azimuthal sar interferogram (azisar) sylvain barbot, institute of geophysics and planetary sciences,...

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