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Sheet
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SAR Synthetic Aperture Radar
Why use microwave frequencies?
- atmospheric attenuation is low at microwave frequencies,particularly 1-10GHz,apart from
resonances due to oxygen and water molecules.
- microwave signals will penetrate cloud and fog,in contrast to visible radiation.
- microwaves can continuously monitor ploar regions and tropical forests that are often in
darkness or covered in clouds.
- SAR is to be used to monitor natural disasters -floods,forest fires,earthquakes etc that are
often accompanied by poor optical visibility.
- fairly narrow beams can be obtained with resonably sized antennas to give acceptable
resolution.
Features of SAR
- a large effective antenna aperture is obtained by mounting the antenna on a moving
platform-an aircraft or a satellite.
- resolutions of down to 10m can be obtained,so that images of the earth’s surface can be
generated.
- complex signal processing is required to extract images,so that real-time operation makes
heavy demands on computer processing power.
- very large amounts of data are generated - as can be seen if say 10 items of information are
generated for each 10m2 of the earth’s surface.
[Exercise :Calculate the number if items of data,given that the earth’s radius is 6000km].
- particularly using satellites,large areas of the earth’s surface can be observed in a short time
so that changes can be observed.
Conventional radar (fixed antenna) - resolution
- the radar detects objects that lie in the antenna beam by the echoes they produce.
- the range to the target is found from the time delay between the transmitted and returned
signal
R =
1
c. TR
2
- the range resolution is determined by the pulse duration τ .A 1uS pulse gives a range
resolution of 150m.
- Pulse Compression is used to improve the range resolution ,without the requirement for a
very short duration,high power pulses.a short pulse is generated to give a good range
resolution,but this is frequency modulated to give a longer,lower power pulse prior to
amplification and transmission.This is achieved using a dispersive filter.The received pulse is
compressed by passing it through a complementary dispersive filter so that it is effectively
shortened ,thereby achieving good range resolution.Range resolutions of about 10m can be
achieved,corresponding to an effective pulse duration of 70nS,
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- the angular resolution (or azimuthal resolution) of a conventional radar is determined by the
angular width of the main lobe of the antenna radiation pattern.This ,in turn,is determined by
the λ/D ratio for the antenna aperture.
- the linear resolution in the cross-range direction depends on the angular width of the
antenna beam and the range to the target area.
- for a typical satellite-borne SAR the slant range is about 900km.
- for SEASAT SAR
frequency = 1.3GHz
hence λ = 23cm.
The antenna length is 10.7m , giving a beamwidth of 23/1070 = 0.022 radians.
Thus, the ground resolution
= 0.022 x 900km = 19km
The conclusion is that the linear resolution in the range direction (about 10m using the pulse
compression) is acceptable,but the linear resolution in the cross-range (azimuthal) direction is
inadequate (19km).
The cross range resolution can be dramatically improved to about 10 using SAR which
comprises
- antenna mounted on an aircraft or satellite moving parallel to the earth’s surface
- sideways looking radar
- regular pulses emitted,data collected for each pulse
- data from all echoes from a given target area are combined to form an image of the area.
Platform movement
velocity v
Antenna
La
Lc
Angular beamwidth in acrosstrack(range) direction
‘Look’ angle (angle of
incidence)
ψ
Ground track vertically
below satellite,
along-track direction
(azimuth)
Slant range to target
Satellite
altitude
swathe
SAR Geometry
Radar footprint determined by antenna
dimensions
2
Across track
direction (range)
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Key parameters for Free-flying SAR satellite systems
Satellite
Seasat
ALMAZ
Agency/country
NASA/USA
USSR
Launch date
1978
1991
Altitude(km)
800
280
Frequency Band (GHz)
L(1.3)
S(3.0)
Polarisation
HH
HH
Incidence angle
23
30-60
(degrees)
Antenna Size (m x m)
10.7 x 2.2
15 x 1.5 (two)
Noise Equiv (dB)
-18
Swathe width (km)
100
25-50
Az resolution (m)/Looks 23/4
15/2
Range Bandwidth
19
Uncoded
(MHz)
Quantisation (bps)
Analog
3
3
E-ERS-1
ESA
1991
785
C(5.3)
VV
23
J-ERS-1
NASDA/Japan
1992
565
L(1.2)
HH
35
Radarsat
Canada
1995
792
C(5.3)
HH
20-50
10 x 1.0
-18
100
25/3
13.5
12 x 2.2
-20
75
30/4
15
15 x 1.6
-21
50-500
28/4
11.5,17.3,30
5
3
4
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SEASAT (1987)
altitude
‘look’ (incidence) angle
Antenna size - along track
- across track
frequency
swathe width
800km
23 degrees
10.7m
2.2m
1.3GHz(λ = 23cm)
100km
10.7m
2.2m
Satellite
movement
θ2
θ1
Along track
870km
23°
800km
Across track
Across-track resolution
Ground resolution
(conventional radar)
Swathe width
from this data:
slant range
beamwidth along track
beamwidth across track
870km
θ1 = 23/1070 = 0.022 radians
θ2 = 23/220 = 0.1 radians
from simple geometry swathe width = 870km x 0.1/cos23 = 95km
along track resolution on ground = along-track width of beam x slant range
= 0.022 x 870km = 19km
This is the resolution of a conventional radar which can only determine whether or not a target lies
within the beam.
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SAR Principle
- the across-track position of a target is determined by a conventional delay-time measurement.
- the along-track position is determined by the Doppler shift of the echo signal.
Pulse emitted
Along track speed v
θ1
φ
Vr = radial velocity of radar w.r.t to target = v.sinφ
Slant range R
targets
A
B
x
Along track
∆x
2v.sinφ ⎞
Change in radar frequency due to Doppler effect ∆f = ⎛⎜
⎟ fo = f D
⎝
c ⎠
- the angular positions - or along-range positions - of two targets within the beam can be
determined by the Doppler frequencies of their echo signals.
- the angular resolution or along-track resolution of the target is determined by the frequency
resolution that can be obtained for the Doppler frequencies.
2v.sinϕ ⎞
f D = ⎛⎜
⎟ fo
⎝
c ⎠
Now ϑ 1 is small (0.02 radians) & φ ≤
∴ sinφ ≈ φ ≈
x
R
1
ϑ1
2
2v x
and f D = ⎛⎜ ⎞⎟ ⎛⎜ ⎞⎟ fo
⎝ c ⎠⎝ R⎠
2v fo
∴ ∆f D = ⎛⎜ ⎞⎟ ⎛⎜ ⎞⎟ ∆x ... difference in Doppler frequency for two targets with separation ∆x
⎝ c ⎠⎝ R ⎠
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Resolution
The ground resolution in the along-track direction ∆x (min) corresponds to the minimum change in
Doppler frequency that can be measured , ∆fD (min).
c ⎛ R⎞
∆x (min) = ⎛⎜ ⎞⎟ ⎜ ⎟ ∆f D
⎝ 2v ⎠ ⎝ fo ⎠
↓
resolution
The minimum change ig f D that can be measured =
Tobs =
1
Tobs
Rϑ 1 R λ
antenna beamwidth measured on ground
= .
=
v La
satellite speed
v
∴ ∆f D (min) =
L a = length of antenna
1
v La
=
.
Tobs
R λ
c ⎛ R⎞ v ⎛L ⎞
∴ ∆x(min) = ⎛⎜ ⎞⎟ ⎜ ⎟ ⎛⎜ ⎞⎟ ⎜ a ⎟ =
⎝ 2v ⎠ ⎝ fo ⎠ ⎝ R ⎠ ⎝ λ ⎠
θ1
1
La ie from Seasat ∆x ≈ 5.4m
2
Tobs = (R. θ1)/v
R. θ1
Speed v
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Limits on SAR PRF (Pulse Repetition Frequency)
Limits on the PRF (equal to the reciprocal of the time interval between successive pulses)
arise because of the requirements of avoiding cross-track range ambiguity and along track
phase ambiguity.
S a t e llit e t r a v e ls p e r p e n d ic u la r
t o t h is p la n e
A & B a r e p o in t t a r g e t s a t
the sw athe ed g es
C ro ss-T r a c k r a n g e a m b ig u ity
R2
R1
C r o s s - t r a c k d ir e c t io n
A
B
S w a t h e w id t h
1
A
0 No pulses
here
1
3
2
τ (PRF)
A
B
2R2
c
2 R1
c
time
3
2
τ‘ (PRF)
Higher PRF
A
A
0
B
time
2R2
c
To avoid cross-track range ambiguity,signal from B must arrive earlier than that for A.ie
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B
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2 R2
⎛ 2R
⎞
< ⎜ 1 + τ ( PRF )⎟
⎝
⎠
c
c
( R2 − R1 ) <
1
c
c. τ ( PRF ) or ( R2 − R1 ) <
2
2( PRF)
Limits on PRF - along track phase ambiguity
v
Satellite path
θ/2
θ/2
Along track
direction
fD(min)
fD(max)
fo
As beam moves over target Doppler frequency changes from fD(max) to fD(min).
f D(max) = f D(min) =
ϑ =
λ
La
2v ϑ
. . fo
c 2
(ϑ is small)
L a = antenna length (along track)
Doppler frequency bandwidth =
2v λ
v
.
. fo =
c 2 La
La
Echo signal is sampled during pulses - sample rate = PRF
Sampling theorum: Sampling rate ≥ 2 f D(max) =
2v
∴ PRF ≥
La
ie minimum PRF ≡ 1 pulse each time antenna moves through
8
1
its length L a
2
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Limits on PRF
Along track resolution ∆x =
∴
La
2
PRF * ∆x ≥ 2v
ie PRF determines along - track resolution
∴Two conditions on the PRF are :
PRF ≤
c
to avoid range ambiguity
2(R2 - R1)
PRF ≥
2v
La
sampling theorem - to avoid phase ambiguity
From these results a suitable compromise must be reached between
- along track resolution
- swathe width
- antenna area
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Focussed SAR
To attain highest along-track resolution of La/2 the observation time Tobs = time taken for
beam to sweep across the target.But in this time the Doppler frequency changes from
+fD(max) to - fD(max).
The solution is to process the SAR data so that it focusses on each along-track target position
in turn.
Pulse emission positions
x
xo
Satellite path
∆R
Closest-approach
Ro range
Ro
Slant-plane Geometry
Target
Constant range line within
swathe
Two-way phase delay to antenna position x,relative to xo
2π
∆φ = - 2⎛⎜ ⎞⎟ ∆R
⎝ λ ⎠
Ro + ∆R =
∴ ∆R ≈
[
R 2o
+ (x − xo )
(x − xo )2
2 Ro
1
2 2
]
since x - x o <<R
To focus on target at xo apply phase corrections ∆φ to echos collected at each antenna
position & then add coherently all returns to find the energy reflected from xo.
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The change in phase with satellite position x for a target at closest approach xo is given by
⎧⎪ 4π x − x 2 ⎫⎪
o
f ( x ) = exp ⎨− j.
.
Differentiate phase term
⎬
(
⎪⎩
λ
)
2 Ro
⎪⎭
Phase term
∴ Instantaneous Doppler frequency fD as a function of the position of the satellite =
2(x - x o )
1 ∂
. .(phase) = λRo
2π ∂x
f = rate ofchange of phase θ = 2πft + φ ;
∂θ
= 2πf
∂t
∴f =
1 ∂θ
.
2π ∂t
To determine the scattering from the target position associated with xo we find the correlation
between this reference function for fD;over the range of positions for which data is collected
for xo,with the actual returns to the satellite at these satellite positions.
This must be done for all ranges Ro across the swathe and for each resolution cell along the
swathe.
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Applications of SAR
Studies of
- Ploar ice.
- Ocean waves.
- Surface/subsurface mapping.
- soil moisture.
- Forest ecology.
- Ship’s wakes
Each type of study dictates different aspects of the
(1) Experimental requirements width,
eg frequency,polarisation ,angle of
incidence,swathe resolution.
(2) System performance resolution
eg EIRP,dynamic range,data
rate,quantisation resolution.
(3) Platform design
eg altitude,launch date/time,mission
duration,orbit
Surface interactions of electromagnetic waves
Characteristics of reflected electromagnetic waves
Surface parameters
- ampltitude
relative permittivity
- phase
depends mainly on
roughness
polarisation
local slope
Surface scattering
at interface between two different media
Volume scattering
by particle distribution in a non-homogenoeous medium.
Surface/subsurface scattering
If surface roughness << λ (radar wavelength)
Example
Libyan desert
- specular reflection i = r
normal refraction
- no vegetation,very smooth surface
1 -2 m of sand on bedrock.
Main dielectric interface is sand - bedrock
optical image shows sand surface.
Microwave image shows detailed map of ancient natural
drainage channels in the rock,beneath the sand.From
these the geological history of the region can be
understood.
Images may help to locate deep water sources in the
region.
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Bragg scattering
- slightly rough surfaces
rms height variation < λ/8
- main application is in the study of ocean waves
Bragg Equation = nλ = 2dsinθ
nλ/2
θ
θ
Ln
- for large angle of incidence the total scattering is a combination of Bragg scattering and
specular scattering.
- natural surface are represented as a series of facets upon which the small-scale surface
roughness is superimposed.
σo
Facet scattering
Bragg scattering
η
Backscatter curve for natural surfaces illustrating the two scattering
mechanisms:Facet scattering for steep incidence angles;Bragg
scattering for shallow incidence angle.
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Ocean waves
- Distinguish long wavelength ocean waves
- wavelength d is 10’s to 100’s of metres
- due to local wind conditions or distant storms
- wave speed is approximately equal to wind speed - infer wind speed
- monitor using ground HF radar
frequency 10 to 30MHz;
wavelength 30m to
10m,an ‘over-the-horizon’ radar that relies
on reflection of signals from the ionosphere.
- short wavelength waves - capillary waves
- wavelengths are ~ cm to 10’s of cm
- due to local wind conditions
- use SARs operating in the 1 to 10GHz frequency range.
- SAR gives wave direction ,wavelength and wave height information.
- information is used to develop ,ocean wave forcast models which are important for
weather forecasting and the prediction of changes in the global climate
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Geology
- Bragg scattering is used to intepret the scattering from sparsely vegetated rock terrains.
- the rock type and age can be inferred from the surface roughness.
Eg sedimentary rocks will be more weathered-and hence rough than igneous rocks older
rocks will be more weathered than rocks
sedimentary and igneous rocks can be distinguished to some extent by the brightness of the
scattering they give.
Study of Forest Canopies - Volume scattering
- due to ‘particle’ distribution in a non-homogenoeous medium.
- the penetration of radiation into a medium - and hence the extent to which volume scattering
is important - depends on the skin depth δ of the medium.
δ =
1
σ is the conductivity ofthe medium; f is the microwave frequency
π . µ. σ . f
- the radar frequency is important because it determines.
- the penetration of the signal into the region,and hence the volume sampled
- the resolution of the objects within the region ,and
- the ability of the radar to distinguish different materials within the region
because their scattering cross-section depends upon the frequency.
- volume scattering is used to study forest canopies
- by comparing the returns at different frequencies and with different
polarizations (vertical & horizontal) the distribution of vegetation at various
heights within the canopy can be inferred.
- the polarisation changes distinguish bewteen returns which arise from single
scattering and multiple-scattering.
- if changes in canopy density over a period are monitored the effects of
environmental changes such as the increase in acid rain can be studied.
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Polar Ice
- different types - and hence ages - polar ice can be distinguished by the scattering they give.
- as with vegetation scattering ,more information about the distribution and development of ice
floes is obtained by comparing the images formed at different microwave frequencies.
- studies of the polar regions are important in investigations of global warming (due to,for
example carbon dioxide emissions) because the effects could be most severe there.
- the growth of sea-ice is a primary mechanism for the removal of carbon dioxide from the
atmosphere.
- knowledge of the position of ice is important for fishing and navigation in the polar regions.
MULTIYEAR
LOWSALINITY,LOWLOSS
SURFACE-VOLUME
SCATTERING
FIRST YEAR:
HIGH-SALINITY
HIGH-LOSS
SURFACE
SCATTERING
OPEN WATER:
HIGH-LOSS
SURFACE
SCATTERING
SEA LEVEL
RIDGE
SURFACE
SCATTERING
GLACIER
ICE
LAKE ICE
VOLUME
SCATTERING
Scattering mechanisms for various ice
types :multiyear,first year and open
water
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WATER
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- more information about the distribution and development of ice floes is obtained by
comparing the images formed at different microwave frequencies
102
T =-10°C
10
Pure Ice
ε = 3 - j0.03
1
Multi-year
ice
Pentration
depth
(m)
First year
ice
10-1
ε = 3.3 - j0.25
10-2
1.5
2
3
4
5
6 7 8 9 10
15
20
Frequency (GHz)
- studies of the polar regions are important in investigations of global warming (due to,for
example,carbon dioxide emissions) because the effects could be most severe there
- the growth of sea-ice is a primary mechanism for the removal of carbon-dioxide from the
atmosphere .
- knowledge of the position of ice is important for fishing and navigation in the polar regions.
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Soil Moisture
- the moisture content of soil varies the relative permittivity of the soil and hence it’s
microwave scattering backscatter cross-section.
24
22
20
18
ε‘
16
14
D ie le c t ric
C o n st a n t
S O IL M O IS T U R E
a t L -B A N D
12
10
8
6
4
ε ‘’
2
0
20
10
30
S o il M o istu re ( % )
C -B and X -B and
L -B and
90
RADAR
W AVELENGTH
80
ε‘
70
L iq u id
W ater
60
50
R eal p art, ε‘
40
D ie le c t r ic
C o nstant
30
I m a g in a r y P a r t
, ε ‘’
20
ε ‘’
10
0
100
30
3
10
1
0 .3
0 .1
W a v e le n g t h ( c m )
Dependance of complex dielectric constant on (a) Soil moisture at L-Band; and (b) Radar
wavelength. (Ulaby et al,1982)
- knowledge of the water content of soil is important for the development of models for the global
hydrological cycle.
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