=e(za°1°)al (2.3.10) 18 r~=-e‘2°'°‘°1bN (2.3.11) For the rest of the reflection coefficients r,-(i=1,2,...,N-1), let r2 i R1: 2 (2.3.12) l-ri ’ SO that, 137, Dr, (~10; MOT—Q; R -R ai+lbi+1 ”10:16 : T11 ("(63); .13.}. 1+1- .- 0111 01.12.». (.- n) n+1. Em and A R- 1 1/2 ri+1=Si+l [fl] (23-14) H- where, +l,l:fai+l>0 SM: —1,ifa,-+1<0 (2.3.15) Once all the reflection coefficients are known, the attenuation coefficients or; can be easily calculated from equation (2.3.9). 2.4 Determination of Attenuation Coefficient from Reflected Signals In section 2.3, it was shown that the ratio of the magnitude of the impulse response determines both attenuation coefficients and reflection coefficients (equations (2.3.9), (2.3.13) and (23.14)). Finding the impulse response in general relies on deconvolution , which involves the inverse Fourier transform of the system spectrum. As will be Shown in chapter 4, 19 because of the existence of noise, frequency band limitations of the FFT as well as other factors, the impulse response obtained through deconvolu- tion is not of the same form as that shown in equation (2.2.1). Thus the magnitudes of the impulse responses used for the calculations of attenua- tion coefficients have some accuracy limitations. Since, the deconvolution technique requires multiple Fourier transforms (to determine X(o)), Y(m) and h(t)), it is time-consuming and not easily implemented in a small system. A simpler and more accurate alternative to deconvolution is to use the magnitudes of reflected signals to determine the attenuation coefficients and reflection coefficients. Consider the model described in section 2.3 and shown in Figure 2.4.1. x(t) x(:) —-D ‘—— Test object 1.— ——- 2’10) Y2“) Figure 2.4.1 Bi-directional ultrasonic interrogation In Figure 2.4.1 x(t) is an incident signal applied to both sides of the object, and y1(t) and y2(t) are the reflected signals, respectively. If h1(r) is 20 the impulse response for x(t) and y1(t), h2(t) for x(t) and y2(t), then the impulse response h1(t) from an object with N boundaries consists of N impulses, or N - h1(r)=2a,8(t—ti) (2.4.1) i=1 where ai is the magnitude of the impulse in the ith interface. The reflected signal y1(t) also contains N echoes corresponding to the N interfaces, so that y1(t) can be expressed as: N y1(t)=2y1.(t) (2.4.2) i=1 where y1 ,(t) is the ith echo in the reflected signal y1(t) due to the ith boun- dary, when interrogated from side 1 of the object. A typical yin-(t) waveforms are shown in Figure 2.4.2. Because all the y1,.(t1’s are the reflections of the incident ”signal .110), they are of the sggjfreguency as _x__(t), and the shapes are similar to that Mn other words,*all_t_he echoes are cnpies of x(t) with different pro- nortionalig constants. That is, fl(t)=co (2.4.3) 3’11 and WP iiih ”III Iiihnuriiir "I" 11111 1. ‘ 1 y 1(‘) . '11" Yum .111. .111. 1 I y 12(1) .111. "1" '11" Yul/(t) Figure 2.4.2 A reflected signal waveform 21 22 yli(t) :c. 3’1(i+1) (2.4.4) where Co and ci are constants. If yum) and yl(i+l)(") are the sampled values of yli(t) and y1(1+1)(t), x(n) is the sampled value of x(t), then by choosing appropriate starting points, we can get —-—"(”) — 2 4 5 yll(n) —Co ( . . ) and ”’02) (2 4 6) ——-=c y 1(i+1)(") for ISiSN. where N is the number of the boundaries in the object. Using deconvolution techniques, we can get the impulse response of y1,(t) and x(t) as follows: With X(n) and Y11(n) the Fourier transforms of x(t) and y1 ,(t), respec- tively, N +351... X(k)=2x(n)e 1" (2.4.7) ":0 N #2131... n=o where: N+1= total sampling points of x(t), y(t) 23 n= the nth sampled point of x(t), y(t) at time t=nT X(k)= the kth component of X(f) Y(k)= the kth component of Y(f) The Fourier transform for the impulse response for y1,(t) and x(t) is then given by: Ylim H —— 2.4.9 lim— X(f) ( ) 01' 2 (n )e -j-2—-kn ylin _Y_l__r(k=) n=0 H1,(k)_ X(k) N 1&1“ (2.4.10) 2x(n)e N ":0 The inverse Fourier transform of ”1.0) provides the impulse response hu(") 2 N -j2—;;kn .21: kn .21: 2331003 j— N kan'fio h,(n)=1 2 H 1 ,(k)e = 2 e 2“ (2.4.11) k=0 N -j—kn Zx(n)e N _ n=0 In a similar manner, the impulse response h(i+1)(‘) for y(i+1)(n) and x(t) is given by: F N -j-2—"kn N 0%“) Eoylfiflfin)‘: h1(1+1)(")= 2 e 2,; 1:0 N -j-—Iar 2x(n)e N "=0 1 From equation (2.4.6), x(n)=coyu(n) h“(n) becomes: N 113%:101 N jailer: N 1'33». Eoyl‘me h11(n)=2H11(k)e =2e 21! 1:0 1:0 N '17“ 2x(n)e ”=0 From equation (2.4.3), it is clear that: erin)”1)’1(i+1)(") So that the ratio of hum) to h1(i+1)(") is: r . N 4%». N j-zlkn ,Eoydn)‘: 28 N 2 1:0 N -j—’5ku 2x(n)e N hu-(H) "=0 l 2 - -IP=C. h1(i+1)(") N fifllm N j. 2T1: kn Eoyrmrfink 28 2 1:0 N filkn 2x(n)e N n M d where c,- is the constant determined in equation (2.4.6). l 24 (2.4.12) (2.4.13) (2.4.14) (2.4.15) (2.4.16) 25 *It has been shown that Min. of We r-i- -. 1.. ' -.. . ,‘1’1110 f th 1 __.-_1____--e inrpulse responses. Since the impulse response for the reflected signals and the incident signal is a train of impulses. WW points._of_the_echoes. Thus, the impulses are the first components in. hli(t)’s, or h1,(0)’s in (2.4.11). The magnitudes ai and ai+1 in equation (2.4.1) become: al=h 11(0) (2.4.17) ai+l=h1(i+1)(0) (2.4.18) and l a 1:111 1(0)::0— (2.4.19) at 1111(0) —-= =C- (2.4.20) “1+1 h1(i+1)(0) ‘ For the opposite side of the model illustrated in Figure 2.4.1, the same conclusions can be drawn. If h2(t) is the impulse response for x(t) and y2(t), then h2(t)=£jb15(t-ti) (2.4.21) i=1 and as in equation (2.4.5) and equation (2.4.6); 26 x(n - 2.4.22 Y2K") O ( ) and y (n) _2' :21,- (2.4.23) y2(i+1)(") . By the procedure shown above: bN=h2.(O)=i (2.4.24) do and bi hzl-(O) = =d- (2.4.25) b(i+l) h2(i+1)(0) ‘ . where d,- is the constant defined in equation (2.4.23) Therefore, equations (2.3.9) and (2.3.13) become 1 aibi-t-l 2 2 I 6' (XE-ELI! [mu-r1- )(1_ri+l )]=4—Ti-Ln [7:(1-r12)(1-ri+121}.4.26) a- b- 1 R- =R- 1+1 1+1 =R- __ . . 1+1 r[ “ibi r crdi (2 4 27) In the above development, we have shown WE;- MILES—0W 0f the W. This provides a convenient method for determining attenuation coefficients and reflection coefficients. The tech- nique is simple to implement in small systems for on-line imaging appli- 27 cations. Furthermore, because of the complex numerical calculations and the frequency band limitations of the FFT algorithm in deconvolution , the ratio of the reflected echoes discussed above will provide more accurate results than deconvolution. In chapter 4, it will be shown that for the ideal case, both techniques give the same result. For measured signals, the two techniques give different results, with the results obtained from the ratio of the echoes more reliable. Chapter 3 Experimental Procedure The various measurement techniques to verify the theoretical develop- ments in section 2.3 and section 2.4 are discussed in this chapter. Section 3.1 presents the system configurations used in the experimental study. Section 3.2 outlines several data processing procedures to calculate the ultrasonic parameters. The measured data and the experimental results are given in section 3.3. 3.1 Experimental Configurations In order to calculate the attenuation coefficient and impedance profile, the knowledge of incident signal and reflected signal waveforms is required. The systems used for recording the incident signal and the reflected signals are shown in Figures 3.1.1, 3.1.2, 3.1.3 and 3.1.4. The purpose of these configurations is to provide a wide range comparison of the different measurement techniques. The following subsections explain these configurations. 3.1.1 Sampling Incident Signal Waveform The system in Figures 3.1.1 and 3.1.2 was used to obtain the incident signal from a lossless acoustic reflection. This was done by observing and 28 29 recording the acoustic ultrasound reflection at the air/water interface._IQtal r E . l . E 1 . Aft}; . . 1 f WWW ' A transducer of frequency 2.25 MHz was used. A Panametrics 5050 Pulse Generator/Receiver was employed to generate pulse signals to the transducer and to received the reflected signals. A low energy, intermediate dampen ultrasound signal was used throughout the experimental study. In Figure 3.1.1, a Tektronix 465 Cathode Ray Oscilloscope was used to display the received signal waveforms. The waveforms were sampled at a 161M112 sampling rate. In Figure 3.1.2, the incident signal was sampled by an A/D conver- sion circuit with a sampling rate of 15MHz. Th: sampled data were sent 11116.5) (131?) passband and {in}? we. The filtered data were displayed on a monitor and also stored on floppy disks. The sampled incident signals from either system above were inputed to a Cordata PC400 microcomputer for further processing. 3.1.2 Sampling Reflected Signal Waveforms 30 _ wafimoooa aqua :8an— _._.m 05w?— “Ban—Eooeomfi 85m 32:6 0M0 new gauche—oh. 333333.?— omen mow—8:35»— can? 31 .8388825 oovUn— 53.80 . _ . _ hogan—89.28 QWN 8.8520 = 95:82 Haw? .532: N._.m 95$.”— uouo>=oo OZ 333333.?— omen 832553 333 32 The reflected signals from a object under test can be obtained in a similar manner, that is to transmit an ultrasound signal to the object and then to receive the echoes from the object. Figure 3.1.3 shows the configuration using an oscilloscope to receive the reflected signal waveforms. The operation and the parameters were the same as those for the incident signal case in Figure 3.1.1. The same ultrasound signal was applied to both sides of the object for the bi-directional interrogation cal- culation discussed in section 2.3. The signal in Figure 3.1.4 was applied to the A/D conversion circuit, similar to the signal in Figure 3.1.2. Both side A and side B were exposed the same ultrasound signal, similar to the case in Figure 3.1.3. Figure 3.1.5 shows still another setup for the measurement methods that will be discussed in section 3.2. In this arrangement, only one side of the object is needed for the ultrasound signal. 3.2 Data Processing Based on the theoretical development in sections 2.3 and 2.4, three different procedures of the attenuation calculation are presented in this section. They are discussed in the following three subsections. 3.2.1 Bi-directional Interrogation 33 _ wEmmoooa 3ch taco—«om m._.m 0.53.”— 5.38880? 9.va 8330 ‘l'illl OMU new 5:9:on 8283:823— omen 850858; N .875 “no... 34 : wfimmoooa Rama 380:3— v._.m 03w."— .8388228 8.9. 52.30 . _ _ _ bean—Eocene: OWN coco—=90 I7 33:8 02 .llll. 338353—2— oncn 8525:5— .83.. amok. _ 35 E mammmoooa Rama 380:3. n._.m 05mm"— cannEooean SQUA— 33.50 {I'll OMU new 5:2.on 333338.?— anon 8938.5— nose 28,—. 36 The experimental setup involved in this method is shown in Figures 3.1.1,3.1.2, 3.1.3 and 3.1.4. Two calculation methods for attenuation and for impedance are described as follows. I) Using the Impulse Response Function 1. An estimate the acoustic impulse response of the object when it is interrogated from either side is achieved as follows: First obtain the sampled incident signal x(n) and the sampled reflected signals y1(n) and y2(n) from side 1 and side 2 of the target. Then transform x(n), y1(n) and y2(n) into frequency domain to obtain X(f), Y1(f) and Y2(f), respectively. The reflection transfer function, H(f), is obtained from both sides of the object as: Y (0 H1m=X—l(r)— (3.2.1) and H2m=Y2-)§% (3.2.2) Finally, the impulse response functions are calculated as: h1(t)=F'1(Hl(f)) (3.2.3) and h2(t)=F"(H2(f)) (3.2.4) 37 where 15"1 is the inverse Fourier transform operator. 2. Obtain the impedance profile and attenuation variation using the impulse response function This was done by applying equation (2.3.9) through equation (2.3.15), assuming the Wand in water to be negligible. Equation (2.3.9) through equation (2.3.15) can be rewritten as: '1=01 (3.2.5) rN'—-bN (3.2.6) For i=1,2,...,N—2, "2 (3 2 7) l l’riz . . a. b. ‘ R. =R.M (3.2.8) 1+1 1 “1b: ‘ R i '+1 2 r i+l=Si+l [1 +1; 1] (329) H- where +1:ifai+1>0 Sin: "l’ifaH1rzaoe ‘ 02 L I. k Water Air Figure 3.2.2 Acoustic transmission and reflection in the single layered object 45 L= thickness of the material along the transmission axis From Figure 3.2.2, it is clear that: —2a 1L a2=(1-r%)r2e (3.2.35) The attenuation coefficient (11 is therefore: 1 “o al=—Ln (1-r%)r2— (3.2.36) 21 [ 02 The ratio -:2- in the equation above can be either the ratio of the impulse 2 response or the ratio of the signal magnitudes, as discussed in subsection 3.2.1. In equation (3.2.36), the reflection coefficient at the water/material interface, r1, needs to be obtained by other means. experimentally, two methods were employed. They are: a) Obtain r1 from an impedance calculation. This is accomplished using the the relationship between impedance and reflection coefficient as shown in equation (2.1.11), which for case here, is: (3.2.37) where the variables were defined in Figure 3.2.2. 21 and 20 are deter- mined as follows: 46 From equation (2.1.2), where: p1=density of the test material c1: velocity of sound in the material . p1 was calculated by measuring the volume and the weight of the test object. c1 was obtained by measuring the travel time of the distance in the . Zo, impedance of water, was found in published data(T able 2.1.2). b) Obtain r1 from a signal waveform From Figure 3.2.2,the relationship: al=rlao (3.2.39) provides the desired reflection coefficient: 01 r1=— , (3.2.40) “0. a Again, a—1 can either be the ratio of the impulse response or the ratio of 0 the signal magnitudes. Once the reflection coefficient r1 is determined, the attenuation coefficient on] of the material can be calculated from equation (3.2.36). 3.2.3 Uni-directional Attenuation Determination without Knowing the Incident Signal 47 The method outlined here is similar to the one in the previous subsec- tion. It requires two different thickness samples of the test material. Knowledge of the incident signal is immaterial as long as the same incident signal applied to both samples. Figure 3.1.5 shows the system configuration for this measurement method. The acoustic reflection and transmission relationship for the two sam-' ples are shown in Figures 3.2.3 and 3.2.4. In Figure 3.2.3, the following notation is used: a0: incident impulse applied to each sample “11‘: impulse response from the first boundary of sample 1 a12= impulse response from the second boundary of sample 1 r1: reflection coefficient at the water/material interface a1= attenuation coefficient of the test material L1= thickness of sample 1 In Figure 3.2.4, the following notation is used: 00: incident impulse applied to each sample a2]: impulse response from the first boundary of sample 2 “22" impulse response from the second boundary of sample 2 r2: reflection coefficient at the material/air interface “o -2a1Ll a0(1-r%)r2e 012 / Water *— L l —_"1 Figure 3.2.3 Sample 1 '1 “o (1+rl)ao "1ao “21 ao( 1 vary-2‘1““ 022 L2 Water fi'fi Figure 3.2.4 Sample 2 49 or]: attenuation coefficient of the test material L2= thickness of sample 2 From an analysis similar to subsection 3.2.2, the transmission and reflection coefficients are given by: alzzao(1—r%)rze-2allll (3.2.41) and 022=ao( 1 -r%)r2e—2alla (3.2.42) Which give the ratio: -2a L g: 00(1—r%)r28 l 1 =e2al(LQ-L1) (3 2 43) “22 ao(l—r%)r2e—2a‘b2 Thus, 1 “12 or = L — . . 1 2(L2—L1) " [an] (3 2 44) The attenuation coefficient or, can be obtained without relying on knowledge of the incident signal or the acoustic reflection. As pointed a previously, the ratio :12- in equation (3.2.44) can be the impulse response 22 or the ratio of the reflected signals. Three different measurement techniques for attenuation variation have been described. The first method introduced, bi-directional ultrasound 50 interrogation, is the most practical one since it can determine the attenua- tion and impedance of a multilayered material. However, it is the most complex in terms of calculations and measurements. The remaining two methods are fairly simple but apply to only single layered material. This limits their usefulness. The technique described in subsection 3.2.3 is the most accurate because it does not rely on assumptions and uses less meas- urement data. Thus it provides a useful laboratory verification. 3.3 Experimental Results The experiments were selected to verify the validity of the measure- ment methods outlined in section 3.2. A test material was investigated under the different measurement configurations. 3.3.1 Results from the Bi-directional Ultrasound Interrogation The model used in the experiment is shown in Figure 3.3.1. It is a single layer structureaan acrylic cast(plexi glass). The incident signal and its frequency spectrum are shown in Figures 3.3.2 and 3.3.3. Since the model is a symmetrical structure, it was interrogated only from one side. The corresponding reflected signal is shown in Figure 3.3.4. The fre- quency spectrum of the reflected signal is shown in Figure 3.3.5. The impulse response obtained is shown in Figure 3.3.6. 51 Plexi glass 1 Water \\ Water 2 \ Figure 3.3.1 Test object 1 // 1! .11. ll . n 1' 1:11 1.11 .111, y 1 V'V.a fi'. '1 Figure 3.3.3 Frequency spectrum of the incident signal 52 echo 1 1 1111. .1111. m 111 111%) . 11 . echo 2 Figure 3.3.4 Reflected signal from test object 1 l . 1111 . 11111111 Magnitude 1.11. 1111111111111“ 1111 1 1) 1 11111 11L . 1 11111 ' 1 x11 11' 1111111111 11111111111111111 1111— Phase for echo 1 51:1 11 11 Magnitude u.-.l11111l1111..1.. ................ 11111 1111“... 1 11111111111111 1111111111111H1111111'11 1.1111111 111111111 111111111111111. p... for echo 2 Figure 3.3.5 Frequency spectrum of the reflected signal 53 1 ii 111 9 H H " .1 L ‘1 3 .111}; u 11 11:11! .111111 a .101111111.I 1 1 1 . . . . l 1,. ‘ '1': 1‘ '.l 'I.i.. 1...}, 1 l 1 1 11'1'11' 1"111'11 ’ 1:. H”. '1' H 11 l 1111"1':Hf11’1" I '1“ ‘l i ‘ 11"1‘1LI ‘ 1111’11'1'1-‘(1'11 l 111i!11!;1111111111111L1111'11I1 u111111111!1111111111111‘1'1‘1111‘11 I 1.1. 1 1114.: L for echo 1 ‘11. I1. 11. ," ' 5 1'1»11'I for echo 2 Figure 3.3.6 Impulse response function in test 1 54 Using two the calculation techniques described previously, the result obtained from the impulse response is given in Table 3.3.1, the result from the ratios of the signal magnitude, the ratio of the peak values and the ratio of the magnitude summation, are shown in Table 3.3.2 and Table 3.3.3. 3.3.2 Result for the Uni-directional Attenuation Determination from Known Incident Signal The model used for this experiment is shown in Figure 3.3.7. The experimental procedure was outlined in subsection 3.2.2. Figures 3.3.8 through 3.3.13 show the sampled signals, their fre- quency spectrums and the corresponding impulse response functions. The reflection coefficient at the water/plexi glass interface Was calculated fol- lowing the two methods discussed in subsection 3.2.3. A 12.75cmx1.1cmx6.35cm, 109.046g sample of the test object was used to calculate the impedance of the test object. The density of the object, p1, was calculated as: p1:109 0463 =1.18146g/cm3=1181.46kg/m3 (3.3.1) 92. 30cm3 The velocity of ultrasound in the test material,cl, was measured as: 01:2805m/s (3.3.2) 55 Water \\\\\§l ---l +— 0.56cm Figure 3.3.7 Test object 2 m Figure 3.3.8 Incident signal for test object 2 Magnitude Phase Figure 3.3.9 Frequency spectrum of the incident Signal W—-*-——- ~ Figure 3.3.10 Impulse response of the incident signal echo 1 -, (Jill. *‘i' ll Tm‘llt' — ‘2 echo 2 Figure 3.3.11 Reflected signal from the plexi glass/air interface 56 .II hIIIIIII IIIIIII IIIIIIII' .' I . M ' I'LIIIIHHII ii i “HUI . i. an . .n. n . llnhnuux. .I IIIJIIIIIIHIJIHI agnlmde I I II I I I II I- III III I III III I I I I . I I I . II IIIII ”LIMIIIIIIIIIIIIITIIIIIMIU MIA?! I I I 7 Phase I I III II IIIIIIII I I ,.'I _ IIII for echo 1 IIII I IIIII I , A - n . . n mm A. 11 211.! III ILA-v III III .. u I I I. I - I ' '. Phase AAA for echo 2 Figure 3.3.12 Frequency spectrum of the reflected signal I II III. I :‘I: I I I II II o _IIII_I&IIIIIII,III II for echo 1 I I. IIII I IIII.IIII I IIIIIIIIII III I ' I for echo 2 Figure 3.3.13 Impulse response in test 2 58 From equation (3.2.38), the impedance of the plexi glass is given by: Z1=plcl=l181.46kg/m3X2805m/F33l4x106kg/mzs (3.3.3) The impedance of water (Z0) was chosen from Table 2.1.2, which is: Zo=1524x103kglmzs (3.3.4) Following equation (3.2.37), the reflection coefficient at the water/plexi glass interface was determined as: Z 1"Zo Z l-I-Zo =0.37 (3.3.5) r1: The reflection coefficient was also obtained by using the other method discussed in subsection 3.2.2. From equation (3.2.40), a 7 r’1--1-= 1.088679x10 —o 45 - - . (3.3.6 a0 2.398081x107 ) where a1 and a0 used are the magnitudes of the impulse response func- tions shown in Figure 3.3.14.and Figure 3.3.11, respectively. These two values of the reflection coefficient were used in the calculations of the attenuation coefficient. The calculation results are tabulated in Table 3.3.4. 3.3.3 Experimental Result for Uni-directional Attenuation without Knowing the Incident Signal Two acrylic blocks with different thicknesses were used in this exper- 59 iment. They are shown in Figure 3.3.14. The sampled signals and their frequency spectrum, as well as the corresponding impulse response func- tions are shown in Figures 3.3.15 through 3.3.23. The attenuation coefficient was calculated following equation (3.2.44). The impulse response magnitudes and the ratio of the peak values of the reflected signals, as well as the ratio of the magnitude summations were used in the calculation. The results are given in Table 3.3.5. The analysis of these experimental results, together with the com- parison of the simulation data, is given in chapter 4. 6O ‘ , £ \\ --I |---- _ "" 1.2cm "' 0.56cm S l 1 amp e Sample 2 Figure 3.3.14 Test object 3 Figure 3.3.15 Incident signal for test 3 iii ‘ ..:i.iiii§’t...... .......... Jill“. 3: ‘li. l I" l '2, w: n Figure 3.3.16 Frequency spectrum of the incident signal 61 Figure 3.3.17 Reflected signal in sample 1 l J I! ,1} 2;.gg' ’I' 'g9 ' '-r-73111!"ll ....... . ..................... Figure 3.3.19 Impulse response in sample 1 62 .I i ‘l- "a . ”H. __ u in :W1 m t 'u 'I ll Figure 3.3.20 Reflected signal from sample 2 41!. mm, JUN" ,umu .umm i "n. :1. L”"".tidhmu A “it! i l. n 't m - u » u ‘l l ' Figure 3.3.21 Frequency spectrum of the reflected signal in sample 2 t l ! llifltdc Figure 3.3.22 Impulse response for sample 2 Table 3.3.1 Result for test object 1 ---us1ng the impulse response function Layer ReflectTDn coefficient Attenuation coefficient (water/plexiglass) (cm-1) Plexiglass 0.37 0.75 Plexiglass 0.45 0.68 Table 3.3.2 Result for test object 1 --—using the signal peak value Layer Reflection coefficient Attenuation coefficient (water/plexiglass) (cm‘l) Plexiglass 0.37 0.40 Plexiglass 0.45 0.33 Table 3.3.3 Result for test object 1 ---using the signal magnitude sum Layer Reflection coefficient Attenuation coefficient (water/plexiglass) (cm-l) Plexiglass 0.37 0.37 Plexiglass 0.45 0.30 Table 3.3.4 Result for test object 2 Layer Reflection coefficient Attenuation coefficient (water/plexiglass) (cm‘l) Plexiglass 0.37 0.63 Plexiglass 0.45 0.56 Table 3.3.5 Result for test object 3 Data type Attenuation coefficient(cm" ) Impulse response 0.58 Signal sum 0.45 Signal peak value 0.44 Chapter 4 Analysis of Experimental Results The experimental results obtained in chapter 3 are compared with simulation data in this chapter. The validity of the measurement tech- niques is discussed. In section 4.1, the experimental data from the impulse response function are analyzed, along with the simulation results. In sec- tion 4.2, the consistency of the two attenuation calculation methods is dis- cussed, based on the simulation data and the experimental results obtained in section 3.3. 4.1 Tradeoffs for Finding the Impulse Response Function The attenuation measurement method introduced in section 2.3 depends heavily on the ability to determine the impulse response function accurately. Theoretically, the impulse response function is a train of impulses, each impulse corresponds to each boundary inside the test material. In practice, however, it is not always the case. Noise may be introduced in the A/D conversion. The finite frequency band of the FFT may cause computation errors. The division operation in deconvolution can even enlarge the effect of those errors. The experhental results in chapter 3 show that even the noises in the impulse response function do 64 65 not distore the impulses in shape, they already effect the magnitudes of the impulses. It is worthwhile to know the limitation of the deconvolution technique for the ultrasound attenuation determination. This was done by simulation. The synthetic ultrasound signals used in the simulation were made close to the actual signals in signal intensity and frequency. Figures 4.1.1 shows the simulation result. As comparison of this result, Figures 4.1.2 shows the measured data and result. From the simulation result, it is clear that the deconvolution technique and the FFT algorithm used in this study are qualified for the attenuation measurement. It turns out the sampled sig- nals need to be processed in order to improve the impulse response func- tion. Two signal processing methods were investigated.‘They are: 1) inter- polation of the sampled signals; 2) correlation to obtain impulse response function. 1) Interpolation of the sampled signals The sampled values of the signals were interpolated by inserting the mean value of two adjoining samples to the middle of these samples. The simulation result without using the interpolation is shown in Figure 4.1.3, as a comparison with the result obtained from the interpolation shown in x0) ‘1 . g | (t) L 41] l‘xki AIULiA y -t‘. v .fi ‘TV I»... Mr) .5 , A Figure 4.1.1 Simulation result l x(t) ll: y(t) lll , ”l i o . ' Q .’ h(t) 1 Al I l l L [Ii 1‘ 1111 g - L A s A A 1 Lil ‘1 l[ L 1‘ 11 AL Y . {vldiil— {It ‘YV'I1VTf '1] [I l ' 'I l 3 Figure 4.1.2 Measured result 67 Figure 4.1.4. The results for the actual signals are shown in Figures 4.1.5 and 4.1.6. These results show the interpolation can improve the impulse response function. For this was a preliminary study of the interpolation effect, only the simple interpolation algorithm was investigated. Other interpolation algorithms may give better results. 2) Correlation to obtain impulse response function The auto- correlation of incident signal and the cross-correlation of the incident and reflected signals can be used to determine the impulse response function. This is derived as follows. Assume: x(t)= incident signal X 0‘): frequency spectrum of the incident signal X*(f)= complex conjugate of X(f) y(t)= reflected signal Y (1‘): frequency spectrum of the reflected signal Y*(f)= complex conjugate of Y(f) rxx(t)= auto-correlation of x(t) rxy(t)= cross-correlation of x(t) and y(t) R30): frequency spectrum of rare) 68 x( I) will olll’l l y“) lillllllllllll ."wrww I'm: *zzzaz': 2! ' ' H H! .lllll.“ ,l lll. . l.l” ll: ll i l Figure 4.1.3 Simulation result without the interpolation x(t) Figure 4.1.4 Simulation result with the interpolation 69 X(t) ‘ i ii I; : él ! :5 y“) M L - .9. ll A l’ l‘ l H t h“) i; r . Figure 4.1.5 Measured result without the interpolation h(t) . I P". ................. . -- - W fl H- W AT, 3L?“ Figure 4.1.6 Measured result with the interpolation 70 Ram: frequency spectrum of rxy(t) h(t)= impulse response H(f)= frequency spectrum of h(t) From the correlation properties, an=X(f)X*(f) (4.1.1) ny(f)=X(f)Y*(f)=X*(f)Y(f) (4.1.2) The frequency spectrum of the impulse response function is given by: R (f) X* Y "1‘? Thus, h(t)=F'1(I-I(f)) (4.1.4) where F'1() is the inverse Fourier transform operator. In the experiment, the incident signal and the reflected signal were processed following the procedure shown above. The result for the actual signals are shown in Figures 4.1.7. It is seen that the improve- ment by this technique is fairly limited. 4.2 Discussion In section 2.4, it was theoretically shown that the ratio of the signal magnitudes can replace the ratio of the impulse response for the determi- nation of the acoustic attenuation. A critical issue upon the validity of this x0) I rug) 13:3); Y(I) "T ”1 Ti é ill, 9'; 'l - My“) if, 4#__. h(t) WI: - :‘firw .. 'W Figure 4.1.7 Measured result using correlation 71 72 method is the consistency of the two ratios in practical environment. A verification of the consistency was done by synthetic signals. The verification is straight forward: for each set of synthetic signals, the corresponding impulse response functions are calculated by deconvo- lution. Then the ratio of the impulses are compared with the ratio of the signal magnitudes. Figure 4.2.1 and Table 4.2.1 show the result for the. first set of data. Figure 4.2.2 and Table 4.2.2 show the case for the second set of data. For the estimate of the signal magnitude ratio, both the peak values and the magnitude summation were used. In Tables 4.2.1 and 4.2.2, the ratio of the impulses and the ratio of the signal magnitudes are identical, which is consistent with the theoreti- cal result. The experimental results in chapter 3, however, are not so consistent. The reasons are the following. The first reason is that the impulse response functions do not consist of only the pure impulses. Thus the magnitudes of the impulses used in the calculation can be different from the "true" magnitudes. For a poor impulse response (Figure 3.3.6), the difference between the two calculation results is large (Fables 3.3.1, 3.3.2, 3.3.3). For a better impulse function (Figures 3.3.19 and 3.3.22), the difference becomes much smaller. In addition, the large variation of the .l. ill x(t) lift fill? t i it . . y(t) “5"!“ 1"!" .lll.3 "UL. ll: l l h(t) 1 Figure 4.2.1 Simulation data 1 i.l {till till; I .'. e y(t) Ill 1th ”J , 4 léiii "'3' i” l h(t) - 7,1,, Figure 4.2.2 Simulation data 2 74 Table 4.2.1 Ratios for simulation data 1 1 L Impulse response Signal magnitude sum Signal peak value 1.000 1.000 ' 1.000 Table 4.2.2 Ratios for simulation data 2 Impulse response . Signal magnitude sum Signal peak value 1.937 2.451 2.000 75 ratios of the impulses in the three experiments indicate the poor accuracy of those ratios. As pointed in chapter 3, the third experiment setup is the most accu- rate one. The results in that experiment are indeed much more consistent than the other two. Hence the result of the third experiment can be con- sidered as the most accurate one. A important observation is that in all the experiments, the results obtained from the signal magnitude ratios are much closer to the result in the third experiment, in comparison of the results from the impulse response function. From these discussions, it is clear that the signal magnitude ratio is more accurate than the ratio of the impulse response, in general. 4.3 Conclusion and Suggestion for Future Study This thesis has developed two methods that can extract both the vari- ation of attenuation coefficient and the variation of reflection coefficient along the path of propagation. The corresponding impedance profile can be easily calculated from the reflection coefficient(equation(3.2.12, 3.234)). The variation of impedance obtained by these techniques should be more accurate than that by the ultrasonic impediography methods, since the latter neglect the attenuation in the medium, whereas the 76 methods outlined in this thesis take into account the ultrasonic attenuation along the path of propagation. In fact, the development of imaging tech- niques utilizing the attenuation coefficient is the main thrust of the research reported here. Between the two methods presented in this thesis, the one utilizing the ratio of the reflected signals is more favorable for imaging applica- tions, because of its simplicity and accuracy. This method depends heavily on the ability to accurately obtain the reflected signals accuracy, it intro- duces other problems such as noise contamination and signal dispression. The attenuation coefficient for biological matter has been found to be fre- quency dispersive so that a large bandwidth may result in nonuniform attenuation of different frequency components. There are several approaches that could improve the accuracy of attenuation calculation’s evaluation. One is to explore different schemes to determine the ratio of the reflected signals. Two methods were outlined to obtain this signal ratio. However, further development may be desirable since the accuracy of the ratio plays a critical role in the method. Another way to improve accuracy may be to apply sophisticated signal processing techniques. In the work reported here, a chebyshev filter was employed which worked well for the test models investigated. As the thickness of the test object increases, the power and hence the signal to noise ratio 77 decreases for reflected echoes from the deep lying boundaries in the object. In that case, other signal processing schemes may be necessary to improve the signal to noise conditions. 9. -78- Bibliography Beretslcy, 1., Farrell, G.A., Improvement of Ultrasonic Imaging and Media Characterization by Frequency Domain Deconvolution, Exper- imental Study with Non-Biological Models, Ultrasound in Medicine, Vol. SB, 1977 ' Giesey, J.J., Automated System for Determining the Acoustic Impulse Response of a Layered Model, MS. Thesis, Michigan State Univer- sky,l986 Ho, 8., Jayasumana, A., Fang, C.G., Ultrasonic Attenuation Tomogra- phy by Dual Reflection Technique, Ultrasonics Symposium, 770, 1983 Jayasumana, M.A.A.P., Acoustic Attenuation and Impedance Charac- terization by Bi-Directional Impulse Response Technique, MS. Thesis, Michigan State University, 1982 . Jonse, J.P., Ultrasonic impediography and Its Application to Tissue Characterization, Recent Advances in Ultrasound in Biomedicine, 1977 . 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