Acoustic microscopy with mechanical scanning—A review

TL;DR: In this paper, the authors present images that show the elastic properties of specimens selected from the fields of material science, integrated circuits, and cell biology, and show how a single spherical surface formed at a solid liquid interface can serve as this ideal lens free from aberrations and capable of producing diffraction limited beams.

Abstract: Acoustic waves in liquids are known to have wavelengths comparable to that of visible light if the frequency is in the gigahertz range. The phenomena of Brillouin scattering in liquids is based on such waves. In helium near 2 K acoustic waves with a wavelength of 2000 A were studied some ten years ago at UCLA. It follows from these observations that an imaging system based on acoustic radiation with a resolving power competitive with the optical microscope is within reach if an ideal lens free from aberrations could be found. Such a lens, which was so elusive at the beginning, is now a simple device and it is the basic component in the acoustic microscope that forms the basis for this review. In this article we will establish the characteristic properties of this new instrument. We will review some of the simple properties of acoustic waves and show how a single spherical surface formed at a solid liquid interface can serve as this ideal lens free from aberrations and capable of producing diffraction limited beams. When this is incorporated into a mechanical scanning system and excited with acoustic frequencies in the microwave range images can be recorded with acoustic wavelengths equal to the wavelength of visible light. We will present images that show the elastic properties of specimens selected from the fields of material science, integrated circuits, and cell biology. The information content in these images will often exceed that of the optical micrographs. In the reflection mode we illuminate the smooth surface of a crystalline material with a highly convergent acoustic beam. The reflected field is perturbed in a unique way that is determined by the elastic properties of the reflecting surface and it shows up in the phase of the reflected acoustic field. There is a distinct and characteristic response at the output when the spacing between the object and the lens is varied. This behavior in the acoustic ieflection microscope provides a rather simple and direct means for monitoring the elastic parameters of a solid surface. It is easy to distinguish between different materials, to determine the layer thickness, and to display variations in the elastic constants on a microscopic scale. These features lead us to believe there is a promising future for the field of acoustic microscopy.

Summary

I I. INTRODUCTION

• MAGING of microscopic objects with optical and electron microscopes has been closely linked to their understanding of physical or biological phenomena.
• The strength of the material itself depends upon these microscopic features.
• It may seem that the tools now available for examining microscopic structures form a complete set satisfactory for every task.
• This desire to examine elastic properties on a microscopic scale has motivated their work on the use of acoustic radiation in a microscope.
• Nevertheless progress to date has permitted us to work over short distances in water with wavelengths less than 1 pm.

II. THE SCANNING PFUNCIPLE

• The "field of view" imaging system where the image appears either on the retina of the observer, on photographic film, or on a fluorescent screen is not a viable alternative for acoustic radiation.
• At first the authors turned to this system as an expedient, but as they gained experience they found that a scanned system has advantages not found in conventional systems.
• This point will become clear in a later section when the authors calculate the response of an abrupt edge for the two systems.
• The scanned system is sensitive to transverse phase gradients in the object.
• And finally, the sequential recording of the image point by point is ideally suited to a system that uses a microprocessor t o manipulate, store, and process the image prior to display.

HI. THE FORM OF THE INSTRUMENT WITH MECHANICAL SCANNING

• If acoustic imaging systems suffer from the absence of photographic film (sensitive to acoustic radiation) they have an enormous advantage (over optics) in that the wave velocity in solids can be larger than that in liquids by a factor of ten.
• In their instrument it generates a plane wave that travels through the sapphire crystal to the spherical lens.
• In the transmission mode (Fig. 2 ) the radiation passes through the object which is supported on a thin Mylar film and it is collected by an output-lens-transducer combination that is similar to the input.
• The return pulse will then be an RF pulse centered at 1100 MHz and of a duration determined by the bandwidth of the acoustic transducer.
• In addition to a system with increased scan speed, other systems have been explored with features that complement and enhance those discussed here.

Iv. PROPERTIES OF ACOUS'ITC WAVES

• It may, at first, seem U M ~C ~S S U Y to write down the elementary equations for acoustic waves-no one would take the space to write out the equations for electromagnetic waves-but the authors feel that it would be useful since acoustic wave properties do FT2 ~~ EPUlLlBRlUM PLANES F i g .
• Sketch of planes and then displacement from equilibrium as used in derivation of wave equation.
• Not have the familiar ring of dielectric constant or permeability.
• The authors will, therefore, limit the discussion to longitudinal, or compressional, waves where the direction of the particle motion coincides with the direction of propagation.
• The differential pressure, or net force, on this thin slice is Tl -T2.

C

• Here c is the elastic constant for the liquid.
• The index of refraction, which determines both the wave velocity and wave impedance for optical waves, varies by less than a factor of two from materialto-material.
• It is for thisreason the biological material exhibits a small contrast for optical waves and a large contrast for acoustic waves.
• The similarity of (4-1) and (4-2) with the one-dimensional form of electromagnetic waves means that the authors can take over those solutions directly.
• The power flow for acoustic waves is given by (4-5).

It thus forms an acoustic antireflection coating [ 291.

• The attenuation of these waves is included by rewriting the propagation in the form exp (+j(kzat)) exp (-aZ) where a is the attenuation coefficient.
• Values for typical solids are shown in Table I .
• The path length for heat flow of this sort decreases as the frequency increases.
• Semiconductors have attenuation coefficients which are intermediate between these values.
• In the second category the authors find liquids with a lower velocity than water but a low-frequency absorption that is enormous.

A . Spatial Frequencies

• In 1973, Cathey wrote 1391 The impression of information onto an electromagnetic wave by modulating some parameter, such as amplitude, frequency, or phase, as a function of time is a familiar concept.
• He goes on in Qlapter 5 to introduce the concept of spatial frequencies and he illustrates how these procedures can be used to deal with imaging problems.
• The authors w i l l hereafter suppress the exponential time factor and use the following notations: u amplitude distribution of the actual function of both A spectrum of plane waves that are used to constitute the x andy; spatial distribution u.
• Nevertheless, they can be included without undue difficulty [441 and the limits can be extended to +m.
• After suitable normalization, this can be written as (5-4).

B. Beam Contours and Computed Images

• The theory as outlined here can be used to calculate beam contours and spatial frequency content of the converging beam.
• When all of these factors are included the distributions change to that given in Fig. 15(b) .
• The authors see that the confocal scanning system (Fig. 17(c )) compares with the incoherent conventional system.
• On the other hand, the amplitude of the output signal should correspond to the phase gradients in the object plane.
• The most pronounced feature in this series is again the contrast reversal in the amplitude images when the lens spacing decreases (Fig. 22 ).

C. The V(Z) Curves

• For the reflection instrument the output voltage as expressed in (5-14) can be used in a unique way to measure some of the elastic properties of the reflecting surface.
• The initial distribution at the transducer is ui(x, y ) , the distribution of the returning field is uO(x, y ) , and the authors have In writing this form they are anticipating the fiial result wherein they monitor V as a function of the parameter 2 ; i.e., the dis- placement of the reflecting object from the focal plane.
• Equation (5-14) can take on a more suitable form by using the transforms described previously.
• Since their problem exhibits circular symmetry about the z axis the authors can replace x' + y 2 by r2 and write [48] (5-1 5) An alternative form of this expression and its derivation may be found in the literature [491.

This V(Z) expression has

• Some results for real cases will be given in a later section.
• When Z is positive the wavefront that impinges on the transducer is spherical with a radius of curvature that depends on 2.
• These simple cases tell us a great deal about the character the authors expect to find in the measured V(2) curves.
• For 2 = 0 the perfect reflector would have the larger reflectivity and would appear brighter in the image (Fig. 25 ).
• The most important feature that has been left out of these examples is the nonuniform illumination of the lens.

D. Reflectance Functions

• The authors needs are somewhat peculiar in that the authors must cover the entire range of incident angles.
• The range near the critical angle is important where the phase relation between the reflected wave and the incident wave undergoes a maximum of change.
• This suggests that acoustic microscopy may one day play a role in t h i s field.
• The various inhomogeneities that show up here are difficult to see in optical images.
• In Figs. 47 and 48 the authors illustrate the appearance of two different devices that were fabricated on the same sapphire wafer.

W. SUMMARY

• In this review the authors have tried to demonstrate that acoustics can compete in a number of ways with optics.
• They represent a new method for viewing microscopic objects.
• The authors want to leave the reader with the impression that there is still more to come.
• Shorter wavelengths will be used with a resulting increase in resolving power.

Full text

1092
PROCEEDINGS
OF
THE
IEEE,
VOL.
67,
NO.
a,
AUGUST
1979
Acoustic
Microscopy
with
Mechanical
Scanning-A
Review
CALVIN
F.
QUATE,
FELLOW,
IEEE,
ABDULLAH
ATALAR,
AND
H.
K.
WICKRAMASINGHE
Invited
Paper
ARrtmet-Ae
waves in
liq-
ne
to
hrVe
-le-
com~~tothatofvip'Me~tifthetrepuencyismthe~
range.
The
phenomena of
BriIIouin
scattering
in
liquids
b
bad
on
arch
waves.
In
helium
near
2
K
acoustic
waved
with
a
wwehgth
of
2000
A
were
studied
some ten yens
ago
at
UCLA.
It follows from
these
observptions
that
an
imagiug
system
baaed
on acoustic
radiation
with
a
resdving
power
competitive with
the
optical
microscope
is
wi~repchifaniderllensfRe~abe~cwldbefound.
Such
a
lens,
which
was
so
elusive at the
besinniqg,
is
now
a
simple
device and it
is
the basic component in
the
acoustic
microec~pe
that
forms the
basis
fa
this
review.
In
this
lrtide
we
win
establish
the chpricteristic properties of
this
new instrument
We
will
review some of
the
simple
prop-
of
acoustic
waves
and show how
a
single
spherical
surface
formed at
a
solid
liquid
interface
can
serve
as
this
ideal
lens
free
from
abern%oas
and
capable
of producing
diffnction
limited
Lwams.
When
this
is
in-
corporPted
into
a
mechanical
sunning
system aud excited with acoustic
Erequencies
in
the
microwave
ranp
imw
can
be
recotded
with
acoustic
wavelengths equal to the wavelength of
visible
light
We
will
present
haps
that show the elastic properties of
specimens
selected from fhe
fields
of
material
science,
integrated
ci~~uit.8,
and
cell
bidogy.
The
in-
formation content in these
images
will
often
exceed
that of
the
optical
microgmphs.
In
the reflection mode
we
illuminate the smooth
surface
of
a
crystallhe material with
a
highly
convewnt acoustic
beam.
The
reflected field
is
perturbed
in
a
unique way that
is
determined
by
the
ehstic properties of the reflecting
surf-
and
it
shows
up in the phe
of the reflected acoustic field.
There
is
a
distinct
and chrrpcteristic
response
at
the
output
when the
spacing
between
the
object
and
the
lens
is
vpied
This
behavior in the acoustic Rflection
micmayp
pro-
vi&
a
rather simple aud direct means for monitoring
the
elasbc
param-
eters of
a
solid
surface.
It
is
easy to
distinguish
between different mate-
riais,
to determine the layer
thickness,
and
to display variations
in
the
elastic constants
on
a
microscopic
sale.
These
features
lead
us
to
be-
lieve
there
is
a
promising
futuxe
for the
Wd
of acoustic microscopy.
I
I.
INTRODUCTION
MAGING of microscopic objects with optical and electron
microscopes has been closely linked to
our
understanding
of physical
or
biological phenomena. It
is
hard to conceive
of a modem laboratory involved with technology
or
the ad-
vancement of science that
is
without a microscope of some
kind. It has been suggested that the number of instruments in
a given country used to extend
our
"vision" beyond the limits
of the unaided eye can
be
used
as
an indicator of the progress
and advancement of that region.
Electronic microstructures and electronic materials form the
basic elements of solid-state electronics-electronics that un-
derlie an ever increasing part of the complex systems that
our
This
research
was
supported
in
part by the
Air
Force Office of Scientific
Manuscript received September 15, 1918;revised February 21,1919.
Research and the NBS/ARPA
Program
on
Semiconductor Electronics.
C.
F.
Quate and A. Atalar are with the Edward L.
Gmzton
Laboratory,
Stanford University, Stanford, CA 94305.
H.
K.
Wlckramasinghe
is
with the Department of Electronic and Elec-
trical
Engineering,
University College London, London, England.
new technology makes possible. The complexity of these sys-
tems comes from
an
acquired ability to control material
uni-
formity and to fabricate devices on a scale that
is
determined
by the wavelength of
light.
We not only exploit
this
wavelength
through lithography for the fabrication of devices but we
also
use
this
radiation to examine structural details with dimensions
of micrometers.
The materials themselves exhibit features with those dimen-
sions either in the form of defects in single crystals
or
in the
alloying of two different materials to produce microscopic
regions with inhomogeneous properties. Other noncrystalline
materials have a grain structure which can be of
this
size. The
strength of the material itself depends upon these microscopic
features.
The entire world of biological structures
is
largely made up
of cellular components that are microscopic in size. The elastic
properties of these components
are
important and they domi-
nate a large number of biomedical problems. The contractile
mechanisms involved with cell movement, other contractile
processes associated with muscle contraction, the deformability
of cells of the blood stream, and the enormous changes in elas-
tic properties that occur when a given cell goes
through
the
mitotic process and divides into two separate
cells
are examples
where the elastic properties are of primary importance.
It may seem that the tools now available for examining
microscopic structures form a complete set satisfactory for
every task. But there
are
limitations-by and large the electron
microscope in the
scanning
version
is
used to examine surface
features and it
is
restricted to objects that can withstand the
environment of the vacuum chamber. The optical microscope
cannot,
be
used to examine the interior of opaque material.
But there
is
a stronger objection to these instruments which
comes from the fact that they cannot be used to examine the
mechanical
or
elastic properties of microstructures. These
elastic properties
are
fundamental-they make a difference
as
to whether the structures
will
hold together. The abiljty to
examine these properties on a microscopic scale would increase
our knowledge by a wide margin. The alloying spikes of alu-
minum and silicon, the adhesion properties of the grains that
form metal alloys and ceramics, the regions surrounding
dis-
locations and faults in single crystals that are highly stressed,
the viscosity and density of intracellular material in biological
cells and tissues-all of these form an enormous area in the
microscopic world, an area that is worthy of study and an area
where we need new tools.
This desire to examine elastic properties on a microscopic
scale has motivated our work on the use of acoustic radiation
in a microscope. Acoustic waves have always held
a
potential
for microscopic imaging simply because the wavelength
of
sound at microwave frequencies
is
small.
In
crystals
of
quartz
0018-9219/79/0800-1092SOO.75
0
1979
IEEE

QUATE
et
al.:
ACOUSTIC MICROSCOPY
WITH
MECHANICAL SCANNING
1093
at low temperatures acoustic waves with a wavelength of 100
A
have been generated and studied
[
1
I.
In liquid helium, wave-
lengths
as
short at 2000
A
have been propagated between two
paralle! surfaces [21. At room temperature
in
liquids the
acoustic wavelengths have been much longer. Nevertheless
progress to date has permitted
us
to work over short distances
in water with wavelengths less than 1
pm.
Much of this article
will
be devoted to the
use
of these waves
in
a focused system wherein the specimen
is
mechanically
scanned to record the image. One primary goal-a goal that
has been realized within the past few months [3] -is the con-
struction of an instrument with a resolving power equal to that
of the optical instrument.
This
article
will
be devoted to a de-
scription of that work and a description of some of the micro-
graphs that illustrate the features that can now
be
studied with
acoustic radiation.
We
will
concentrate almost entirely on the version of the
acoustic microscope that uses mechanical scanning and acoustic
lens
[4].
Before we proceed with the
full
description we
will
point out that the essential component in the system is a simple
spherical lens formed at the interface between a solid such
as
sapphire with a
high
velocity of sound and a liquid such
as
water with a low sound velocity. There is no spherical aberra-
tion in this lens and it cq be used to focus the acoustic beam
into a waist with a diameter that
is
less than one wavelength.
In water this wavelength
is
equal to that of visible light
(0.5
pm) for a frequency of
3
GHz. The acoustic micrographs at
this frequency are beginning to approach the optical micro-
graphs in quality.
The material in
this
article
is
confined for the most part to
instruments operating above 1 GHz.
This
region
is
attractive.
There we can compete with the optical microscope in resolving
fine detail and we enjoy this competition. Work in the field of
acoustic microscopy below 1 GHz is important but it
will
not
be included here since it has been covered
in
previous review
articles
[
5
1
-[
121
.
The early work of Korpel
[
51 and the cur-
rent work of Kessler
[
121 on laser scanning systems has estab-
lished principles and pointed to areas
of
investigation
[
13)
where acoustic radiation can play a unique role. The work of
Tsai
[
141 has demonstrated the utility of acoustic waves as a
method of probing bonds between opaque materials. Wilson
[
151 and Weglein
[
161 have studied integrated circuits with
the acoustic microscope and they argue that increased contrast
in their acoustic micrographs provides information that
is
not
available in optical micrographs.
In
France, Bridoux and
Torquet
[
171 in their work have shown that this instrument is
useful for opaque objects such as fossils. Attal
[
181 and Wick-
ramasinghe
[
191 have taught
us
that the phase of the output
signal contains as much information about the image as does
the amplitude of the signal.
In
Japan, Chubachi [20] has
shown that piezoelectric transducers can be fabricated directly
on the curved surface of the lens and thereby eliminate the
spurious pulses that rattle around inside the crystal that forms
the acoustic cell. In England, Bennett, Payne, and Ash
[
21 ]
have demonstrated that acoustic microscopy
is
useful for
studying the electrolytic deposition of metallic layers. In addi-
tion, this field has been discussed in several articles of a more
general interest
[
221
-[
261
.
II.
THE
SCANNING
PFUNCIPLE
The “field of view” imaging system where the image appears
either on the retina of the observer, on photographic film, or
on a fluorescent screen
is
not a viable alternative for acoustic
radiation. Other meansmust
be
found. Piezoelectric
films
are
efficient, highly sensitive and they operate over a wide range
of frequencies. These could be used to build
an
array of de-
tectors in the form of an acoustic retina.
In
such an may
careful attention would have to be given to both the phase and
amplitude of the signal from each element. The degree of
complexity
in
this
system was such that we found that we
were continually working on arrays. It was the microscope it-
self that held our interest. A single piezoelectric detector and
a mechanically scanned object
is
an alternative. An imaging
system based on scanning the beam
is
tightly focused and the
image field is constructed point by point as the object
is
moved
in
a raster pattern through the focus of the beam.
At first we turned to
this
system
as
an expedient, but as we
gained experience we found that a scanned system has advan-
tages not found in conventional systems.
The primary drawback for the mechanical scanning system
is
the speed. It
is
slow. Several seconds are required to build up
a single frame
as
compared to television rates of 30 frames per
second. This
will
be overcome in time for we have built me-
chanical systems that operate at 10 frames per second but the
work to be reported here
will
be limited to the systems which
use
slow scans.
The advantages inherent to scanning systems with focusing
were not obvious in the beginning. It
is
now becoming evident
that scanning systems which record a single point at a time
exhibit properties different from those that display the entire
field of view.
In
the scanned system there
is
no problem with
coherent radiation. Since the energy at the focus
is
confined
to a diameter that is less than one wavelength in dimension
there are no interference fringes of the type that are common
with optical microscopes that use coherent laser radiation.
These fringes arise from the scattered radiation from two points
on the object that are separated by many wavelengths. This
point
will
become clear in a later section when we calculate
the response of an abrupt edge for the two systems.
The scanned system
is
sensitive to transverse phase gradients
in the object.
In
transmission
this
is an important source of
contrast. In the reflection mode the highly focused beam
makes it possible to study small variations in the elastic con-
stants across the surface of a solid specimen. This turns out to
be
an important source of contrast in reflection images. These
two points
will
be discussed at some length later on
in
this
review. And finally, the sequential recording of the image
point by point
is
ideally suited to a system that uses a micro-
processor to manipulate, store, and process the image prior to
display. The cost of memories
is
decreasing with time, and
microprocessors
will
be
important elements
in
future
microscopes.
HI.
THE
FORM
OF
THE
INSTRUMENT
WITH
MECHANICAL
SCANNING
If acoustic imaging systems suffer from the absence of photo-
graphic film (sensitive to acoustic radiation) they have an enor-
mous advantage (over optics) in that the wave velocity
in
solids
can be larger than that
in
liquids by a factor of ten. The sketch
of Fig. 1
is
useful for explaining this advantage. The large
velocity ratio means that there
is
a
large angle of refraction,
for a wave is traveling through the solid-liquid interface (Fig.
l(a)).
This
has two consequences
in
the microscope: 1) with
a spherical interface, rays approaching from the solid will
leave in a direction that
is
nearly radial (Fig.
1
(b)), 2) with a
plane interface waves approaching from the liquid
will
find a
critical angle for total internal reflection which
is
much smaller
than that encountered
in
optics (Fig. l(c)).

1094
PROCEEDINGS
OF
THE
IEEE,
VOL. 67, NO.
8,
AUGUST 1979
LIQUID
Fig.
3.
Scanning acoustic microscope-Mechanical components.
(Cour-
tesy of
R. C.
Addison.)
(c)
Fig.
1. Illustration of strong refraction of acoustic waves at a liquid-
solid interface (TIR-total internal reflection). (a) Snell’s
law.
(b) Lens. (c) Reflector.
PIEZOELECTRIC
ZnO
LAYER
-EN
METAL
ELECT-
RADIATW
@
yTRANSDUCER
-\
@
rLENS
:@
>REFLECTING
OBJECT
-
PIEZOELECTRIC
TRANSDUCER
Fig.
2.
Sketch of microscope geometry for transmission.
The
first
factor permits us to construct a simple, single
sur-
face lens that
is
free from aberrations and focuses the beam to
a
diffraction limited waist. The second factor permits
us
to
use the reflection mode and sense the elastic properties of the
reflecting surface.
The acoustic components of the microscope are shown in
Fig.
2
for the transmission mode.
A
photograph of the me-
chanical components for
this
mode
is
presented in Fig.
3.
The
essential parts of the reflection mode microscope are shown in
Fig.
4.
Referring to Fig.
2,
we b.egin with the electrical input
signal
to the piezoelectric transducer. It
is
a sputtered film of zinc
oxide sandwiched between the two
films
of gold.
This
trans-
ducer
is
extensively used
in
a variety of microwave acoustic
devices
[27].
It has proved to be efficient (50-percent conver-
sion effective) and it operates at frequencies that exceed 10
GHz.
In
our instrument it generates a plane wave that travels
through the sapphire crystal to the spherical lens. The ratio of
x
x-y
SCANNING
FG.
4.
Sketch of microscope components for reflection.
the radius of the transducer to that of the lens
as
well
as
the
transducer-lens spacing must be carefully adjusted. The lens
is
in the Fresnel zone of the radiating transducer and
it
is
sur-
prisingly easy to pick a combination of dimensions that
will
result
in nonuniform illuminations of the lens.
At
the lens
surface the impedance ratio between sapphire and water
is
nearly
50
:
1
and
this
must
be
overcome with a quarter-wave
matching layer. Various combinations have been suggested-
gold-quartz
[281
,
glass
[29]
,
Arsenic-Tri-Selenide 1171
-
and they
all
are effective. Carbon
films
with an acoustic imped-
ance of
9
X
lo6
kg/m2-s may
be
ideal for this purpose but
they have not yet been used.
With the sapphire-water combination the
beam
converges to
a focus with a focal length that
is
15 percent greater than the
radius of curvature.
In
the transmission mode (Fig.
2)
the
radiation passes through the object which
is
supported on a
thin Mylar film and it
is
collected by an output-lens-transducer
combination that
is
similar
to the input.
In
this
mode where
we
use
continuous radiation
it
is
possible to monitor either the
change
in
amplitude or the change
in
phase of the signal
as
the
object
is
scanned.

QUATE
et
al.:
ACOUSTIC MICROSCOPY WITH MECHANICAL SCANNING
1095
r----
-
1
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AI
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I
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MASTER
CRYSTAL
CLOCK
I!
a95-
1.25
GHZ
I
S8H
4
BPF
I,
/I
CRT
DISPLAY
-
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SCAN
CONTROL
-
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CIRCUITRY
.-c
[-I
A
Fig.
5. Block diagram
of
the acoustic reflection microscope centered
at 1100
MHz.
The object itself
is
mechanically translated through the beam
waist by the loudspeaker shown in Fig.
3.
This
unit moves the
object
with
simple harmonic motion along a straight line at a
frequency of
60
Hz over a distance of
0.2
mm. A micrometer
drive
is
used to lift the loudspeaker through this same distance
in a time equal to several seconds.
This
slow scan speed
(5-10
slframe) makes it necessary to
store the image by some method before display. We use two
methods: 1) a scan converter, and
2)
direct writing on film.
In
the reflection mode (Fig.
4)
the radiation
is
pulsed
so
that the reflection from the object can
be
distinguished in
time from spurious pulses that come from other reflecting
points within the system. A block diagram of the reflection
mode system
is
shown in Fig.
5.
An
avalanche transistor pulser
excites the piezoelectric transducer through the circulator.
The pulsewidth
is
selected such that the frequency content
of the pulse covers the operating frequency range of the acous-
tic system.
As an example, a pulse of duration
500
ps can excite the
acoustic system centered at 1100
MHz.
The return pulse will
then be an RF pulse centered at 1100 MHz and of a duration
determined by the bandwidth of the acoustic transducer.
After being amplified this pulse
is
detected and its amplitude
is
used to modulate the intensity (Z-axis) of a television moni-
tor. The images are recorded by photographing the face of
this monitor
[
301 .
In
addition to a system with increased scan speed, other sys-
tems have been explored with features that complement and
enhance those discussed here. Two are of primary interest.
The nonlinear system where the output transducer
is
tuned to
the second harmonic of the input; in this system the nonlinear
properties of the object itself can
be
monitored
[
3
1
1.
In
another system the
axis
of the output lens is moved from the
colinear alignment as shown in Fig.
2
to
an
off-axis position
1321.
It
is
then possible to detect the energy that
is
scattered
through a wide angle by the object. It
is
analogous to dark
field imaging in some ways since the output transducer does
not detect the direct signal from the input when the object is
absent.
Iv.
PROPERTIES
OF
ACOUS'ITC WAVES
It may, at first, seem
UM~C~SSUY
to write down the elemen-
tary
equations for acoustic waves-no one would take the space
to
write
out the equations for electromagnetic waves-but we
feel
that
it
would
be
useful
since acoustic wave properties do
FT2
~~
EPUlLlBRlUM
PLANES
Fig.
6.
Sketch of planes and then displacement from equilibrium
as
used
in
derivation
of
wave
equation.
not have the familiar ring of dielectric constant or permeabil-
ity. For that reason we
will
write out the differential equa-
tions. The wave equations
that
come from these are convenient
for defining the terms that we deal with throughout the text.
Acoustic waves come in a variety of forms-shear, longitudi-
nal, and surface-but in liquids the longitudinal wave represents
the only mode of propagation. We
will,
therefore, limit the
discussion to longitudinal, or compressional, waves where the
direction of the particle motion coincides with the direction of
propagation.
In
the sketch of Fig.
6
we illustrate two parallel planes spaced
by a distance Az. The medium
is
liquid with a density
PO.
The stress on plane 1
,
denoted by TI, and on plane
2
by T2,
represents the force per unit of area on these planes. The
differential pressure, or net force, on this thin slice is Tl
-
T2.
The net force acting to compress the slice is (-aT/az)Az since
T2 is given by T1
+
(aT/az)Az. Compressive force will
be
taken as positive. The mass per unit area of this slice
is
poAz.
Newton's Force Law gives us the relation
-
(aT/az)az
=
p0az aulat
or
aT/az
=
-poaulat.
(4-1)
Here
U
is
the velocity of the material
in
the slab. It
is
to be
distinguished from the wave
U,
velocity which
will
appear
later. If plane 1
is
displaced from its equilibrium value by an
amount
5
the material velocity
U
is
equal to
at/&.
If the
dis-
placement from equilibrium of plane
1
,
51,
is
equal to
5'
,
the
displacement of plane
2,
the slab
is
merely translated along the
z-axis. But
if
&
is
less
than
51
the slab
is
compressed by
an
amount
f1
-
fz
=-(as/az)Az.
The
strain
S
is
equal to
(fl
-
fz
)/Az
or
-
at/&.
If
we differentiate with
mct
to the time

1096
PROCEEDINGS
OF
THE IEEE,
VOL.
67,
NO.
8,
AUGUST
1979
DENSITY (0
/cm3)
Fig.
7.
Chart
of
material parameters
for
acoustic
waves.
(Courtesy
OK
C. Eggleton.)
and invert the order of differentiation, we
find
We can invoke Hooke’s Law,
T
=
cS,
and write
aulaz
=
-
-
aT/at.
1
(4-2)
C
Here
c
is
the elastic constant for the liquid.
The two equations (4-1) and (4-2) give
us
the wave equations.
We assume lossless one-dimensional propagating waves in the
form exp
(-j(kz
-
at))
and the equations take the form
kT=
WPOU
kU=
(a/c)T.
(4-3)
We find the relation for
k
to be of the form
k
= =
f
a/vs
(4-4)
where
vs
=
a.
With the forward wave
(k
=
+a/vs)
we have
T
=
U
=
Zo
U
and with the backward wave
(k
=
-
a/vs)
we have
T
=
Here
Zo(E6)
is
the characteristic impedance of the
acoustic wave. It
is
related to the wave velocity through the
relation
ZO
=
pov,.
These three parameters
are
conveniently
plotted in the form
as
given in Fig.
7.
There we see that the
wave velocity (m/s) and acoustic impedance (kg/m2-s) for
different materials can vary by more than a factor
of
ten.
This
-zo
u.
large variation underlines the crucial difference between acous-
tic imaging and optical imaging. The index of refraction, which
determines both the wave velocity and wave impedance for
optical waves, varies by less than a factor of two from material-
to-material. It
is
for thisreason the biological material exhibits
a small contrast for optical waves and a large contrast for
acoustic waves.
The similarity of (4-1) and (4-2) with the one-dimensional
form of electromagnetic waves means that we can take over
those solutions directly. The power flow for acoustic waves is
given by
(4-5)
The reflectivity of a wave at an interface by two materials
of
impedance
Zol
and
Zo2
is
given by
Ref
=
z02
-
ZOl
z02
+ZOl
(4-6a)
and the transmission (amplitude) through the interface
is
given
by
Trans
=
2ZOl
ZOl
+
z02
(4-6b)
It
also
follows that the reflection at an interface can
be
reduced
and the transmission improved with a matching layer one quar-
ter wave in thickness with an impedance equal to
(ZOI 202)”~.
It thus forms an acoustic antireflection coating
[
291.
The attenuation
of
these waves
is
included by rewriting the
propagation in the form exp
(+j(kz
-
at))
exp
(-
aZ)
where
a
is
the attenuation coefficient.
This
parameter
has
a strong