Synthetic Aperture Radar (SAR) Basic Principles & Concepts
Irena Hajnsek Earth Observation and Remote Sensing Institute of Environmental Engineering ETH Zurich Email:
[email protected] German Aerospace Center (DLR) Microwaves and Radar Institute (DLR-HR) Pol-InSAR Research Group VU 1 > Autor Name
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German Aerospace Center (www.dlr.de) DLR is Germany’s Aerospace Research Center and Space Agency 31 research institutes and scientific / technical facilities DLR Oberpfaffenhofen: mostly space activities 5 research institutes 3 technical facilities including: –
German Space Operations Center (GSOC);
–
German Remote Sensing Data Center (DFD).
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Electromagnetic Spectrum
Microwave Window
Optical Window
Electromagnetic spectrum and attenuation caused by Earth’s atmosphere VU 3 > Autor Name
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35,3 km
21,3 km
1994: Shuttle Radar Lab SIR-C/X-SAR
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X (3cm)
CETH(5cm) Zü Zürich – DBAUG - IFU - Earth Observation Chair L (23cm)
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Infrared Image (Spaceshuttle Columbia)
Radarbild (Spaceshuttle Endeavour) Endeavour)
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Unique Characteristics of Microwave Remote Sensing Independent of Weather Conditions: Penetrate clouds, rain, (smoke); (Lower Frequencies) Penetrate into / through a wide class of natural cover types as: Sand / Ice / Vegetation; Sensitive to objects of dimensions from cm to m: (Complementary to Optical and IR remote sensing); Very accurate (differential) distance measurements (employing interferometric techniques); (Active) Microwave systems are able to operate day and night.
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Range Resolution
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Christian Hülsmeyer: Inventor of Radar (1904)
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Radar Measurement Principle Range distance ro
co
(Velocity of light)
Tx
co
object
Rx
Received echo signal (back-scattered signal of imaged object): Total time delay =
Total distance = Velocity of light
2 . ro co t (time)
receive
transmit ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
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(Slant) Range Resolution Pulse Duration τ
Range difference Δro
co Tx
co Rx Δro Time difference Δt =
Total range difference Velocity of light
=
2 .Δr roo co
Δro
co Tx
co Rx Δro Two scatterers can be resolved because they have different time delays VU 13 > Autor Name ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair i.e. because their echoes arrive at different times
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(Slant) Range Resolution Pulse Duration τ
Range difference Δro
co Tx
co Rx Δro Time difference Δt =
Total range difference Velocity of light
=
2 .Δr roo co
Δro
τ
co Tx
co Rx Δro When the time difference Δt (i.e. the difference of time delays) becomes VU 14 >smaller Autor Name ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair than the pulse duration τ then the objects cannot be separated from each other ! Microwaves and Radar Institute > 30.05.2006
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(Slant) Range Resolution Range resolution: The min. distance between two objects that can still be separated from each other i.e. the distance that corresponds to a time difference Δt equal than the pulse duration τ
δr
co Tx
co Rx Δro Time difference Δt := Pulse duration τ =
2 Range resolution = Velocity of light
2δ c
δr
→ rRange resol.:
cτ 2
The range resolution is independent on the distance between the sensor and the scatterer; it depends only on
δr
the pulse duration τ that is inverse proportional to the pulse bandwidth W:
cτ c 2 2W
Example: A pulse bandwidth of W=100MHz leads to a range resolution δr=1.5m (corresponding to a pulse VU 15 > Autor Name duration of τ=10ns) . ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
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The Dilemma The energy of a pulse defines the (maximum) distance that a object can be detected:
Range distance ro
Received signal energy ERX from an object at distance r0: The energy of the transmitted pulse and pulse duration τ: E Tx PTx τ
Object
ERx ~
ETx r04
EisTxgiven by product of instantaneous peak power P
P is limited by the sensor hardware – especially in the case of spaceborne sensors so that for increasing the pulse energy long pulses are required. But on the other side: For achieving a high spatial resolution short pulses (realised by wide bandwidths) are required. The solution is to use pulse modulation. Commonly used: Linear frequency modulation (FM Chirp) ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
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Amplitude variation
Linear Frequency Modulated Pulse
FM Chirp
The frequency f0 is linearly changed along the pulse time
fr ( t ) k r t
Frequency variation
τ 2
Frequency variation
τ 2
τ:= Pulse duration
τ τ t 2 2
kr maybe positive (Up-Chirp) or negative (Down-Chirp)
The bandwidth
Wr : is Δfindependent on the pulse
length τ. So it becomes possible to generate pulses
Wr Δf
with large pulse lengths τ and large bandwidths Wr
kr
τ 2
τ 2
Phase Modulation
with
Chirp bandwidth
Wr : k r τ
Pulse compression gain
Cr 10 log10 ( Wr τ r )
time
φr ( t ) πk r t 2
Phase modulation
Note: The phase of the chirp has ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair a
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Matched Filter The high range resolution is achieved after reception: The long chirp(ed) pulse so(t) is compressed using a “matched filter”. The output pulse uo(t) will have the same total energy of the input pulse so(t) but will be significantly shorter.
n(t)
Matched filter xo(t)
so(t)
ho(t)
uo(t)
u 0 ( t ) s 0 ( t ) h 0 ( t ) s 0 ( T ) h 0 ( t T ) dΤ
where stands for convolution
The matched filter function ho(t) is given by the complex conjugated, time-reverted transmitted shirp h0 ( t ) m s0 ( t ) ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
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Range Compression by Convolution
τ
Range SAR Signal
t Convolution
Reference Function
t
δr
e
Point Target Response
t ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
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Range Compression by Convolution Range SAR Signal
t Reference Function
Convolution
t
δr
e
Point Target Response
t ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
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Matched Filter Assuming white Gaussian noise (e.g. thermal noise): ►Pulse compression with matched filtering leads to best possible Signal-to-Noise ratio.
τ
The length of the compressed pulse is limited by the bandwidth of the chirp:
1 Wr
Examples of transmitted pulses:
Pulse with 10 ns width
Chirp with 5 s width and 100 MHz
leads to 1,5 m resolution.
bandwidth leads to 1,5 m resolution
(Bandwidth=100MHz)
(after pulse compression).
Gain in the average power by using chirp signal:
G = 5 s / 10 ns = 500 !!! VU 21 > Autor Name
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Radar Types Nadir Looking Implementations:
Side Looking Implementations
Radar Altimeters
Scatterometers
Radar Sounders
Imaging Radars (SLAR & SAR)
Left (A) and right (B) echoes are not separable.
A
The side looking geometry resolves the left-right ambiguit
B
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Basic Radar Block Diagram
Transmitter Antenna
Radar Pulse Circulator
Receiver
Transmitter: generates generates aa high high power power pulse pulse •• Transmitter: Data Recording
Circulator (Switch): (Switch): switches switches transmitted transmitted pulse pulse to to antenna, antenna, •• Circulator returned echoes echoes to to receiver receiver returned Antenna directs directs transmitted transmitted pulses pulses towards towards the the target target area area •• Antenna Receiver amplifies amplifies the the received received signal signal and and converts converts to to base base band band •• Receiver
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Side-Looking Imaging Geometry
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z
• Pulsed radar system • Two-dimensional imaging (azimuth x slant range) Antenna Azimuth Range
• Timing of the Radar: Tx
Tx Rx
Swath
x
y
Rx
Illuminated area T = 1/PRF
PRF = Pulse Repetition Frequency ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
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Slant Range 2 Ground Range Resolution δr θ d Depression Angle
cτ 2
Slant Range resolution:
Look Angle θ 0 (or Incidence Angle)
δr
cτ c 2 2Wr
Wr:= Chirp bandwidth τ := Pulse duration δr
cτ 2
is the “natural” radar range coordinate Ground Range resolution: δGr
δr cos(θ0 )
Ground range is Slant range δr
δGr
cτ 2
projected on the geoid δr
cτ 1 2 cos(θ0 )
δGr
cτ 2
cτ 1 2 cos(θ0 ) VU 25 > Autor Name
Slant Range 2 Ground range transformation by resampling
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Radar measures distance !!!
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Shadowing
Shadows: Areas in the scene that are not illuminated for example when the incidence angle is larger than the negative terrain slope
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Foreshortening
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Compression of topo features in the scene Becomes stronger when the the (local) terrain slope becomes closer the incidence angle.
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Layover
Incidence angle = the (local) terrain slope.
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Layover
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Extreme case of foreshortening that occurs When the incidence angle becomes smaller than the (local) terrain slope.
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Azimuth Resolution
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Real Aperture Radar Angular resolution:
θa
λ da
Spatial resolution (Az):
δa θaR0
λ R0 da
d δa (R ) A p e r t u r e
θa
da
R0
R0
δa (R )
x
δa (R )
The azimuth resolution decreases with increasing distance to the scatterer. High azimuth resolution requires high frequencies, large antennas & small ranges.
y
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Real Aperture Radar Angular resolution:
θa
λ da
Spatial Resolution (Az):
λ R0 da
d δa (R )
R e a l A p e r t u r e
δa θaR0
θa
da
R0
R0
δa (R )
δa (R )
Example Example1: 1:X-Band X-Band Airborne Airbornesystem, system,50 50MHz MHzbandwidth, bandwidth,33mmantenna, antenna,3000 3000mmrange range
r ==33m m r
a == 30 30m m a
Example X-BandSatellite Satellitesystem, system,50 50MHz MHzbandwidth, bandwidth,12 12mmantenna, antenna,800 800km kmrange range Example2: 2:X-Band
x y
r ==33m m r
a == 2000 2000m m !! a
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Synthetic Aperture Radar
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SAR Basic Principle
swath width
a
x y
• Pulsed radar system • Radar system must be coherent (stable local oscillator). Phase information is preserved
• Two-dimensional imaging (azimuth x slant range) • Azimuth resolution is independent on range distance ! ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
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SAR Azimuth Resolution
• Angular resolution of synthetic antenna:
v P Platform velocity
θSA
λ d a 2L SA 2R0
• Length of the synthetic aperture: S y n t h e t I c A p e r t u r e
L SA δa θaR0
L SA
θa
R0
λ R0 da
• Azimuth resolution: a
θa
δSA θSAR0
da 2
Azimuth Resolution = Half Antenna Length in Azimuth
x The azimuth resolution is independent on range (i.e. the distance to the scatterer).
y
It is determined only by the size of the real antenna. ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
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SAR Azimuth Resolution
S y n t h e t I c A p e r t u r e
L SA L SA
θa
R0
R0
x The loss of resolution with increasing range (i.e. distance to the scatterer) is
y
compensated by the increase of the sythetic aperture. ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
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Synthetic Aperture Formation Lsa Point Target Flight Direction
Beamwidth of Real Aperture Antenna
SAR Sensor
Two-dimensional received SAR signal
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SAR Phase History
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•Phase history
v P Platform velocity
φ( t ) 2
4π 2π 2π v P2 t 2 r( t ) R0 λ λ R0 λ
Range variation r(x): S y n t h e t I c
r( x ) R02 x( t )2 R0
x2 v2 t2 R0 P 2R0 2R 0
where: x : v P t
L SA
θa
R0
A p e r t u r e
• Frequency variation:
r(x)
fa ( t )
1 1 dφ( t ) 2 v P2 ω(t ) t 2π 2π dt λ R0
• Doppler Rate:
x
κ a :
due to the quadratic range var.
2 v P2 λ R0
• Azimuth (or Doppler) Bandwidth:
y
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W :
2v t λR
2v P2 R0θa 2v P da λR 0 v P
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SAR Azimuth Signal v P Platform velocity Phase history S y n t h e t I c
L SA
Amplitude variation
θa
R0
A p e r t u r e
Frequency variation
r(x)
PRF 2
x
PRF 2
Azimuth (Doppler) Bandwidth
y
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2D-SAR Image Formation Raw data
Range compressed data
range range
Image data
azimuth
azimuth
azimuth Range reference
Azimuth reference
function
function
point target
range
far range
Near range amplitude
azimuth ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
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Sp. Res: 3 x 3 m ISLR Az: -15.1 dB ISLR Rg: -14.1 dB ISLR 2D: -11.5 dB
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Spatial Resolution: 3>xAutor 3m VU 48 Name Microwaves and Radar Institute > 30.05.2006
SAR Imaging Modes
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Az
Rg
Comparison: ScanSAR vs. Stripmap vs. Spotlight (TerraSAR-X)
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Comparison: ScanSAR vs. Stripmap (TerraSAR-X) ScanSAR (HH) 150 MHz 17 m resolution 1 (az) x 6.9 (rg) looks 7.25 m spacing θincid ≈ 19.7° .. 30.4° ascending orbit
Stripmap (HH) 150 MHz 7 m resolution 3 m spacing 2.9 (az) x 3.4 (rg) looks θincid ≈ 24.8° .. 28.1° descending orbit
3 days time separation
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ScanSAR EEC-RE 17 m res.
illumination
~3 km x 4 km
ScanSAR
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Stripmap
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Squint Angle & Doppler Centroid • Phase history
v P Platform velocity
φ( t ) 2 S y n t h e t I c
where:
θa θs
L SA
R0
A p e r t u r e
r(x)
x
4π 2π 2π v P2 ( t t 0 )2 r( t ) R0 λ λ λ R0 t 0 :
R0 sin(θ s ) The scatterer appears vP earlier/later due to the squint angle
• Frequency variation: fa ( t ) fD κ a t
2v P sin(θ s ) 2v P2 t λ λR 0
due to the linear due to the quadratic range variation range variation 2v P sin(θ s ) λ
• Doppler Centroid:
fD :
• Doppler Rate:
κ a :
2 v P2 λ R0
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SAR Azimuth Signal v P Platform velocity Phase history S y n t h e t I c
Frequency variation
θa θs
L SA
R0
A p e r t u r e
r(x)
PRF fD 2
x
PRF fD 2
Azimuth (Doppler) Bandwidth
y
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Moving Targets
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•Phase history
v P Platform velocity
S y n t h e t I c
Amplitude variation
2 2 4π 4π 2π ( v a v P ) t φ( x ) R0 vr t λ λ λ R0
Range variation r(t):
v L SA
vr
R0
A p e r t u r e
va
r(t) (R0 vr t)2 (vat vPt)2 R0 vr t
(va vP )2 t2 2R0
• Frequency variation: 2 2( v a v P )2 fa ( t ) v r t fD κa t λ λR 0
r(x) • Doppler Centroid (due to vr): (causes an azimuth shift)
x
2v r λ
2( v a v P )2 λ R0 (azimuthal velocities changes the doppler rate)
• Doppler Rate:
y
fD :
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κa :
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Tehachapi Loop, California, 19.12.2007 VU 61 > Autor Name Microwaves and Radar Institute > 30.05.2006
azimuth
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V range
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SAR History History of SAR 1951
Doppler beam sharpening concept
Carl Wiley, Goodyear
1958
First focused SAR Image
University of Michigan
1960
First operational airborne system (UPD-1)
Univ. Michigan/Texas Instrum.
Airborne SAR with digital processing
Military industry, USA
1978
First SAR satellite (SEASAT)
NASA/JPL, USA
1979
Real-time airborne SAR processing
MDA, Canada
Digital SAR processing with workstations
NASA/JPL, USA
1991
First European SAR satellite (ERS-1)
ESA
1994
First demonstration of fully polarimetric, multi frequency spaceborne SAR (SIR-C/X-SAR)
NASA, USA,DLR, Germany / ASI, Italy
2000
First single-pass interferometric mission in space (SRTM)
NASA, USA, DLR, Germany
2002
First dual-polarised SAR satellite (ASAR/ENVISAT)
ESA
2007
Launch of TerraSAR-X (first German civilian radar satellite)
2010
Launch of TanDEM-X
early 1970
early 80s
DLR / Astrium
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Air- and Spaceborne Sensors
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Commonly Used Frequency Bands Frequency band
Frequency range
Application examples
VHF
300 KHz -
300 MHz
Foliage/Ground penetration, biomass
P-Band
300 MHz -
1 GHz
soil moisture, biomass, penetration
L-Band
1 GHz
-
2 GHz
agriculture, forestry, soil moisture
C-Band
4 GHz
-
8 GHz
ocean, agriculture
X-Band
8 GHz
-
12 GHz
agriculture, ocean, high resolution radar
Ku-Band
14 GHz
-
18 GHz
glaciology (snow cover mapping)
Ka-Band
27 GHz
-
47 GHz
High resolution radar
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Polarimetric Airborne SAR Sensors
AES1
AIRSAR
DOSAR
RENE
AeroSensing (D) GulfStream Commander X-Band (HH), P-Band (Quad)
NASA / JPL (USA) DC8 P, L, C-Band (Quad)
EADS / Dornier GmbH (D) DO 228 (1989), C160 (1998), G222 (2000) S, C, X-Band (Quad), Ka-Band (VV)
UVSQ / CETP (F) Écureuil AS350 S, X-Band (Quad)
ESAR
EMISAR
MEMPHIS / AER II-PAMIR
STORM
DLR (D) DO 228 P, L, S-Band (Quad) C, X-Band (Sngl)
DCRS (DK) G3 Aircraft L, C-Band (Quad)
FGAN (D) Transal C160 Ka, W-Band (Quad) / X-Band (Quad)
UVSQ / CETP (F) Merlin IV C-Band (Quad)
PISAR
RAMSES
PHARUS TNO - FEL (NL) CESSNA – Citation II C-Band (Quad)
NASDA / CRL (J) ONERA (F) GulfStream Transal C160 ETH(Quad) Zü - Earth Zürich – DBAUG - IFU L, X-Band P, L, S, C,Observation X, Ku, Ka, Chair W-Band (Quad)
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Spaceborne SAR Missions since 1978
SEASAT
ERS-1/2
J-ERS-1
SIR-C/X-SAR
NASA/JPL (USA) L-Band, 1978
European Space Agency (ESA) C-Band, 1991-2000 & 1995-today
Japanese Space Agency (NASDA) L-Band, 1992-1998
NASA/JPL, L- and C-Band (quad) DLR / ASI, X-band April and October 1994
RADARSAT-1
SRTM
ENVISAT / ASAR
ALOS / PALSAR
Canadian Space Agency (CSA) C-Band, 1995-today
NASA/JPL (C-Band), DLR (X-Band) February 2000
European Space Agency (ESA) C-Band (dual), 2002-today
Japanese Space Agency (JAXA) L-Band (quad), 2005
CosmoSkymed
TerraSAR-X
SAR Lupe BWB Germany X-Band, 2006
ASI / Alenia German Aerospace Center (DLR) / Astrium X-Band (dual), (quad), 2007 ETH Zü rich – DBAUG - IFU - Earth X-Band Observation Chair Zü2007
RADARSAT-2 Canadian Space Agency (CSA) VU 68 > Autor Name C-Band (quad), 2007 Microwaves and Radar Institute > 30.05.2006
33
ENVISAT/ASAR
Launch: 28.02.2002 MIPAS
MERIS
AATSR SCIAMACHY MWR
GOMOS DORIS RA-2 LRR
Size: 26 x 10 x 5 m, Weight: 8.2 t
ASAR
Most ambitious RS satellite for environmental monitoring Unique combination of 10 RS instruments ESA ETH Zü Chair Zürich – DBAUG - IFU - Earth Observation
ALOS/PALSAR
Wavelength
0.236 m
Chirp Bandwidth
14 MHz
Peak Transmit Power Duty Cycle Noise Figure Antenna Size (Tx , Rx) Quantisation
Launch date Weight Solar Power Orbit Altitude Revolution Yaw steering Inclination Attitude error
ASAR-Antenna (ca. 10 m x 1.33 m VU 69 > Autor Name and 320 T/R-Modules) Microwaves and Radar Institute > 30.05.2006
January 2006 4000kg ~7Kw@EOL Sun Synchronous 691.65 km 14+27/46 ON 98.16 degrees ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair 0.4e-4°
2 kW 3,5 % (7 % / 2) 4 dB 8.9 m x 3.1 m 5 bit (BAQ)
VU 70 > Autor Name Microwaves and Radar Institute > 30.05.2006
34
Launch date: 14. Dec 2007 Frequency 5.405 GHz (C-band) Repeat cycle: 24 days
ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
VU 71 > Autor Name Microwaves and Radar Institute > 30.05.2006
Launch date: 14. June 2007 PPP with EADS ASTRIUM GmbH Wet mass: 1209 kg Size: 5 m height 2.4 m diameter
Solar Generator
Thrusters
X-Band Radar Antenna 384 Transmit/Receive Modules S-Band TM/TC Antenna X-Band Downlink Antenna Data Rate: 300 MBit/sec ETH Zü – DBAUGMass - IFU - Earth Observation Chair Zürich State 256 Gbit Solid Memory
VU 72 > Autor Name Microwaves and Radar Institute > 30.05.2006
35
Information Content -Speckle -Radiometric Resolution -Radar Cross Section -CS’s
VU 73 > Autor Name
ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
E
Imaginary
Received Electric Field: | E | A
: R
4
Microwaves and Radar Institute > 30.05.2006
E A exp( i )
Scattering Amplitude R Phase
Real
R Distance Antenna-Scaterrer
Image Intensity
~
| E |2 A 2
Single Single scatterer scatterer in in the the resolution resolution cell cell
Deterministic Scatterers (Point Scatterets) ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
VU 74 > Autor Name Microwaves and Radar Institute > 30.05.2006
36
| E | A
2 :
4
E R2
Imaginary
Received ReceivedElectric ElectricField: Field:
| E | A
1 :
R1
3 :
R1
4
R3
Real
R2
| E | A
4
E A exp( i )
R3
The Themovement movementofofthe thescatterer scattererwithin withinthe the resolution resolutioncell cell isisassociated associated totoaachange changeofof the thephase phaseofofthe thereceived receivedsignal signal… …
… …due duetotothe thechange changeofofthe the Antenna-Scatterer Antenna-Scattererdistance. distance. Image Intensity
~
| E |2 A 2
is not changing ! VU 75 > Autor Name
ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
Microwaves and Radar Institute > 30.05.2006
Received Electric Field:
E
Am exp( im ) m
The The received received signal signal isis given given by by the the coherent (i.e. vectorial) sum of coherent (i.e. vectorial) sum of the the signals signals received received from from each each scatterer scatterer inin the theresolution resolutioncell. cell.
Im
Am A
m :
4
Rm
Re
“Random Walk” Process
m mscatterers scatterers within withinthe theresolution resolutioncell cell
Stochastic Scatterers (Distributed Scatterets) ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
VU 76 > Autor Name Microwaves and Radar Institute > 30.05.2006
37
The The movement movement ofof the the scatterers scatterers within within the the res. res.cell cell isisassociated associated toto aa change change ofof phase phase and and amplitude amplitude ofof the the received receivedsignal. signal.
Im
Re
“Random Walk” Process
Image Intensity
changes !
Stochastic Scatterers (Distributed Scatterets)
VU 77 > Autor Name Assumption: ofof–the resolution than ETH Zü DBAUG - IFU - Earthcell Observation Chair Zürich Assumption:Wavelength Wavelengthλλ 30.05.2006
Phase Image
Probability density function (pdf) of the phase of a SAR image of distributed scatterers with fully developed speckle. pdf ( )
Uniform Distribution [- π,π]: ► No information in the phase of a single SAR image.
ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
VU 80 > Autor Name Microwaves and Radar Institute > 30.05.2006
39
Fully Developed Speckle
E
Received Electric Field:
NS
A
m
exp( iφ m )
m 1
When:
The number of scatterers is large within the resolution cell; The scatterers are independent from each other; Amplitude Am and phase φm are independent random variables; The phase φm is uniformly distributed between –π and π;
Then:
Fully developed speckle:
In terms of the central limit theorem: Re{ E } and Im{ E } are independent random Gaussian variables with zero mean and the same standard variation σ.
pdf (Re{ E })
1 Re{ E } exp( ) 2σ σ 2π
pdf (Im{ E })
1 Im{ E } exp( ) 2σ σ 2π
The pdf of the Intensity I (Re{ E }) 2 (Im{ E }) 2 is
pdf (I)
The pdf of the Amplitude A I is
pdf ( A )
1 I exp( ) 2σ 2 2σ 2 A A2 exp( ) 2 σ 2σ 2
Exponential distributed
Rayleigh distributed
VU 82 > Autor Name
ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
Microwaves and Radar Institute > 30.05.2006
Speckle in Multi-Look Images Multi-Look: Incoherent summation (average) of resolution cells. The average can be performed in the frequency domain … by averaging images of individual frequency parts in range and/or azimuth; or in the spatial (time) domain … by averaging individual resolution cells in range and/or azimuth.
Multi-Look Intensity
IML
1 N aN r
N a Nr
I
k
Ik
where
k 1
Nr Na
… Intensity of the kth resolution cell … Number of res. cells used in Rg / Az
L Nr N a … Number of Looks The pdf of the Multi-Look Intensity is:
pdf (I)
LL IL 1 1 L I exp( ) (L 1)! ( 2σ 2 )L 2σ 2
Gamma distributed
The same mean 2σ 2 but a reduced standard deviation by a factor L compared to the 1 look intensity
The pdf of the Multi-Look Amplitude is: pdf ( A )
2LL A ( 2L 1) LA 2 exp( ) Gen. Gamma distributed 2 L (L 1)! ( 2σ ) 2σ 2
VU 83of > Autor Name Speckle can be reduced at the expense of spatial resolution by increasing the number looks. ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair Microwaves and Radar Institute > 30.05.2006
40
MGD-SE Spatial Resolution: 3 x 3m ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
VU 84 > Autor Name
Microwaves and Radar Institute > 30.05.2006
MGD-RE Spatial Resolution: 7 x 7m VU 85 > Autor Name (~ 9 Looks)Microwaves and Radar Institute > 30.05.2006
41
What does the Radar measure ? Radar reflectivity (backscattered signal) of the target as a function of position. 1 The radar transmits a pulse (pulse travelling velocity is equal to velocity of light)
2. Some of the energy of the incident radar pulse is reflected back towards the radar. … and is measured by the radar. It is known as Radar Backscatter o (Sigma Nought or Sigma Zero).
ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
VU 86 > Autor Name Microwaves and Radar Institute > 30.05.2006
What does the Radar measure ? Normalized radar cross-section (backscattering coefficient) is given by:
o (dB) = 10. Log10 (energy ratio) Whereby: received energy by the sensor energy ratio = “energy reflected in an isotropic way”
The backscattered coefficient can be a positive number if there is a focusing of backscattered energy towards the radar
or The backscattered coefficient can be a negative number if there is a focusing of backscattered energy way from the radar (e.g. smooth surface) ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
VU 87 > Autor Name Microwaves and Radar Institute > 30.05.2006
42
Backscattering Coefficient o
Typical scenario
Levels of Radar backscatter Very high backscatter (above -5 dB)
Man-Made objects (urban) Terrain Slopes towards radar very rough surface radar looking very steep
High backscatter (-10 dB to 0 dB)
rough surface dense vegetation (forest)
Moderate backscatter (-20 to -10 dB)
medium level of vegetation agricultural crops moderately rough surfaces
Low backscatter (below -20 dB)
smooth surface calm water road very dry terrain (sand)
VU 88 > Autor Name
ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
Microwaves and Radar Institute > 30.05.2006
ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
Microwaves and Radar Institute > 30.05.2006
VU 89 > Autor Name
43
Radar image color composit (Shuttle Imaging Radar-C) Two large ocean eddies next to sea ice in the Weddell Sea, Antarctica, on October 5, 1994, The eddies sweep up loose bits of sea ice, mostly pancake ice, in their rotating currents. Very new ice is seen in the darkest areas. First- year ice is green. Open ocean is blue. The image has a size of 240km by 360 km. L-band VV is blue, L-Band HV is green, and C-band VV is red.
ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
VU 90 > Autor Name Microwaves and Radar Institute > 30.05.2006
91 > Autor Name Bergen, Norway, March 13,VU2008
ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
Microwaves and Radar Institute > 30.05.2006
44
VU 92 > Autor Name
ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
Microwaves and Radar Institute > 30.05.2006
ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
Microwaves and Radar Institute > 30.05.2006
Surface Scattering
VU 93 > Autor Name
45
VU 94 > Autor Name
ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
Microwaves and Radar Institute > 30.05.2006
ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
Microwaves and Radar Institute > 30.05.2006
VU 95 > Autor Name
46
Multi-Parameter SAR Acquisitions -Multi-Temporal -Multi-Angular -Multi-Frequency -Polarimetric
ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
VU 96 > Autor Name Microwaves and Radar Institute > 30.05.2006
F-SAR (DLR), Kaufbeuren, X-Band
ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
VU 97 > Autor Name Microwaves and Radar Institute > 30.05.2006
47
F-SAR (DLR), Kaufbeuren, X-Band, vollpolarimetrisch
ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
VU 98 > Autor Name Microwaves and Radar Institute > 30.05.2006
Polarimetric SAR
X-band PI-SAR / Test Site: Gifu-Japan
VU 99 > Autor Name R:HH-VV G:HV+VH B:HH+VV
ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
Microwaves and Radar Institute > 30.05.2006
48
Frequency and Polarisation Diversity
C-band R: HH G: HV B: VV
L-band P-band VU 100 > Autor Name ETHHH Zü Zürich R: G:– DBAUG HV B:- IFU VV- Earth Observation Chair R: HH G: HV B: VV
C-band
L-band
Beaufort Sea, 1998 AIRSAR / NASA-JPL
Microwaves and Radar Institute > 30.05.2006
P-band R: C-TP, G: L-TP, B: P-TP
ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
VU 101 > Autor Name Microwaves and Radar Institute > 30.05.2006
49
Multitemporal
Az Rg
High Resolution Spotlight Image (300 MHz): Australia, Sydney, Harbor Bridge
1. Layer: Dec 12, 2007 2. Layer: Jan 1, 2008 3. Layer: Jan 12, 2008
ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
VU 102 > Autor Name Microwaves and Radar Institute > 30.05.2006
Multitemporal
Az
High Resolution Spot Light Image (300 MHz): Australia, Sydney Harbor Bridge
1. Layer: Dec 12, 2007 2. Layer: Jan 1, 2008 3. Layer: Jan 12, 2008
ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
VU 103 > Autor Name Microwaves and Radar Institute > 30.05.2006
50
Rg
Drygalski Glacier Oct 2007 – Jul 2008
6 m/day
by Remote Sensing Technology Institute
ETH Zü Zürich – DBAUG - IFU - Earth Observation Chair
19/04/06
RGB Pauli
06/06/06
VU 104 > Autor Name Microwaves and Radar Institute > 30.05.2006
05/07/06
VU 105 > Autor Name Multitemporal L-band Quad-Pol - AGRISAR Campaign 2006 ETH Zü - IFU - Earth Observation(E-SAR) Chair Zürich – DBAUG Microwaves and Radar Institute > 30.05.2006
51