IUTWHWIHWWHWII 31293 10725 8570 This is to certify that the thesis entitled Automated System For Determining The Acoustic Impuise Response Of A Layered Mode] presented by Jeffrey James Giesey has been accepted towards fulfillment of the requirements for Masters degree in Elect. Engr. @gW Major‘g rofessor Date MW /2, /7/’é 0-7639 MS U is an Affirmative Action/Equal Opportunity Institution MSU LIBRARIES —_ RETURNING MATERIALS: Piace in book drop to remove this checkout from your record. FINES wiII be charged if b00k is returned after the date stamped below. 3m. 2213.. m3 . . _ . d 100 023:. AUTOMATED SYSTEM FOR DETERMINING THE ACOUSTIC IMPULSE RESPONSE OF A LAYERED MODEL BY Jeffrey James Giesey A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Electrical Engineering and System Science 1986 4274/!” ABSTRACT AUTOMATED SYSTEM FOR DETERMINING THE ACOUSTIC IMPULSE RESPONSE OF A LAYERED MODEL BY Jeffrey James Giesey Present ultrasonic imaging techniques make use of only the magnitude of the receiving signal. A method was developed which gives the impedance profile of a layered material from the acoustic impulse response. In this thesis an automatic system was developed to calculate the acoustic impulse response of a layered model. The system was tested with three different transducers and two different models. Three different filtering methods were also investigated. The results showed that in most cases, the layers of the models could be seen in the impulse response by using this system. Also, the resolution of the system was greater than that of conventional ultrasonic imaging. ACKNOWLEDGMENTS I would like to thank L.T. Wu for his help in developing some of the software used for this thesis, and Dr. Robert Barr and Dr. H. Roland Zapp for their helpful suggestions. Finally; I thank Dr. Bong Ho, my advisor, for his guidance on this work and my education. ii TABLE OF CONTENTS List of Tables. . . . . . . . . . . List of Figures . . . . . . . . . . Chapter 1 Introduction. . . . . . . Chapter 2 Theoretical Considerations. 2a. 2b. 2c. 2d. 2e. Introduction . . . . . . . Impedance Derivation . . . Attenuation Imaging. . . . Bandwidth Considerations . Ideal Cases. . . . . . . . Chapter 3 System Hardware . . . . . 3a. 3b. 3c. 3d. 3e. 3f. Introduction . . . . . . . Computer . . . . . . . . . Bus Buffer . . . . . . . . Range Gate Controller. . . A/D Conversion Board . . . Ultrasonic Pulser/Receiver Chapter 4 Experimental Results and Future Possibilities. . . . . . . . . 4a. 4b. 4c. Introduction . . . . . . . Data Acquisition . . . . . Experimental Results . . . iii 4d. Future Possibilities Appendix A Fourier Transform. Appendix B Algorithm for Reducing Noise Components from Spectrum. Appendix C System Software. Bibliography. iv Page LIST OF TABLES Page Table 1: Summary of Results. . . . . . . . . . . . . 58 Figure Figure Figure Figure Signal Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 1: 2: 3: 4: S: 6: 7: 3: 9: 10: ll: 12: 13: 14: 15: 16: 17: 18: 19: 20: LIST OF FIGURES Definition of Variables. . . . . . . . Determination of the Impulse Response. Bidirectional Interrogation. . . . . . Typical Frequency Spectrum of Input Ideal Model. . . . . . . . . . . . . . Ideal Impedance Profile. . . . . . . . Ideal Impulse Response . . . . . . . . Spectrum of Figure 7 . . . . . . . . . Less than Ideal Impulse Response . . . Spectrum of Figure 9. . . . . . . . . System Diagram. . . . . . . . . . . . Input and Output Timing Diagram . . . Bus Buffer. . . . . . . . . . . . . . Range Gate Controller . . . . . . . . A/D Conversion Board. . . . . . . . . Data Transfer Timing Diagram. . . . . Waveform x(t) Recording . . . . . . . Waveform y(t) Recording . . . . . . . Model 1 . . . . . . . . . . . . . . . MOdel 2 O O O O O O O O O O O O O O 0 vi Page Figure 21: Typical Input: 1.00 MHz, Focused, Nonfiltered. . . . . . . . . . . . . . . . Figure 22: Typical Output: 1.00 MHz, Focused, Nonfiltered. . . . . . . . . . . . . . . . Figure 23: Typical Input: 1.00 MHz, Focused, Filtered . . . . . . . . . . . . . . . . Figure 24: Typical Output: 1.00 MHz, Focused, Filtered . . . . . . . . . . . . . . . . Figure 25: X(f) for 2.25 MHz, Focused Transducer . Figure 26: X(f) for 2.25 MHz, Unfocused Transducer Figure 27: X(f) for 1.00 MHz, Focused Transducer . Figure 28: Y(f) for Trial 1. . . . . . . . . . . . Figure 29: H(f) for Trial 1. . . . . . . . . . . . Figure 30: h(t) for Trial 1. . . . . . . . . . . . Figure 31: H(f) for Trial 2. . . . . . . . . . . . Figure 32: h(t) for Trial 2. . . . . . . . . . . . Figure 33: H(f) for Trial 3. . . . . . . . . . . . Figure 34: h(t) for Trial 3. . . . . . . . . . . . Figure 35: H(f) for Trial 4. . . . . . . . . . . . Figure 36: h(t) for Trial 4. . . . . . . . . . . . Figure 37: H(f) for Trial 5. . . . . . . . . . . . Figure 38: h(t) for Trial 5. . . . . . . . . . . . Figure 39: H(f) for Trial 6. . . . . . . . . . . . Figure 40: h(t) for Trial 6. . . . . . . . . . . . Figure 41: H(f) for Trial 7. . . . . . . . . . . . Figure 42: h(t) for Trial 7. . . . . . . . . . . . vii Page Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 50: 51: 52: H(f) h(t) H(f) h(t) H(f) h(t) H(f) h(t) H(f) h(t) for for for for for for for for for for Trial Trial Trial Trial Trial Trial Trial Trial Trial Trial 11 11 12 12 Viii Page CHAPTER 1 INTRODUCTION Ultrasonic waves have been used to produce images in medical applications since the 1970's. .Almost all imaging schemes so far have only made use of the magnitude of the returned signal. A much more useful image of an object can be produced by displaying the acoustic impedance and attenuation of that object. So far work done on impedance and attenuation imaging has been limited to a few researchers whose work involved hand digitizing the return ultrasound signal. Thus, the images done so far take more work to obtain and could not be considered a practical means of imaging. It is the goal of this project to automate the signal acquisition and signal processing to produce an acoustic impulse response from which the impedance and attenuation images can be found. This project will enable future improvements to be made in the signal processing and eventually produce a practical way to produce both acoustic impedance and attenuation images. The basic principle behind ultrasonic imaging is to produce a pressure wave with a transducer and apply the wave to the medium to be imaged. This wave propagates through the medium until it reaches a material with a different acoustic impedance. At the boundary of these two materials, part of the wave will be transmitted through the second medium and part of the wave will be reflected back to the transducer. This reflected wave can be detected by the same transducer and displayed. Presently, there are two types of images produced that account for the vast majority of ultrasonic images. They are called A-mode and B-mode. For an A-mode image, the return signal is envelope-detected and the amplitude is displayed on a CRT as a function of time. The acoustic signals are then translated from functions of time to functions of distance by dividing time by the speed of sound in the material. Therefore, time and distance are used interchangeably. The A-mode display is used to locate boundaries between layers of difference impedances. Applications include estimation of liver size, location of brain midline, and measurement of eye structure. For a B- mode image, the signal is envelope-detected similarly to an A-mode except it is displayed as a line of dots called pixels with the brightness of the individual pixels corresponding to the amplitude of the signal at that point. By combining many different angles of transducer orientation, a two-dimensional image is produced. B-mode imaging is most widely used in fetal monitoring and other imaging. It is believed that a plateau has been reached using these two imaging techniques and others that use envelope detection. This plateau was reached mainly because these schemes only utilize a small portion of the returned signal. An imaging scheme was developed by J.P. Jones in which the whole signal, both magnitude and phase, was used. This method makes use of all the spectral information to determine the impedance profile of the material. This thesis extends the scheme into ultrasonic imaging. The acoustic impedance is a measure of the pressure required to give a particle of a medium a certain velocity. For example, air has a lower acoustic impedance than water, so pressure waves travel in water much more easily than through,airu .An impedance image is developed by taking the input waveform and the output waveform and deconvolving them in the frequency domain to find the impulse response. The theory will be reviewed later in this thesis. The relation is: t d/hIT) d1 = 1/2 1n [z(t)/20] o In order to find the impulse response, we first find the incident waveform x(t) and the reflection waveform y(t). Then, we take the Fourier transform of both to get X(f). Dividing Y(f) by X(f), we obtain the frequency domain impulse response H(f). We then take the inverse Fourier transform to get the impulse response hit) with which the impedance profile z(t) can be found. This scheme has the advantage over the present techniques in that: 1. It gives the direction of the impedance change, not just the magnitude. This scheme will tell if the boundary is between a higher to lower impedance medium or a lower to higher impedance medium. 2. It gives the value of impedance for a layer relative to the initial impedance, not just the preceeding layer. Thus, if the acoustic impedance is known for any of the layers, the acoustic impedance is known for the entire medium. 3. It greatly improves the resolution of the image because the impulses of the impedance profile are significantly narrower than those of regular envelope detection. Another image that can be evaluated from the impulse response is the acoustic profile. Attenuation is the measure of the decrease on intensity as a pressure wave travels through a medium. In order to form the attenuation profile the medium needs to be interrogated from both sides. The goal of this thesis is to perform the necessary data acquisition and signal processing to compute an impulse response. It is organized into four chapters. The first chapter introduces the subject and the second explains some of the theory involved in ultrasound. Chapter three describes the hardware developed to carry out the imaging and explains its operation. Chapter four presents and discusses experimental results, and is followed by suggestions for future work for the imaging system. CHAPTER 2 THEORETICAL CONSIDERATIONS In order to understand the project it is essential to first review some of the basic ultrasound principles. With these basic principles, we can derive the equations that relate the impulse response to the impedance profile. This section will also take a brief view of the necessary theory to do acoustic attenuation measurement, and will be followed by a discussion of the bandwidth considerations and some solutions to bandwidth problems. Finallyy we will look at two ideal cases which will enable us to compare the actual experimental results with what should be expected. 2a. Review of General Ultrasound Principles As noted before, an ultrasound image is created by sending a pressure wave into a medium. When this pressure wave reaches a change in material, part of it is reflected back and part of it is transmitted through the medium. Mathematically, the wave can be expressed with a standard wave equation describing the pressure at a particular point and time. v2p(x.t) = p/k £9, where p = pressure, p= density of the material, k = wavenumber with k =wc, c = wave velocity, and w: radian frequency. The solution to the equation is of the form p(X.t) = poexpi-j(wt-kx)] The amplitude of the pressure at a given point is P(X) = poexm-ax) where: 0: attenuation constant From the continuity equation V5pu +9? = 0 where u = the particle velocity and the density is relatively constant we find that V5u + l/kfi? a 0 This gives us the relation -%=o% so if iii-”35‘ a‘t-rjw we get P =I3CU where c = w/k = the velocity of propagation of the ultrasound wave If we define z = pc as the acoustic impedance of the material we get the handy form of p = zu relating the particle velocity to the pressure. The intensity of the wave is derived from the kinetic energy since KB I 1/2 pu2 E '7 = (KE)C where I is the intensity. So I 1/2 pen2 and the amplitude of the wave at a point is described by and part is transmitted. and where and Snell's law, I(x) = 10 exp(-20x) pi+ Pr: pt When the wave reaches a boundary, part is reflected By using the boundary conditions cosai- vr c039,: v, coset acoustic acoustic acoustic particle particle particle angle of angle of angle of pressure of the incident wave pressure of the reflected wave pressure of the transmitted wave velocity of the incident wave velocity of the reflected wave velocity of the transmitted wave incident wave reflected wave transmitted wave (see Figure 1) we can find the reflection coefficient (the ration of the reflected pressure over the incident MATERIAL 1 C1 .21 MATERIAL 2 (32 .22 Figure 1: Definition of Variables 10 pressure) and the transmission coefficient (pressure over the incident pressure). If the incident wave is moving perpendicular to the surface, the reflection coefficient simplifies to r = (2, -2.)/(z,- + z.) (1) and the transmission coefficient simplifies to = ZZj/(Zj + 2,) (2) where z. = acoustic impedance of the first material 2, = acoustic impedance of the second material the intensity of the wave is proportional to the square of the pressure divided by the impedance so the intensity reflection and transmission coefficients are equal to the square of the pressure coefficients times the ratio of the impedances. This gives the reflection coefficient R=(z; -z.)2/ (2; +2.)2 the transmission coefficient T=4zi-zi /(z; +2.)2 They are related to T = (R + l) The other general aspect of ultrasound waves that is important to this thesis is the resolution of the standard techniques. For envelope detection the resolution is generally accepted to be equal to the wavelength in the best case. To get an estimate of this, a 1.00 MHz wave 11 propagating through liver tissue (with velocity of propagation = 1545 m/s) would have a resolution of only = c/f = 1.5 mm. It is because of this poor resolution that ultrasound is not suitable for many applications. 2b. Impedance Derivation Biological tissue is normally'acoustically'complex, however there is some order to it. The macro structure of the tissue suggests a multi-layered, nonplanar, laminated structure. Since the lateral variations in material can be reduced by focusing the transducer to a desired depth, it is fairly safe to use a planar, multilayered structure to test the system. However the following assumptions must be made: 1. Only first order reflections are used. 2. Each layer is homogeneous (i.e. constant impedance in layer). 3. The boundary between layers is small compared to the layer itself. 4. There are no large differences in impedance (i.e. small reflections). The following terms must be defined: x(t) = input waveform y(t) = output waveform X(u» = frequency spectrum of input YUM) = frequency spectrum of output H(u» = frequency spectrum of impulse response h(t) = impulse response 12 acoustic impedance of the nth layer N ll reflection coefficient at the nth boundary H II (see Figure 2) The derivation of the relation between the impedance profile and the impulse response is as follows. The impulse response will be the sum of all the reflections from the various boundaries. Neglecting attenuation we can see from Figure 2 that: h(t) = rganc‘flt - tn) (3) and I a1: R, a2= (121+ 1) R2(R1- 1) a3: (R,+ 1)(R2+ 1)1=23(R1 - 1)(R2 - 1) so mi 2 an: Rnfl(1 - R.) i=1 putting this into equation 3, we get m 0-1 2 h(t) = Z Rnflu - R.) on: - t.) n=1 i=1 or h(tn) = Rnifllu - R?) The ratio of two successive reflections n and n + 1 equals n-1 h(tn) _ Rn [In - R2) _ Rn (4) h(tnn) Rm [3] (1 - 1275 RM (1 - R?) taking the natural logarithm of both sides h__(__tn) = 1n [ Rn h(tn——_:—1) Rnn (1 - R?) or 13 Rn+1 Rm_1 R,n \\ ‘\ 1+Rn 1‘Rn+1 Rm / ‘rz’ ~'\ ‘8 ~\ \\ t"1 t2 t3 tn tn+1 t:m-l tIn Figure 2: Determination of the Impulse Response l4 1nth> mic no to; mi 2 0 ID WATER E CORN OIL 0 Figure 19: Model 1 It 12mm 1mm 18mm DH‘— 4 :5 WATER :2 CORN OIL I: O Figure 20: Model 2 40 signal processing schemes tried were no filtering, a simple low pass filter, and single peak detection. The simple filter used an averaging scheme x(n) = (x(n-1)+x(n)+x(n+l)) /3 and ignored signals that were under a set threshold. The result was a wave form that was zero at al 1 places except where there was a reflection. The single peak detection was done manually by eliminating all signals except the single peak of the reflection. As an extensive amount of data was collected, only selected portions of it will be presented here. Figure 21 shows the typical input x(t) of the 1.00 MHz fOcused transducer without filtering. Figure 22 shows a typical nonfiltering output y(t) for this transducer. Figures 23 and 24 show the input and output received respectively of the 1.00 MHz transducer with the sample filter applied to the signal. Both outputs were for Model 1. The output signals for Model 2 had waveforms spaced closer together and the signals from the other transducers had a different base frequency, but all inputs and outputs were of similar nature. Figures 25, 26, and 27 show the input frequency spectrum X(f) for the 2.25 MHz focused, 2.25 MHz unfocused, and 1.00 MHz focused transducers respectively. These plots show that the majority of the signal energy is found in a region about the center frequency of the transducer. This demonstrates the band-limited nature of the signal and 41 800 .. 600 a 400-- 200 - - magnitude 0 -200 ' V .400- ~600" 0.00 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.00 USCG Figure 21: Typical Input: 1.00 MHz, Focused, Nonfiltered 500 3' 400 '- 300 '- 200 ‘- 100 " A. . . magnitude 0 .- ~ IN”. , ,. ., . . -100 q. ' ' -2oo-- -3oo-» -4oo‘- -500" 0.00 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.00 U560 Figure 22: Typical Output: 1.00 MHz, Focused, Nonfiltered 42 5003 400" 300 *- 200 '1 100 ' magnitude 0. )n -100 ' -200 ‘ V -300 - .400 u 0.00 0.60 1.20 1.00 2.40 3.00 3.60 4.20 4.80 5.40 6.00 0880 Figure 23: Typical Input: 100 MHz, Focused, Filtered 400 a 300 ‘- 200 . 100 ‘- 0 - rnagnflude' ' -100 . ~200 4 -300 -- -400 «I -500" 0.00 0.60 1.20 1.30 2.40 3.00 3.60 4.20 4.80 5.40 6.00 U800 Figure 24: Typical Output: 1.00 MHz, Focused, Filtered 43 35 7- 3o .. 25 -- magnitude 15 a)- 10 ‘- 51p o 1 . .11 0.00 0.49 0.98 1.47 1.96 2.45 2.94 3.43 3.92 4.41 4.90 MHz Figure 25: X(f) for 2.25 MHz, Focused Transducer 30 -- 25 .. 20 - magnitude 15 - 1o :- 0 1 “ 0.00 0.49 0.98 1.47 1.96 2.45 2.94 3.43 3.92 4.41 4.90 MHz Figure 26: X(f) for 2.25 MHz, Unfocused Transducer 44 justifies the use of a windowing filter discussed in Section 2d. Figure 28 shows the output spectrum Y(f) for the 1.00 MHz transducer interrogating Model 1 (Trial 1). The spectrum shows that again the majority of the energy is contained in a band about the center frequency. The major difference between X(f) and Y(f) is that the output spectrum has an oscillatory spectrum imposed on it. This effect is called scalloping. When Y(f) is divided by X(f), this oscillatory spectrum should come out giving a spectrum similar to the spectrum of an ideal impulse response (Figure 8). Figures 29 through 52 present the impulse response frequency spectrum H(f) and the impulse h(t) for twelve different trials. Due to variability in the range gate setting and in the mounting of the transducer in the model, the impulse responses were framed so that the first reflection always occurred at 0.60 usec. The speed of sound in acrylic is approximately 1660 m/sec, so for Model 1 (6 mm of acrylic) the second echo should have occurred at 4.2 usec and for Model 2 (1 mm of acrylic) the echo should have occurred at 1.2 usec. The impulse responses were judged by two criteria. First is the ability to observe two distinct peaks in the impulse response that corresponds to the two boundaries. The second criteria was if the location of the peaks in h(t) corresponded to the 45 903 80'‘ 70 " 60 up so a)- magnitude 40 -- 30 a 20 ‘- 10* o a an. 0.00 0.49 0.98 1.47 1.96 2.45 2.94 3.43 3.92 4.41 4.90 MHz Figure 27: X(f) for 1.00 MHz, Focused Transducer 80 u 70 -- fl ,0 .. A 50 up magnitude 40 -- 30 u 20 .- 10 u 0 W 0.00 0.49 0.98 1.47 1.96 2.45 2.94 3.43 3.92 4.41 4.90 MHz Figure 28: Y(f) for Trial 1 46 magnitude , A 0.00 0.49 0.98 1.47 1.96 2.45 2.94 3.43 3.92 4.41 4.90 MHZ Figure 29: H(f) for Trial 1 40 -- ,,.. 3 20 0 1°" ‘A‘t IOAII II magnitude 0 - ', v .. ' I y 'A ”I“ .10 q 0.00 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.00 11800 Figure 20: h(t) for Trial 1 47 magnitude . W 0.00 0.49 0.98 1.47 1.96 2.45 2.94 3.43 3.92 4.41 4.90 MHz Figure 31: H(f) for Trial 2 Z: I 1:. II... I I (II (1 (pm .20 .. -30 -- U .40 - -50-- 0.00 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.00 U890 Figure 32: h(t) for Trial 2 rnagnfiude 48 4.0 ~- 3.5 ~- 3.0 .. 2.5 «- 2.0 '- L5-- 1.0 '- 0.5 - 0.0 0.00 0.49 0.98 1.47 1.96 2.45 2.94 3.43 3.92 4.41 4.90 MHz Figure 33: H(f) for Trial 3 rnagnhude Figure 20 ~- 1: J‘AAAA‘ III .N .10" "Vi”tvi) -20 . .30 .. .404- 0.00 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.00 U890 34: h(f) for Trial 3 magnnude 49 10' 0‘ 0.00 0.49 0.98 1.47 1.96 2.45 2.94 3.43 3.92 4.41 4.90 MHz Figure 35: H(f) for Trial 4 magnnude Figure ”H‘HA‘AVHA‘ A 3:” 'VHH' y‘ ”W -15 ‘- -2o-- 0.00 0.60 1.20 1.30 2.40 3.00 3.60 4.20 4.80 5.40 6.00 U596 36: h(t) for Trial 4 SO 14-- 12 .- 10 in magnitude 01 0.00 0.40 0.98 1.47 1.96 2.45 2.94 3.43 3.92 4.41 4.90 MHz Figure 37: H(f) for Trial 5 1.0 l 0.9 ' 0.8 ' 0.7 ' 0.6 ' V magnitude 0.5 ' NCHDUTPUH' 0.4 ' 0.3 ' 0.2 ' 0.1 - o.o«WWWWW 0.00 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.00 usec Figure 38: h(t) for Trial 5 51 (A) magnitude 0 0.00 0.49 0.98 1.47 1.96 2.45 2.94 3.43 3.92 4.41 4.90 MHZ Figure 39: H(f) for Trial 6 30 ID 2... A magnum 1:" ‘1 H A. ., A‘ ,i Hi WI" WV”! -20 ~- -30.. 0.00 0.60 1.20 1.80 2.40 3.00 3.60 4.22 4.80 5.40 6.00 U880 Figure 40: h(t) for Trial 6 52 magnitude 3 ‘- 1 1D 01 0.00 0.49 0.98 1.47 1.96 2.45 2.94 3.43 3.92 4.41 4.90 MHz Figure 41: H(f) for Trial 7 30 n 20 .. 10' magnitude .10 -- 0.00 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.00 USBC Figure 42: h(t) for Trial 7 53 magnitude 8 ‘- 21X o. 0.00 0.49 0.98 1.47 1.96 2.45 2.94 3.43 3.92 4.41 4.90 MHz Figure 43: H(f) for Trial 8 magnltude 0 - i 0.00 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.00 usec Figure 44: h(t) for Trial 8 magnitude 4 - - Figure magnitude Figure 2‘. ‘1- 54 0.00 0.49 0.98 1.47 1.96 2.45 2.94 3.43 3.92 4.41 4.90 MHz 45: H(f) for Trial 9 40 ~- 30 nu 20 «- 10 ID o‘.vi .10.. v .20 .. .30 .i “Hi“‘ifliivii‘ ‘Hiifih, ”i'Hi‘i' ' WM i 0.00 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.00 U590 46: h(t) for Trial 9 55 —A GOO :’€ 1 I l ‘ magnitude l U O‘N01FUIGVG Lt l 0.00 0.49 0.98 1.47 1.96 2.45 2.94 3.43 3.92 4.41 4.90 MHz A Figure 47: H(f) for Trial 10 40 ~- 30 u 20 I. 101- 0. i Mimi iiil‘i'iim'i' ”H .20 .. u .30 -- U -40 ~- 0.00 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.00 U880 Figure 48: h(t) for Trial 10 magnitude 1O '- Figure rnagnnude Figure 56 20 u 18 ~- 16 n 14 «- 12 ~- 3.. 6" 4.. 21- o mmwmm .- o.oo 0.49 0.93 1.47 1.96 2.45 2.94 3.43 3.92 4.41 4.90 MHz 49: H(f) for Trial 11 40 T so -- h 20 .- 10.. o. ‘L it“ L‘H'idfilw" -10 . -20 .. V -30 . -40 l. 0.00 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.00 USBC V “W”. wy 50: h(t) for Trial 11 magnitude 10 -- Figure magnitude Figure S7 20 T 13 .. 16 .. 14 -- 12 u 4:- 0.00 0.49 0.9 1.47 1.96 2.45 2.94 3.43 3.92 4.41 4.90 MHz 51: H(f) for Trial 12 4o «- 30 - 20'- W‘HH‘L‘ ‘i V” 1' .10 .. .20 -- -3o -- .40 -» .50.. 0.00 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.00 usec 52: h(t) for Trial 12 58 anticipated location in time. Table 1 summarizes the trial parameters and the results. TABLE 1: SUMMARY OF RESULTS Trial # TRANSDUCER EQQEL FILTER RESULTS FIGURES 1 1.00 focused 1 none good 29, 3O 2 1.00 focused 1 simple poor 31, 32 3 1.00 focused 1 single peak good 33, 34 4 1.00 focused 2 none good 35, 36 S 1.00 focused 2 simple unstable 37, 38 6 2.25 focused 1 none good 39, 40 7 2.25 focused 1 simple fair 41, 42 8 2.25 focused 2 none poor 43, 44 9 2.25 unfocused 1 none fair 45, 46 10 2.25 unfocused 1 simple good 47, 48 11 2.25 unfocused 2 none good 49, 50 12 2.25 unfocused 2 simple poor 51, 52 There are several general observable trends. First, the impulse response method improves resolution. The theoretical limit of resolution of an envelope-detected signal is the wavelength of the signal. For a 1.00 MHz signal in acrylic this is IJSnmL Figure 36 clearly shows two boundaries .6 usec or 1 mm apart. The second trend was 59 that the frequency of the transducer did not seem to make much difference. If there were any advantages, it would have been the 1.00 MHz transducer, as more of its signal was contained in the bandwidth of the system. The two focused transducers seem to have given a more accurate measure of distance than the unfocused transducer. Trials 9, 11, and 12 show an error in the location of the boundaries. A possible explanation for this could be multiple reflection paths observed by the transducer due to the dispersity of the unfocused beam. Finally, and probably most surprisingly, the simple filter and threshold detection had an adverse effect in most cases. The nonfiltered signals probably worked adequately because noise components canceled each other out when taking H(f). The filter and threshold detector could have caused the unstable transformer in Trial 5 and degraded the signal enough to change the impulse response. The exception to this was the single peak detection, but this scheme is difficult to implement automatically while preserving the signal. 4d. Future Possibilities This thesis has pointed to the possibilities of using the impulse response to find both the impedance and attenuation profiles. Thus the obvious next step is to do 60 this. .Although the system did a reasonably good job of finding boundaries in the impulse response, there will be a problem in finding the impedance and attenuation profiles for two reasons. First, the noise level in non-boundary regions is significant. This will tend to produce noise in the profiles. Secondly, the impulse response at the boundary is not always a single peak, but a series of positive and negative peaks. This effect will also corrupt the profile. There are several approaches that could be taken to alleviate these problems. The easiest way to improve the profile would be to write a sorting program that would detect peaks that are truly part of the impulse response, and ignore those created by noise and bandwidth limitations. Another way to increase the accuracy of the impulse response would be to increase the sampling frequency. The present rate of 14.67 MHz could be increased to the system limit of 20 MHz. The system would then record the wave form in more detail and give better results. In theory this would improve the resolution of the system. One final way to improve the system is to explore different signal processing schemes. The present ones were chosen because of their simplicity. The two most obvious avenues to explore would be the actual acquisition filter and threshold detection. The other would be to perform the iterative techniques on H(f) to restore 61 frequencies outside the range f1,f2. There is work to be done before impedance and attenuation imaging are practical. The automated system for determining the impulse response performed well in finding the impulse response of the models. This system is a step closer to that realization. APPENDICES APPENDIX A APPENDIX A FOURIER TRANSFORMER The Fourier transformer used to calculate the impulse response for this thesis was performed on Michigan State University Cyber 750. The specific routine used was the FFTCC. This routine is resident in the Hustler Auxiliary Library and will take the fast Fourier transformer of a complex waveform and return a complex waveform. The number of samples used in the transform was 296, whereas the number of samples used from the signal was 120. All other points were set to zero. This gave an impulse response of 148 usable points (the other 148 are mirror points from the transform). If a wider range of observation is desired both the number of samples and the number used in the transform will have to be increased. 62 APPEND I X B APPENDIX B ALGORITHM FOR REDUCING NOISE COMPONENTS FROM SPECTRUM The following process was used to try to eliminate the noise from the spectrum of the impulse response H(f). First the notation used H(f) = the actual spectrum of the impulse response Ho(f) = the spectrum of the impulse response plus noise N(f) = the spectrum of the noise W(f) = windowing function used H'(f) = estimate of the actual spectrum The process: 1. 2. Obtain Ho(f) by dividing Y(f) by X(f) Calculate the window function W(f) given by W = cos2n(i-io) forio-Ai