Page 51 - Radar Technology Encyclopedia

aperture illumination approximation, four-thirds earth radius 41

ter in the y-z (azimuth) plane. A(z) is a complex function, hav- While the physical shape of a reflector or lens antenna
ing both amplitude and phase: may be rectangular, the aperture distribution (illumination)
A(z) = |A(z)| exp jY(z) function produced by a feed horn generally has an elliptical
where |A(z)| = illumination amplitude and Y(z) = illumination shape, leading to beamwidths and sidelobe levels that are bet-
phase. At an angle f, the contributions from a particular point ter predicted as resulting from an elliptical aperture. DKB
on the aperture will be advanced or retarded in phase by 2p(z/ Ref.: Johnson (1993), p. 2.19.
l)sinf radians. Each of these contributions is weighted by the
A synthetic aperture is created by taking advantage of the
factor A(z). The field intensity is the integral of these individ-
motion of a radar platform to extend the effective antenna
ual contributions across the face of the aperture.
aperture beyond the limits of its actual physical dimensions.
For a given field intensity pattern, E(f), the aperture illu-
In a side-looking synthetic aperture radar (SAR), the effective
mination can be found from
beamwidth of the radar is no longer described by conven-
¥ tional (real) antenna relationship q = K l/D, where the
1 æ 2pz ö 3 q
Az () --- ò E f() exp – j --------- sin f dsin f beamwidth constant K » 1 depends on aperture weighting,
=
q
l è l ø
e
– ¥ but by q = K ¢l/L , where L is the effective length of the
e
s
q
which may be used as the basis for synthesizing an antenna aperture and K ¢ » 0.5. Narrowing of the beamwidth in a syn-
q
pattern, or finding the aperture illumination that yields the thetic aperture radar is subject to certain fundamental con-
desired antenna pattern E(f). straints: (1) the length L can be no longer than the width of
e
Maximum antenna gain and minimum beamwidth are the region illuminated by the real aperture: L £ Rq , and (2)
3
e
realized with a uniform aperture illumination; i.e., one that is L £ (Rl) 1/2 . The second limitation applies to an unfocused
e
constant over the aperture and zero everywhere else. Such SAR, where the aperture size must be such that the phase
illumination will lead to an antenna pattern of the (sin x)/x front can be considered a plane wave. This limitation can be
form, with the intensity of the first sidelobe 13.3 dB below removed in a focused SAR by compensating for the curvature
peak gain. There exists a large variety of useful illumination of the spherical wavefront (i.e., applying a phase correction at
functions, and low sidelobes can be obtained by using func- each “element” of the synthetic array). See RADAR, syn-
tions such as a cosine or a Taylor function. Antennas with the thetic aperture; ANTENNA, synthetic aperture. PCH
lowest sidelobes are those with illumination functions for Ref.: Skolnik (1980), Ch. 7; Skolnik (1990), Ch. 6
which the amplitude tapers to a small value at the aperture
aperture tapering (see aperture illumination).
edges. Lower sidelobes are produced with greater amplitude
tapering, but at the expense of a wider mainbeam width and APPROXIMATION
lower mainbeam gain. Controlling the antenna pattern in this
detection probability approximation (see DETECTION
way is referred to as aperture tapering. A table describing
probability).
many of the functions commonly used, and listing the side-
lobe levels, beamwidth factors, and efficiencies, is given in The flat-earth approximation is applicable to very-short-
the article on WEIGHTING. Some typical illumination range targets in height finding, giving a sufficiently good esti-
functions are given in Table W3. (see also PATTERN, mate of target height as
antenna). PCH, SAL
h = h + Rsin q
Ref.: Skolnik (1990), p. 7.37. t r t
where h is the radar antenna height, R is the measured target
aperture illumination efficiency (see antenna directivity). a
range, q is the measured or estimated target elevation angle,
t
aperture matching (see ARRAY aperture matching). and h is the estimated target height. SAL
t
A passive aperture is one that focuses energy received from Ref.: Skolnik (1990), p. 20.14.
a true source outside the antenna (as opposed to an active The four-thirds earth radius approximation expresses the
aperture). refractive effects of the troposphere in terms of straight ray
paths over a spherical earth whose radius is ka, where k = 4/3
A rectangular aperture consists of rows and columns of
6
and a = 6.5 ´ 10 is the true radius of the earth (see ATMO-
radiating elements with an aperture illumination defined
SPHERE, refraction). The refractive index implied by this
along those coordinates. The beamwidth of a uniformly illu-
model varies linearly in the lower atmosphere:
minated rectangular aperture of width w is q = 0.886l/w, and
3
the sidelobe level is -13.3 dB. In many cases, the illumination
functions in the x-and y-coordinates are separable: nh () n –= 0 k h
1
=
gx y ,( ) gx () gy ()
where n » 1.000313 is the refractive index of the atmosphere
0
In that case, the antenna patterns in each coordinate may be - 8
at the surface and k » 4 ´ 10 per meter is the assumed gra-
1
calculated separately, each being the Fourier transform of the
dient of refractive index with respect to height, h. In general,
corresponding illumination function.