Azimuthal SAR Interferogram(azisar)

Sylvain Barbot,Institute of Geophysics and Planetary Sciences,

Scripps Institution of Oceanography,University of California at San Diego

forward look interferogram

θ

α

ϕΔ

)sin(4

1 θαλπϕ −Δ=Δ r

r

backward look interferogram

rr

Δθ

αϕΔ

)sin(4

2 θαλπϕ +Δ−=Δ r

r

range d

irecti

on

range direction

))sin()(sin(4

21 θαθαλπϕϕϕ ++−Δ=−=Δ r

r αθλπϕ sincos

8rr

Δ=Δ

double difference interferogram

double difference suppresses topography and most of troposphere delays.measurement is still ambiguous, but no more relative (Δ0 ||Δr||.cos θ= 0)

rr

Δ

Geometry

L

efficient look direction

L3

λα =

antenna width

wavelength L

r θπϕcos

38

rΔ

=Δ

first fringe Δπ occurs for ||Δr||= 3L/8=3.75m (no wavelength dependence)

Lrπϕθ

83

cosΔ

=Δr

α is the efficient look angle

α

angular energy distribution

βα

L

λ LdL

dL

L

L

λ

θθλ

π

θθλ

πθα

λ

λ

31

)(sinc

)(sinc

/

0

/

0 ≈=

∫

∫

angle first moment from energy distributionReal Aperture Radar

)ˆ(ˆˆ)ˆ.( ιιιι ××+= rrrrrr

insar dbldiffstill not measured

ι a

plane of sight

rr

azimuth (satellite track)incidence

quake slip

arr ˆ.cosrr

=Δ θ

aararar ˆ).ˆ.()ˆ(ˆrrr

+××=

Azimuth View Angle

azimuth

emitted pulse

h=800 km

S=5 km

L=10 m

fo=5.3 GHz

range

Synthetic Aperture Radar

dt

df dop

π⋅

⋅=

21

€

=0 + 2 ⋅2π

λ⋅ R + v ⋅ t( )

1/ 2

€

f dop = 2 ⋅v ⋅ t

λ ⋅R

€

Bdop = 2 ⋅v ⋅T int

λ ⋅R

vLRT

1int ⋅⋅≈λ

L

vB dop ⋅=2

Doppler frequency

Instantaneous phase

Total Dopplerbandwidth

2

Lresolutionspatial =

R

aziθ

L vr

nearest range

Illumination duration Tint

Azimuth Compression

Fd > 0

Fd = 0

Fd < 0

sensor

target

How to filter for look directions ?

Range and look direction variation with time

Look Direction

Doppler analysis

lines of equi-Doppler

lines of equidistanceflight line

illuminated area

Range/Doppler reference system

How to filter for look direction ?

θλ

sin2v

fD =

Local ground incidence angle

Doppler analysis

case of a zero Doppler centroid

2/intT

dopBt

dopf

2/intT−lookcentral

lookbackward

vr

lookforward

intT

Doppler frequency varies linearly with time

Doppler analysis

Doppler frequency variation with time/space

Frequency spectrum in azimuth

(antenna pattern modulation)

f

azifS )(

dopB

2/intTt

dopf

2/intT−

intT

Doppler centroid

vr

Doppler analysis

Image spectrum=Doppler frequency *antenna spectrum * scene impulse response

zero Doppler centroid

vr

dopf

vr

dopf

2/intT− 2/intT

dopB

intT

dopB

intT

2/intT− 2/intT

Doppler analysis

Non-zero Doppler centroid case

non-zero Doppler centroid

forward look forward lookbackward lookbackward look

Doppler Power Spectrum

Doppler frequency / PRF

Aliasing Limit (DFT)

Doppler centroid ~ 0.75

Doppler analysis

back

war

d lo

ok

forward look

back

war

d lo

ok

Doppler analysis

Doppler shift (freq. domain) = azimuth modulation (time domain)

Doppler with range

fd(r)/f0=a2r2+a1r+a0

Dopplerat acquisition

Doppler centroid modulation

IeI

IeIlffi

tlfi

d

d

)/(2

2

0~

~

π

π

=

= Δ

Now easy to take backward and forward look

shifted to center

DFT

back

war

d

backward

forward

forw

ard

no need forDoppler

compensation

Hector Mine azimuth interferogram