EE/Ae 157 b
Interferometric Synthetic Aperture Radar
EE/Ge 157 b, Week 3
3-1
PRINCIPLES OF IMAGING RADAR CHARACTERISTICS OF RADAR WAVES
•
The propagation of radar waves are governed by Maxwell’s equations. From these equations, one can derive the so-called free-space wave equation: 2
E •
2 c 2r
E0
The solution to this free-space wave equation is of the form:
E Ae i kr t •
There are three parameters in this wave solution that we commonly exploit in radar remote sensing: – Amplitude and polarization provides information about scattering properties and structure – Frequency diversity allows us to learn more about the size of scatterers – Phase information is used in interferometry to reconstruct three-dimensional topography, as well as small changes to topography
EE/Ge 157 b, Week 3
3-2
PRINCIPLES OF IMAGING RADAR TYPES OF IMAGING RADARS
Structural Information Polarimeter
Polarimetric Interferometer
Spectral Information Spectrometers EE/Ge 157 b, Week 3
Elevation Information Interferometer
Spatial Information Imaging Radar 3-3
RADAR INTERFEROMETRY HOW DOES IT WORK?
A2 B RADAR
A1
Antenna 1 Antenna 2
Return could be from anywhere on this circle
Return comes from intersection
SINGLE ANTENNA SAR EE/Ge 157 b, Week 3
INTERFEROMETRIC SAR 3-4
RADAR INTERFEROMETRY TRIGONOMETRY
•
The radar phase difference for a common transmitter is 1
4
•
;2
2
2
2
A1
B
+
For the spaceborne case, B From the law of cosines, we find that ( ) 2 2 B 2 2 B cos 2 B sin( ) 2 B sin( )
•
A2
z
0
h
Z(y)
The phase difference is directly proportional to the electrical length of the interferometer baseline
EE/Ge 157 b, Week 3
y
SIMULTANEOUS BASELINE
3-5
RADAR INTERFEROMETRY Phase Difference in the Absence of Topography (B=60m, alpha=45,wavelength=5.66 cm, altitude = 234 km)
Radar Look Direction
EE/Ge 157 b, Week 3
360 Degrees
Radar Movement
3-6
RADAR INTERFEROMETRY Phase Difference is a function of the ELECTRICAL Length of the Baseline (B=60m, alpha=45, altitude = 234 km)
Wavelength = 5.66 cm
EE/Ge 157 b, Week 3
Wavelength = 24 cm
3-7
RADAR INTERFEROMETRY Example: Mt. Shasta, California
EE/Ge 157 b, Week 3
3-8
RADAR INTERFEROMETRY Mt Shasta Phase Difference (B=60m, alpha=45,wavelength=5.66 cm, altitude = 234 km)
Radar Look Direction
EE/Ge 157 b, Week 3
Radar Movement
3-9
RADAR INTERFEROMETRY TRIGONOMETRY (continued)
•
Now let 0 represent the look angle to a point on a “flat earth” as shown in the figure. Then
A2
z
sin sin 0
A1
B
sin 0 cos 0
•
In terms of the interferometric phase, it means we can write
•
2
B sin 0
B cos 0
The first term represents the phase difference measured for the “flat earth,” i.e. in the absence of any topography. If we remove the so-called “flat earth phase,” we are left with
flat •
2
2
+
0
h
Z(y)
B cos 0
y
This is the so-called “flattened interferogram”
EE/Ge 157 b, Week 3
3 - 10
RADAR INTERFEROMETRY Mt Shasta Flattened Interferogram (B=60m, alpha=45,wavelength=5.66 cm, altitude = 234 km)
EE/Ge 157 b, Week 3
3 - 11
RADAR INTERFEROMETRY SENSITIVITY TO TOPOGRAPHY
•
The elevation of the image point is found from z y sin 0
•
• •
A1
The so-called ambiguity height is the elevation change required to change the flattened phase difference by one cycle sin 0 ha B cos 0
A small ambiguity height means good sensitivity to topography If the elevation is the scene varies by more than the ambiguity height, the phase will be “wrapped”, since we only measure phase modulo 360 degrees.
EE/Ge 157 b, Week 3
A2
z B
+
0
h
Z(y)
y
3 - 12
RADAR INTERFEROMETRY Ambiguity Height Baseline = 60 m, Baseline Angle = 45 Degrees, Altitude = 234 km
Ambiguity Height in Meters
3000 L-Band
2500
C-Band
2000
1500
1000
500
0 20
30
40
50
60
70
Look Angle in Degrees EE/Ge 157 b, Week 3
3 - 13
RADAR INTERFEROMETRY PHASE UNWRAPPING
Phase z
8
Phase
2 0
EE/Ge 157 b, Week 3
4 2 0
y
ACTUAL ELEVATION PROFILE
6
y
WRAPPED PHASE
y
UNWRAPPED PHASE
3 - 14
RADAR INTERFEROMETRY Ambiguity Height & Phase Wrapping Relief exceeds ambiguity height, resulting in wrapped phases
Wavelength = 5.66 cm
EE/Ge 157 b, Week 3
Relief does not exceed ambiguity height; Phase is not wrapped
Wavelength = 24 cm
3 - 15
RADAR INTERFEROMETRY HOW IS IT IMPLEMENTED?
B
SIMULTANEOUS BASELINE Two radars acquire data at the same time EE/Ge 157 b, Week 3
B
REPEAT TRACK Two radars acquire data from different vantage points at different times 3 - 16
RADAR INTERFEROMETRY COMPARISON OF TECHNIQUES
IMPLEMENTATION
ADVANTAGES
DISADVANTAGES
Simultaneous Baseline
• Known baseline
• Difficult to get adequate baseline in space
• No temporal decorrelation
• High data rate from two radars
• Typically better performance
• Typically higher cost
• Lower data rate from one radar
• Temporal decorrelation
• Lower cost
• Baseline not well known and may be changing
Repeat T rack
• Depending on orbit, any baseline can be realized
EE/Ge 157 b, Week 3
3 - 17
INTERFEROMETRIC SAR PROCESSING GEOMETRY
Ra nge S phe re
D opple r C one Ba se line Ve ctor Aircra ft Position
Ve locity Ve ctor
Pha se C one
S ca tte re r is a t inte rse ction of Ra nge S phe re , D opple r C one a nd Pha se C one
EE/Ge 157 b, Week 3
3 - 18
EE/Ge 157 b, Week 3
3 - 19
PRINCIPLES OF IMAGING RADAR SAR IMAGE PROJECTION Radar Image Plane
A three-dimensional image is projected onto a two-dimensional plane, causing characteristic image distortions: • b’ appears closer than a’ in radar image LAYOVER
b’ a’
c’
d’
• d’ and e’ are closer together in radar image FORESHORTENING
e’ f’
g’
b c
EE/Ge 157 b, Week 3
d
i’
h
e a
h’
• h to i not illuminated by the radar RADAR SHADOW
f
g
i
3 - 20
RADAR INTERFEROMETRY EXAMPLE: TOPSAR DATA
EE/Ge 157 b, Week 3
3 - 21
RADAR INTERFEROMETRY IS IT POSSIBLE TO USE THE SPACE SHUTTLE TO MAP THE EARTH? (1994)
•
• • •
With the weight of a typical radar payload, the shuttle can be launched into an orbit with 57 degrees inclination, and altitude
