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Description  |
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BACKGROUND OF THE INVENTION
This invention relates to the art of surface scanning and imaging, and more
particularly to a new and improved ultrasonic method and apparatus for
surface scanning and imaging.
One area of use of the present invention is in fingerprint scanning and
imaging, although the principles of the present invention can be variously
applied to imaging surface topology using ultrasound. In optical
techniques for fingerprint scanning, reflections from small air pockets
under the fingerprint ridges reduce the image quality thereby requiring
image processing techniques which are quite complex and costly to
implement and which themselves can cause unwanted artifacts or possibly
remove valid components of the image. Another problem with optical
techniques is that once the ridge structure of a finger is worn smooth
enough optical systems no longer are able to acquire good quality images.
It would, therefore, be highly desirable to provide a system and method for
imaging surface topology which provides high quality images thereby
reducing the complexity and cost of subseqent image processing and which,
in the case of personal identification, has the capability of imaging
structures which lie beneath the surface of the skin which can be used for
identification.
SUMMARY OF THE INVENTION
It is, therefore, a primary object of this invention to provide a new and
improved system and method for imaging surface topology.
It is a further object of this invention to provide such a system and
method which provides high quality images so as to reduce the complexity
and cost of subsequent image processing.
It is a more particular object of this invention to provide such a system
and method for use in fingerprint scanning and imaging.
It is a further object of this invention to provide such a system and
method for use in personal identification which has the capability of
subdermal imaging.
It is a more particular object of this invention to provide such a system
and method which is efficient and effective in operation and which is
relatively simple in structure.
The present invention provides an ultrasonic system and method for imaging
a surface wherein a C-mode ultrasonic scan is performed over a fixed area
of the surface and range gating is applied to that area at a selected
location from the surface to a given depth below the surface. For use of
the system and method in fingerprint imaging, a live finger is placed upon
a scannable surface, the portion of the finger on the surface is scanned
using the ultrasonic energy, and ultrasonic energy returned from the
finger portion is received to capture an electronic image of the pattern
of ridges and valleys of the fingerprint.
The ultrasonic imaging system comprises a probe for providing a directed
output ultrasonic beam to scan the surface and to receive ultrasonic
echoes from the surface, a pulser-receiver to cause the probe to provide
the output beam and to provide signals in response to the returned
ultrasonic echoes, signal processing means for detecting and processing
return echo signals from the pulser-receiver and a computer for storing
and displaying information contained in signals from the processing means
and for controlling operation of the processing means. The probe includes
first means for scanning the surface along one direction, second means for
scanning the surface along another direction, the two directions
preferably being orthogonal. In accordance with another aspect of the
present invention, the fingerprint image is analyzed in the spatial
frequency domain.
The foregoing and additional advantages and characterizing features of the
present invention will become clearly apparent upon a reading of the
ensuing detailed description together with the included drawing wherein:
BRIEF DESCRIPTION OF THE DRAWING FIGURES
FIG. 1 is a diagrammatic view illustrating an aspect of optical fingerprint
scanning;
FIG. 2 is a diagrammatic view illustrating aspects of depth of penetration
in optical scanning;
FIG. 3 is a diagrammatic view illustrating reflection and transmission of
ultrasound at an interface;
FIG. 4 is a graph in the form of the resonant curve of an ultrasonic
transducer;
FIG. 5 is a diagrammatic view illustrating behavior of incident and echo
ultrasonic pulses at two interfaces;
FIG. 6 is a diagrammatic view illustrating lateral resolution of return
ultrasonic echos;
FIG. 7 is a diagrammatic view illustrating depth of focus for two different
ultrasonic transducers;
FIG. 8 is a diagrammatic view illustrating Snell's Law for ultrasonic
lenses;
FIG. 9 is a diagrammatic view illustrating a converging ultrasonic lens;
FIG. 10 is a longitudinal sectional view of an ultrasonic transducer used
in the system of the present invention;
FIG. 11 is a block diagram of the ultrasonic imaging system according to
the present invention;
FIG. 12 is a graph including waveforms illustrating operation of the system
of FIG. 11;
FIG. 13 is a longitudinal sectional view of the probe of the system of FIG.
11;
FIG. 14 is a top plan view of the probe of FIG. 13;
FIG. 15 is a diagrammatic view illustrating a sector scan swept by the
acoustic mirror in the probe of FIGS. 13 and
FIG. 16 is a diagrammatic view illustrating a relationship between the
acoustic mirro and lens in the probe of FIGS. 13 and 14;
FIG. 17 is a diagrammatic view of a ray trace of the ultrasonic beam from
the probe of FIGS. 13 and 14 as the beam strikes a scatter reflector;
FIG. 18 is a diagrammatic view of a ray trace of the ultrasonic beam from
the probe of FIGS. 13 and 14 as the beam strikes a specular reflector;
FIG. 19 is a diagrammatic view illustrating ultrasonic return pulses seen
by the transducer in the probe of FIGS. 13 and when echoing a specular
reflector;
FIG. 20 is a diagrammatic view illustrating ultrasonic return pulses seen
by the transducer in the probe of FIGS. 13 and when echoing a scatter
reflector;
FIG. 21 is a schematic diagram of a circuit for implementing the system of
FIG. 11;
FIG. 22 is a program flow chart illustrating the software for controlling
operation of the computer in the system of FIG. 11;
FIG. 23 is a graph including waveforms providing a timing diagram
illustrating operation of the program of FIG. 22;
FIG. 24 is a block diagram illustrating a character recognition system
based on spatial filtering;
FIG. 25 is a schematic diagram of an illustrative optical spatial filtering
system;
FIG. 26 is an enlarged image of a portion of a finger print illustrating a
bifurcation and a ridge ending;
FIG. 27 is an enlarged grey scal finterprint image;
FIG. 28 is a spatial frequency representation of the fingerprint image of
FIG. 27;
FIG. 29 is an enlarged image of a fingerprint bifurcation and the psatial
frequency representation thereof;
FIG. 30 is an enlarged image of a fingerprint ridge edning and the spatial
frequency representation thereof;
FIG. 31 is an enlarged image of a fingerprint parallel ridge structure and
the spatial frequency representation thereof;
FIGS. 32a-f are enlarged images of spatial freuqncy representations of
detected minutia from a spatial frequency analysis of the fingerprint of
FIG. 27; and
FIG. 33 is a map of the detected minutia of FIG. 32.
DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENTS
A more complete understanding of the ultrasonic method and apparatus for
surface scanning according to the present invention perhaps can be
obtained best from a brief consideration of optical systems. The almost
unlimited number of optical imaging systems presently in existence use a
multitude of different approaches to scanning that are targeted at many
different applications. However, for purposes of illustration, only those
systems that rely on Frustrated Total Internal Reflection or FTIR as the
basis for obtaining an image will be considered. The theory of FTIR is
that light incident on an interface going from a higher index of
refraction to a lower one will be totally reflected if the incident angle
is large enough. If on the other hand the incident of refraction between
the two surfaces is closely matched, a significant amount of absorption
and scattering takes place. Several systems use this concept as the basis
for generating an image. One of the more classical examples and the one
which will be emphasized herein is that of fingerprint scanning. Referring
to FIG. 1, a finger 1 is placed upon an optical interface such as a prism
2 and a light source (usually a laser) scans the finger to obtain an
image, relying on the ridges of the finger to completely contact the
surface of the prism thus causing the light source to be scattered.
However, often small air pockets form under the ridges thereby reflecting
the light as opposed to scattering it. This creates a very poor quality
image that must be improved by image processing techniques. Often, these
image processing techniques or algorithms cause unwanted artifacts or
possibly remove valid components of the image. Always, these techniques
are quite complex and costly to implement. However, prior to understanding
the problems associated with scanning the fingerprint, general fingerprint
pattern recognition theory must first be understood.
A variety of fingerprint processing algorithms have been developed and
experimented with over the years, each with a varying degree of success.
The basic idea behind all of these algorithms is to identify and locate
unique points of the fingerprint referred to as minutia. The two
predominant types of minutia are ridge endings and bifurcations. A ridge
ending is formed when a ridge of a fingerprint no longer continues along
its path, it simply stops or ends. A bifurcation on the other hand is
formed when a ridge of a fingerprint splits (bifurcates) into two ridges
or, conversely, when two ridges merge into one ridge. Fingerprint
identification algorithms are concerned with identifying every minutia of
the fingerprint (both ridge endings and bifurcations) and associating with
each minutia found, three positional identifiers (x, y, and theta). These
three parameters locate the minutia in an arbitrary (but fixed) cartesian
coordinate system where x and y map the position of the minutia and theta
defines its angle of orientation with respect to one of the axes. A match
between two fingerprints is made when the x, y, and theta of one
fingerprint match (or nearly match) the x, y, and theta of another print.
Essentially, there are two basic methodologies which have been used to
provide an image of the fingerprint to be processed. The first technique
is to generate an inked impression of the fingerprint. This is done by
applying ink to the finger to be printed and rolling the finger onto a
piece of paper or cardboard. The inked image is then placed under an
optical scanner where it is scanned, digitized and placed into the memory
of the computer responsible for processing the fingerprint. There are,
however, a number of problems and deficiencies with this approach
especially when viewed in the realm of security systems. The first and
foremost deficiency with this approach is the need to ink an individual's
finger or hand. Certainly in some applications such as law enforcement,
the inconviencing of the individual being printed is not a primary
concern. However, if the application is general security such as that
which is required for access control, the inconviencing of the individual
is of prime importance and generally rules out the use of any type of
inking procedure.
The second concern with this approach falls into the category of equipment
and material use. Over several years it has been demonstrated that
standardizing the type of ink to be used, along with the material it is to
be printed on, is not as trivial of a problem as it appears. Furthermore,
different inks and different papers all affect the overall final quality
of the image as it is scanned into the computer.
The third (and certainly not last) problem with this procedure is the
training of the individual responsible for obtaining the print. Factors
such as too little ink, too much ink, improper pressure on the finger when
rolling, etc., greatly affect the overall outcome of the image. In
addition, if the individual to be printed is resistant to being printed in
any way, the potential for obtaining a good quality print is far less.
The second methodology for obtaining an image of a fingerprint is to scan
the finger directly. This approach is referred to as "live scan". The idea
behind the devices used to scan the finger is based on the concept of
Frustrated Total Internal Reflection or FTIR. Live scan readers that
employ this technique rely on the fact that the interface established
between the finger and the optical surface (usually a prism but perhaps a
lens) can generate both reflection and scattering based upon the relative
indices of refraction of the fingerprint valleys and ridges versus the
glass prism. That is, the prism has a high index of refraction. When
interfaced to a valley of a fingerprint (i.e. air) which has a low index
of refraction, the light is reflected back to a photosensor for data
conversion and storage. When the prism is interfaced to a much higher
index of refraction such as skin (i.e., the ridge of the fingerprint), the
light is scattered and absorbed. The amount of light reflected back to the
photosensor is significantly less than before. The recorded image is a
grey scale image of the fingerprint.
The single most important problem behind using the concept of FTIR for
fingerprint imaging lies in the ability to ensure that the ridge of the
finger completely comes in contact with the optical element. Often, the
finger is very dry and lacks any type of skin oil or moisture. As a
result, when a finger is placed down upon the optical interface, small air
gaps, although microscopic in size, are thick enough to completely reflect
the light back to the photosensor and thus be interpreted as a valley (the
space between the fingerprint ridges) instead of a ridge. The net effect
is a very spotty image. These spots may eventually be detected as false
minutiae and therefore cause the fingerprint to be improperly matched
against other fingerprints.
In addition to air pockets between the ridge of the finger and the glass
interface being formed by dry skin, two other similar conditions must be
considered. They are irregularly shaped ridges and sweat pores.
Irregularly shaped ridges are those ridges that have nicks and gouges in
them and this type of ridge occurs quite often. This too results in air
pockets being formed at each nick and gouge. Sweat pores also present a
similar problem. Sweat pores are tiny openings found along the ridge
structure and appear in the final image when scanned optically. However,
when a fingerprint is obtained using an inking process, these sweat pores
are filled in with ink and never seen. This results in two completely
different images of the same finger which causes significant problems for
the image processing software.
Another type of problem occurs if the finger to be imaged is extremely oily
or moist as opposed to extremely dry. In this case, the entire ridge of
the finger is coated with a thin film of oil. The skin oil with its index
of refraction acts very similar to the air pockets caused by dry skin and
causes the incident light ray to be completely reflected as opposed to
scattered by the irregular surface of the ridge. Here, the entire ridge is
unable to be imaged and the print image becomes completely unreadable.
This results from the fact that the thickness of the oil or moisture
needed to completely reflect the incident light wave is very thin. The
actual "thickness" needed to reflect the light is defined by how deep the
light will travel into the second medium before it is completely
reflected. This depth, known, as the depth of penetration, is a function
of the wavelength of the incident light used and the index of refraction
(n1 and n2) of the two interfacing surfaces. Referring to FIG. 1, the
depth of penetration is given by
##EQU1##
Assuming that the optical element is glass and that the interfacing medium
is air, then for an angle of incidence of 45.degree., the thickness of the
air pocket needed to completely reflect a light wave of wavelength equal
to 3 um is given by
dp=902nm (2)
Thus, for air pockets of thickness greater than that defined in equation
(2), the underlying ridge structure is never seen by the light ray. As can
be seen from equation (1), the depth of penetration can be altered by
changing the frequency of the incident light, the angle of incidence, or
the index of refraction (of the optical element usually via some form of
surface coating). This effect is shown in FIG. 2. In fact, all of these
parameters have been the subject of much research in the hopes of defining
an optimum set of parameters. Although great improvements were able to be
achieved, this fundamental problem is still a major source of poor image
quality when optically imaging the finger directly.
Even with the improvements made to this approach, however, there are a
number of problems that affect the overall implementation in a real world
environment when interfacing to large masses of people. The first of these
problems is that the image quality varies significantly between dry versus
oily or wet fingers as previously discussed. This is partially due to the
fact that dry fingers usually result in a thin layer if air existing
between the ridges of the finger and the prism. In these cases, it is very
difficult to distinguish between ridges and valleys and the resulting
image becomes very blotchy. Furthermore, it has been documented that the
optical system is sensitive to not only dry versus wet fingers, but also
smokers fingers versus non-smokers fingers, different skin colors, and the
menagerie of dirt, grease and grime that can be found on the end of the
fingers.
Finally, both of the above mentioned approaches (inking and live scan)
suffer from a common shortcoming. It has been found over the years that
certain occupations cause the ridge structures of the finger to be worn
very thin. Occupations that require the repeated handling of abrasive
surfaces such as banktellers handling money, bricklayers, etc. Once the
ridge structure is worn fine enough, the optical systems are no longer
able to acquire good quality images since the surface structure is not
even there to image. This is a significant shortcoming of these approaches
since one of the very institutions that could utilize a high security
system based on fingerprint identification is the banking industry.
However, unlike optics, an ultrasound approach according to the present
invention offers the ability to image below the surface of the finger.
Therefore, if no ridge structure exists or if the ridge structure is too
fine to produce a reasonable signal to noise ratio, then sub-dermal
features can be used as a means of identification. Any unique sub-dermal
structure could be used for this purpose with special attention being
given to the arteries and veins. It is well known that the arteries and
veins of the fingers are quite numerous and even different between the
left and right sides of an individual. Therefore, by obtaining an image of
these structures, a person's identity can be established much like using
the fingerprint. Thus using ultrasound according to the present invention
provides a means for obtaining these images which, when used in
conjunction with the fingerprint, will produce substantially higher
performance ratios with respect to the accuracy of recognition, i.e. false
acceptance rates and false rejection rates.
The basic principle behind the ability to use ultrasound as an imaging
modality is governed by the principles of general wave theory analysis and
common to several other modalities in one form or another (i.e. optical,
electromagnetic, etc.). The principle is that an acoustic wave upon
striking an interface will be partially transmitted and partially
reflected provided that an acoustical impedance mismatch exists at the
interface. Therefore, by collecting the echoes of the transmitted wave, an
overall image of the acoustical discontinuities of the object in question
can be made. When an ultrasonic beam strikes a surface that is smooth and
regular (such as the valley of air found in a fingerprint), the angle at
which it is reflected is quite predictable and is referred to as a
specular return echo. However, when the beam strikes an irregular shaped
surface (such as the ridges of the fingerprint or the blood vessels
internal to the finger) the beam is scattered in many directions and is
referred to as a scattered return echo. In the case of a specular
reflector as shown in FIG. 3, the amount of reflection that is caused by
the interface is dependent upon the ratio of the acoustical impedances of
the two interfaces and the angle at which the incident wave strikes the
interface.
It is imperative to understand the reflection and transmission behavior of
ultrasound upon striking a very thin gap such as a small air pocket. For
the purposes of this explanation, a small air gap internal to a second
structure shall be used as an example. As an incoming acoustic wave of
unlimited length strikes the air gap, the wave is split into a reflected
and transmitted wave. After passing through the air gap, the transmitted
wave is again split a second time. The result is a sequence of reflections
in both directions inside the air gap. On either side a sequence of waves
leaves the air gap which are superimposed. The individual waves are
intensified or weakened depending on the phase position.
Letting Z.sub.1 represent the acoustic impedance of the the material and
Z.sub.2 represent the acoustic impedance of air, then the ratio of the two
impedances can be abbreviated by
m=Z.sub.1 /Z.sub.2 (3)
Defining the thickness of the air gap to be d, then an expression for the
acoustic transmittance D and the acoustic reflectance R is given by
##EQU2##
Both expressions are periodical and have a minimum and maximum value as
regular intervals as defined by minima of R and maxima of D occuring at
d/wavelength=0, 1/2, 2/2, 3/2, etc. and maxima of R and minima of D
occuring at d/wavelength=1/4, 3/4, 5/4, etc. These relationships hold only
for infinitely long waves, i.e. continuous waves. However, in the case of
the very thin air gap, even a short pulse is equivalent to a wave train of
long duration because the width of the gap is much smaller than one
wavelength. The results therefore apply to pulse transmission. The
reflection coefficient R is the ratio of the reflected acoustic pressure
wave Pr to the incident acoustic pressure wave Pi or R=Pr/Pi, assuming the
reflecting interface is infinitely thick (several wavelengths). The
reflection coefficient for very fine air gaps, i.e. thin interface, in any
material can be calculated from equation (5). The significance is that if
the air gap is thin enough the reflectivity is near zero. This allows
imaging past thin layers of air trapped between the finger and lens which
is not possible by the optical approach. Reflection coefficients of 1% are
readily measured yet, when viewing the transmittance, virtually no change
is detectable with such a fine gap.
An important component of an ultrasonic imaging system is the probe which
in turn, includes the piezoelectric transducer, the required lensing
system, mirrors, rotating prisms, etc. The transducer requirements or
parameters are tightly coupled to the specific application and for the
most part are concerned with resolution and attenuation. These parameters
include frequency, quality factor, axial resolution, lateral resolution
and focal length.
The selection of the desired operating frequency for the piezoelectric
transducer is determined by the attenuation coefficient of the propagating
medium, depth of penetration, and resolution required for the particular
application. Generally, the limiting resolution (and the more critical one
for C-scan imaging which will be discussed presently) is lateral or
traverse resolution as opposed to axial or longitudinal resolution as will
also be described. The lateral resolution of an ultrasonic imaging system
is directly proportional to the frequency of the system. A good `rule of
thumb` is that the maximum resolution that can be obtained is on the order
of a single wavelength. The wavelength of ultrasound in water at a
frequency of 30 MHz for example, can be calculated as follows:
##EQU3##
Two other influencing factors on operating frequency are the attenuation
coefficient of the propagating medium and the depth of penetration
required to obtain the image. There are essentially four causes of wave
attenuation in a medium:
1. Divergence of the wavefront
2. Elastic reflection at planar interfaces
3. Elastic scattering from irregularities or point scatterers
4. Absorption.
Many materials, including human tissue, have been empirically characterized
with respect to their acoustic attenuation. The measure is a composite of
the above mentioned causes of attenuation and is usually given in terms of
db/MHz/cm. Table I gives the acoustic attenuation of some biological
samples at a frequency of 1 MHz. As is easily calculated, the return
signal level of an ultrasonic beam operating at 30 MHz in soft tissue and
imaging a vessel 1 cm below the surface is:
=(1.5 db)(30 MHz)(2 cm round trip distance)
=90 db
It is very easy to quickly exceed the signal to noise ratio of any high
sensitivity receiver used to process the return signal. Thus, a practical
limit exists between the required resolution and depth of penetration
needed for obtaining an image.
TABLE I
______________________________________
Acoustic Attenuation at 1 MHz
Attenuation Coefficient
Material (db/cm)
______________________________________
Air 10
Blood 0.18
Bone 3-10
Lung 40
Muscle 1.65-1.75
Soft Tissue 1.35-1.68
Water 0.002
______________________________________
The quality factor or `Q` of a transducer is a measure of its frequency
response about its resonant frequency. The Q of a transducer is directly
related to the axial resolution of the system as well as the amount of
radiated acoustic energy. Very high Q transducers have poor axial
resolution and radiate small amounts of acoustic power. These transducers
are highly efficient however and are usually operated in a continuous wave
(cw) mode as in the case of doppler flowmeters. Low Q transducers offer
very high resolutions and radiate considerably more acoustic energy into
the neighboring medium(s). These transducers are usually operated pulsed
mode as in pulse-echo imaging systems.
The Q of a transducer is calculated as the ratio of the resonant frequency
to the frequency width of the half power points as shown by the curve 10
in FIG. 4 and is given by
Q=f.sub.1 /.sub.13 f (6)
Another form of the definition of Q in terms of energy is given by:
##EQU4##
From this it is readily determined that as the amount of energy radiated
from either or both faces of the piezoelectric element increases, i.e.
energy lost per cycle increases, then the Q of the transducer decreases.
Likewise the converse is also true. Thus, if the goal is to design a
system with a broadband frequency response, then the Q of the transducer
must be low. To accomplish this, the mediums interfacing to the faces of
the crystal must have matching or near matching impedances in order to
maximize the radiated energy. In transducers used for biological scanning,
the one face of the crystal is generally placed on the surface of the skin
which represents a much better impedance match than that of air, thus
immediately lowering the Q of the transducer. To ensure that no layers of
trapped air lie between the face of the crystal and the surface of the
skin, often a gel-like substance with an acoustic impedance similar to
that of tissue is applied to the skin. Since the acoustic impedance of
skin is generally several hundred times greater than that of the
piezoelectric element, the overall effect on the Q of the transducer is
minimum.
To lower the Q of the transducer even further, the back face of the
transducer is generally mounted using some type of epoxy with an acoustic
impedance much lower than that of air. This will cause energy to be lost
through the back face as well as the front face. The overall effect is
that the total amount of power available to radiate into the medium to be
imaged has decreased, but this is generally overshadowed by the improved Q
of the transducer. A concern in allowing energy to be lost through the
back face is that it does not find its way back to the crystal resulting
in some type of standing wave or artifact. Therefore, the epoxy used to
mount the element is generally filled with particles of aluminum or
tungsten. This turns the epoxy into a good ultrasonic absorber and the
energy radiated from this face is lost.
Axial resolution is the ability of a transducer to distinguish between two
objects spaced in a plane parallel to the direction of beam propagation,
also known as the longitudinal plane. As shown in FIG. 5, a single
incident pulse 11 striking a medium 12 with two reflecting interfaces
13,14 causes two echoes 15,16 back to the transducer. To determine the
distance between the two interfaces, the total time between echoes is
measured (dividing by 2 for roundtrip time), and multiplied by the
velocity of sound in that medium. Thus, a measure of axial resolution is
given by the relationship
d=tc/2.
From FIG. 5 it can be seen that as the two interfaces 13,14 are moved
closer together, the time between successive echoes decreases. Eventually,
as the two interfaces 13,14 are moved close enough together, the time
between the two echoes 15,16 will no longer be distinguishable (i.e. the
two echo pulses will appear as one long pulse to the receiving
electronics). In order to provide as much separation as possible between
the two echoes, it is desirable to have the ringing of the radiated
pressure wave (and hence, the reflected wave) be as short as possible.
Therefore, very low Q transducers are used when axial resolution is of
prime importance. This is generally the case when multiple images at a
variety of different depths are desired. In this case, the return echoes
are only captured during a specific period of time. This time represents
the round trip delay time associated with the particular depth or range
that is being imaged. This technique is referred to as range gating and
will be discussed in further detail presently.
Lateral resolution is defined as the minimum distance that can be resolved
between two points in the transverse plane. This distance is essentially
dictated by the size of the beam as measured in the plane in which the
objects reside. FIG. 6 provides a diagrammatic approach in determining
lateral resolution. Two distinct objects are sonified by a beam 21 of beam
width `d` which is swept across the objects. When the objects are far
apart (a distance greater than `d`), two distinct echoes 22,23 are
returned. Knowing the sweep rate of the transducer and measuring the time
between the two returns, the distance between the two objects can be
determined. As the objects are moved closer together, the return echoes
also move closer together. When the return echoes appear right next to one
another, yet still distinguishable, the distance between the two objects
is the minimum resolvable distance. This distance is defined as the
lateral resolution and as can be seen from FIG. 6, is approximately equal
to the size of the spot. Should the objects continue to move closer
together, the individual echoes begin to merge with one another making the
determination of two distinct echoes ambiguous. It should be noted however
that the ability to detect small changes in amplitude of the returned
signal will improve the lateral resolution of the system. Many systems
often provide an adjustment on the overall receiver gain and/or
sensitivity in order to be able to adjust the system's resolving power.
Naturally, in order to maintain the maximum level resolving capability, the
spot size must be kept to a minimum for reasons previously discussed. The
size of the beam is smallest at the focal point of the transducer.
Therefore, any objects that are to be imaged should reside in a plane
located at the focal distance. Often this is difficult to do because of a
number of application specific problems. The question then becomes how
much larger does the beam get as it moves away from the focal point.
Another way of stating this is how deep is the region within which the
size of the spot falls within certain limits of is optimum size. The
answer to this question is referred to as the depth of focus. The depth of
focus is defined as the region surrounding the focal point where the spot
size is within 1.414/d of its optimum size `d`. FIG. 7 shows the depth of
focus for two different transducers. Transducer A has an aperture size
equal to that of transducer B. Transducer B however has a much shorter
focal length than transducer A. This results in a much small spot size at
the focal point (thus providing better lateral resolution) but diverges
much more rapidly as the distance from the focal point increases. It is
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