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REMOTE SENSING BY ACOUSTIC VIDEO PULSE TECHNIQUES

By

Nai-Hsien Wang

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 Systems Science

1988

ABSTRACT

REMOTE SENSING BY ACOUSTIC VIDEO PULSE TECHNIQUES
By

Nai-Hsien Wang

This thesis derives the formulas for acoustic wave equations in terms of
an attenuation constant and the phase constant in material. The transmission.
coefficienLand Went are We-
guency) in dispersive media. According to the analytical results, the
waveforms of the transmitted signal and the reflected signal depend not only
on the characteristics of the medium, but also the frequency components of
the incident signal. One can identify the different media by the reflected
video pulse shapes and their spectral distributions. Experiments were

designed and performed to show the validity of the theory.

Acknowledgements

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. Di Ye for his help in the experiments. Most importantly, I would
like to thank my parents, Mrs. and Mr. Chiou—Yueh and Chin-Chi Wang.

Because of their encouragement and support, I was able to write this thesis.

Table of Contents

List of Tables ............................................................................... vi
List of Figure ............................................................................... vii
Chapter 1 Introduction ................ 1
Chapter 2 Theoretical Considerations ......................................... 5
2.1 Review of Basic Ultrasound Principles ......................... 5
2.2 The Acoustic Plane Wave Equation .............................. 7
2.3 Transmission and Reflection Coefficients ..................... 12
2.4 Damping and Attenuation .............. 16
2.5 Video Pulse Probing Techniques ................................... 22
2.6 Analogy between Ultrasonic Waves
and Electromagnetic Waves ............................................ 24
Chapter 3 Experimental Procedure .............................................. 27
3.1 Experimental Configurations ......................................... 28
3.2 Data Processing ............................................................. 31
Chapter 4 Analysis of Experimental Results ............................... 40
4.1 Experimental Results ..................................................... 40
4.2 Discussion ...................................................................... 41

4.3 Conclusion and Suggestion
for Future Study ............................................................... 77

iv

Bibliography ................................................................................ 80

List of Tables
Table 2.1.1 Approximate Values of Ultrasonic
Velocities of Various Media ......................................... 7
Table 2.2.1 Characteristics of Some Materials ............................ 12

Table 2.6.1 Analogy between Ultrasonic Waves
and Electromagnetic Waves ........................................ 26

Table 4.2.1 The Mean Value of Magnitude and
Power of the First Reflection ........................................ 64

Table 4.2.2 The Approximate Reflection Coefficients ................ 71

vi

List of Figures
Figure 1.1.1 A Gaussian video pulse .......................................... 3

Figure 1.1.2 The spectrum of a Gaussian
video pulse .................................................................. 3

Figure 1.1.3 The reflected signals from
some materials ............................................................ 4

Figure 2.2.1 Infinite homogeneous medium with
plane applied pressure .................................. ‘ .............. 8

Figure 2.3.1 Transmission and reflection
at an interface .............................................................. 13

Figure 3.1.1 The block diagram of the
experimental configurations ........................................ 29

Figure 3.2.1 The waveform(l) reflected from
water/aluminum interface ........................................... 34

Figure 3.2.2 The waveform(2) reflected from
water/aluminum interface ........................................... 34

Figure 3.2.3 The correlation of waveform(l)

and waveform(2) ......................................................... 35
Figure 3.2.4 The spectrum of waveform(l) ................................ 36
Figure 3.2.5 The spectrum of waveform(2) ................................ 36
Figure 3.2.6 The average waveform reflected from

water/aluminum interface ........................................... 37
Figure 3.2.7 The spectrum of average waveform ....................... 37

Figure 3.2.8 The spectral difference between
the waveform(l) and the average
waveform spectra ........................................................ 38

vii

Figure 3.2.9 The Spectral difference between
the waveform(2) and the average
waveform spectra ........................................................ 39

Figure 4.1.1 The waveform reflected from water/air
interface (the incident signal) ..................................... 42

Figure 4.1.2 The waveform reflected from
water/air interface ........................................................ 43

Figure 4.1.3 The spectrum of incident signal ................ 44

Figure 4.1.4 The spectrum of waveform reflected
from water/air interface .............................................. 44

Figure 4.1.5 The spectral difference between
incidence and water/air
reflection spectra ......................................................... 45

Figure 4.1.6 The waveform reflected from
water/aluminum interface ............................. . .............. 46

Figure 4.1.7 The waveform reflected from
water/plexiglass interface ........................................... 47

Figure 4.1.8 The waveform reflected from
water/composite material interface ............................ 48

Figure 4.1.9 The waveform reflected from
water/wood interface ................................................. 49

Figure 4.1.10 The waveform reflected from
water/rubber interface ................................................ 50

Figure 4.1.11 The waveform reflected from
water/ stone interface .................................................. 5 1

Figure 4.1.12 The spectrum of waveform reflected
from water/aluminum interface ................................. 52

Figure 4.1.13 The spectrum of waveform reflected

viii

from water/plexiglass
interface ..................................................................... 52

Figure 4.1.14 The spectrum of waveform reflected
form water/composite material
interface ..................................................................... 53

Figure 4.1.15 The spectrum of waveform reflected
from water/wood
interface ..................................................................... 53

Figure 4.1.16 The spectrum of waveform reflected
from water/rubber
interface ..................................................................... 54

Figure 4.1.17 The spectrum of waveform reflected
from water/stone .
interface ..................................................................... 54

Figure 4.1.18 The spectral difference between
incidence and water/aluminum
reflection spectra ........................................................ 55

Figure 4.1.19 The spectral difference between
incidence and water/plexiglass .
reflection spectra ........................................................ 56

Figure 4.1.20 The spectral difference between
incidence and water/composite
material reflection spectra .......................................... 57

Figure 4.1.21 The Spectral difference between
incidence and water/wood
reflection spectra ........................................................ 58

Figure 4.1.22 Theispectral difference between
incidence and water/rubber
reflection spectra ........................................................ 59

Figure 4.1.23 The Spectral difference between
incidence and water/stone

ix

reflection spectra .....................................

Figure 4.2.1 The waveforms of the

reflected signals .......................................

Figure 4.2.2 The spectra of the reflected signals

Figure 4.2.3 The spectral difference between the
incidence and the

reflection spectra .....................................

Figure 4.2.4 The autocorrelation of incident signal

Figure 4.2.5 The crosscorrelation of incident
waveform and waveform reflected

from water/air interface ..........................

Figure 4.2.6 The crosscorrelation of incident
waveform and waveform reflected

from water/aluminum interface ..............

Figure 4.2.7 The crosscorrelation of incident
waveform and waveform reflected from

water/plexiglass interface .......................

Figure 4.2.8 The crosscorrelation of incident
waveform and waveform reflected from

water/composite material interface .........

Figure 4.2.9 The crosscorrelation of incident
waveform and waveform reflected from

water/wood interface ..............................

Figure 4.2.10 The crosscorrelation of incident
waveform and waveform reflected from

water/rubber interface ............................

Figure 4.2.11 The crosscorrelation of incident
waveform and waveform reflected from

water/stone interface ..............................

................... 60

................... 65

.................... 69

.................... 7O

.................... 73
.................... 73
.................... 74
.................... 74
.................... 75
.................... 75
........... 76

.................... 77

CHAPTER 1

Introduction

Most ultrasonic imaging systems use echo returns from boundaries of
different acoustic impedances to show material properities. The image
shows properties related to boundary variations. It is the purpose of the
research reported here to Show that the material characteristics can be
extracted from the shape of the echo pulse when a narrow video pulse exci-
tation is used. Although the video pulse technique has been used for a
variety of applications in target identification by electromagnetic waves, it
has not been applied to acoustic probing in spite of the advantage of lower
operation frequencies and lower wave attenuation, since the attenuation
coefficient is directly related to frequency. In addition to the lower operat—
ing frequency, another attractive feature is that the velocity of an acoustic
wave ( about 1500 m/sec in water) is five orders of magnitude lower than
that of the electromagnetic wave in free space. Based on the relationship
between frequency and wavelength for any propagating wave, u = f A. , the
acoustic wave should have much shorter wavelength which in turn provides

superior range resolution.

The video pulse radar signal contains a broadband of frequencies. For

example, a signal that is approximately Gaussian in shape, as shown in Fig.

1

2
1.1.1, can be to expressed through its Fourier Transform as a spectrum of
frequencies from about DC to 400 KHz. Each frequency component pro-
pagates through the material with a different velocity and attenuation
depending upon the target and material properties. When all the reflected
frequency components are received by the receiving antenna (transducer),
the output will be a video pulse which resembles a spread version of the
transmitted pulse. The reflection of each of the spectral components is
determined by the characteristics of the medium from which it is reflected.
This is due to the fact that the reflected pulse must satisfy the boundary con-
ditions at each interface. For electromagnetic wave propagation, the dom-
inant characteristics of the medium are the conductivity and the dielectric
constant. For ultrasonic waves, the propagation and reflection depend on the

medium density, elasticity, and viscosity.

Theoretically, the characteristics of a medium can be determined if the
reflected and incident pulses are known. Conversely, if the incident pulse
and the characteristics of the medium are known, it is possible to calculate
the reflected pulse shape. By using a Gaussian video pulse in the time
domain as the incident pulse, and by taking typical values of density, elasti-
city, and viscosity of media, it is possible to calculate the reflected pulse
from materials such as soil, wood, stone and metal ( Figure 1.1.3 ). The cal-

culated pulse shapes show that the reflected pulses are different for different

media.

 

 

 

Figure 1.1.1 A Gaussian video pulse

magnitude ‘

 

Figure 1.1.2 The spectrum of a Gaussian video pulse

incident signal

 

 

wood

plexiglass

 

soil

rock ——

 

 

steel

 

Figure 1.1.3 The reflected signals from some materials

CHAPTER 2

Theoretical Considerations

This chapter provides the theoretical analysis for the acoustic video
pulse probing techniques. In the first section, some related ultrasound prin-
ciples are reviewed. The acoustic plane wave equation is derived in the
second section. In the third section, the transmission coefficient and the
reflection coefficient are determined from the boundary conditions at inter-
faces. In reality, ultrasound propagating through a medium will have some
energy loss, so the damping and attenuation properties should also be taken
into consideration. This problem will be discussed in section 2.4. The pro-
perties of the acoustic video pulse will be explained in section 2.5. Since the
acoustic wave is very similar to the electromagnetic wave, the commonelity

will be formulated in section 2.6.

2.1 Review of Basic Ultrasound Principles

Ultrasound is the name given to those waves with frequencies ahoyejfL
_K_H_z (above the audible range). Ultrasonic waves consist of propagating
periodic disturbances in an elastic medium. The particles of the medium
vibrate about their equilibrium positions either perpendicular to or parallel to

the direction of propagation. Since the parallel vibrations are dominant and

5

6
of lower propagation losses only these variations will be considered. The
propagation of the resulting motion-strain effects away from the source
results in a longitudinal compression wave that transmits mechanical, or
acoustic, energy away from the source. The vibratory motion of the medium
is strongly dependent on the ultrasound frequency and on the state of the
medium. Table 2.1.1 provides that the values of velocity of longitudinal
sound waves in various materials. Velocity in solids are the highest, those

in liquids and biological soft tissues are lower, and those in gases are lowest.

The relationship between frequency and wavelength of a wave is given

by

7. = % (2.1.1)

where u is the propagation velocity, f the the frequency of the wave, and 2. is
the wavelength. Since the propagation velocity of ultrasound
(1.5x103 m/ sec in water) is much lower than that of an electromagnetic
wave (3x108 m/sec in free space), the wavelength of ultrasound is five ord-
ers of magnitude smaller for a given frequency. For a frequency of 5 MHz,
the wavelength of ultrasound is approximately 0.3 mm while for an elec-
tromagnetic wave it is 60 meters. Because of the much shorter wavelength,

the use of ultrasound for detection will give much higher resolution.

Table 2.1.1 Approximate values of ultrasonic velocities of various media [1]

 

 

 

Medium Sound Velocity (m/sec)
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

 

 

 

2.2 The acoustic plane wave equation

In this section, we will investigate sound propagation in an infinite
homogeneous medium in equilibrium. The coordinate system is shown in
Figure 2.2.1. If a force is applied in the x-direction, it will result in a uni-

form pressure p (xo,t) to the y-z plane at a distance x0 from the origin. Due

8
to this applied force, the particles will experience a displacement in the x-
direction. Particles at the location x0 will also be displaced. If we consider
a small differential volume element with incremental length dx and area A in

the plane of the applied force, the equilibrium volume, V, of the element will

 

 

 

be
V = A dx (2.2.1)
I
I U dt
V“. \T'.
, l
I
no, u :m, n I
——.. __.. '
i l
I l
'o I 'o ‘ ‘1 l
0 N ' V ' r -—o-
y

 

Figure 2.2.1 Infinite homogeneous medium with plane applied pressure

As a result of this compressional force the differential volume changes to

V’ = A (dx+d§) = A (dx + %E- dx) (2.2.2)

where d§ represents a compressional displacement.

Therefore, the change in volume is

W = V’ - V = A ($5- dx) (2.2.3)

9
Conventionally, the strain produced in the volume element is defined as the

ratio of the volume change to the original volume:

- ._ .41 _ 2%
strain = V — ax (2.2.4)

According to Hooke’s law, ' 'n ' l i i

is constant, This relationship can be expressed as

 

p = —k-a-§- (2.2.5)

r—*

where k is the coefficient; of elasticity. The negative sign in Eq. (2. 2. 5)
(SS

 

results from a positive pressure in the x-direction giving a strain in the nega-
tive x-direction.
We can define the particle velocity u as the time rate of change of parti-

cle displacement. That is,

u(x,t) = % (2.2.6)

The partial derivative of Eq.(2.2.5), with respect to time, gives:

£911.: k§(%§) _ _k_ (2.2.7)
at
01'
fl. _ ii
3x _ k 81‘ (2°28)

If the applied pressure varies with time, the pressure magnitude will be
a function of distance,x, as well as of time, t. From Newton’s second law of

motion, the acceleration of a material element resulting from an applied

10

pressure is:

.35 z - 25;. (2.2.9,

The negative sign in Eq. (2.2.9) results from a net acceleration to the right

for a negative spatial pressure gradient. In Eq. (2.2.9) p is the medium den-
sity.

Eq.(2.2.8) and Eq.(2.2.9) are the coupled equations relating to pressure

particle velocity. By decoupling these equations, it is possible to obtain the

acoustic plane wave equations

$12). = fig; (2.2.10)
and,
2%! = fig;— (2.2.11)
The general solution for pressure and particle velocity are
p = p(0)e“"""""’ (2.2.12)
u = u(0)ej(‘”"'K") (2.2.13)

 

K = m7p'7k" 2.3.71 ,Czfl? (2.2.14)

The wave number K is in general a complex quantity. It consists of the

phase constant B and the attenuation constant or,

K = B-joc (2.2.15)

1 1
From Eq.(2.2.12), Eq.(2.2.l3) and Eq. (2.2.9), the relationship between

pressure and particle velocity is

p = 99—11 (2.2.16)
K
The characteristic acoustic impedance is defined as the ratio of digressure

to particle speed. From Eq.(2.2.15), the acoustic impedance Z can be

expressed as

= = 99.
z _ u. K 96 VELWE‘K’ (2217)

For a lossy medium, the acoustic impefice is a complex quantity. For a
lossless medium the attenuation constant or is zero, and the wave number

reduces to K = B, which gives a real acoustic impedance.

Under the lossless assumption, the phase velocity vp is

v = —- = — (2.2.18)
1. ” B WK

sti im edance for :lossle medium can be written as
\I’
Z : pvp (2.2.19)
For an attenuation constant of zero, the mass density, the longitudinal wave

   

Therefore, the

velocity and the acoustic impedance of some materials are shown in Table

2.2.1.

Table 2.2.1 Characteristics of some materials [6]

 

 

 

Acoustic
Material Mass Density Longitudinal Im edance
kg/m3 Velocity, m/s x10 kg/mZ-s
Air (20°C) 1.21 340 411x10-6
Water (20°C) 1,000 1,480 1.5
Aluminum 2,695 6,350 17.1
Plexiglass 1,182 2,680 3.17
Silicon rubber 1,010 1,030 1 .04
Lead 1 1,400 1,960 22.3
Copper 8,900 4,700 42
Iron (steel) 7,830 5,950 46.6

 

 

2.3 Transmission and reflection coefficients

When an acoustic plane wave is incident to a boundary between two
different media, it will be partially reflected. The ratio of the characteristic
impedances of the two media determines the magnitude of the reflection
coefficient and transmission coefficient. Assume there is an acoustic plane
wave propagating from medium 1 to medium 2, as shown in Figure 2.3.1.

B 5 EV
Wstates that the angles of incidence and reflection are equal when

the wavelength of the wave is small compared to the dimensions of the

13

reflector. That is,

9i = 6,. (2.3 e 1 )
From relationship between 0,- and 0,, the angle of transmission, is:
sine,- u 1

sine, = E (2'32)

 

Medium 1

.

/
/%/’2

Figure 2.3.1 Transmission and reflection at an interface ,

|
|
P l
l
l

      
    
 

In the equilibrium state, the pressure on both sides of the boundary

remains the same in order to maintain aétationary boundary) This gives

pi + ,- = (2.3.3)
Furthermore, the normal component of the particle velocity must be the

14

.same_on both sides of the boundary or else the Mamediamnnotmmain in

 

 

 

 

 

 

 

T ~.-’ MI (‘TAA
contact._Thus, ‘Y 0
uicosei — u,cosO, = u,cos0, (2.3.4)
From Eqs.(2.2.16) and (2.3.4), we have
. K cos0- K c030 K cost)
[’1 1 r _ pr 1 r = pt 2 t (23.5)
Pl P1 Pz
Solving Eqs.(2.3.3) and (2.3.5), the pressure ratios are
K 1 K 2
—-—cosO; - ——cos0,
55- = p 1 p2 (2.3.6)
Pi K 1 K 2
—cose,- + —cose,
Pl 92
and
2K 1
c039,-
53- = pl (2.3.7)
Pi K 1 K 2
—cosG,- + —cosO,
Pr 92

For normal incidence 0,- = 0, = 0, the pressure amplitude ratios are reduced

 

t0
K1 K2
Pr pl 92
Re ection coe cient R = — = (2.3.8)
fl fii Pi K1 K2
—_ + _—
PI 92
2K 1
Transmission coefi‘icient T = fl = p1 (2.3.9)

 

Pi K1 K2
——+—
PI 92

15
Using the acoustic impedance definition Z =mp/K, the reflection coefficient

and transmission coefficient can be reduced to:

22-21

R = -— W0.3.10
Zz+Z1 RU M‘ 1% ( )(0)
1 WA“ I 3 “SI
QQY %\30v%\
222 - (<6 ‘7‘
— —— .4. 2. .11
22+21 ( 3 )

Up to this point, the reflection and transmission coefficients were
expressed in the time domain. Using the Fourier Transform the reflection

and transmission coefficients can be expressed in the frequency domain as

well.

The Fourier Transform of p (x, t) is defined as

P(x,00) = j p(x,t)e-f°‘dt (2.3.12)
Because the reflection coefficient 1: and the transmission coefficient [are

independent of time, the R and T can be written as

 

K1 K2
P 0,0.) " z —z
R ___ r( ) = P1 p2 = 2 1 (2.3.13)
Pi(0,(0) K1 + K2 22 +21
Pr Pz
2K1
Pt(0:w) Pl ZZZ

 

 

_. = = —— 2.3.14
Pi(0,(t)) K1 + K2 Zz +21 ( )

Pl Pz

16

2.4 Damping and attenuation

As discussed in section 2.2, the acoustic wave equation (Eqs.(2.2.10)
and (2.2.11)) was derived for the condition that the wave propagating
through the medium suffers no energy loss, that is, the acoustic wave pro-
pagates in the medium without attenuation. Ideal materials of this kind do
not exist, although weakly damped materials are often approximated as
ideal. Elastic damping usually depends on temperature, frequency, and the
type of vibration. At room temperature, acoustic lesses in many materials
may be adequately described by either assuming theoelasticity k is a complex
quantity or lg"addingmscons_dan1ping_term.

In the following section, both of these approaches are used to obtain the
attenuation constant a and phase constant B. The results from these

approaches are then compared and discussed.

2.4.1 Complex elasticity

In a lossy medium the elasticity k becomes a complex number, that is,

k = k, + jki (2.4.1)
From Eq.(2.2.14), the wave number K becomes

 

K = (Np/(k, + jki) (2.4.2)
and jK contains real and imaginary parts:

17

jK = a+jB (2.4.3)
If we insert Eq.(2.4.3) into Eq.(2.4.2) and equate the real and imaginary

parts the following relationships result:

(0 p k,
2 2 _
B k} + k3
2043 _ ___—“’2 p k" (2 4 5)
— k3 +k3 ° '

Using these equations, the attenuation constant or and the phase constant B

can be expressed in terms of to, p, k, and k5:

 

.11 +(ki/k,)2 —1

 

 

 

 

 

or = 03W [ 2 2 1” (2.4.6)
k, + k5
\jl +(k-/k )7 +1 1
[3 = W [ 2‘ ’2 3 (2.4.7)
k, + k;
or, alternatively k,- and k, in terms of or and B as:
2 2 2
(0 9(13 -a )
2 2.4.8
- = 20°29” (24 9)
t ([32 + a2)2 ° '

k-
In the case of a low loss medium, that is when (—‘--)2 < < 1 , the a and
CAL—___. B
1 b
reduce to

k- .
a : g’w-kLN—Fp/ . (2410)
r

18

 

k
2 (6.1.37); [1—-8—(-,:-)2] (2.4.11)

2.4.2 Damping force

The second approach to obtaining the attenuation and phase constants is
to consider the damping force term in the wave equation. In an ideal loss-
less medium, Hooke’s law describes the linear relationship between pressure

and strain:

8
Pideal = -GS (2.4.12)

where c is a proportional constaii—t: called elastic stiffness constant, while S is

 

strain, as defined in Eq.(2.2.4).
The damping force in material can be put in the form:

BS

 

Pdamping = - 11$ - (2.4.13)
where n is the material viscosity.
The total pressure becomes
BS
p : pideal +pdamping = _ (ks +1137 (2-4-14)
For a one-dimensional problem, the strain is
S _3_§_ (2.4.15)

: 3x

19

From Eqs.(2.2.6) and (2.4.15) we get

 

3_u _ .815 _ 9i
3x _ axa: — 0: (2.4.16)
Taking a partial derivative with respect to time in Eq.(2.4.14), we obtain:
a ——c-al—n 82“ (2417)
a: — ea 3th ' '

From Newton’s second low of motion, Eq.(2.2.9), the spatial derivative of

pressure and the time derivative of particle velocity are related by

22 = _ 29.
8x p at (2.4.18)

Following the same procedure used in section 2.2 to decouple Eqs.(2.4.17)

and (2.4.18), the acoustic plane wave equations including attenuation

 

becomes:
EK=£12E+EEL (2419)
3:2 9 3x2 9 szat . '
and,
azu c 8214 1 33u
__ = _ __— + 2.4.20
3:2 p x2 P (9th ( )
Again, the general solutions for pressure and velocity are
p = p(0)ej‘“"""‘) (2.4.21)
u = u(0)ej(‘°“Kx) (2.4.22)

where

K = B— jor (2.4.23)

20

Using these solutions, the following equations are obtained:

pmzp = 6‘sz + 1'1]sz (2.4.24)

pro2 = 6K2 + jnKzto (2.4.25)
With K 2 = B2 - 2aB j — a2, and both a and B real, the following equations

are obtained by equating the real and imaginary parts of Eq. (2.4.25).

c(|32 - 62) + 2aBT10) = p662 (2.4.26)

n0)(B2 — 62) - 2ch = 0 (2.4.27)
Solving Eqs. (2.4.26) and (2.4.27) for real on and B, gives:

 

 

 

 

2
2 1 CPOJ 2
0t - - \II + 03/ —1 2.4.28
2 01202 +c,)[ (n c) 1 ( )
and
2
2 1 CPO) 2
— — l + 05/ + 1 2.4.29
Finally,

 

1A
1 c
or = o) {-2— (112032P+ C2) [‘11 +(r103/c)2 4]} (2.4.30)

 

 

 

1/‘2
B = (o {% ("20:21:62) NI +(1100/c)2 +11} (2.4.31)

The above equations give the general solution for the attenuation constant a

and phase constant B. We can express c and n in terms of or and B as:

(02( 2 _a2)
6‘ = £0323 a2), (2.4.32)

21

2pm20tB

 

 

= 2.4.33
"m (02 +62)2 ( )

or,
= 29995 2 4 4
n (132 +02)2 ( ° '3)

For the low frequency approximation (IL—f2)2 < <1, the following

simplifications result:

2
0t 2 flz-cz—Vp/c [1 —(n03/c)2]%

2
2 11°; _ l 112 2 v2
26 \I—p/c [1 2( c ) 1 (2.4.35)
2
z 3226—V—p/c (2.4.36)

B = W11 aid-“$0”

z (Np/c [1 — %—(363)2] (2.4.37)
2 (m/p/c (2.4.38)

From Eqs.(2.4.36) and (2.4.38), when the frequency of the acoustic wave is

c . . .
low ( (D< 4?) ), the attenuation constant 1s proportron to (02, and the phase

constant is proportion to (o. For very low frequencies, the attenuation

approaches zero. For higher frequencies the attenuation increases rapidly.

For a given frequency, the attenuation constant or is proportion to the
square root of the medium density. As the viscosity constant increases, the

attenuation constant also increases. If the the elasticity stiffness constant

22

increased, the attenuation constant decreases.

By comparing the results of these two approaches, that is, using com-
plex elasticity or using an added damping force, the same results conclu-
sions can be drawn. From Eqs.(2.4.6), (2.4.7), (2.4.30) and (2.4.31), we
found that the real part k, of the complex elasticity plays the same role as
the elasticity c in the lossless case. The imaginary part k,- of the complex
elasticity is analogous to the damping constant 11 times angular frequency

0). That is,

k, (——-)c

k,- <——> 110)

2.5 Video pulse probing techniques

Reflection coefficients and transmission coefficients are crucial factors
in determining wave propagation in media with different materials proper-
ties. When the incident wave is a narrow band signal, the reflection
coefficient and the transmission coefficient are usually constant. This is not
true for a broad band signal. The basic principle of using video pulses is to
exploit the broad band signal characteristics to detect media variations. The
broadband signal form the transducer is dispersed by the frequency depen-

dent reflection and transmission at the interfaces of different acoustic

23
impedances of different media. The energy of the reflected wave or of the
transmitted wave depends on the frequency dependent reflection coefficient

or the frequency dependent transmission coefficient.

A necessary requirement for using video pulses is that thewayefoanL

id 11 w in 'm fre uen must well kn wn. When

the video pulse impings on the interface between the_first_an.d.second_media,
the mflectedmemahmjflimquemmmmeach modified by its
(own frequency dependenflreflection coefficient. The reflected signal spec-

trum contains the information necessary to characterize the unknown media.

The Fourier spectrum of the incident pressure wave is given by:

P,(x, 00) = j p,(x,:)e “fwd: (2.5.1)

If x is set to zero at the interface of two media, the pressure in the frequency
domain at the interface is:

Pi(0,(1)) = F <p (0,t)> (2.5.2)

where F < - > = I ° e"j‘°‘dt is the Fourier transformation.

—“

In section 2.3, it was shown that the reflection coefficient is independent
of time, so that the Fourier Transform of the reflected wave at the interface

in the frequency domain is given by:

24

P,(0,60) = Pi(0,0))R (2.5.3)
and the reflected pressure wave at the interface in the time domain is

p,(0,t) = F-1 <P,(0,0))> = F‘1<P,-(0,00)R> (2.5.4)

where F "l< - > = 511;- I - ejm‘dm is the inverse Fourier transform and R

is the time independent reflection coefficient.

A detected signal a distance d from the interface has the form:

“1K rd

Pr(d,l‘) = Pr(0,t)e (2.5.6)
The signal to be detected is thus given by:
p,(x,t) = Re F‘1<P,-(O,00)R >e_jK1d } (25.7)

= Re{ F—l< F<p,-(0,t)> R> e_jKld}

The real part of the pressure is taken since only this signal can be detected

experimentally.

2.6 Analogy between ultrasonic waves and electromagnetic waves

The equations for the acoustic plane waves have many similarities to
electromagnetic waves. As shown in Table 2.6.1, the pressure and particle

velocity of the acoustic wave play the same role as the electrical field and

25
magnetic intensity of the electromagnetic wave. The magnitude of the pres-
sure provides the potential energy and the particle velocity provides the
kinetic energy. The density and the reciprocal of the elasticity are analogous

to the permeability and permittivity, respectively.

 

 

 

Ultrasound Electromagnetic wave
pressure p electric field E
particle velocity u magnetic intensity H

momentum density pu

 

 

Strain s = I,’ _
elastzcuy k
density p
1
elasticity k

wave number K = (mip/ k
. (0
phase velocrty v = F

wave equation

£9317. ___ 9.22.2
8x2 16 3:2
82—14 ___ 9.122.
8x2 ’6 Biz

 

magnetic flux density B = 11H

electric flux density D = 8E

permeability u
permittivity 8

wave number K = (ml-tre-
phase velocity v = 5B)-

wave equation

 

81:2 11.8 Biz
8211 = 82H
3x2 pr: BIZ

 

 

26

Table 2.6.1 Analogy between ultrasonic waves and electromagnetic waves

CHAPTER 3

Experimental Procedure

In order to analyze the characteristics of an unknow medium, we must
detect and process the reflected or transmitted waveform. Although the
Iramur‘I . . ’Om .0" III ' '1 Im. II .n I' 1. II. d-Iium,
1113, more difficult to obtain because of Jhemediumdimensinns_Further-
more, the implementation of a transmission configuration requires two trans-
ducers while the reflection technique uses only one transducer. Thus the

echo mode of operation is the choice of preference.

In order to demonstrate the theory developed, a single layer target is
used for simplicity. The ultrasonic transceiver transducer is submerged in
water. When the ultrasonic pulse hits the water/target interface it generates
a reflected wave which travels back to the transducer. By comparing the
reflected wave and the incident wave, the reflection coefficient of the inter-
face can be determined. Two experimental procedures are performed, the

w is recorded inmaLtime and drew
through various signal fiprocessieggtechniquesfito retrieve information about

the target. For accurate waveform recording, a high sampling analog-to-

digital converter is required. According to the Nyqnistrriteria, the sampling

Wust be atJeast hwice )he highest frequency component of the

27

28
signal. The W In the
experiments reported here with a transducer frequency of 2.25 MHz a sam-
pling rate of 14.667 MHz about 3.26 times of the Nyquist rate was chosen.
Additional data processing of the recorded signal is performed by various
algorithms.

In section 3.1 the experimental configurations are presented and in sec-

tion 3.2 the data processing algorithms are discussed.

3.1 Experimental Configurations

In order to determine the properties of a medium, the characteristics of
the incident signal and reflected signal waveforms must be known. The sys-
tem shown in Figure 3.1.1 is used to obtain the signal from the water/target

interface.

3.1.1 Sampling the incident signal waveform

The video pulse technique requires that a broadband signal, ideally an
impulse, be transmitted for optimum material characterization. Experimen-

tally, a pulse of less than SOBsec is transmitted.

For subsequent analysis, a detailed incident wave sent out by the trans-

ducer has to be known precisely. A simple way to obtain such a waveform

29

 

hogan—5882:.

2.va 32:60

 

 

h< c8388

 

 

 

.
_
_
_

 

engage—822:.

Q~-N 8.8580

 

Econ—on 2.9

 

 

 

mecca—swung 3.88598 05 .3 Efimfle £83 05. :a 0.5m."—

 

 

NIZ 53.3
.3328 a}.

 

 

 

 

 

 

 

 

cozuoomtoflg
cwcn
83055:?—

 

33>»
3qu

 

 

 

 

 

30
is as follows. The acoustic impedance of water is about 3650 times larger
than that of air (refer to Table 2.2.1), the reflection coefficient of the
water/air interface is practically equal tg__-_1..,that is, a complete reflection.
For a short water path, the Wan be
As a result, the reflected wave from water/air interface can be treated as the

incident wave except the signal waveform is being inverted.

In the experiments, a transducer of frequency 225 MHz is used. A
Panametrics 5050 Pulse Generator/Receiver is employed to generate pulse
signals to the transducer and to receive the reflected signals.

In Figure 3.1.1, the signal is sampled by an A/D conversion circuit with
a sampling rate of 14.667 MHz. The sampled data will be sent to a
Cromemco Z-2D microcomputer, and be transferred to an IBM personal

computer AT for further processing.

3.1.2 Sampling Reflected signal waveforms from objects

The reflected signals from an object under test can be obtained in a
similar manner. That is, the transducer transmits an ultrasound pulse to the
water/object interface and then receives the echoes. The reflected signal is
sampled at 14.667 MHz and the sampled data is processed in a microcom-

puter to obtain the characteristics of the object.

31

3.2 Data processing

The signal received from the system shown in Figure 3.1.1 is the data in
the time domain. These signals are transformed into the frequency domain.
The reflection coefficients at different frequencies are calculated from the
frequency components. Signal extraction is complicated by the fact that
noise exists and by system jitter. Improvement in experimental accuracy is

achieved by signal processing and by statistical methods. Softwareprncess-
ing is pmfenedknghaccurachhile hardware cimuiUIListQLLayro-

cessing.

 

Data processing consists of three main parts: correlation, averaging and

spectral analysis.

3.2.1 Correlation and averaging

A video pulse contains many frequency components. Every frequency
component contributes information to the final result. Therefore, one should
take as many frequency components as possible. However, if too wide a
band is taken, noise will be overwhelming. One way to increase the signal-
to-noise ratio is to use W The zero mean station-
ary noise is averaged to zero so that the signal-to-noise ratio will increase by

W if N signals are averaged.

32

Noise reduction results from averaging and also from signal matching.
Due to the system uncertainty (jitter), the phase of each signal is different.
Thus signal phase alignment is necessary before signal averaging. The
phase difference of two signals can be detected by calculating the correla-
tion between them. The position of the peak value of the correlation func-
tion will be the distance between these two signals. After the distance
between two signals has been detected, one can be aligned in order to do the
averaging.

We will use a real experimental example to show how the correlation
and average work. Figures (3.2.1) and (3.2.2) are two original waveforms
reflected from a water/aluminum interface. It can be seen that these
waveforms have significant noise present. In order to reduce the noise, the
correlation is calculated as shown in Figure 3.2.3 to find the distance
between them. Based on the calculated distance, waveform (2) can be
shifted and averaged with waveform (1). For a twelve waveform correlation
and average, the resultant waveform is shown in Figure (3.2.6). The average
waveform is smoother and contains less noise. Comparing the spectrum of
each waveform ( Figures (3.2.4), (3.2.5), and (3.2.7)-(3.2.9)), we see at the
high frequency noise is filtered by the averaging process. Thus correlation
and averaging are excellent techniques for increasing the signal—to—noise

ratio.

33

Fourier Transform and inverse Fourier Transform

After the signal averaging process is completed, the frequency spectra
of the signal is obtained from its Fourier transform. A general purpose Fast
Fourier Transform routine was developed for calculating the spectrum and
displaying the phase as well as the magnitude of each frequency component.
In addition, some weighting windows may be added to further improve the
results. The weighting windows includes various types, such as the rec-
tangular, triangular, Hamming, and Hanning windows. In addition to the
Fourier Transform, the inverse Fourier Transform is avaliable for time

domain representation.

34

I.“ file: “01.1 n : 18? display raise iron 15. to 3.

Figure 3.2.1 The waveform(l) reflected from water/aluminum interface

NM filo: “01.2 n = 1027 display range {m 150 to 3.

m A M A AVAVA'DM AW

 

 

 

 

 

Figure 3.2.2 The waveform(2) reflected from water/aluminum interface

35

l'ilo “1.1.11 1 “101.21. iron -75 to 75 , 13:21:57, 02-01-1988
"IX : 91653.29 at x = 5 , aux 982655.39 at x : 2

All I...

 

I

Figure 3.2.3 The correlation of wavefonn(1) and waveform(2)

36

 

 

12. points FIT input file :[Illl.l!tl 21:16:25. 02-01-1588

Figure 3.2.4 The spectrum of waveform( 1)

 

120 points m in“ filo :hlllJNI 21:10:10, 02-01-1988

Figure 3.2.5 The spectmm of waveform(2)

37
am filo: alums II = 1B7 display man In- 150 to see

1‘ ‘fl M A [\TIAL 1:“ W \1‘\Afu~u‘\fJ\/Wv‘w‘vj(

Figure 3.2.6 The average waveform reflected from
water/aluminum interface

"ll. “II ill] '1] ".F.
II II "

I. Ilnlllllh _ m .IIIIIIIIII .ll

12. points m in!!! file :[IIOLM'H 21:22:10. 02-01-1988

Figure 3.2.7 The spectrum of average waveform

38

8.8% 5.8053 owflog on. can
ASE—80>“? 05 303.3 connect? 358% 05. w.N.m 033m

sip “my?“ a.

t?
J

lrb b .b—b——~— P .P n n: b b n b — b L
. 1‘ 1“ d 111 1‘. q d 4.1 4“ —1 ‘d- ‘ 4.1-‘4 d ‘ ifi ““ [1 4‘

 

 

aazééisfia 4293:: as .332: .333 5:22“

39

88on Enact; owfiuzw 05 can
ASE—80$; 05 5253 ooaocotmn 3.500% 2F add 0.5mm"—

. \»_b_.___r. —_ .. . .
<J 444

p . . .. r»__ h__._... p p

—\‘1¢1 ‘D 1d‘dq 1‘ q

5
~.«4.— 4 it“—

 

 

aaad-~a-~a.mmuamud~

.~e=~a-~_q new .na~.do_a_ .Ha.~o_aH ggg.o~aa

CHAPTER 4

Analysis of Experimental Results

The experimental results obtained from the system described in chapter
3 are listed in section 4.1. The characteristics of each tested material are
analyzed in section 4.2. In section 4.3, some conclusions are provided and

suggestions for future study presented.

4.1 Experimental Results

4.1.1 The Incident Signal

Using the setup in Figure 3.1.1 and the method described in section
3.1.1, the inverse incident waveform was obtained and shown in Figure
4.1.1. The waveform in Figure 4.1.1 is an averaged waveform of twelve
reflections from the water/air interface. Figure 4.1.3 is the spectrum of the
averaged incident waveform. It is observed that about 90 percent of the

energy is within the frequency band from 1 MHz to 5 MHz.

In order to ensure that the experimental results are repeatable, the
reflected signal from the water/air interface was measured on different days.
Figure 4.1.2 is the average of eight waveforms and Figure 4.1.4 shows its

spectrum. The results of the second set of data is very close to the first. In

40

41
addition to comparing the signal in the time domain, we can also compare
them in the frequency domain (Figure 4.1.5). The spectral difference
between the two appears to be small. In other words, the experimental

results are time independent and repeatable.

4.1.2 The Signals reflected from Tested Materials

Several materials are tested by the video pulse system. They are alumi-
num, plexiglass, composite material, wood, rubber and stone. Both the
reflected waveforms and the spectrum of each material are shown in Figures

(4.1.6)-(4.1 .17).

4.2 Discussion

In order to reduce noise from the return signal, twelve reflected
waveforms from the same target were averaged to increase the signal-to-

noise ratio by \112 = 3.464. This process proved to be extremely valuable.

In chapter 2, we have shown that the reflection coefficient can be

expressed in terms of material densities and wave propagation constants as,

Eq. (2.3.8),

K —K
R: 192 291 (4.2.1)

K192+K291

 

where K = [3 — joc.

2:55:46 01-28-1988
Data File IairOZ
No. 04 files, n I 12 42
Correlation range from 200 to 350
Max difference between two data file dmax I? 50

The distance between [air02.2] and [air02.avgl is 4 with cmax I 86385
The distance between [air02 .3] and Eair02.avgl is 3 with cmax I 89646
The distance between [air02.4] and Cair02.avg] is 5 with cmax I 85249
The distance between [air02.5] and tair02.avg] is 7 with cmax I 83110.5
The distance between Cair02.6] and [air02.avg] is 6 with cmax I 86301.98
The distance between Eair02.7] and £a1r02.avg] is -4 with cmax = 89236.3
The distance between [air02.8] and Eair02.avg] is -1 with cmax I 84794.29
The distance bitween tair02.9] and [air02.avg] is 5 with cmax I 83125.5

The distance between Eair02.101 and [air02.avg] is 9 with cmax I 86480.1
The distance between Cair02.11] and [air02.avgl is -3 with cmax I 89371. 02
The distance between Eair02.12] and [air02.avq] is 7 with cmax I 85661.79
am lilo: “I“.u’ e1 : 1" display page he. 2“ to 35.

J\ Farce—h

 

rm mo: aim.” n1 : ms links new has 1. to 7.

 

Figure 4 1 1 The waveform reflected from water/air interface
( the incident signal )

14:59:40 01-28-1988

Data file Iair03

No. of files. n I 8 43
Correlation range from 200 to 940

Max difference between two data file dmax -? 50

The distance between tair03.21 and [air03.avgJ is 7 with cmax - 92441

The distance between'tair03.31 and [air03.avgJ is 10 with cmax - 87669
The distance between tair03.4l and Cair03.avgl is 10 with cmax . 88168.67
The distance between tair03.5] and Cair03.avgl is 8 with cm.” a 93342.
The distance between tair03.6] and Eair03.avgJ is 7 with cmax I 90498.42
The distance between Cair03.7] and tair03.avg] is 7 with cmax - 91774.5
The distance between Eair03.8] and tair03.av9] is 12 with cmax I 90769.45
III. file: ailll.avs a1 3 ill‘ display range tree zae c. 35.

n l

 

 

 

 

 

I“ file: we.” I! : 1C6 dime! 1'” tree 1. to 7.

 

Figure 4.1.2 The waveform reflected from water/air interface

 

 

 

ill illill

'l'l All"

 

 

 

 

 

 

 

 

 

 

118 points m in“ file :lairflJfll I5:C:§. fl-fl-im

Figure 4.1.3 The spectrum of incident signal

 

 

his. ...... ht

‘ 11. ”is” m in!“ file :laii'flJfll 05:57:82. 02-01-1900

 

Figure. 4.1.4 The spectrum of waveform reflected from
water/air interface

45

<l-

. denounce c5583

23 00:0205 5222— oooouotzc 8.58% 05. n46 0.33"—

D
J

bib-Pthb-P

141‘ “‘ ‘l

.8...“ a. was. am a.

e I d

.a-::: p
4

J.“‘ “‘.‘ 4 1‘ d 1 ‘

 

 

32.3.3222:

522.2 .5 ii: £83 23

11:54:43 01-18-1988
Data file Ia101

No. of files, n I 12
Correlation range from 300

150 to

Max difference between two data file dmax -’ so

The distance between [a101.2] and Ca101.avq] is 3 with Cmax a 96297
The distance between Ca101.3] and Ea101.avql is i with one“ a 37593.5
The distance between Ca101.41 and Ca101.avg] is -13 with cmax . 95325.33
The distance between [a101.53 and ta1D1.avgJ is 9 with cmax . 95472.75
The distance between Ca101.6] and [a101.avql is 9 with cmax I 92636.2
The distance between [a101.7] and Ca101.avg] is 5 with cmax 3 95707.49
The distance between [a101.8] and [a101.avq] is 9 with cmax - 96216.43
The distance between talOi.9J and [a101.avq] is -1 thh cmax - 95103

The distance between Ca101.10] and [a1¢i.avq] 15 3 with cm.” 8 86399.66
The distance between (a101.11] and [a101.avq] 13 7 with cmax . 94257.91
The distance between Ca101.12] and ta101.avg] 13 1 with cmax 8 92187.16

III. file: alIl.30! a1 = III? 15. to 3..

i l

5.1. 1110: alIl.l'! a1 : 1"?

display passe free

 

 

 

 

 

diltll! PI... 9!!! 1.. to 7..

Figure 4.1.6 The waveform reflected from water/aluminum interface

 

14:46:34 01-27-1988
Data file nglass01

No. of files. n = 12
Correlation range from

200 to

350

Man difference between two data file dmau =“ 30

The distance between [pglassOI.2] and [pq1a5501.avg] is
The distance between [pgla5501.3] and qu155501.aug] is
27582.5

The distance between Epglass01.4] and qulassfii.avgl is
27020.01

The distance between EpglassOi.S] and qulass01.avql ii
The distance between Cpqlass01.:] and [pqlas501.avgl 15
27036.79

The distance between [pgl=ssOl.7] and Cpq1a5501.avg1 15
27845.57

The distance between [oqlaas01.al and [pqiassni.avg] is
25183.29

The distance between Cpqlassfli.9l and [pglassOi.aV9] 1’
26005, 75

The distance between Epglasaoi.iu] and Epgla5501.avg] is

27112.44

The distance
27120.7

The distance between [pqlassti
25779.36

not: tile: psiassll.aes

between Epglasswi.lll and Epgiassfll.3vq] is

.12] and [pglassOl.aqu is

n1 : 1626 display range (nan 206 to 350

vvv v ‘

taro tile: nelassll.ans n1 : 1626 disalas range tron ill to Til

 

 

“Wm

S'wlth

14 with

a.
-)

13

~19 with

-7 with

with

with

with

with

12 with

8 with

Figure 4.1.7 The waveform reflected from water/plexigalss interface

with

47

cmax I 27186
cmax a

C1113}: a

cmax I 27662

C1113}: .

cmaa 3

CHIC}: 3

cmax I
cmax a

cmax ‘

50‘” a

12:2

8:37 02-01-1988

Data f i l e Icomp02

No. of files, n I 12
Correlation range from 200 1 to 350
Max difference between two data file dmax I? 20

48

Th. distance between Ecomp02.2] and tcomp02.avgl is 10 with cmax I 2390
Th. distance between [comp02.3 and Ecomp02.avg] is 5 with cmax I 30313
The distance between tcomp02.4] and [comp02.avgl is 3 with cmax I.324O1.33
The distance between Ccomp02.5] and Ccompt)2.avgl is 9 with cmax 1 32156.75
The distance between [comp02.6l and Ccomp02.avgl is 8 with cmax 31794.79
Th. distance between tcompC)2.7J and [comp02.avgl is 7 with cmax I 33269.5
The distance between EcompD2.8] and (commitmavgj 1. 13 with cmax - 750801.29
The distance between [comp02.9l and (comp02.avgl is 13 with one): I 30539.13
The distance between [compoZJOl and Ccomp02.avgl is 11 with cmax I 32910
The distance between tcomp02.11] and Ecomp02.avgl is -18 with cmax I 32840.8

The distance between Ccomp02.12l and Ecom902.avgl is 9 with
In file: Man a1 : 1B1 displas rinse free 28 1a 358

 

MI tile: and.” n1 : 181 diselas an. Inn 1. to 7.

 

Figure 4.1.8 The waveform reflected from water/composite
material interface

cmax I 30293.83

13:02:18 02-01-1988 49
Data file Iwood01

No. of files, n I 12

Correlation range from 200 to 350

hex difference between two data file dmax :7 10

The distance between £wood01.2] and Ewood01.avgl is D with cmax
The distance between twood01.3] and [woodOl.avgJ is 4 with cmax
The distance between Cwood01.4l and twood01.avgl is 4 with cmax
The distance between [wood01.51 and [wood01.avgl is O with cmax
The distance between twood01.6l and twood01.avgl is 3 with cmax
The distance between Cwood01.7l and [wood01.avgl is -1 with cmax
The distance between Cwood01.81 and twood01.avg] is ‘7iuith cmax
The distance between [wood01.9] and twood01.avg] is -5rwith cmax

34089
32275.5
35639.99
35272.5
33639.62
32888.17
35159.99
35866

The distance between Cwood01.101 and twood01.avgl is ‘3 with cmax I 35641.89
The distance between £wood01.11] and [wood01.avgl is 8 usith cmax I 33395.1
The distance between Cwood01.12] and twood01.avgl is 4 uvith cmax I 36560.54

Ill. 1110: eaedll.avy n1 = 1I31 displas Pins! '80! III to 350

 

Ill! llle: eeell|.aey n1 : ill? display sanye (ran 1.6 to 76!

 

 

 

Figure 4.1.9 The waveform reflected from water/wood interface

 

2:19:08

02-01-1988

Data file Irub02

No. of Giles,
Correlation range from

Max

The
The
The
The
The
The
The
The
The
The
The

III. lilo: lsbII.l'!

I!!! file: IIIII.IUI

difference between two data file

distance
distance
distance
distance
distance
distance
distance
distance
distance
distance
distance

n I 12

between
between
between
between
between
between
between
between
between
between
between

vvvvvv

200

Erub02.2]
[rub02.31
[rub02.4]
Crub02.5]
[rub02.61
Erub02.7]
Crub02.8]
[rub02.93

Crub02.iOJ and Erub02.av9] is -36 with
Erub02.iiJ and Crub02.avgl is -6 with
(rub02.i2] and Erub02.avg] is
si : ill? lflsplas tense tree all to

 

to

and
and
and
and
and
and
and
and

350

dmax I?

£rub02.avg]
Crub02.avgJ
[rub02.av91
[rub02.avg]
CrubO2.avgJ
[rub02.avg]
[rub02.avgl
Crub02.avql

sizilfl’ turnanelnenne Hi to fl”

40

is
is
is
is
is
is.
is
is

0 with

-15 with

-4 with

-i7 with

-l with

-20 with

-8 with
with

-2

2 with

v V .

50

cmax I 42174
cmax I 43782
cmax I 40974.33
cmax I 40989
cmax I 39868
cmax I 40999.34
cmax I 36785.29
cmax I 37717.5
cmax I 39757.55
cmax I 37525.2
cmax I 37581.1

Figure 4.1.10 The waveform reflected from water/rubber interface

I

12:49:14 02-01-1988
Data tile IstoneOi
n I 1:
Correlation range from :00 t

Max difference between two data file

No. of files,

The distance
The distance
The distance

The distance
The distance

The distance
The distance
The distance
The distance

The distance
92052.21
The distance

em “10: sienna” si : 1.6

em lilo: sheen.“ n1 : ms

between

between'

between

I
between
between
between
between
between
between

between

between

Estone01.2
[stone01.3]
[stoneGi.4J

Cstone01.5]
Estone01.6]
Estone01.7]

Estone01.8]
[stone01.9]

Estone01.10] and [stone01.avg] is
[stone01.iil and Estone01.avg] is -12 with

[stone01.12] and EstoneOi.avgJ is

and
and
and

and
and
and

and
and

’50

dmax =2 80
Estone01.avg]
EstoneOi.avg]
CstoneDi.avgJ
Estone01.avg]
EstoneOl.avgJ
EstoneOi.avgJ

Estone01.avgl
Estone01.avg]

displas range (lee 2|. is 35.

displas elm free 1' to 7'

is
is
is
is
is
is
is
is

D with
-52 with
-56 with

-42 with
‘39 with
-38 with
-‘4 with

-3 with
2 with

1 with

Figure 4.1.11 The waveform reflected from water/stone interface

51

cman = 88899
cmax I 92041
cmax I 92744.3‘
cmar I 85527.25
cma> I 87300.0:
cmax = 88888.5

cmax = 87038.68

cmax I 91152.13
cmax I 89838.h

cmax =

cmax I 90121.9'

52

JIM _ “manual... i

12. leists '11 islit file :1alIl.€ftl 10:16:14. CI-Il-i’.‘

 

Figure 4.1.12 The spectrum of waveform reflected from
water/aluminum interface ’

 

.Le “AA-“AAAMH -- M Ln LM‘.

m piste m in“ file “513501an 10:24:38, 02-01-1908

Figure 4.1.13 The spectrum of waveform reflected from
water/plexigalss interface

53

AL 0‘ ‘ w

h

 

 

 

l

110 points It! input file :lcufllJi‘tl 10:01:15. l-01-1900

Figure 4.1.14 The spectrum of waveform reflected from
water/composite material interface

 

 

-AAAA A -A- -. ale 4‘

130 points 11'! input file :lseedlithl 10:20:01. 02-01-1900

Figure 4.1.15 The spectrum of waveform reflected from
water/wood interface

54

 

120 leists 511 is’It file :lru502.ffll 10:00:12. 02-01-1900

Figure 4.1.16 The spectrum of waveform reflected from
water/rubber interface

 

120 points 11'! ins: lilo :isteseOiJiil 13:00:01. 02-01-1300

Figure 4.1.17 The spectrum of waveform reflected from
water/stone interface

55

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59

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was 3:029: .8223 3=Eot€ 158% 2C. mmAé 89mm

 

Lb-nnp-pn—b — P‘ .‘ ———bL-———_—P——nppb bun-p! -- Pp nninb bh-——_—————-Pb-——— 1 ‘ — — L—Phb-b-rr

__= _ a . . . _ ___—

 

 

 

 

 

 

aaaééausnfl .3532: 2; £132.33 43.8.3 .238“

61

We have then,

_ (Blpz - [3291) -J'(0I1l32 - azpl)

R - .
([3192 + [3291) -J(0¢1P2 + 0291)

 

(4.2.2)

When the operating frequency is low, or (362)2< <1, the attenuation

coefficient a and phase constant B can be greatly simplified. From Eqs.

(2.4.37) and (2.4.39), we have

2

a = 32%vp‘ic“ (4.2.3)
B z W (4.2.4)

Then, the reflection coefficient becomes

 

 

w<pc)/( 67-1]-'[M«l( c)/( “—331
22 P11 1261 922 911 26

R = 2 {4.25)
. mm 11200
[\l(92€2)/(91017 + 1] -J[‘2——\/(chz)/(PIC 17 + —]
01 262

 

 

 

Judging from this expression, the reflection coefficient R can be evaluated
when the medium density p, elastic stiffness constant c, viscosity constant T]
and the operation frequency (a) are known. The medium density and the
acoustic propagation velocity for most materials are published. The elastic

stiffness constant c can be obtained indirectly as follows:

The acoustic propagation velocity v is

62

_“l
B
Using the approximate value for phase constant B in Eq. (4.2.4), the velocity

v:

(4.2.6)

becomes

v ‘~" Vc/p (4.2.7)

With this, the elastic stiffness c becomes
6 .. 2
~ pv (4.2.8)

An alternate way to obtain the viscosity constant is to use the attenuation

expression of the medium (Eq.(2.4.30) or Eq.(4.2.3)).

Water was chosen as the first medium in our experiments. The density
of water is 1000 kg/m3 and the acoustic velocity is about 1500 m/s.
Assuming no attenuation in water, the viscosity constant reduces to zero.
The elastic stiffness constant is about 2.25x109 N/m2 from Eq. (4.2.8).

With this stiffness constant, the reflection coefficient becomes:

 

-- (D
[Wozc2)/(2.25x10”) - 11 +11%]
R = n (20 (4.2.9)
N<p2c2>/(2.25x10i2) + 11-11-57]

 

 

In the following subsections, we will discuss the expermental results in
three ways. 1) By comparing the signals in the time domain. 2) By compar-
ing the spectral differences between the reflected waveform and the incident

waveform, and 3) by determining the sign of the reflection coefficients.

63

4.2.1 Time domain signals

In the time domain it is easy to find the magnitude and damping of each
signal. Figure 4.2.1 is the time domain representation of the signals for all
materials tested. It can be seen that the magnitude and the damping of
waveforms are different for different materials. For the signals in Figure
4.2.1, the power of each signal may be calculated by squaring the magnitude
of the waveform. The mean value of the magnitude and the power of the

first reflection of each signal is shown in Table 4.2.1.

Incident signal

From Table 2.2.1, the acoustic impedance of air is about 411 kg/m2°sec
and that of water about l.5><10‘5 kg/m2°sec. We may use Eq. (2.2.10) to get

the reflection coefficient at the water/air interface, as:

RWer/air 2 4.99945
which is very close to -1. Base on this, we can say that the signal reflected

from the water/air interface is similar to the incident signal except the phase

has been changed by 180°.

In Table 4.2.1, we list two values for the reflected signals from the
water/air interface. They are detected by the same setup but at different

time. Theoretically, the power of the incident signal must be greater than

64

- —-——- -- -—..—o.—

Table 4.2.1 The mean value of magnitude and power of the first reflection

 

Second medium average magnitude power of the first reflection
W

Air 1 (Incidence) 134.50 80946.57
Air 2 135.09 83813.83
Aluminum 133.77 89956.47
plexiglass 133.77 22289.42
composite material 133.71 27672.30
wood 133.62 30567.79
rubber 134.08 33940.06

stone, 133.67 856.44

 

 

 

the power of the echo signals. It is surprising to see that the power of the
water/aluminum reflection is greater than that of the water/air reflection.
This may be due to the fact that the power of each incident signal is different

or the the incident beam is not normal to the target surface, such that only

part of the reflected power is received by the transducer. This may also

65

Air

 

.1

5..

ml .
I

Stone (+20 as)

Figure 4.2.1 The waveforms of the reflected signals

66
explain why the power of two reflected signals detected at different time

from water/air interface are slightly different.

Signal reflected from water/target interface

For a given input, the power of a reflected signal depends on the square
of the reflection coefficient. The absolute values of reflection coefficients

are given in Table 4.2.1.

From the published characteristics of materials, one can calculate the
theoretical values of the reflection coefficients. For example, the density,

the elasticity stiffness constant, and the viscosity of aluminum [3] are:

pa, = 2695 kg/m3
ca, 2 11x1010N/m2
1101 = 35X10"5 N-sec/m2

From Eq. (4.2.9), the reflection coefficient is

R z (11.478—1)+ jm16x10-15
“mm“ (11.478 + 1) - ja) l6x10‘15

 

= 0.840

From the value of Rwy/a, we can conclude that about 70.6 percent (

Rfimfial = 0.8402 = 0.706) of the incident energy will be reflected from the

water/aluminum interface.

Taking plexiglass as an example, the characteristics of which are

67

ppgm, = 1182 kg/m3
cm, 2 8.5x109N/m2

The reflection coefficient is

(2.113 — 1) + j (upgm,m)/(1.7x101°)
(2.113 + 1) — j (np8,a,,m)/(1.7x101°)

 

Rwater/pglass :

(C lass
pg )2, WC

 

If we assume the imaginary part is small, that is npglass< <
may approximate the reflection coefficient as

Rwater/pglass :: 0358
Therefore, about 12.8 percent ( Rama/pg)“, = 0.3582 = 0.128) of the energy
will be reflected from the water/plexiglass interface.

From the theoretical analysis, the ratio of the reflection coefficient is

R
water/a1 : 0.840 2 2.346

Rwater/pglass 0°35 8

 

From the experimental results,

 

 

Rwater/al ~ P ower water/a1 11,5

Rmer/pglass ~ Powerwater/pglass
~ 89956.47 ]1,¢z : 2.01

" [22289.42

The experimental results are within 15 percent of the theoretical results.

68
4.2.2 The spectral difference between the reflected waveform and the

incident waveform

The signals are transformed into the frequency domain by a FFT rou-
tine. Figure 4.2.2 is the spectrum of each signal detected. The spectral dis-
tribution of the reflected wave should be similar to that of the incident wave,
when the reflection coefficient is real. Figure 4.2.3 is the spectral difference
between reflected signal and incident signal. For comparison, the spectra
have been normalized with respect to the incident power. From the spectral

difference, one should be able to identify the nature of the target.

4.2.3 The sign of the reflection coefficient

From the power content of each reflected signal, one can evaluate the
absolute values of the mean reflection coefficients. The sign of the
reflection coefficient, however, can not be determined from such informa-
tion. The sign of the reflection coefficient can be determined by correlation
techniques. If the positive peak in the crosscorrelation of two signals is
greater than the negative peak, the two signals must be in phase. Otherwise,
they are out of phase. Since the reflection coefficient of the water/air inter-
face is negative, we may determine the sign of reflection coefficient by

correlating the echoes from the water/air reflection and the water/target

reflection.

 

 

 

 

 

 

 

 

.. ‘ 69
Aluminum
. - . numb. .. -
Composite material "mm“ mm“!
Rubber
...|||mlmll||h- M .. .I. .2. -..(||lllnmlll|m ..

 

Figure 4.2.2 The spectra of the reflected signals

70

Aluminum W~:fi Affi; 4%

 

 

Plexiglass WW V-Ill- - WWW-“W

Composite material ulllhl II A V II Illlil:

 

Wood W W. ‘“ WWW

 

 

Rubber %+ g - W

01134567.!

 

Figure 4.2.3 The spectral difference between the incidence
and the reflection spectra

71

. .m‘“—~‘

Table 4.2.2 The approximate reflection coefficients

 

Second medium approximate reflection coefficient

 

m

Aluminum +0.840
plexiglass +0.208
composite material +0.258
wood -0.285
rubber -O.317
stone -0.008

 

 

 

Figures 4.2.4 - 4.2.11 show the correlation of each signal with the
water/air reflection. From these figures, we find that the reflection
coefficients of water/aluminum, water/plexiglass, and water/composite
material are positive, while those of water/wood, water/rubber, and
water/stone are negative. If we take Rwamm = 0.840 as the reference, we
get the results shown in Table 4.2.2 for the approximate reflection

coefficients for other materials.

72
The more accurate reflection coefficients can be obtained from the spec-
tra of the incident and reflected signals at each frequency component, since

the reflection coefficients at different operation frequencies are different.

73

File leirflanl l [air-8.3.91. hen -75 to 75 . 09:55:12. 02-01-1908
m1: = 8.74.76 at x = O , -MX $7.05.“ at x = 3

”A” Ill

vv VV

v

Figure 4.2.4 The autocorrelation of incident signal

File [airflavgl I labile”), free -7.'1 to 75 , 10:“:26, 0241-1900
4M! = men.” at x :-5 . mt :-72930.5 at x :-2

AAA“

-v UV

 

A

U ‘JflvkvA

Figure 4.2.5 The crosscorrelation of incident waveform and
waveform reflected from water/air interface

74

I'll. [airfldnl l (alumni. fun -75 to 75 . 10:16:34. 02-01-1900
m = 77213.13 at x :-36 , -MX 3'7””.45 at x :41

VJ if M

U V'"

 

Figure 4.2.6 The crosscorrelation of incident waveform and
waveform reflected from water/aluminum interface 3

File him...” I (”India”). In. -75 to 75 . 10:26:55. I-Il-lm
"I! = 36965.24 at x = 1.6 . 4!! #0943.” at x : 21

AA AA [AAWAV

V V V

 

Figure 4.2.7 The crosscorrelation of incident waveform and
waveform reflected from water/plexigalss interface

75

File lair-flJu) 6 [confides]. (m -75 to 75 . 10:09:52. 02-01-1960
"I! : 39077.66 at x :-15 . 4!! run. at x :-10

WW

 

Figure 4.2.8 The crosscorrelation of incident waveform and waveform
reflected from water/composite material interface .~

flle Imam”) 6 (“0401.3“), Iron -75 to 75 , 10:33:07. I-01-1900
9H! : 062.56 at x =-3 , ~IX =-45533.31 at x = 0

M A
V V

Figure 4.2.9 The crosscorrelation of incident waveform and
waveform reflected from water/wood interface

76

I'll. [mum] 0 (“A"). Iron '75 to 75 , manna-014m
m = 67956.62 at x = 16 . -MX =-«9fi.77 at x : 13

VAVAVA A A A A A AVAV¥
V UV V W

 

Figure 4.2.10 The crosscorrelation of incident waveform and
waveform reflected from water/rubber interface

lilo lairI.ml 2 [stationary]. 7m -75 to 75 . 13:12:13. I-01-19I
M! = 65736.6 at x =-5 . -M! =-61256.72 at x :-2

vAVAfi/‘VA VAUAVAUAVA AWAVAVAVAV:

 

Figure 4.2.11 The crosscorrelation of incident waveform and
waveform reflected from water/stone interface

77

4.3 Conclusion and Suggestion for Future Study

This thesis has derived the formulas for acoustic wave equations in
terms of the attenuation constant a and the phase constant B in material
media. The transmission coefficient and the reflection coefficient which
turned out to be functions of frequency and the characteristics the of media
were obtained. From the result of the derivation, the waveforms of the
transmitted and the reflected signals depend not only on the characteristics
of the medium, but also on the frequency components of the incident signal.
With this in mind, it is possible to identify different media by their reflected

video pulse shapes. The theory is verified by the expermental results.

Using the acoustic wave for remote sensing gives higher range resolu-
tion than using electromagnetic waves. The reason is that the wavelength of
acoustic waves in a medium is five orders of magnitude shorter than that of
the electromagnetic wave in free space. In addition to the shorter
wavelength advantage, the operating frequencies for acoustic waves can be
much lower than that for the electromagnetic waves. As a result, the signal

is easier to record and process.

One essential requirement for the video pulse technique is that the
reflected signal must be recored accurately, due to the fact that the shape of

the reflected signal carries the media information. Therefore, a high sam-

78
pling rate analog-to—digital converter is needed. Once the signal is recorded,

the data can be processed by software on a computer.

Experimentally, the approximate reflection coefficients can be deter-
mined by measuring the power ratio and evaluating the crosscorrelation of
the reflected and the incident signals. The power ratio determine the mean
magnitude and the peak of crosscorrelation determines the sign of the
reflection coefficient. The precise reflection coefficients can be obtained
from the spectra of the incident signal and of the reflected signal at each fre-

quency component.

Although it is possible to obtain the medium density, the elasticity con-
stant and the viscosity from the reflection coefficient, we did not obtain the
experimental values in this thesis. In order to obtain these values, a much
narrower video pulse must be used, so that a broader frequency spectrum
can be sent to give a broader dispersive response from the media. By com-
paring the reflection coefficient at each frequency component, the charac-

teristics of the materials can be determined.

Judging from the preliminary results of this work, we see that the video
pulse technique has a high potential for application in many areas such as in
cancer detection, nondestructive evaluation of materials, and remote sensing

in land and sea environments. Before this technique can be applied in the

field, further theoretical as well as experimental must be carried out.

79

[1]

[2]

[3]

[4]

[5]

[6]

[7]

80
Bibliography

Stewart, H. F., Stratmeyer, M. E., An overview of Ultrasound:
Theory, Measurement, Medical Application, and Biological Effects,
U.S. Department of Health and Human Services, July, 1982.
Ronold W. P. King and Charles W. Harrison, J r., The transmission
of electromagnetic waves and pulses into the earth , J. of Applied
Physics, Vol. 39, No. 9, Aug. 1968, pp.4444-4452.
B. A. Auld, Acoustic fields and waves in solids , Vol. I, John
Wiley & Sons, 1973, pp.1-190.
Officer, Introduction to the theory of sound transmission ,
McGraw-Hill 1958, pp.1-83.
Leenong Li, Attenuation Measurement by Ultrasonic Techniques,
A Thesis for Master of Science, Department of Electrical Engineer-
ing and System Science, Michigan State University, 1987. pp. 17-
60.
Velimin M. Ristic Principle of Acoustic Devices , John Wiley &

Sons, 1983, pp.1-51.

Simon Ramo, John R. Whinnery and Theodore Van Duzer,

Fields and waves in communication electronics , 2nd ed., John

Willey & Sons, 1984.

81
[8] Robert T. Beyer and Stephen V. Letcher, Physical Ultrasonics ,

Academic Press, 1969.

[9] J. Szilard, Ultrasonic Testing- non-conventional testing techniques

, John Willey & Sons, 1982.

[10] J. Blitz, M. Sc., and A. Inst. P., Fundamentals of Ultrasonics ,

Butterworths, 1963

[1 l] P. Filippi, Theoretical Acoustics and Numerical Techniques ,

CISM, 1983.

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