RADAR AND SYNTHETIC APERTURE RADAR BASICS

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RADAR AND SYNTHETIC APERTURE RADAR BASICS

• Dr. Jakob van Zyl
• RADAR SCIENCE AND ENGINEERING SECTION
• JET PROPULSION LABORATORY
• CALIFORNIA INSTITUTE OF TECHNOLOGY
• 4800 OAK GROVE DRIVE
• PASADENA, CA 91109

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OUTLINE

• PRINCIPLES OF IMAGING RADAR
• RADAR INTERFEROMETRY FOR HEIGHT MAPPING
• SIMULTANEOUS ACQUISITION
• REPEAT TRACK
• DIFFERENTIAL INTERFEROMETRY FOR CHANGE DETECTION

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PRINCIPLES OF RADARHOW DOES RADAR WORK?

• RADAR Radio Detection And Ranging
• Since radar pulses propagate at the speed of
  light, the difference to the target is
  proportional to the time it takes between the
  transmit event and reception of the radar echo

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PRINCIPLES OF IMAGING RADARREAL APERTURE RADAR
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PRINCIPLES OF IMAGING RADARTHE RADAR EQUATION

• The SNR is derived from the radar equation
• where
• Peak transmit power
• Antenna gain (one way)
• Transmit system loss
• Receive system loss
• Operating noise figure
• Boltzmanns constant
• Noise temperature
• Bandwidth
• Pulse length
• Antenna length

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PRINCIPLES OF IMAGING RADARTHE RADAR EQUATION

• In order to improve the signal-to-noise ratio for
  a fixed radar frequency, one has (among others)
  the following options
• Increase the transmitted power. This is usually
  limited by the power available from the
  spacecraft or aircraft.
• Increase the antenna gain. This requires larger
  antennas, severely affecting the launch mass and
  volume.
• Increase the pulse length. This means poorer
  resolution.
• Decrease bandwidth. This also means poorer
  resolution.
• Fly lower. Increases atmospheric drag, requiring
  more fuel for orbit maintenance.
• Signal modulation is a way to increase the radar
  pulse length without decreasing the radar range
  resolution
• All civilian spaceborne SARs, and most civilian
  airborne SARs use linear FM chirps as the
  modulation scheme.

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PRINCIPLES OF RADAR IMAGINGSYNTHETIC APERTURE
RADAR
BOTH RANGE AND AZIMUTH RESOLUTIONS ARE
INDEPENDENT OF DISTANCE TO TARGET!
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PRINCIPLES OF RADAR IMAGINGSAR IMAGING
COORDINATE SYSTEM
RADAR
NADIR
FLIGHT
TRACK
FLIGHT
TRAJECTORY
CONSTANT DOPPLER LINES
ILLUMINATED AREA
CONSTANT DISTANCE LINES
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PRINCIPLES OF RADAR IMAGING POINT TARGET RESPONSE

• The radar system transmits a series of chirp
  pulses
• The target will be in view of the radar antenna
  for a limited time period. During this period,
  the distance to the target is
• Usually, so that

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PRINCIPLES OF RADAR IMAGING POINT TARGET RESPONSE

• The phase of the returned signal is
• The instantaneous frequency of the transmitted
  wave is
• This signal has a bandwidth of B centered around
  fc

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PRINCIPLES OF RADAR IMAGING CORRELATION WITH
POINT TARGET RESPONSE

• This signal has an envelope shown on the right
  that is centered at r(t) and has a 3 dB width
  of
• This corresponds to a range resolution of
• The phase of the signal, ignoring the carrier
  term, is
• It is this phase term that provide the
  interferometric and polarimetric information

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PRINCIPLES OF RADAR IMAGING RANGE-DOPPLER
PROCESSING

• The phase of the range compressed signal is
• The last approximation on the right is valid when
  the antenna beamwidth is very narrow, and is
  usually a good approximation for most higher
  frequency airborne SAR systems
• The expression above is that of a chirp signal
  with a bandwidth of
  where T is half the time that the target is in
  the field of view of the antenna
• Note that the bandwidth of the azimuth chirp is a
  function of the range to the target.
• The range-Doppler processing algorithm uses this
  fact to first perform matched filter range
  compression, followed by matched filter azimuth
  compression

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PRINCIPLES OF RADAR IMAGING RANGE-DOPPLER
PROCESSING
Raw SAR Data
Range Compressed Data
SAR Image
Azimuth Compression
Range Compression
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PRINCIPLES OF RADAR IMAGING CLASSICAL SAR
PROCESSING GEOMETRY
insert sphere
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PRINCIPLES OF IMAGING RADARSAR IMAGE PROJECTION
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PRINCIPLES OF IMAGING RADARAZIMUTH AMBIGUITIES
Reference Synthetic Aperture Radar Systems
Signal Processing, by Curlander and McDonough,
Wiley, 1991
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PRINCIPLES OF IMAGING RADARRANGE AMBIGUITIES
Reference Synthetic Aperture Radar Systems
Signal Processing, by Curlander and McDonough,
Wiley, 1991
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TYPES OF IMAGING RADARS
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SAR POLARIMETRYSCATTERER AS POLARIZATION
TRANSFORMER

• Transverse electromagnetic waves are
  characterized mathematically as 2-dimensional
  complex vectors. When a scatterer is illuminated
  by an electromagnetic wave, electrical currents
  are generated inside the scatterer. These
  currents give rise to the scattered waves that
  are reradiated.
• Mathematically, the scatterer can be
  characterized by a 2x2 complex scattering matrix
  that describes how the scatterer transforms the
  incident vector into the scattered vector.
• The elements of the scattering matrix are
  functions of frequency and the scattering and
  illuminating geometries.

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SCATTERING MATRIX

• Far-field response from scatterer is fully
  characterized by four complex numbers
• Scattering matrix is also known as Sinclair
  matrix or Jones matrix
• Must measure a scattering matrix for every
  frequency and all incidence angles

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POLARIMETER IMPLEMENTATION
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POLARIZATION SIGNATURE

• The polarization signature (also known as the
  polarization response) is a convenient graphical
  way to display the received power as a function
  of polarization.
• Usually displayed assuming identical transmit and
  receive polarizations (co-polarized) or
  orthogonal transmit and receive polarizations
  (cross-polarized).

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OBSERVED POLARIZATION SIGNATURES SAN FRANCISCO
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OBSERVED POLARIZATION SIGNATURES L-BAND
POLARIZATION SIGNATURES OF THE OCEAN
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RADAR INTERFEROMETRYHOW DOES IT WORK?
A2
B
A1
Antenna 1
Antenna 2
Return comes from intersection
SINGLE ANTENNA SAR
INTERFEROMETRIC SAR
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RADAR INTERFEROMETRYHOW IS IT DONE?
REPEAT TRACK Two radars acquire data from
different vantage points at different times
SIMULTANEOUS BASELINE Two radars acquire data
at the same time
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RADAR INTERFEROMETRYCOMPARISON OF TECHNIQUES
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RADAR INTERFEROMETRYTRIGONOMETRY
SIMULTANEOUS BASELINE
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INTERFEROMETRIC SAR PROCESSING GEOMETRY
insert sphere
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RADAR INTERFEROMETRYPHASE UNWRAPPING
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RADAR INTERFEROMETRYHEIGHT ERROR SOURCES
(Reference Zebker, et al., IEEE GRS 32, p.825,
1994)
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DIFFERENTIAL INTERFEROMETRYHOW DOES IT WORK?
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DIFFERENTIAL INTERFEROMETRYERROR SOURCES

• Uncompensated differential motion
• Atmospheric effects
• Temporal decorrelation
• Layover

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EMERGING SAR TECHNIQUESPOLARIMETRIC
INTERFEROMETRY

• Polarimetric interferometry is implemented by
  measuring the full scattering matrix at each end
  of the interferometric baseline
• Currently there are no single baseline systems
  that can acquire this type of data
• During the last three days of the second
  SIR-C/X-SAR mission the system was operated in
  the repeat-pass interferometric mode, and some
  fully polarimetric interferometric data were
  acquired
• Using the full scattering matrix one can now
  solve for the optimum polarization to maximize
  the interferometric coherence
• This problem was first analyzed and reported by
  Cloude and Papathanassiou
• Using interferograms acquired with different
  polarization combinations, one can also for
  vector differential interferograms
• These vector differential interferograms have
  been shown to measure large elevation differences
  in forested areas, and cm-level elevation
  differences in agricultural fields

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EMERGING SAR TECHNIQUES POLARIMETRIC
INTERFEROMETRY COHERENCE

• Given two complex radar images, the coherence is
  defined as
• When the full scattering matrix is measured, the
  generalized coherence can be written as
• To optimize the coherence, one has to solve this
  expression for the two complex vectors

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EMERGING SAR TECHNIQUES VECTOR DIFFERENTIAL
INTERFEROMETRY

• The vector differential interferometric phase is

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EMERGING SAR TECHNIQUES TOPOGRAPHY FROM
POLARIMETRY

• A technique to infer topography from polarimetric
  signatures is under development by a group led by
  Schuler at the Naval Research Laboratories in the
  USA
• This technique is based on the fact that if a
  surface is tilted in the azimuth direction, one
  observes a shift in the maximum of the
  polarization signature
• The scattering matrix of a slightly rough surface
  tilted by an angle a with respect to the
  horizontal is

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EMERGING SAR TECHNIQUES POLARIZATION SIGNATURE
OF A TILTED SURFACE
ORIENTATION ANGLE
ORIENTATION ANGLE
ELLIPTICITY ANGLE
ELLIPTICITY ANGLE
Flat Surface
Tilted Surface
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EMERGING SAR TECHNIQUES TOPOGRAPHY FROM
POLARIMETRY

• By measuring the shift in the maximum of the
  polarization signature, the tilt of the surface
  in the azimuth direction can be estimated.
• In vegetated areas, P-Band data are used since a
  tilted surface will show a similar behavior if
  the trunk-ground interaction term is relatively
  strong
• The accuracy with which one can measure the
  surface tilt is determined by the signal to noise
  ratio
• Once the surface tilts (surface slopes) are
  known, the slopes are integrated in the azimuth
  direction to find the topography as a series of
  azimuth profiles
• Ground control points are needed to find the
  correct absolute height, and to tie different
  azimuth profiles together
• By using data acquired in a crossing flight
  pattern, the topography can be derived requiring
  only a single ground control point
• While the accuracy of this technique is not as
  good as that of interferometry, crude digital
  elevation maps can be produced.