U.S. patent number 3,877,012 [Application Number 05/349,334] was granted by the patent office on 1975-04-08 for planar phased array fan beam scanning system.
This patent grant is currently assigned to General Electric Company. Invention is credited to Everett A. Nelson.
United States Patent |
3,877,012 |
Nelson |
April 8, 1975 |
PLANAR PHASED ARRAY FAN BEAM SCANNING SYSTEM
Abstract
Array element phase commands used to scan the beam of a planar
phased array are conventionally obtained by adding to the beam
shaping phases, phases obtained by sampling a linear (planar)
function of position on the array surface. When this technique is
applied to phase shaped fan beams, the beam acquires an
increasingly curled or warped shape as the scan angle is increased.
To offset this tendency, the scanning phase commands are obtained
by sampling a function which becomes increasingly nonlinear
(warped) as scan angle is increased.
Inventors: |
Nelson; Everett A. (Whitesboro,
NY) |
Assignee: |
General Electric Company
(Utica, NY)
|
Family
ID: |
23371940 |
Appl.
No.: |
05/349,334 |
Filed: |
April 9, 1973 |
Current U.S.
Class: |
342/371;
342/377 |
Current CPC
Class: |
H01Q
3/34 (20130101) |
Current International
Class: |
H01Q
3/30 (20060101); H01Q 3/34 (20060101); H01q
003/26 () |
Field of
Search: |
;343/1SA |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Tubbesing; T. H.
Claims
What is claimed as new and desired to be secured by Letters Patent
is:
1. In a beam steering computer for connection between an array
control computer and a logic manifold in a phased array radar
system, the combination comprising:
a first function generator connected to the array control computer
for generating a first signal indicative of a scanning function for
producing a selected shape beam to comprise a term in a phase
command;
a second function generator controlled by the array control
computer for producing a second signal indicataive of
.sqroot.k.sup.2 -[.gamma.'(x.sub.n)+ k sin .phi..sub.o].sup.2 where
.gamma.' is the derivative of the scanning function, k is
2.pi./.lambda. , .lambda. is the wavelength of the phased array
radar system output, x.sub.n is the x plane location of a phased
array element, x axis being vertically disposed and .phi..sub.o is
a value of aximuth angle;
horizontal and vertical sweep command generators constructed and
arranged to produce horizontal and vertical sweep phase signals;
and
signal integration means for combining said first signal with said
vertical sweep signal and said second signal with said horizontal
sweep signal and for passing said combined signals as a phasing
command to said logic manifold whereby a planar, vertically
disposed phased array beam is generated and scanned over an azimuth
range without distortion of said planar configuration.
Description
BACKGROUND OF THE INVENTION
This invention relates to phased array technology radio wave
propagation and more particularly to directive scanning of a phased
array beam.
A planar phased array consists of a plurality of array elements,
the radiation from which adds and cancels to provide a beam. The
beam scanned by the phased array is determined by the phase
commands provided to each element. The present invention is
particularly applicable to planar phased arrays having large
apertures in terms of radiated wave length. Fan beam scanning is
used, for example, in airborne radar for ground mapping. While the
present invention is discussed in many aspects in terms of fan beam
scanning, it should be realized that this is only by way of
exemplification, and the present invention is also applicable, for
example, to pencil beam scanning and other forms of shaped beam
scanning in accordance with the teachings of the present
invention.
In conventional prior systems, a linear function has been utilized
for scanning a fan beam. The linear function is sampled, and added
to the phase command for each array element. While the ideal fan
beam would have a generally planar three dimensional shape, the fan
beam of a conventionally scanned planar phased array will in
general have a conical shape. Consequently, for a ground mapping
beam scanned in the conventional way, the intersection of the beam
with the ground is a hyperbolic arc, rather than the desired
straight line. The intersection only approaches a straight line
asymptotically at longer ranges. Deviation of the hyperbolic arc
from the straight line is greater at short ranges, and increases
rapidly with scan angle. This effect is commonly known as beam
curling. The result of beam curling is gain reduction and
directional error. The analogy may be drawn of an operator looking
at a radar display of a curled beam and the person looking at an
object at the bottom of the swimming pool. To both, the object from
which returns are received are at a place other than where it
appears to be. At moderate to large scan angles, the short range
portion of the cathode ray tube ground map display of returns from
a conventionally scanned planar phased array will be both distorted
and washed out.
SUMMARY OF THE INVENTION
It is therefore an object of the present invention to provide a
planar phased array scanning system in which beam curling is
minimized.
It is also an object of the present invention to scan a planar
phased array by sampling of a warped function rather than a linear
function.
It is another object of the present invention to provide a method
and means for scanning a planar phased array to provide a fan beam
that is more nearly planar rather than conical in shape, whereby a
beam directed from the air toward the ground has an intersection
with the ground that is a straight line.
It is yet another object of the present invention to provide a
method and means for scanning a planar phased array whereby gain
variation with scan angle is minimized.
It is a general object of the present invention to provide a method
and means for scanning a planar phased array in which distortion
and directional error is minimized.
Briefly stated, in accordance with the present invention, there is
provided a means of scanning a planar phased array beam in which
scanning phases are obtained by sampling a warped function. The
warped function is determined from the derivative of the phase
function used to obtain the desired beam shape. The amount of
warping is increased as scan angle increases in order to compensate
for the increasing tendency of the scanned beam to curl.
BRIEF DESCRIPTION OF THE DRAWINGS
The means by which the foregoing objects and features of novelty
are achieved are pointed out with particularity in the claims
forming the concluding portion of the specification. The invention,
both as to its organization and manner of operation, may be further
understood by reference to the following description taken in
connection with the following drawings.
Of the drawings:
FIG. 1 is illustrative of a sphere in the far field of the aperture
of a planar phased array illustrating various forms of antenna
beams;
FIGS. 2 and 3 are geometrical illustrations useful in understanding
the theory of operation of the present invention;
FIG. 4 is a block diagramatic representation of one means for
implementing the present invention; and
FIGS. 5 and 6 are charts useful in understanding the operation of
the present invention.
DESCRIPTION OF THE PREFERRED EMBODIMENT
Referring now to FIG. 1, there is illustrated a sphere in the far
field of the aperture of a planar phased array at an origin O. The
far field is defined by stating that lines from any point on the
aperture to a point in the far field are substantially parallel.
The x axis is vertical, and the y and z axes are horizontal. The
origin O may be viewed as the position of a planar phased array in
an aircraft having a heading along the z axis and flying in the y-z
plane. In this conceptualization, the ground may be represented as
a y'-z' plane parallel to the y-z plane.
A fan beam is a beam having a major lobe with a highly elliptical
cross section. For ground mapping purposes, the major diameter of
the ellipse is large with respect to the minor diameter. For
purposes of the present exemplification, the fan beam is described
in terms of the major diameter. Due to resolution of a radar system
and conventional shaping of a fan beam, it is proper to approximate
the fan beam as having a cross section being a line. In FIG. 1, the
curve 1 represents the intersection of an unscanned fan beam with
the far field sphere. All lines drawn to the beam lie in a plane,
here the x-z plane. The projection of the curve 1 on the y'-z'
plane lies along the z' axis. It is desired to scan the beam
through an azimuth angle .theta. and maintain the same beam shape,
namely a scanned beam 2 intersecting the far field sphere along a
great circle and having an intersection 3 with the y'-z' plane
which is a straight line. In this manner, no directional error
appears in the return wave. This form of accurate scanning is
achieved with mechanical scanning since the entire antenna rotates.
However, to scan a phased array, phase commands must be provided to
provide a resultant beam which is scanned while the antenna itself
does not rotate about the x axis.
An explanation of the relation of the mathematical function
utilized to the beam produced and of beam steering by element
phasing is found in Allen, J. L. "Array Antennas: New Applications
For An Old Technique," I.E.E. Spectrum, Nov. 1964, pp 115-130. The
conventional form of phased array scanning by sampling a linear
function produces a scanned beam 6. The beam 2 comprises an arc
which at all portions is of constant azimuth for a given angle
.theta.. However, the conventionally scanned beam 6 for a given
angle .theta. is not of constant azimuth, but is at a constant
angle to the y axis. All lines drawn to the curve 6 from the origin
O form the side of the cone. Therefore, the beam 6 is said to be
curled. The intersection 7 of the beam 6 with the y'-z' plane is a
hyperbolic arc. Deviation of intersection 7 from intersection 3 is
indicative of directional error of the beam 6. The directional
error is at its greatest value at short ranges from the x axis and
also increases rapidly with increasing values of .theta..
In order to illustrate this problem, the equations by which
conventional scanning is expressed are examined. It has been the
convention to assume that the phase scanning of the beam of a
planar aperture of an arry implies the superposition on the
aperture of a phase distribution that is a linear function of the
position on the aperture. It is an inherent characteristic of such
a phase scanned beam to tend to retain its shape in cosine space
independent of scan angle. This leads to the above described
distortion, as, for example, of a fan-shaped beam known in the art
as a csc.sup.2 .phi.cos.phi. beam frequency used for ground mapping
(where -.phi. is the dip angle, or angle below the horizontal
plane). This examination is made with reference to FIG. 2 in which
FIG. 2a is a spherical plot illustrating direction angles and the
radial unit vector u.sub.r ; FIG. 2b is a plot of cos .alpha..sub.x
vs. cos .alpha..sub.y (defined below) illustrating cosine space;
and FIG. 2c is a plot of a sphere in far field of the aperture,
similar to FIG. 1.
Consider an array of N identical element radiators in the x-y plane
(FIG. 2a). The array is large enough so that edge effects may be
assumed negligible. Let the location of an element n be given by
.rho..sub.n = u.sub.x x.sub.n +u.sub.y y.sub.n (1)
and let the relative current at a reference point be A.sub.n
=.vertline.A.sub.n.vertline.e.sup.- .sup.j.psi. , where u is a unit
vector and .psi. is a phase function. Then, the field intensity in
the radial direction u.sub.r is given by ##SPC1##
where k=2 .pi. and f(u.sub.r) is the field intensity of a single
element in the array environment when A.sub.n =1 for that element.
The summation in equation (2) is called the array factor. In fact,
it is the radiation pattern of an array of isotropic elements. When
f(u.sub.r) is very broad (as it almost always is) the shape of the
radiation pattern of a large aperture is usually determined
primarily by the array factor. The subscript o is used below to
indicate a direction or angle in which a beam is steered.
F(u.sub.r) is a maximum when the contribution of all the elements
add in phase. Therefore, let
.psi. .sub.n =k.rho..sub.n.sup.. u.sub.ro (3)
Equation (2) can then be written ##SPC2##
and the shape of F is that of the familiar pencil beam with its
peak scanned to the direction u.sub.ro.
In order to demonstrate that this expression yields a beam which is
warped at various scan angles, let .alpha..sub.x .alpha..sub.y, and
.alpha..sub.z be the direction angles of u.sub.r to the x, y and z
axis respectively. (See FIG. 2a). Then,
u.sub.r =u.sub.x cos .alpha..sub.x + u.sub.y cos .alpha..sub.y +
u.sub.z cos .alpha..sub.z (5)
From equation (1)
.rho..sub.n.sup.. (u.sub.r -u.sub.ro) = x.sub.n (cos .alpha..sub.x
- cos .alpha..sub.xo ) + y.sub.n (cos .alpha..sub.y - cos
.alpha..sub.yo) (6)
Therefore, the array factor F.sub.a of equation (4) can be written,
##SPC3##
It should be noted that, in the space defined by FIG. 2b, the shape
of F.sub.a is independant of (cos .alpha..sub.xo, cos
.alpha..sub.yo). This property of planar apertures is not
restricted to pencil beams.
Let .gamma. (x) be a non linear function of x such that when
.psi. .sub.n = .gamma. (x.sub.n) (8)
ground map beam is formed in the x-z plane. It is assumed that the
desired shaped beam extends from 5.degree. to 45.degree. below the
y-z (horizontal) plane and has all of its power in a region very
close to the x-z plane. This corresponds to .alpha..sub.x =
95.degree. and .alpha..sub.y = 135.degree.. The intersection of the
beam with a sphere in the far field of the aperture is indicated by
the heavy black arc in FIG. 2c.
Conventionally, such a beam has been scanned by superimposing on
the aperture the linear phase function k.rho..sub.n.sup.. u.sub.ro
so that the element phase commands are now obtained from
.psi. .sub.n = k .rho. .sub.n .sup.. u.sub.ro + .gamma. (x.sub.n)
(9)
The array factor then becomes ##SPC4##
When beam scanning of a shaped beam is defined in this manner, it
can be seen from equation (12) that the shape of F is still
independent of (cos.sub.xo,cos.sub.yo) in cosine space (FIG. 2b).
This means the beam will retain its shape on constant direction
cosine arc. At moderate to large scan angles (the definition in
numerical terms of "moderate to large" depending on the particular
application), this retention of shape constitutes beam warping.
Restrict u.sub.ro to the y-z plane. Then
.psi..sub.n = ky.sub.n cos .alpha..sub.yo +.gamma. (x.sub.n)
(11)
and equation (10) becomes ##SPC5##
The present invention comprises means for providing a non-linear
phasing function based on the derivative of the conventional beam
function. In this manner, the dimensional error due to change in
slope as the intersection 7 of FIG. 1 approaches the x axis is
minimized. The theory of operation of the present invention is set
forth below in order to demonstrate the manner in which beam
curling is substantially eliminated. FIG. 3 is utilized in this
explanation. FIG. 3a is a representation or a circular, planar
array aperture; FIG. 3b is a plot of a phase function utilized and
FIG. 3c is a plot of a sphere in the far field of an aperture,
similar to FIG. 1.
If the intersection with ground (i.e., the y'-z' plane of FIG. 1)
of a ground map beam formed by a planar phased array is to be a
straight line through the x axis, the intersection of the beam with
the far field sphere must be an arc of constant .theta.. A scanning
procedure that approximates this desired result will be
developed.
The pattern of a large (in wave lengths) planar array can be
approximated by that of a large continuous distribution of
electromagnetic sources. Therefore, since it is also more
convenient to do so, the phasing function for scanning a ground map
beam will first be developed for a continuous aperture. Then the
element phase commands, .psi..sub.n , as given by equation (3) or
equation (9), can be approximated by a continuous function of
aperture position. It will be designated .psi.(.rho.) .
Thus, for the continuous aperture, equation (3) can be replaced
by
.psi. (.rho.) = k .rho. .sup.. u.sub.ro (13)
where .rho.represents the location of any point on the aperture,
rather than the discrete element locations. Adding a constant to
the right side of equation (13) will have no effect on the beam.
This will be done for later convenience and equation (13) will be
rewritten as follows:
.psi. (.rho.) = k.rho. .sup.. u.sub.ro + B (14)
the circular aperture illustrated in FIG. 3a will be used as an
example. Let .gamma. (x) be the function required to obtain the
desired unscanned ground map beam in the x-z plane. To scan this
beam in the conventional manner, equation (9) can be rewritten for
application to a continuous aperture as
.psi. (.rho.) = .gamma.(x) + k .rho..sup.. u.sub.ro (15)
or, using the notation of equations (2) and (5)
(.rho.) = .gamma.(x) + kx cos .alpha..sub.xo + ky cos
.alpha..sub.yo (16)
For the moment, let cos .alpha..sub.yo = 0 (.alpha..sub.yo =
90.degree.). Thus, the beam is scanned in the x-z plane, only. The
intersection of this beam with the far field sphere is indicated by
the dark arc in the x-z plane of the FIG. 3c. Now, suppose
.alpha..sub.xo is held constant and the beam is scanned away from
the x-z plane. The intersection of the beam with the far field
sphere is now indicated by the dark constant .alpha..sub.yo arc of
FIG. 3c. The dotted arc represents the desired beam intersection
which is a constant .theta. arc (See FIG. 1).
Divide the aperture of FIG. 3a into incremental strips such as the
one shown at x=x.sub.i. On each incremental strip, approximate the
x dependent terms of equation (16) by a straight line function.
.beta..sub.i (x) = m.sub.i x+b.sub.i (17)
Replacing .gamma. (x) + kx cos .alpha..sub.xo in equation (16) by
.beta..sub.i (x), the phase function for strip i becomes
.psi..sub.i (.rho.) = .beta..sub.i (x) + ky cos .alpha..sub.yo
(18)
which is a linear function of position on the strip.
Now, suppose that the power radiated by each incremental strip of
the aperture is directed to a given segment of the radiation
pattern on a one for one basis. For instance, suppose that all the
power radiating from strip i passes through the beam cross section
segment indicated by .DELTA..alpha..sub.xi in FIG. 3c. Holding
.alpha..sub.xo constant as the beam is scanned away from the plane,
the segment .DELTA..alpha..sub.xi moves along a constant
.alpha..sub.x arc. However, if each beam strip can be independently
phased, then each beam segment can be placed on the desired arc,
instead of the constant .alpha..sub.y arc. Thus, the desired beam
intersection could be obtained. Since .psi..sub.i (.rho.) is
separable in x and y, each beam segment can be steered to the
constant .theta. arc, .theta.=.theta..sub.o, if the proper value of
.alpha..sub.yo or .alpha..sub.yi is used in equation (18) for each
aperture strip. That is each strip must be scanned by applying the
equation.
.psi..sub.i (.rho.) = .beta..sub.i (x) + ky cos .alpha..sub.yi
(19)
Considering FIGS. 1 and 2a it can be seen that
cos .alpha..sub.yi = cos .phi..sub.i sin .theta..sub.o sin
.phi..sub.i = cos .alpha..sub.xi (20)
Therefore, it is necessary to find .alpha..sub.xi for each strip.
Each strip can be scanned by application of equation (14). Let
.psi..sub.i (.rho.) = kx cos .alpha..sub.xi + ky cos .alpha..sub.yi
+ B (21
from equation (19) and (21) it can be seen that
.beta..sub.i (x) = kx cos .alpha..sub.xi + B
Comparing equations (17) and (22)
cos .alpha..sub.xi = 1/k m.sub.i (23)
Therefore,
cos .phi..sub.i = sin .alpha..sub.xi = .sqroot. k.sup.2 -
m.sub.i.sup.2 (24)
Substituting equations (20) and (24) into equation (19) yields
.psi..sub.i (.rho.) = .beta..sub.i (x) + y sin .theta..sub.o
.sqroot.k.sup.2 - m.sub.i.sup.2 (25)
of course, in the limit as .DELTA. x.sub.i .fwdarw. 0
m.sub.i = d/dx .beta..sub.i (x) (26)
When x = x.sub.1,
.beta..sub.i (x) = .gamma.(x) + kx cos .alpha..sub.xo = .gamma.(x)
+ kx sin .phi..sub.o
and
m.sub.i = .gamma.' (x) + k sin .phi..sub.o (28)
where .gamma.'(x) =d/dx .gamma.(x): Thus, in the limit equation
(25) can be rewritten
.psi.(.rho.) = .gamma.(x) +kx sin .phi..sub.o +y sin .theta..sub.d
.sqroot.k.sup.2 -[.gamma.'(x) +k sin .phi..sub.o].sup.2 (29)
This is the phase function desired to minimize the curl of a phase
scanned fan beam. To apply equation (29) to a planar array, simply
sample the function of each element position thus.
.psi..sub.n (.rho..sub.n)= .gamma.(x.sub.n) +kx.sub.n sin
.phi..sub.o +y.sub.n sin .phi..sub.o .sqroot. K.sup.2 -[.gamma.'
(x.sub.n)+k sin .theta..sub.o].sup.2 (30)
In order to compare the phase function of equation (30) to the
conventional phase function equation (9) may be rewritten in terms
of functions of azimuth and elevation as follows:
.psi..sub.n = .gamma.(x.sub.n)+kx.sub.n sin .phi..sub.o +ky.sub.n
sin .theta..sub.o cos .phi..sub.o (31)
Utilizing the relationship cos.sup.2 .phi.=1- sin.sup.2 .phi. ,
equation (31) may be rewritten as follows:
.psi..sub.n =.gamma.(x.sub.n)+ kx.sub.n sin .phi..sub.o +ky.sub.n
sin .theta..sub.o .sqroot.1-sin.sup.2 .phi..sub.o (32)
By comparing the radicals of equations (32) and (30), it is seen
that the apparatus of the present invention provides a correction
to the scanning function dependent upon .gamma.', the slope
thereof. Consequently, the apparatus of the present invention
operates to provide improved scanning of the radar beam.
Referring now to FIG. 4 there is illustrated in block diagrammatic
form a phased array system constructed in accordance with the
present invention. An array control computer 20 which is well-known
in prior systems provides beam direction angles based on beam
direction requirements and aircraft attitude to a beam steering
computer 21 coupled thereto. The beam steering computer corresponds
to the prior art computer providing the linear phasing commands
described above. Outputs from the beam steering computer 21 are
provided to a logic manifold 23, which provides phase commands to
phase shift drivers 24. The logic manifold 23 comprises prior art
interface circuitry between the beam steering computer 21 and the
phase shifter drivers 24 which provide the phase commands to the
antenna elements 25. Radio frequency energy is provided to the
antenna elements 25 at an input port 26 from a well-known radio
frequency source (not shown). One form of array may include two
thousand antenna elements 25. Only four are illustrated for
simplicity.
The array control computer 20 provides signals comprising digital
words representing trigonometric functions of the beam direction
angles which are characterized in the present exemplification as
being provided at output terminals 30-36. Focusing phase command
digital words are provided at an output terminal 32, and commands
for enabling selected elements 25 are provided at an output
terminal 33. These commands are all provided in prior systems of
the type described.
The beam steering computer 21 may take many forms in accordance
with the present invention. In the present exemplification, the
beam steering computer 21 is illustrated as including a pencil beam
phase command generator 40 which is included in prior beam steering
computers of the type described. A ganged electronic switch 41 is
provided and connected such that in one position the output
terminal 30 is connected to the pencil beam phase command generator
40 and in its other position, the output terminals 31, 34, 35 and
36 are connected to a plurality of other generators 42 through 45.
In other words, in operation, for providing a pencil beam, a prior
art method of scanning is used and for generating a fan beam, the
present invention is utilized. Therefore, in FIG. 4, the switch 41
is illustrated in its second position. When the switch 41 is in its
first position, the digital words representing trigonometric
functions of the beam direction angles are coupled to the pencil
beam phase command generator 40 which provides an output to an
adder 48. Focusing phase commands are provided to the adder 48 from
the focusing phase command generator 49, which has an input coupled
to the output terminal 32. Pencil beam phase command words are
coupled to the logic manifold 24 from the adder 48.
In accordance with the present invention, the switch 41 is coupled
in its second position, and the output terminal 36 is coupled to an
azimuth scan command generator 42, terminal 34 to a non-linear
function generator 43, terminal 35 to an elevation scan generator
44, and terminal 31 to a linear scan generator 45. The azimuth scan
generator 42 provides the digital word indicative of y.sub.n sin
.theta..sub.o for determining the relative phase of one array
element 25 to another in a horizontal direction in order to achieve
azimuth scanning. The non-linear function generator 43 provides a
digital word representing .sqroot.k.sup.2 -[.gamma.'(x.sub.n)+k sin
.theta..sub.o].sup.2 which is indicative of the derivative of the
fan beam command function in order to compensate for beam curling
in accordance with the above-described derivation. The outputs of
the generators 42 and 43 are provided a multiplier 60. The
generator 44 provides a linear command in the form of a digital
word representing kx.sub.n sin .phi..sub.o determining relative
phase of one array element 25 to the next in a vertical direction
for determining the angle of depression of the fan beam. The linear
scan generator 45 provides the basic fan beam function
.gamma.(x.sub.n) in accordance with the teachings of the
above-described publication. Outputs of the generators 44 and 45
are coupled to an adder 61. In order to provide the command signal,
the outputs of the multiplier 60 and adder 61 are coupled to an
adder 62 which provides an input to an adder 63 for combining the
steering command with a focusing command coupled to the adder 63
from the focusing phase command generator 49. The output of the
adder 63 is connected to the logic manifold 24, whereby phase
commands in accordance with the present invention are coupled to
the array elements 25.
In operation, phase commands are provided to the elements 25 in
accordance with the above-described derivation. Each of the
generators 42-45 is constructed in a well-known manner and it may
utilize handbook circuitry. Otherh circuitry for providing the
desired phase commands will suggest itself to those skilled in the
art.
In operation, phase commands are provided to the array elements 25
in accordance with the above derivation. FIGS. 5a and 5b are
respectively illustrative of typical prior art and present
invention plots of beam amplitude versus azimuth angle. In FIGS. 5a
and 5b, the solid line curves represent cross-sections of the beam
scanned at different azimuth angles, and for one elevation angle,
dotted lines connect corresponding corss-sections of a beam scanned
to different azimuth angles. FIG. 5a shows the ground map beam in
the x-z plane (FIG. 1) and in five scanned positions. For each beam
position, five cross-sections of the ground map beam are shown.
Ideally the cross-section peaks should line up for each beam
azimuth position. For the conventionally scanned case of FIG. 5a,
every beam position shows significant beam skew, while in FIG. 5b,
beam skew becomes severe only at the heel (i.e., for larger values
of .phi.) of the beam and only for the extreme angle. Further, gain
loss at the heel of the beam in FIG. 5b is almost negligible, while
comparatively large in FIG. 5a, as indicated by the slope of the
dotted lines drawn in FIGS. 5a and 5b.
FIG. 6 is a plot of the intersection with the ground of beams of
arrays scanned conventionally and in accordance with the present
invention, for an aircraft at a given altitude. The y and z axes of
FIG. 6 correspond to those of FIG. 1. The prior scan is illustrated
in dashed lines while the scan of the present invention is
illustrated in solid lines. For the exemplification of FIG. 6, the
aircraft is at an altitude of eight miles. Deviation of the beam
from a straight line going to the origin of the plot of FIG. 6 is
minimized in accordance with the present invention. Consequently,
positional distortion is minimized, and the return beam produced in
accordance with the present invention may be used in conjunction
with a conventional radar display rather than a display requiring
compensation for a positional distortion.
What is thus provided according to the present invention are a
method and apparatus for scanning a phased array to produce a
unidirectional beam of substantially constant azimuth by sampling a
non-linear function for the phase command to compensate for beam
curling which is produced by sampling a linear phase command.
* * * * *