Dynamically focussed array

An array of sonic transducers, useful for medical ultrasonic imaging, has individual sections thereof separately coupled for forming separate beams of sonic energy which converge, respectively, to separate foci along a common axis of the beams. The ratio of the diameter of the radiating aperture of the array relative to a wavelength of the sonic energy is chosen to provide a moderate degree of focusing so that the depth of field at one focus blends with the depth of field of the next focus. Thereby, there is formed a continuous region of substantially uniform intensity of sonic radiation along the common beam axis. Circuitry is provided for selecting one or more specific foci dependent on the bounds of a selected region to be insonified. Upon reception of sonic energy, circuitry is provided for selecting one or more specific foci as a function of the time of travel of an echo from a subject being observed to approximate a continuously varying focus in accordance with distance from successive points of reflection within the subject.

BACKGROUND OF THE INVENTION 
Sonic imaging systems have been utilized for biological and medical 
situations were interior points of a subject are to be observed. 
Typically, such imaging systems employ a source of sound in the form of an 
array of a relatively large number of small transducers or, alternatively, 
in the form of one or more large transducers having a size commensurate 
with the overall size of the array. The source of sound may provide for 
parallel rays of radiation to focus at infinity, or may provide converging 
rays to focus at a nearby point. 
By way of example, the U.S. Pat. No. 3,967,234 which issued in the name of 
Jones on June 29, 1976, shows the use of arcuate transducers to provide 
converging beams of radiation for focusing at a nearby point to produce 
better resolution in the near field. A similar source of sound, but being 
composed of an array of ultrasonic transducers having a preset curvature 
for focusing the radiant energy, is shown in the U.S. Pat. No. 3,587,561 
which issued in the name of Ziedonis on June 28, 1971. 
A problem exists in the use of the foregoing systems for imaging a 
biological or medical subject in that, generally, the systems are only 
focused at one predetermined range from the source of sound. Attempts at 
variable focusing by use of a transducer array with a tapped delay line 
for each transducer have resulted in excessive complexity and cost for a 
commercially acceptable system. By way of example in a medical imaging 
system, such as the imaging of the internal portion of a living creature, 
it may be desirable to accurately discriminate between bone material at 
one depth and flesh material at a second depth. However, the use of the 
foregoing fixed-focus sound sources requires the selection of a 
predetermined depth which will be focused, while points of interest at 
other depths will not be as well resolved. 
SUMMARY OF THE INVENTION 
The aforementioned problems are overcome and other advantages are provided 
by a system which focuses radiant energy at a plurality of foci. In 
accordance with the invention, the system incorporates an array of 
radiating elements wherein individual regions of the array form converging 
beams of radiant energy which focus, respectively, at individual foci 
spaced apart along a common axis of the beams. The principles of the 
invention apply both to electromagnetic energy and to sonic energy since 
both forms of energy are produced by radiating elements which may be 
placed in an array. The ratio of a diameter of a radiating aperture of the 
array to a wavelength of the radiant energy is chosen to provide for a 
moderately sharp focusing of the respective regions of the array so that 
the depth of field at one focus blends with the depth of field at the next 
focus. For example, in a preferred embodiment of the invention, a 
radiating aperture is provided which has a diameter equal to forty 
wavelengths, and which produces three foci with a spacing between the foci 
of eighty wavelengths. In the case of an array having circular symmetry 
about the beam axis, radiant energy of substantially uniform intensity is 
found within an elongated cylindrical region in front of the array and 
enclosing the foci. 
In the case of medical ultrasonic imaging, the regions of the array may be 
separately activted upon transmission and reception of sonic energy 
directed toward a subject which is to be imaged. One or more of the 
regions of the array are activated for illuminating a specific region 
within the subject to be imaged. Upon reception of the echoes reflected 
from the subject, individual regions, or groups of the regions, of the 
array, are sequentially activated in synchronism with the time of 
propagation of the radiant energy through the subject to provide for a 
dynamic focusing of the array. The dynamic focusing permits the array to 
be focused at the points within the subject from which echoes of the 
radiant energy emanate. 
The array may have a flat face or a curved face. In the case of the flat 
face, the array is composed of a set of radiating elements with focusing 
being accomplished by means of phase shifters or delay units coupled to 
each of the radiating elements to impart a phase shift or delay to 
electrical signals coupled to the radiating elements. The phase shift or 
delay is selected to produce a curved wavefront of radiation having a 
radius of curvature centered at the desired focus. In the case of the 
curved face, the array is focused by placing the radiating elements along 
a set of concave surfaces of constant radii of curvature, with the 
respective centers of curvature being at the desired foci. A separate 
curvature is applied for each of the foci. For the transmission of sonic 
energy from a planar array, the radiating elements take the form of 
relatively small sonar transducers fabricated of a piezoelectric material. 
Alternatively, in the case of a curved array transmitting sonic energy, a 
single large arcuate transducer may be utilized in lieu of a set of 
relatively small transducer elements positioned about the curved face of 
the array. The array of radiating elements takes the form of concentric 
circular regions wherein the innermost region is focused at the nearest 
focus while the outermost region is focused at the furthest focus. 
In the case wherein the system provides an image of sites within a subject 
such as a human being, the array is advantageously placed against the 
subject, as in medical diagnostic imaging of a human being by sonic 
energy. Individual regions of the array are selected by a switch in rapid 
sequence to vary the focus as a function of the range of sites from which 
echoes emanate. To facilitate the description of the invention, the 
following description will relate to a sonic imaging system, it being 
understood that the description applies in an analogous fashion to a 
system utilizing electromagnetic radiation, such as a laser radar which 
may be focused at nearby points. 
In one embodiment of the invention, three groups of sonic transducer 
elements are arranged in a planar array of concentric circular regions 
wherein the middle and the outer regions are of annular shape. Phase 
shifters providing fixed values of phase shift are employed for shifting 
the phases of signals of transducers in each of the circular regions. 
Thereby, for each circular region there is provided a wavefront which 
converges toward a fixed focal point upon transmission, and diverges from 
the fixed focal point toward the array upon reception. Delay lines having 
preset values of delay are preferred in lieu of the phase shifters for 
wide band signals since the delay lines have a wider bandwidth than the 
phase shifters. A different focal point is formed by each of the three 
regions. 
For forming each of the focal points during reception of an echo, the 
transducer signals from each of the regions are separately combined to 
produce a sum signal for each region. The sum signal corresponds to an 
echo emanating from the vicinity of the site of the focus of the 
respective region. Circuitry, including a selector switch, sequentially 
selects a sum signal or a combination of sum signals as a function of the 
time of travel of an echo in the subject to provide effectively a dynamic 
focusing of the imaging system, the focus changing with the depth of the 
reflecting sites within the subject from which the echoes emanate. 
Thereby, enhanced resolution of individual points within the subject is 
provided to produce a sharper image of these points on a display. 
In an alternative embodiment of the invention utilizing an array with three 
regions arranged on separate spherical surfaces, the outer and the middle 
regions of the array employ coaxial annular transducers disposed on 
spherical surfaces, while the central region employs a circular transducer 
having a spherical surface. Each of these three transducers has a concave 
cross-section to provide for the focusing of the sonic energy, the three 
transducers providing a set of three focal points. The selection of a 
focal range is accomplished by the selective switching of the three 
regions as has been described above for the first embodiment.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
Referring now to FIGS. 1 and 2, there is seen a system 20 for producing 
images of points 22 within a subject 24, the images being portrayed upon a 
display 26 of the system 20. The system 20 comprises a planar array 28 of 
annular sonic transducers 30 arranged in individual regions about a common 
axis 32 of the array 28. The transducers 30 may be fabricated of a 
piezoelectric material, such as lead-zirconate-titanate, with electrodes 
(not shown) attached to the material in a conventional manner. The system 
20 further comprises a module 34 of transmit/receive circuits 36 which are 
coupled to respective ones of the transducers 30. Upon transmission, a set 
of signals is applied by the transmitter 38 via a line 40 and the module 
34 to the transducers 30. The signals coupled via the line 40 are seen to 
fan out to individual ones of the circuits 36. Echo signals reflected from 
sites within the subject 24 and incident upon the transducers 30 are 
coupled via the circuits 36 and line 42 to a receiver 44. 
In accordance with the invention, the array 28 comprises a central circular 
region 47 having a short focal length, an inner annular region 48 having a 
medium focal length, and an outer annular region 49 having a long focal 
length. Signals radiated by individual ones of the transducers 30 in the 
respective regions 47-49 are provided with phase shifts by corresponding 
phase shifters 52 in the transmitter 38, while signals received from the 
transducers 30 are provided with phase shifts by corresponding phase 
shifters 54 in the receiver 44. Each of the phase shifters 52 and 54 
provides a single fixed value of phase shift. The receiver 44 comprises 
amplifiers 56 which are coupled to the input terminals of the respective 
phase shifters 54 whereby signals seen fanning into the amplifiers 56 from 
the line 42 are amplified to a sufficient magnitude for operation of the 
phase shifters 54. The transmitter 38 includes a set of amplifiers 58 for 
amplifying the power of signals provided by the phase shifters 52 to a 
sufficient magnitude for transmission into the subject 24. Also included 
in the transmitter 38 is a selector switch 60 operated by a knob 62 for 
selectively coupling a signal, produced by a signal generator 64, to the 
transducers 30 of one or more of the regions 47-49. 
The rays of radiation from the central region 47 are identified in FIG. 1 
by the legend A, the rays from the regions 48 and 49 being identified 
respectively by the legends B and C. While the rays from each of the 
regions 47-49 are focused at their respective focal points 22, it has been 
found advantageous, as will be explained hereinafter, to utilize the rays 
from a plurality of the regions 47-49 for the imaging of sites within the 
subject 24 at specific ranges from the array 28. As shown in FIG. 1, and 
by way of example, the rays A focus at a point 22 located at a distance of 
60 mm (millimeters), the rays B focus at the point 22 located at a 
distance of 120 mm, and the rays C focus at a point located at a distance 
180 mm from the array 28. All the focal points are on the axis 32. For 
receiving echoes from subject matter located at a distance in the range of 
30 mm to 90 mm, only the transducers 30 of the central region 47, 
producing the rays A, are excited. For subject matter located at a 
distance in the range of 90 to 150 mm, the transducers 30 in both the 
regions 47-48, providing the rays A and B, are excited. For subject matter 
located at distances greater than 150 mm, the transducers 30 of all three 
regions 47-49 providing the rays A, B and C are excited. 
The switch 60 is provided with three fixed contacts, labeled A, B and C, 
for coupling the signal from the generator 64 to the transducers 30 of the 
corresponding regions of the array 28. A sliding contact 66 of the switch 
60 rotates past the fixed contacts and is sufficiently long for contacting 
all three contacts A, B and C simultaneously as shown in FIG. 1, the 
sliding contact 66 contacting only the contacts A and B, or simply the 
contact A upon rotation of the sliding contact. The sliding contact 66 is 
rotated by the knob 62 for selectively energizing the regions 47-49 of the 
array 28 in accordance with the range of distances of the subject matter 
to be imaged such that the rays A are radiated for short distances, the 
rays A+B are radiated for medium distances, and the rays A+B+C are 
radiated for long distances. The switch 60 may also be provided with a 
smaller contact 68 for individually selecting either the rays A, B, or C. 
The system 20 also comprises summers 71-75, a switch 76, a clock 78, a 
range counter 80 and a filter 84. The clock 78 provides timing signals for 
synchronizing the operation of the display 26 with the operation of the 
counter 80 and the signal generator 64. The switch 76 is portrayed as a 
mechanical switch to facilitate the explanation of its operation; however, 
it is understood that the switch 76 operates electronically in response to 
a digital signal of the counter 80 representing the range of subject 
matter from which echoes emanate in the subject 24. A sliding contact of 
the switch 76 selectively couples signals from one of three terminals #1, 
#2 and #3. 
The summer 71 sums together the transducer signals of the central region 
47, corresponding to the rays A, and applies the sum to terminal #1 of the 
switch 76. The summer 72 sums together the transducer signals of the inner 
annular region 48, corresponding to the rays B, and applies the sum to the 
summer 74. The summer 74 combines the output signals of the summers 71-72 
and applies the combined signal, corresponding to the rays A+B to terminal 
#2 of the switch 76. Similarly, the summer 73 sums together the transducer 
signals of the outer annular region 49 and applies the sum to the summer 
75, the summer 75 combining the sums of the summers 73-74 and applying the 
combined signal, corresponding to the rays A+B+C to the terminal #3 of the 
switch 76. Thereby, in response to a range signal from the counter 80, the 
switch 76 applies the corresponding set of transducer signals to the 
filter 84 for presentation of the display 26. The filter 84, as well as 
the phase shifters 52 and 54, have a sufficiently wide pass band to 
accommodate the transducer signals. The filter 84, preferably, is matched 
to the waveform of the signal provided by the generator 64 to maximize the 
power of received echo signals relative to background noise. 
In the preferred embodiment of the invention, the array 28 has an exemplary 
diameter of 30 mm. The wavelength of sonic energy produced by the array 28 
has an exemplary value of 3/4 mm in water (or human tissue) at an 
exemplary frequency of 2 MHz. The transducers 30 each have a radiating 
aperture with an exemplary dimension in their radial direction of 1/2 mm, 
this being equal to 3/8 wavelength. 
In operation, the phase shifters 52 coupling signals to the transducers 30 
of the central region 47 are each preset with individual values of phase 
shift to produce a curved wavefront for radiation emanating from the 
central region 47, the wavefront being curved about the near focal point 
22. Similarly, the phase shifters 52 coupling signals to the transducers 
30 of the inner annular region 48 and the outer annular region 49 are each 
provided with individual values of phase shift for providing curved 
surfaces of wavefronts emanating from the respective regions 48-49, the 
wavefronts being curved respectively about the middle focal point 22 and 
the far focal point 22, respectively. Thereby, the phase shifters 52 
provide for the focusing of the signals from the array 28. Similar 
comments apply to the operation of the phase shifters 54 for providing a 
focusing upon reception of the echoes from the subject 24. In response to 
a timing signal of the clock 78, the signal generator 64 provides the 
waveform of the signal to be transmitted by the transducers 30. The clock 
78 further provides timing pulses to the counter 80, which counts these 
pulses to provide the time elapsed from the transmission of the signal of 
the generator 64. 
A feature of the invention is the dynamic focusing which can readily be 
accomplished since the three regions of FIG. 1 are preset to focus at 
their respective focal lengths. The time elapsed between the transmitted 
signal and the reception of an echo from a site within the subject 24 is a 
measure of the distance, or range, of the site from the array 28. The 
counter 80 drives the switch 76 to couple echoes from different focal 
regions as a function of range. Thus, at short ranges, the display 26 is 
presented with signals received via the central region 47 of the array 28, 
while for moderate ranges the display 26 is presented with signals 
received by the combination of both the central region 47 and the inner 
annular region 48. At large ranges, the display 26 is presented with 
signals received by the combination of the three regions 47-49 of the 
array 28. The use of all three regions 47-49 at the longer ranges, while 
only the region 47 is used at close range, provides greater uniformity of 
sound intensity at the various ranges without significant degradation of 
focal spot size. 
The knob 62 of the switch 60 is utilized to select the optimum mode of 
transmission. Thus, by way of example, if all regions within the subject 
24 are of equal interest, then the switch 60 is set as shown in the figure 
such that all transducers 30 of the array 28 are transmitting. However, if 
subject matter at moderate or nearby ranges is primarily of interest, then 
the switch 60 is set for coupling the signals, respectively, via the 
contacts A and B or only via the contact A. If desired, the sliding 
contact 68 may be utilized for coupling signals by the contact B or the 
contact C. 
Referring also to FIG. 3, there is seen a schematic diagram of a delay line 
which may be utilized in lieu of a phase shifter 52 or 54 in an 
alternative embodiment of the invention wherein the focusing of the 
radiant energy is to be accomplished by a delaying of the transducer 
signals rather than by providing the phase shift as has been described 
with reference to FIG. 1. The delay line takes the form of an 
inductor-capacitor ladder circuit with terminating resistors at the input 
and output terminals thereof. Such a delay line has an exemplary bandwidth 
of approximately 10 MHz (megahertz) which is well in excess of the 
frequency of the radiant energy, such frequency being typically on the 
order of 1-2 MHz which is used in sonic imaging for medical diagnostic 
purposes. Thereby, a burst of the radiant energy having a duration of 
approximately one cycle of the radiant energy can be accommodated by the 
system of FIG. 1, the corresponding electrical signal being readily 
propagated through the delay line of FIG. 3 without significant 
distortion. 
Referring also to FIG. 4, there is shown a cross-sectional view of an 
alternative embodiment of the array 28 of FIGS. 1 and 2, the alternative 
embodiment of FIG. 4 being identified by the legend 28A. Annular sonic 
transducers 30A of FIG. 4 are arranged in three regions 47A, 48A and 49A 
which correspond respectively to the central region 47, the inner annular 
region 48 and the outer annular region 49 of FIG. 2. The embodiment of 
FIG. 4 differs from that of FIGS. 1 and 2 in that the front faces of each 
of the regions 47A-49A are concave with radii of curvature directed 
respectively from each of the three focal points 22 of FIG. 1, this being 
in contradistinction to the planar surfaces of the regions 47-49 of FIGS. 
1 and 2. The radius of curvature of the central region 47A of FIG. 4 is 
directed from the nearest of the points 22 while the radii of curvature of 
the regions 48A and 49A are directed respectively from the points 22 at 
120 mm and 180 mm in FIG. 1. 
The concavity of each of the regions of the array 28A provides a curved 
wavefront of radiation and a focusing of the radiation from each of the 
regions to the respective focal points 22 on the array axis 32. Since the 
curvature of the wavefronts provided by the array 28A is the same as that 
provided by the planar array 28 of FIG. 1 in conjunction with the phase 
shifters 52 and 54, the phase shifters 52 and 54 may be deleted, or be set 
for equal values of phase shift, when the array 28A is utilized. A further 
feature of the array 28A is the displacing, or stepping, of the respective 
regions 47A-49A relative to each other along the array axis. The stepping 
results in a shifting of the nominal phase of the groups of rays A, B and 
C relative to each other to provide for a constructive addition of the 
respective radiation at numerous points along the axis 32 of FIG. 1. The 
stepping may be accomplished physically by the physical locations of the 
regions 47A-49A as shown in FIG. 4, or electrically by the use of delay 
lines, such as that of FIG. 3, in which a fixed delay is imparted to 
sigals of one region relative to another of the regions 47A-49A. An 
adjustment in the location of the regions 47A-49A will be described with 
reference to FIG. 10. The constructive addition results in uniformity of 
energy density along the axis 32 will be seen in the graphs of FIGS. 
12-14. Alternatively, the set of phase shifters 52 and the set of phase 
shifters 54 may be used to impart a phase taper to the transducers 30A in 
one or more of the regions 47A-49A to alter the positions of the 
corresponding focal points 22 along the axis 32. If desired, switches (not 
shown) may be employed for bypassing the phase shifters 52 and 54 whereby 
the phase taper may be selectively introduced to establish additional ones 
of the focal points 22 for the dynamic focusing. 
Referring also to the diagram of FIG. 5, and with reference to the case of 
the planar face of the array 28 of FIGS. 1 and 2, the focusing at the 
respective focal points is accomplished, as has been noted hereinabove, by 
introducing phase shifts to signals transmitted by and incident upon the 
transducers 30 by the phase shifters 52 and 54. The magnitudes of the 
phase shifts as a function of position along the array 28 are shown by the 
diagram and are maintained constant during the transmission and reception 
of the sonic energy. For each transducer 30, the amount of the phase shift 
compensates for signal delay experienced in the transition from the 
concave regions 47A-49A of FIG. 4 to the planar faces of the corresponding 
regions of FIG. 2. Similarly, when delay lines, such as that of FIG. 3, 
are utilized in lieu of the phase shifters 52 and 54, calculation of the 
compensating delay follows the calculation of the phase shift shown in 
FIG. 5 for the exemplary wavelength of 3/4 mm. For the exemplary dimension 
of array size and focal distances shown in FIG. 1, it is seen that the 
outer diameter of each of the regions of the arrays 28 and 28A bears a 
ratio of 1:6 relative to the corresponding focal distances. As seen by the 
trignometric construction of FIG. 5, the necessary phase compensation for 
the planar surface approaches a magnitude of approximately .pi./3 radians 
at the outer radius of any one of the regions 47-49 relative to locations 
at the inner radii of the corresponding regions. The foregoing explanation 
also applies to the alternative phase taper for the array 28A of FIG. 4 
and to a line array which will be described in FIG. 7. 
If desired, the array 28 may be translated in position along the surface of 
the subject 24 by conventional means, represented by a scanner 90, to 
provide a two dimensional presentation on the display 26, wherein the Y 
coordinate represents depth within the subject 24 while the X coordinate 
represents distance along the surface of the subject 24. The scanner 90 
produces a signal at its X terminal which is coupled to the X terminal of 
the display 26 for driving the X axis of the display 26 in correspondence 
with the X position of the array 28. By way of alternative embodiments, it 
is also noted that the switch 76 may also be provided with a small moving 
contact (not shown) such as that described previously with to the switch 
60, plus additional contacts coupled directly to the output terminals of 
the summers 72 and 73 whereby signals may be coupled individually from the 
regions B and C. Such a switching arrangement may prove useful in 
eliminating off-axis signals in the vicinity of a focal point 22. However, 
the switching arrangement actually shown in FIG. 1 is generally preferred 
because of the uniformity of intensity provided at intermediate points 
between the focal points 22 as will be described hereinafter. 
Referring now to FIG. 6, there is seen a further embodiment of the array 28 
of FIG. 1, the alternative embodiment of FIG. 6 being identified by the 
legend 28B. The array 28B is similar to the array 28A of FIG. 4 in that 
concave radiating surfaces are employed. However, in lieu of the numerous 
annular transducers having a relatively thin form for providing each of 
the three regions 47A-49A of FIG. 4, the embodiment of FIG. 6 employs a 
single annular transducer for each of the regions 48B and 49B, and a 
single bowl-shaped transducer for the region 47B. The radiating surface of 
each of the transducers has the curvature of a spherical surface. Focusing 
of radiant energy with the array 28B is accomplished in the same manner as 
taught previously with reference to the array 28A. However, great 
simplicity of the electronic circuitry is provided in that only three 
transducer elements are employed in the array 28B. 
Referring now to FIG. 7, there is seen a system 20A which is an alternative 
embodiment of the system 20 of FIG. 1, the system 20A comprising a line 
array 28C of rectangular transducers 30B in lieu of the circular array 28 
of annular transducers 30 in the system 20. The array 28C of FIG. 7 is 
coupled via the module 34 of transmit/receive circuits, and then via the 
line 40 to a transmitter 38A, and via the line 42 to a receiver 44A. The 
transmitter 38A comprises the switch 60 and the amplifiers 58 and is 
coupled to the generator 64 as is the case with the transmitter 38 of FIG. 
1. Also, the receiver 44A comprises the amplifiers 56 which are coupled to 
the summers 71-73 as is the case with the receiver 44. 
In accordance with a feature of the invention, both dynamic focusing (as 
was taught for the system 20 of FIG. 1) and beam steering are provided for 
the line array 28C of FIG. 7. The combination of dynamic focusing and beam 
steering is provided by phase shifting circuits 52A and 54A which 
incorporate both a fixed phase shifter 96 and a variable phase shifter 98. 
For steering a beam through a scan angle which is less than approximately 
20 degrees from the nominal axis of the radiation pattern, the focusing 
can be accomplished by the use of the fixed phases, as is provided by the 
phase shifters 52 and 54 of FIG. 1, plus a variable phase shift which is 
tapered linearly from one end of the array 28C to the other end of the 
array 28C to tilt the wavefront for focusing at a point off the axis of 
the array. For a nominal axis of the radiation pattern which is inclined 
at a relatively large angle, greater than 20 degrees, the acuity of the 
focus is diminished and additional compensating electronic circuitry is 
needed. 
The fixed values of phase shift are provided by the shifters 96, and the 
variable shifters 98 provide phase shifts according to digital control 
signals from read-only-memories 100 in response to an address from an 
address generator 102. The address generator 102 provides an address in 
accordance with the desired scan angle. The address may be designated 
manually by an encoder (not shown) in the generator 102, or the address 
may be provided by a counter (not shown) which is in the generator 102 and 
is responsive to timing signals from the clock 78 of FIG. 1. Each of the 
memories 100 stores a set of values of phase shift for the phase shifters 
98, and produces the aforementioned control signals in accordance with the 
phase shift required to direct the axis of the radiation pattern in in the 
desired direction. 
FIG. 8 shows an array 28D mounted on a support 104 through which 
transducers 30C of the array 28D are coupled to the module 34. The array 
28D may also be referred to as a line array, and may be regarded as a 
slice of the array 28A of FIG. 4. The array 28D of FIG. 8 may be utilized 
in lieu of the array 28C in the system 20A of FIG. 7, in which case the 
fixed phase shifters 96 may be deleted since the focusing is accomplished 
by the curvatures of the regions of the array 28D in a manner analogous to 
that explained above with reference to the array 28A of FIG. 4. 
Referring now to FIG. 9, there is seen a diagrammatic view of the concave 
radiating surfaces of the array 28D of FIG. 8, the diagrammatic view being 
equally applicable to a cross-section of the arrays 28A-B of FIGS. 4 and 
6. The arcs representing the surfaces of the respective regions are shown 
exaggerated in order that the curvature be more visible. The arcs are 
shown extended to intersect the axis 32 and have been positioned so as to 
be tangent at a common point on the axis 32. 
Referring also to FIG. 10, there is seen a mechanical arrangement for 
supporting the regions 47B-49B of the array 28B of FIG. 6. The mechanical 
supporting structure comprises yokes 151 and 152 which are affixed to the 
regions 48B-49B, respectively, of the array 28B. The region 47B is affixed 
to a pedestal 154 having a keyway 156 therein for sliding on a rail 158 
which is rigidly secured to the center of the yoke 151. Similarly, the 
yoke 152 is provided with a keyway 160 for sliding on a rail 162 which is 
rigidly secured to the central portion of the yoke 151. Double threaded 
screws 163-164 having knobs 166 thereon are threaded between the central 
portion of the yoke 151 and, respectively, the pedestal 154 and the yoke 
152 for urging the pedestal 154 and the yoke 152 into positions relative 
to the yoke 151. Thereby, the region 47B and the region 49B may be 
displaced along the axis of the array 28B relative to the region 48B to 
adjust the relative phases of the groups of rays A, B and C which were 
seen in FIG. 1. Following the construction of FIG. 9, the surfaces of the 
regions 47B-49B of FIG. 10 may be viewed as extending to the axis 32. The 
tangents to such extensions of the curved surfaces of the respective 
regions 47B-49B at the axis 32 are parallel to each other. By turning the 
knobs 166 for adjusting the screws 163-164, the respective tangents may be 
made to coincide as shown in the diagrammatic view of FIG. 9. 
Alternatively, the regions 47B-49B may be displaced relative to each other 
so as to eliminate the stepped appearance and providing a continuous 
surface for the entire array 28B. 
Referring now to FIG. 11, there is seen a diagrammatic view similar to that 
of FIG. 9, FIG. 11 showing dimensions of the array 28D of FIG. 8 in terms 
of wavelengths, the diameters also being seen in centimeters. The 
displacements between the regions of the array are shown as 0.12 
wavelengths in the axial direction between the central region and the 
inner annular region, and a distance of 0.16 wavelengths in the axial 
direction between the inner and outer annular regions. The aperture 
diameters are shown respectively as 13 wavelengths, 27 wavelengths and 40 
wavelengths for the three regions of the array. The depth of the radiating 
surface of the array as measured along the axis is 0.8 wavelengths. For 
ease of mathematical analysis, it is more convenient to describe the 
curved line array 28D of FIG. 8 than the two dimensional bowl-shaped 
arrays of FIGS. 4 and 6. Accordingly, in the ensuing FIGS. 12-14, a curved 
line array having the dimensions outlined in FIG. 11 is to be utilized. 
Referring now to FIGS. 12-14, there is presented a set of graphs showing 
patterns of the intensity of radiation at locations both on the axis and 
off the axis of a curved line array 28D of FIG. 8 having the dimensions 
shown in FIG. 11. These graphs closely approximate the radiation patterns 
for a bowl-shaped array such as that of FIGS. 4 and 6 wherein the 
dimensions in a longitudinal axial plane are those portrayed in FIG. 11. 
The focal points are located at distances of 60 mm, 120 mm and 180 mm in 
front of the array, these being the same locations as was described 
previously with reference to FIG. 1. In developing the graphs of the FIGS. 
12-14, it is assumed that the central region producing the group of rays A 
is activated from 0 to 90 mm distance, that the central region and the 
inner annular region for the groups of rays A and B are activated for 
distances in the range of 90 to 150 mm, and that all three regions for 
providing the groups of rays A, B and C are energized over the range of 
distances 150 mm to 200 mm. It is seen that the radiation pattern can be 
brought to a focus of intermediate acuity over the aforementioned range of 
distances. In particular, it is noted that, with reference to the fourth 
graph of FIG. 12, the size of the focus is generally less than one-half 
centimeter throughout the range of 20 centimeters. If the array had only a 
single curved region, rather than the three regions outlined in FIG. 11, 
then the focal spot would have increased to 2 centimeters at some points 
within the 20 centimeter range. The first graph of FIG. 12 shows the power 
per unit area (or intensity) in decibels along the axis of the array while 
the second graph shows the intensity in decibels of the first sidelobe of 
the radiation pattern. The third graph shows the beam width as measured at 
the first sidelobe of the radiation pattern while the fourth graph, as 
already noted, gives the width of the focal spot. 
In the description of the array of FIG. 7, it was shown that the axis of 
the radiation pattern can be scanned relative to the axis of the array. 
Accordingly, in FIG. 13 there is presented a set of graphs which 
correspond to the four graphs of FIG. 12, the graphs of FIG. 13 providing 
the intensity on the axis of the beam, the intensity on the first 
sidelobe, the width at the first sidelobe and the width of the focal size 
for a radiation pattern which has been steered 20.degree. off of the array 
axis. FIG. 14 portarys the foregoing four relationships for the case of a 
radiation pattern, or beam, which has been steered at an angle of 
30.degree. relative to the array axis. The focus retains its acuity and 
substantial uniformity of size for beam steering angles less than 
25.degree.. 
As was noted hereinabove, the graphs of the FIGS. 12-14 were developed for 
the situation wherein the tangents to the curves of FIGS. 9 and 11 
coincide at the axis 32. However, by altering the positions of the arcs, 
as by the mechanism described in FIG. 10, the size of the focus can be 
optimized. 
It is understood that the above-described embodiments of the invention are 
illustrative only and that modifications thereof may occur to those 
skilled in the art. Accordingly, it is desired that this invention is not 
to be limited to the embodiments disclosed herein but is to be limited 
only as defined by the appended claims.