2.1 synthetic aperture radar (sar), grundlagenkeydel.pixelplaat.de/uploads/file/erlangen...

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1Institut für Hochfrequenztechnk und RadarsystemeQue

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1Institut für Hochfrequenztechnk und Radar

2.1 Synthetic Aperture Radar (SAR), Grundlagen

Vorlesung: Hochauflösende Radarsysteme

WS 2007/08,

Friedrich-Alexander-Universität Erlangen Nürnberg

Lehrstuhl für Hochfrequenztechnik

Wolfgang Keydel

DLR Oberpfaffenhofen, Institut für Hochfrequenztechnik und Radarsysteme

e-mail: [email protected], Web: http://www.keydel.com

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Bandwidth, B; Puls Length, τP; Range Resolution, δrg

333 psec1nsec2 nsec3,3 nsec10 nsec20 nsec100 nsecτP

5 cm

3GHZ

30 cm

500MHz

15 cm0,5 m1,5 m3,0 m15 mδrg

1GHz300MHz100 MHz50 MHz10 MHzB

, =B τP

c cBrg= =1

2 2δ τP

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Side-Looking Imaging Geometry

SN

P G TD

r kT F Lave

tot

=2 2

3 404

λ σπ ( )

SN

P G TD

r kT F Lave

tot

=2 2

3 404

λ σ0 Δd δrg

π ( )

Δd dr=

λ

SN

P G TD

r kT F dLtot

ave=2

3 304

λ3σ0 δrg

π ( )

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Auflösungszellen am Boden (Pixel)

Boden-Entfernung

Ground Range (rg)

AuflösungsgeometrieH

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Remote Sensing Terminology

Radar PulsNear Range

Far Range

Incidence Angle θi

Pixel: GroundResolution Element

Antenna Foot Print

Nadir

Swath Width

Grazing Angle

vT

ψ

θHaz

θHel

θiψ

Depression Angle

Look Angle resp.

Off NadirRange Bin = ½ Pulslänge

GroundRange

Slant Range

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E-SAR image (X-band) processed in real-time,

3 x 3 m resolution, 6 looks

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The Basic Principle of SAR

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Two dimensional SAR Scheme,

Received Doppler Frequency:

z

x

Δrr0

re

vt=x

r

LS = vTD

θHθ

f v t v tD = ≈2 2λ

ϑλ

ϑsin ( ) ( )

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SAR Foot Print Scheme

S

θH

x = vt

yGround Range

δrg

δaz

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L vfsDB

D=

2Δ

Δ Δϑ Δf v t v xrD ≈ =

2 2λ λ

( )

Beam Forming with Fixed Filter Bfix = ΔfD

1/Bmin ≤ Tmax = Time necessary to shift fD through the whole Filter Bandwidth

Corresponding Synthetic Aperture:

für Bmin = ΔfD and Tmax= ΔT

Optimum Resolution obtainable by use of a fixed Filter

rv2

Tx

rv2

Tf 2

D

λΔΔ

λΔΔ

==

2

xDB

222min r

v22r

rv2

rv2B ⎟

⎠⎞

⎜⎝⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛== δ

λλ

λλ

δ λxDB Dv

r f=2

Δ λv

rB=2

δ λxDB

r=2

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Geometric SAR Azimuth Resolution

Length of the synthetic aperture (Θa≤ 30°)

Azimuth Resolution = Half Antenna Length in Azimuth

Beam Width of the Synthetic Antenna: Θsa= da/2r0

Azimuth resolution

δsa= da/2

Synthetic Antenna Length = Ground Strip

Courtesy Alberto Moreira, DLR

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Tracking Filter leads to Matched Transmit Receive System

allows Use of Total Dwell Time TD & Largest Synthetic Aperture LS

SAR

General Valid Relations (for θH ≤ 30°)

θH = λ/d and L = θH r

dazd=2

Optimum Theoretical Azimuth Resolution for Focussed SAR

(Strip Map Mode)

L vT vB

rLS D

S= = → =azδ λ

2

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Synthetic Apertur RadarBasically Coherent Scatterometer

with

Very High Sophisticated Data Evaluation and Processing

Basis: Construction of Very Large Antenna along a flight path by means of Data Processing

Unfocussed SAR:neglects inherent Phase Differences with respect to a fixed Point

Azimuth Resolution (unfocussed) δazunfoc = ½√λR

Focussed SAR:Resolution independent of Wavelength & Distance

Azimuth Resolution δaz = d/2

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14Institut für Hochfrequenztechnk und RadarSAR is an Antenna

r0r-

n

rn

Flight Direction

SAR Sensor

Point Target

r0 rnr-n

ReceivedAzimutSignal

Two Way Antenna Pattern

SAR Processor Detection

Coherent Summation Convolution

Point Target Response

SAR Resolution

Phase Correction

Real Antenna

Beamwidth

The Antenna: System Determining Element for SAR


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SAR Block Diagramm

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SAR Range Equation

Normal Radar Equation (Hall)

SAR Radar Equation Point Target

SAR Radar Equation Area Target

T rvD

az=

2λδ

SN

P G Tr kT F L

ave D

tot

=2 2

3 404

λ σπ ( )

SN

P Gr kT F v L

ave

az tot

=2 3

3 304 2

λ σπ δ( )

SN

P G

r kT F vLave rge

tot

=2 3

03 3

04 2

λ σ δ

πa f ( )

σ σ δ δ= o az rge

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All SAR Design Equations contain Antenna Parameter!!

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SAR – RAR Comparision

Im-prove-ment

SAR

RAR

Contrast (S/C = SCR)Area Target (C/N = CNR)Point Target (S/N =SNR)Type

=

(SNR)SAR = =

(SNR)SAR BτP(PRF)λrvrg

=δ 2(SNR)RAR

(PRF)d

v2

(SNR)SAR=

(SNR)RAR

BτPrλdδαζ

(SCR)SAR=

(SCR)RAR

=

P GR kT F BτP(PRF) Ltot

ave=2 2

3 404

λ σπ

(SNR)RAR

= dr B P rg

σσ λ τ δ0

(S/N)RAR

=

P G

R kT F (PRF)Lave rg

tot

2 30

3 304

λ σ δ

π

(SNR)RAR

azrg=

σσ δ δ0

(S/N)SARP GR kT F v L

ave

az tot

=2 2

3 304 2

λ σπ δ

P G

R kT F vLave rg

tot

=2 3

03 3

04 2

λ σ δ

π

(SNR)SAR

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Pulse Repetition Frequency

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Pulse Repetition Frequency (PRF)Dominating Factor in SAR Design

Principal Limitations:Ú Azimuth & Range AmbiguitiesÚ Swath Coverage- & Extension RequirementsÚ Forbidden PRF Bands due to

h Altitude Line Echo (ALE)h Altitude Variationsh Earth Curvature & Orbit Excentricities

Lower Limit: 2vd-1 < PRFTransmitter must be pulsed before platform moves ½ the Antenna Length d

Upper Limitdefined by Range Ambiguity Requirements Impulse needs for crossing the Swath along rgmax the Time tgmax= c (2 rgmax)-1

22

vd

PRF crg

≤ ≤max

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Pulse Spectrum Scheme Moving Pulse Doppler Radar

Single Spectral Line Fine Structure

Pulse Spectrumwith

Ambiguities

Single Spectral Lines

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PRF Limitations due to Altitude VariationsAllowed PRF Bands for X-Band Satellite

Ambiguity Limit1064 HZ

m = Number of allowed

Range Ambiguities

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PRF choice for X-SAR/SRTMTransmit & Nadir Interference Limitations

Objective: A fixed combination of PRF and Off-nadir angle• takes into account the historical development and restrictions,• avoids transmit and preferably nadir interferences and• yields a good interferometric performance.

1200 1400 1600 1800PRF / Hz

10

20

30

40

50

60DLR

nadir interference

transmit interference

Orbit height = 233 km

Off-

nadi

r ang

le /

deg

Off-

nadi

r ang

le /

deg

Orbit height = 249 km

1200 1400 1600 1800PRF / Hz

10

20

30

40

50

60DLR

nadir interference

transmit interference

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System Parameters of the X-SAR Instrument

• Orbit height from 233 km to 249 km (coverage requirement of C-Radar)

• PRF limited to eleven fixed values ranging from 1240 Hz up to 1736 Hz

• Off-nadir angle > 51° to avoid interference with Attitude and Orbit Determination Avionics (AODA)

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Ambiguities

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X-SAR Ambiguities

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Airport Zürich Klothen with & without Ambiguitiescaused by 6,8° Antenna Squint Angle

Ambiguities E-SAR, X-VV, θHH= 12°, v = 70 msec-1

Near Range 2805m, Far Range 5355mCourtesy Alberto Moreira, DLR

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Ambiguities due to Multipath Reflection (Bridge)

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Μυλτι−Φρεθυενχψ Ε−ΣΑΡ−Ιμαγε (Λ, Χ, ανδ Ξ−βανδ)

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x

Phase Information is decisive for SAR

r0r

r ≈ r0

Transmitted: VT= V1 sinωt Received: Vr= V2 sin(ωt + ωDt)

Linear Frequency Modulation

2 2

0

vrλ

Chirp Steepness: Bandwidth Required: B vr

TfD D=2 2

0λv

=2δaz

r r vt r r vtr

r r vtro

202 2

0

2

02

0

2

2

= + − ≈

≈ +

==>

Two Way Phase: =>ϕ πλ

ω π ϕ πλ

= + = = =2 2 40

2 2

0

2

0r v t

rf d

dtvr

tD D

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Azimuth Signal

V = 70 msec-1, λ = 5,6 cm, r0 = 5000 m

Phase/Degree

Frequency/Hz

Normalized Anplitude


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Phase ReferencePhase contents all Target Information required. Quadratic Demodulation provides Phase Information with INPHASE (I) & QUADRATURE (Q) Component.

Target Position at t=0 where fD = 0

Further Information by Correlation with Reference Function for Point Target Sref(t) = Ssig (t)

So(t) at Correlator Output

I (t) A v tr

t Q t A v tr

t

S (t) I t jQt j v tr

t A

o o

sigo

= =

= + = =

cos sin

exp

2 2

2 1

2 2

2

πλ

πλ

πλ

&

with

S (t) = S (t)S (t - )dt = exp expcor sig ref* τ π τ

λπ τ

λ−

+

−

+

− −∫TD

TD

o oTD

TD

j vr

j vr

t dt

2

2 2 2

2

22 2

S ( ) = expcor τ π τλ

πλ

τ− j vr

c v Tro

D

o2

2 2 2sin

∫

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RAR – SAR Point Target Signal Comparision


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SAR Processing uses Pulse Response Function in bothAzimuth and Range Impulse Response Function

s x B T cB x x

v

s r B T cB r r

c

az az Daz

rg rg rgrg

=−

=−

sin

sin

π

π

0

02

( )

( )


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Influence of Weighting

Impulse response function with Hamming weighting (= 0.54) w ( t ) =


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Quality MeasuresPeak Sidelobe Ratio & Integrated Sidelobe Ratio

PSLR =Power within Sidelobes

Power within Main BeamISLR =

Power within Sidelobes

Power within Diagram

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Characteristics of Impuls Response Function


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SAR, Measured I- & Q-Signals

Point Target, Frequency Modulated Signals

L-Band, H = 400m, r0 = 1590m, v = 60m sec-1

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Raw Data

SAR Image


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Unfocussed SAR

T rvD =λδ az

z

x

Δrr0

re

Vt=x

r

LS = vTD

θHθ

Focussed SAR needs Phase Compensation during Dwell Time

Unfocussed SAR ignores Δr ≤ λ/16

Required Dwell Time for Specified δaz

θH= d/r0

Δr ≤ λ/16 ==> Maximum Apertur Length for Unfocussed SAR

(LS/2)2 = ro2 - ro

2 ≈ 2ro(re - ro )

L r dSunmax ≤ 0

2Resolution obtainable for Unfocussed SAR

δ azunfoc= 2λr1

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Depth of Focus (DOF) Defines Nr. of Reference Functions required over the Whole Swath

x = vt

S

θH

yGround Range

δrg

δaz

DefinitionDoF = 2Δr0

Required Accuracy to match a given quadratic Phase Reference Function to the considered Range

Maximum allowed Phase Error IΔr - Δr0I =λ/8

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Depth of Focus (DOF) Defines Nr. of Reference Functions required over the Whole Swath

Definition: DoF = 2Δr0

Required Accuracy to match a given quadratic Phase Reference Function to the considered Range for

Maximum allowed Phase Error IΔr - Δr0I =λ/8

r r L drdr

r drdr

r rr

r

r L

Lr

r r r Lr

s

o s

202

2

00

0

0

02

2

2

02

0 0

2

02

22 2

2

1 18

2 2 8

= + → = = → =

+

≈ −

− = =

ΔΔ

Δ Δ Δ λ

λδλ

2

2

20

0 822 az

LrrDOF ==Δ=

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λδ 2

az8

Depth of Focus (2):

DOF =

The depth of focus becomes smaller as δaz is made smaller.

Example:X = 5 cm, δaz = 3 m DOF ≈ 1.44 km

Processing of a 4.3 km swath requires 3 different reference functions.

If δaz = 50 cm under the same conditions: DOF ≈ 40 m 10 references are required increasing the processing complexity.

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SAR Data Flow


2.1 synthetic aperture radar (sar), grundlagenkeydel.pixelplaat.de/uploads/file/erlangen...

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