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Interferometric Synthetic-Aperture Radar (InSAR) and Applications

Chris Allen (callen@eecs.ku.edu)

Course website URL www.cresis.ku.edu/~callen/826/EECS826.htm

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OutlineSyllabus

Instructor information, course description, prerequisites

Textbook, reference books, grading, course outline

Preliminary schedule

Introductions

What to expect

First assignment

Radar fundamentalsActive RF/microwave remote sensing

Electromagnetic issues

Antennas

Resolution (spatial, range)

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SyllabusProf. Chris Allen

Ph.D. in Electrical Engineering from KU 1984

10 years industry experience

Sandia National Labs, Albuquerque, NM

AlliedSignal, Kansas City Plant, Kansas City, MO

Phone: 785-864-3017

Email: callen@eecs.ku.edu

Office: 321 Nichols Hall

Office hours: Tuesdays and Thursdays2:00 to 2:30 p.m. and 3:45 to 4:30 p.m.

Course descriptionDescription and analysis of processing data from synthetic-aperture radars and interferometric synthetic-aperture radars. Topics covered include SAR basics and signal properties, range and azimuth compression, signal processing algorithms, interferometry and coregistration.

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SyllabusPrerequisites

Introductory course on radar systems (e.g., EECS 725)

Introductory course on radar signal processing (e.g., EECS 744)

TextbookProcessing of SAR Databy A. HeinSpringer, 2004, ISBN 3540050434

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SyllabusReference books

Synthetic Aperture Radar Processingby G. Franschetti and R. LanariCRC Press, 1999, ISBN 0849378990

Digital Processing of Synthetic Aperture Radar Databy I. Cumming and F. WongArtech House, 2005, ISBN 1580530583

Spotlight-Mode Synthetic Aperture RadarC. Jakowatz, et al,Springer, 1996, ISBN 0792396774

Synthetic Aperture Radar: Systems and Signal ProcessingJ. Curlander and R. McDonoughWiley, 1991, ISBN 047185770X

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Grades and course policiesThe following factors will be used to arrive at the final course grade:

Homework, quizzes, and class participation 40 %Research project 20 %

Final exam 40 %

Grades will be assigned to the following scale:A 90 - 100 %B 80 - 89 %C 70 - 79 %D 60 - 69 %F < 60 %

These are guaranteed maximum scales and may be revised downward at the instructor's discretion.

Read the policies regarding homework, exams, ethics, and plagiarism.

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Preliminary scheduleCourse Outline (subject to change)

SAR system overview and signal properties 1 weeks(data recording, nonideal motion, layover and shadowing, moving targets)

SAR radar range equation and associated geometries 2 weeks(side-looking, squint, and spotlight modes)

SAR signal processing 3 weeks(range and azimuth compression, range migration, autofocus)

SAR signal processing algorithms 2 weeks(range-Doppler, scaling, omega-k)

Interferometry 6 weeks(registration, decorrelation, phase unwrapping, implementation, terrain mapping, surface velocity mapping, change detection, single-pass vs. multi-pass)

Class Meeting ScheduleJanuary: 15, 20, 22, 27, 29February: 3, 5, (10th to 12th NSF Site Visit), 17, 19, 24, 26March: 3, 5, 10, 12, (17th to 19th Spring Break), 24, 26, 31April: 2, 7, 9, 14, 16, 21, 23, 28, 30 May: 5, 7

Final exam scheduled for Friday, May 15, 1:30 to 4:00 PM

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Introductions

Name

Major

Specialty

What you hope to get from of this experience(Not asking what grade you are aiming for )

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What to expectCourse is being webcast, therefore …

Most presentation material will be in PowerPoint format Presentations will be recorded and archived (for duration of semester)

Student interaction is encouragedStudents must activate microphone before speaking

Please disable microphone when finished

Homework assignments will be posted on websiteElectronic homework submission logistics to be worked out

We may have guest lecturers later in the semester

To break the monotony, we’ll try to take a couple of 2-minute breaks during each session (roughly every 15 to 20 min)

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InSAR

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Your first assignmentSend me an email (from the account you check most often)

To: callen@eecs.ku.edu

Subject line: Your name – EECS 826

Tell me a little about yourself

Attach your ARTS form (or equivalent)

ARTS: Academic Requirements Tracking System

Its basically an unofficial academic record

I use this to get a sense of what academic experiences you’ve had

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SAR image of Los Angeles area

SEASAT Synthetic Aperture Radarf: 1.3 GHz PTX: 1 kWant: 10.8 x 2.2 m B: 19 MHzx = y = 25 m pol: HHorbit: 795 km DR: 110 Mb/s

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SEASAT suffered a massive electrical short in one of the slip ring assemblies used to connect the rotating solar arrays to the power subsystem.

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SAR image of Gibraltar

ERS-1 Synthetic Aperture Radarf: 5.3 GHz PTX: 4.8 kWant: 10 m x 1 m B: 15.5 MHzx = y = 30 m fs: 19 MSa/sorbit: 780 km DR: 105 Mb/s

Nonlinear internal waves propagating eastwards and oil slicks can be seen.

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PRARE: precise range and range rate equipment

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Radar fundamentals (review)ERS-1 Synthetic Aperture Radar

Radar center frequency, f: 5.3 GHz• C-band, = c/f = 5.7 cm

c = 3 x 108 m/s

Antenna dimensions, ant: 10 m x 1 m (width x height)• Approx. beamwidth, /antenna dimension az 0.057 m/10 m = 5.7 mrad or 0.32° el 0.057 m/1 m = 57 mrad or 3.2°• Antenna gain, G 4/(az el)• G(dBi) = 10 log10(G)

dBi is dB relative to isotropic antenna

• G = 4/(0.057 x 0.0057) = 38700 or 46 dBi• Minimum along-track resolution, ymin = ℓ/2

ℓ is antenna’s along-track dimension

• ℓ = 10 m, ymin = 5 m, y = 30 m > ymin

Bandwidth, B: 15.5 MHz• Range resolution (slant range, cross-track), r = c/2B r = c/(2 x 15.5 MHz) = 9.7 m• Ground resolution (cross-track), x = r /sin is the incidence angle

Pulse duration, : 37.1 s• Pulse compression ratio, B = 575 (28 dB)

B(dB) = 10 log10(B)

• Blind range c/2 = 5.6 km

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Radar fundamentals (review)ERS-1 Synthetic Aperture Radar

Sampling frequency, fs: 19 MSa/s, 5 b/sample, I/Q• Nyquist requires fs ≥ 15.5 MSa/s

• fs = 1.23 Nyquist rate (23% oversampling)

Orbit altitude, h: 780 km• Orbital velocity, v,

for Earth, = 398,600 km3/s2

• Ground velocity, vg,

Re = 6378.145 km

• v = 7.46 km/s, vg = 6.65 km/s

• Minimum pulse-repetition frequency, PRFmin = 2v/ℓ

• PRFmin = 2(7460)/10 = 1490 Hz

• 1720 Hz ≥ PRF ≥ 1640 Hz (from ERS specs)

Look angle, : 23°• sin = (1 + h/Re) sin = 26°• Ground resolution, x = r /sin x = 22 m

s/km,hRv e

hRRvv eeg

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Radar fundamentals (review)ERS-1 Synthetic Aperture Radar

Ground swath width, Wgr: 100 km• Slant swath width, Wr = Wgr sin • Wr = 43.8 km

• Echo duration from swath, s = + 2 Wr/c

s = 37.1 s + 292 s = 329.1 s

Data rate, DR: 105 Mb/s• Samples/echo = 329.1 s x 19 MSa/s = 6250 Samples/echo• Sample rate = PRF x Samples/echo• Sample rate = 1640 x 6300 = 10.3 MSa/s• Data rate = Sample rate x bits/sample = 10.3 MSa/s x 10 bits/Sa = 103 Mb/s

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Ka-band, 4″ resolutionHelicopter and plane static display

f: 35 GHz

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Sandia’s real-time SARSandia SAR system

LynxCountry USADate 1998Frequency 15.2 to 18.2 GHzPolarization VVBeamwidth (deg) 3.2 az, 7 el.Slant range 7 to 30 kmSwath width 2600 pixelsTransmit power 320 WNoise equivalent RCS -30 dBsmNF 4.5 dBSampling (8 b @ 125 MS/s)Mode stripmap / spotlightResolution (slant & azimuth) 0.3 / 0.1 mMass 125 lbsProcessing stretchSquint angle (deg) 45 to 135Weather restriction 4-mm/hr rainfall rateUAV platforms Predator, I-GNAT, Prowler IICrewed platforms Blackhawk, KingAir 200

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Radar fundamentals (review)Radar range equation, received signal power, and signal-to-noise ratio

For a monostatic radar system and a point target

Where

Pt is the transmitted signal power, W

Pr is the power intercepted by the receiver, W

G is the gain of the antenna in the direction of the targetR is the range from the antenna to the scatterer, m is the target’s radar scattering cross section (RCS), m2

is the wavelength of the radar signal, m

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22t

rR4

GPP

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Radar fundamentals (review)Receiver noise power, PN

k is Boltzmann’s constant (1.38 10-23 J K-1)

T0 is the absolute temperature (290 K)

B is receiver bandwidth, Hz

F is receiver noise figure

Signal-to-noise ratio (SNR) is

may be expressed in decibels

W,FBTkP 0N

FBTkR4

GPPPSNR

043

22t

Nr

SNRlog10dBSNR 10

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Radar fundamentals (review)Example: Sandia Lynx SAR

Radar center frequency, f = 16 GHz

Transmit power, PT = 320 W (55.1 dBm)

dBm: dB relative to 1 mW

Slant range resolution, r = 0.3 m (1 ft)

Receiver noise figure, FREC = 2.8 (F = 4.5 dB)

Antenna beamwidths, 3.2° x 7°

Range to target, R = 30 km (18.6 miles)

Target RCS, = 0.001 m2 (-30 dBsm) = ° x y

Find the Pr , PN , and the SNR

First derive some related radar parameters

Wavelength, = c/f = 0.01875 m

Antenna gain, G 4/(az el) G = 1840 or 32.6 dBi

Bandwidth, B = c/2r B = 500 MHz

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Radar range equation exampleFind Pr

Solve in dB

Pr(dBm) = Pt(dBm) + 2G(dBi) + 2 (dB) + (dBsm) – 3 4(dB) – 4 R(dB)

Pt(dBm) = 55.1 G(dBi) = 32.6 (dB) = -17.3 (dBsm) = -30

4(dB) = 11 R(dB) = 44.8

Pr(dBm) = -156.3 dBm or 2.3 10-19 W (0.23 aW)

Find PN

Solve in dB

PN(dBm) = kT0(dBm) + B(dB) + F(dB)

kT0(dBm) = -174 B(dB) = 87 F(dB) = 4.5

PN(dBm) = -82.5 dBm or 5.6 pW

Find SNRSNR = – 156.3 – (– 82.5) = -73.7 dB or 4.3 10-8

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22t

rR4

GPP

W,FBTkP 0N

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Radar fundamentals (review)Signal processing improves SNR

Pulse compression gain, BAssuming = 20 s yields a 40-dB pulse compression gain

Coherent integration improves SNR by NN is the number of integrations

N = synthetic-aperture length * PRF / velocity

Synthetic-aperture length, L = az R, L = 1675 m

Assume velocity = 36 m/s (Predator UAV cruise speed is 130 km/h )

Assuming a 1-kHz PRF

N = 46500 or 46-dB improvement

Therefore the SNR from a -30-dBsm target is 12.3 dBMany measurements require SNR > 10 dB

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Airborne SAR block diagram

New terminology:Magnitude imagesMagnitude and Phase ImagesPhase HistoriesMotion compensation (MoComp)Autofocus

Timing and ControlInertial measurement unit (IMU)GimbalChirp (Linear FM waveform)Digital-Waveform Synthesizer

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Airborne SAR real-time IFP block diagram

Image-Formation Processor

New terminology:Presum (a.k.a. coherent integration)Corner-turning memory (CTM)Window Function

Focus and Correction VectorsRange Migration and Range WalkFast Fourier transform (FFT)Chirp-z transform (CZT)

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InSAR Coherent Change Detection

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Backscattering

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Radar response to extended targetsThe preceding development considered point target with a simple RCS, .

The point-target case enables simplifying assumptions in the development.

Gain and range are treated as constants

Consider the case of extended targets including surfaces and volumes.

The backscattering characteristics of a surface are represented by the scattering coefficient, ,

where A is the illuminated area.

A

unitless,p,p;, s0

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22t

rR4

GPP

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Factors affecting backscatterThe backscattering characteristics of a surface are represented by the scattering coefficient,

For surface scattering, several factors affect Dielectric contrast

Large contrast at boundary produces large reflection coefficientAir (r = 1), Ice (r ~ 3.2), (Rock (4 r 9), Soil (3 r 10), Vegetation (2 r 15), Water (~ 80), Metal (r )

Surface roughness (measured relative to )RMS height and correlation length used to characterize roughness

Incidence angle, ()

Surface slopeSkews the () relationship

PolarizationVV HH » HV VH

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Surface roughness and backscatter

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Backscatter from bare soil

Note: At 1.1 GHz, = 27.3 cm

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Backscattering by extended targets

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Detecting flooded lands

Combination of water surface and vertical tree trucks forms natural dihedral with enhanced backscatter.

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Detecting flooded lands

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Doppler shifts and PRF

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Doppler shifts and radial velocityThe signal from a target may be written as

c = 2fc

and the relative phase of the received signal,

A target moving relative to the radar produces a changing phase (i.e., a frequency shift) known as the Doppler frequency, fD

where vr is the radial component of the relative velocity.

The Doppler frequency can be positive or negative with a positive shift corresponding to target moving toward the radar.

rad,R2

2Rk2

Hz,v2

R2

dt

d

2

1f r

D

Rk2tj0

ceEtE

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Doppler shifts and radial velocityThe received signal frequency will be

ExampleConsider a police radar with a operating frequency, fo, of 10 GHz.

( = 0.03 m)

It observes an approaching car traveling at 70 mph (31.3 m/s) down the highway. (v = -31.3 m/s)

The frequency of the received signal will be

fo – 2v/ = fo + 2.086 kHz or 10,000,002,086 Hz

Another car is moving away down the highway traveling at 55 mph (+24.6 m/s). The frequency of the received signal will be

fo – 2v/ = fo – 1.64 kHz or 9,999,998,360 Hz

R2ffff cDc

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Doppler shifts and radial velocityGiven the position, P, and velocity, u, both the radar and the target, the resulting Doppler frequency can be determined

The ability to resolve targets based on their Doppler shifts depends on the processed bandwidth, B, that is inversely related to the observation (or integration) time, T

Instantaneous position and velocity Relative velocity, u

Radial velocity component

uRadar

uTarget

u = uRadar - uTarget

Hz,T1fB D

uRadar uTarget

PRadarPTarget

RRadar path

Target path

u

R (unit vector)^ ^

=

uRadial = u R

uTangential

u

uR = u cos()

fD = 2 u cos() /

^

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Pulse repetition frequencies (PRFs)The lower limit for PRFs is driven byDoppler ambiguities

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Doppler ambiguitiesTo unambiguously reconstruct a waveform, the Nyquist-Shannon sampling theorem (developed and refined from the 1920s to

1950s at Bell Labs) states that exact reconstruction of a continuous-time baseband signal from its samples is possible if the signal is bandlimited and the sampling frequency is greater than twice the signal bandwidth.

Application to radar means that the pulse-repetition frequency (PRF) must be at least twice the Doppler bandwidth. For side-looking SAR (centered about 0 Doppler), the PRF must be twice the highest Doppler shift.

For the case where the Doppler frequency shift will be 250 Hz (a 500-Hz Doppler bandwidth), the PRF must be at least 500 Hz.

[The Nyquist-Shannon theorem also has application to signal digitization in the analog-to-digital converter (ADC) requiring that the ADC sampling frequency be at least twice the waveform bandwidth.]

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PRF constraintsRecapping what we’ve seen—

The lower PRF limit is determined by Doppler ambiguities

The upper PRF limit is determined by the range ambiguities

EclipsingFurthermore, for systems that do not support receiving while transmitting, various forbidden PRFs will exist that will eclipse the receive intervals with transmission pulses, which leads to

where Tnear and Tfar refer to signal arrival times for near and far

targets, is the transmit pulse duration, and N represents whole numbers (1, 2, 3, …) corresponding to pulses

bandwidthDopplertheisf,f2PRF DDmin

rangesunambiguoutheisR,R2

cPRF u

umax

farnear T

NPRF

T

1N

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Spherical Earth calculationsSpherical Earth geometry calculations

Re Earth’s average radius (6378.145 km)

h orbit altitude above sea level (km)

core angle

R radar range

look angle

i incidence angle

i

sin

R

sin

R

sin

hR e

i

e

coshRR2hRRR ee2

e2e

2

Re

Re

NadirPoint

h R

i

Radar Position

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Spherical Earth calculationsSatellite orbital velocity calculations (for circular orbits)

Re Earth’s average radius (6378.145 km)

h orbit altitude above sea level (km)

v satellite velocity

vg satellite ground velocity

standard gravitational parameter (398,600 km3/s2 for Earth)

s/km,hRv e

hRRvv eeg

Re

hRfRn

swath

Radar VelocityAntenna pattern

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Spherical Earth calculationsSwath width geometry calculations

Re Earth’s average radius (6378.145 km)

Rn range to swath’s near edge

Rf range to swath’s far edge

Wgr swath width on ground

Wr slant range swath width

n core angle to swath’s near edge

f core angle to swath’s far edge

i,m incidence angle at mid-swath

enfgr RW

nfr RRW

Re

Re

h Rf

n

f

Rn Wri,m

Wgr

m,igrr sinWW

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PRF constraints

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PRF constraints

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PRF constraints

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Antenna length, velocity, and PRFGiven an antenna length, ℓ

wavelength,

velocity, v

We know

The Doppler bandwidth, fD, is

Therefore PRFmin is

2

v22sin

v2fD

vvv

fD

(small angle approximation)

v2f2PRF Dmin

Note that PRFmin is independent of

Aircraft casev = 200 m/s, ℓ = 1 mPRFmin = 400 Hz

Spacecraft casev = 7000 m/s, ℓ = 10 mPRFmin = 1.4 kHz

fD < 0

ℓv

fD > 0

antenna

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Three moving targets traveling on a runway at the Patuxent River Naval Air Station.

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Real-aperture side-looking airborne radar(SLAR)

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Side-looking airborne radar (SLAR)SLAR systems produce images of radar backscattering mapped into slant range, R, and along-track position.The along-track resolution, y, is provided solely by the antenna. Consequently the along-track resolution degrades as the distance increases. (Antenna length, ℓ, directly affects along-track resolution.)

Cross-track ground range resolution, x, is incidence angle dependent

Ry az

sin2

cx p where p is the compressed

pulse duration

y

xx

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Side-looking synthetic-aperture radar (SAR)

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Synthetic-aperture radar (SAR)Synthetic-aperture radar is an imaging radar concept that was developed in the early 1950s by Goodyear Aircraft Company.

It is remarkable in that when fully processed, SAR images have very fine resolution that are range independent.

Numerous variations of SAR have been derived from the basic concept and these include inverse SAR (ISAR), interferometric SAR (InSAR), and ScanSAR.

The basis concept for SAR appears fairly simple though upon inspection it is more complex.

The core concept may be thought of in at least five different ways:

Synthesized antenna aperture

Doppler beam sharpening

Correlation with reference point-target response

Matched filter for received point-target signal

De-chirping of Doppler frequency shift

Optical focusing equivalent

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Synthetic-aperture radar (SAR)In SAR systems a very long antenna aperture is synthesized resulting in fine along-track resolution.For a synthesized aperture length, L, the along-track resolution, y, is

As with SLAR, the cross-track resolution, x, is incidence angle dependent

L, is determined by the system configuration.For a fully focused stripmap system, Lm = azR (m), where

az is the azimuthal or along-track beamwidth of the real antenna (az /ℓ)

R is the range to the target

For L = Lm, y = ℓ/2 (independent of range and wavelength)

For unfocused SAR, the maximum synthetic aperture length, Lum, is

For L = Lum,

sin2

cx p

L2Ry

)m(,2RLum

)m(,2Rrau

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Synthetic-aperture radar (SAR)In the fully focused stripmap SAR mode, the synthetic-aperture length is determined by the length of the flight path during which a target in the antenna’s field of view.

RRL azm

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Synthetic-aperture radar (SAR)In spotlight mode, the synthetic aperture length L may exceed Lm because the antenna is steered to illuminate the

region of interest as the system passes by, and

where (radians) is the change in aspect angle over which the target is viewed.

For small , y /(2)

m,2sin4

y

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SAR data collection modes

In strip mode, the along-track resolution (y) is determined by synthetic-aperture length (L)

In spotlight mode, y /(2) where (radians) is the change in aspect angle over which the target is viewed.

2/y

L2Ry

RRL az

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Inverse SAR (ISAR)Inverse synthetic-aperture radar (ISAR) (not to be confused

with InSAR) involves forming range-azimuth radar images of a moving target using a stationary radar.

Synthetic aperture formation requires only relative motion and is not restricted to a moving radar system.

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Inverse SAR (ISAR)While primarily used in military applications, ISAR does have scientific value.

Radar images of 3.5-km asteroid 1999 JM8 at a range of 8.5x106 km (22x Earth-Moon separation distance).Images labeled A were produced from data collected by Arecibo and have 15-m range resolution.

Images labeled G produced from data collected by Goldstone. G1 has 38-m resolution, G2 has 19-m resolution.

A

A

G1

G2

Aug 5, 1999 July 28, 1999

Aug 2, 1999Aug 1, 1999

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Arecibo Observatory

Funded by National Science FoundationOperated by Cornell University

Located in Puerto Rico

1-MW transmitterf: 2.38 GHz, : 12.6 cm

305-m diameter, non-steerable reflector (Earth’s largest curved focusing dish)

Collects data for: radio astronomy (passive),terrestrial aeronomy (study of Earth’s upper atmosphere),planetary radar studies

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Goldstone Solar System RadarPart of NASA/JPL Deep Space Network (DSN)

Located in California

Fully-steerable 70-m parabolic reflector500-kW transmitter

f: 8.560 GHz: 3.5 cm

Operates in both monostatic and bistatic modes with New Mexico’s twenty-seven 25-m antennas Very Large Array or Arecibo