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Synthetic Apetue Rd Pocessing SAR nd IFSAR Giogio Fnceschetti Univesit Fedeico II Npoli Itly 1

REFERENCE TEXT Giogio Fnceschetti Riccdo Lni SYNTHETIC APERTURE RADAR PROCESSING TECHNIQUES CRC Pess BOCA RATON Fl 1999

3

Tle of content Bsic concepts Pocessing Intefeometic SAR 4

Bsic Concepts Geomety Response in Time Domin Response in Fequency Domin 5

I. Geomety 1. Cylindicl efeence coodinte system 6

. Boesight stip mode illumintion geomety 7

3. Boesight cquisition geomety in the () plne 8

9 II. SAR esponse in time-domin 1. Tnsmitted wvefom fo the chip cse () ( ) ( ) τ ω n n t t t t P t j t f ect ep 1 ( ) ( ) α ep n n t t j t t P

1. Received wvefom fom unity sctteed t fte heteodine with ( ) [ ] w c R t t c R t t P c R j t t f n n n n n ect ep τ ω ( ) R n + ) ( ϑ

3. Chnge of Coodintes ct t t t n R R + ( ) n 4. Nomlize to R L to X cτ 11

1 5. Received wvefom with ( ) ( ) ( ) g dd h γ ( ) ( ) τ π γ γ c j ep ( ) [ ] w R L j R c X R c X P g ep ect τ τ L X π

III. SAR esponse in fequency-domin 1. SAR signl spectum H ( ) d d h( ) ep( j ) ep( j ) G ddγ ddγ whee ( ) d d g( ) ep( j ) ep( j ) ( ) ep( j) ep( j) G( ) ( ) d d g( ) ep[ j( ) ] ep[ j( ) ] is the SAR tnsfe function. Simplest cse H ( ) ddγ( ) ep( j) ep( j) G( ) Γ( ) G( ) 13

Pocessing Asymptotic evlution of integls Tnsfe Function epnsion Now Focus SAR Wide Focus SAR 14

I. Asymptotic evlution of integls 1. Type of integl I ( Ω) dtf ( t) ep[ jωq( t) ] with Ω >> 1. Asymptotic evlution q I () t q( t ) s ( ts ) ( ) t t q ( t ) ( Ω) ~ dtf ( t) ep[ jωq( t )] q +! s s s ep jωq s ( t t ) s ~ πj Ωq s f ( t ) ep[ jωq( t )] s s 15

3. Emples F ( ) 1/ dq ep[ jq] ep[ jq ] ~ ect ep j 1/ 16

17 II. Tnsfe function evlution ( ) f f f X c p X c R f R L p R c X R L p p R c X q p ω π ε τ + τ π τ ε + + τ + + Ψ τ 1 1 1. Convenient evlution fom Let we hve ( ) ( ) [ ] [ ] [ ] ( ) [ ] Ψ q q P q j dq p w p j dp G ect ep ep 1

Fo chiped signl G with Ψ ( ) dp ep[ jψ ( p) ] w [ p ] dq ep[ j ( q) ] ect[ q] ( q) 1 Ψ q q L ( p) p R Ψ + 1 + 1 ε π fτ 18

19. Asymptotic evlution ( ) ( ) ( ) [ ] ( ) [ ] j w j w G ep ect ep ect ~ π π Ψ Ψ with ( ) + ε + + ε Ψ w L L L ect 1 1 4

3. Simplest SAR tnsfe function epession Epnsion ound leds to + ε + ε + ε L L L 1 4 / 1 1 nd with Accodingly ( ) + ε + ε Ψ 1 4 4 1 4 4 ( ) j j G 4 ep ect 4 ep ect

1 4. Resolution f f f L X L d d G H j j d d G H G H / / 1 / )] ' ( )]sinc[ ' ( )sinc[ ( ) *( ) ( '] ']ep[ ep[ 1 ect ) ect ( ) *( ) ( ) ( ) ( ) ( Γ Γ τ π π γ π

III. Tnsfe function epnsion 1. SAR tnsfe function eclled ( ) ( ) ( ) [ ] ( ) [ ] ( ) 1 1 4 ep ect ep ect ~ + ε + + ε Ψ Ψ π Ψ π L L L j w j w G

3. Tnsfe function phse epnsion ound Let ( ) ( ) ) ( ) ( + Ψ Ψ K with ( ) ( ) ( ) 1 1 1 1 4 + ε + + ε + ε + + ε Ψ Ψ L L L K L L L

we hve K with µ v ζ ( ) µ ( ) + v( ) + ζ( ) ( ) ( ) ( ) 4 4 4 ε ε 4

III. Now focus SAR 1. Simplest ppoimtion Assume µ v ζ G ( ) G ( ). SAR pocessing Fom H ( ) G( ) Γ( ) we get * ( ) H ( ) ( ) Γ G 5

3. Emples Refeence Imge 6

Uncompensted µ ( ) tem 7

Uncompensted v( ) tem 8

IV. Wide focus SAR 1. Stting point H G ( ) G ( ) ddγ( ) ep( j) ep[ j( + K( ) ) ] ( ) Γ[ + K( ) ] with K ( ) µ ( ) + v( ) Accodingly H ( ) G( ) Γ[ ( 1+ v( ) ) + µ ( ) ] G( ) Γ[ Ω( ) + µ ( ) ] Ω( ) 1+ v( ) 9

. Rnge pocessing FT 1 ep * 1 [ H ( ) G ( ) ] dep[ j ] Γ[ Ω( ) + µ ( ) ] jµ ( ) Ω ˆ π ( ) γ Ω( ) 3

3. Simplest cse v so tht Ω 1 H ( ) G ( ) Γ[ + µ ( ) ] 31

4. Chip scling Ω B C D A B D ( 1+ B D) ( 1+ B D) 3

Rnge pocessing 33

Full pocessing 34

Intefeometic SAR Bsic pinciples Decoeltion effects Phse Unwpping techniques Emples 35

I. Bsic pinciples 1. Geomety Single imging senso Dul imging senso 36

Reltions ( + δ ) + l l sin( ϑ β) z led to H cosϑ z z ϑ + δ sin ϑ δ ϑ δ l cos. Intefeometic phse 4π [ ] δ * ( ) Ph γˆ ( ) γˆ ( + δ ) ϕ 1 so tht z sin ϑ l cos ( ϑ β) sin ϑ z ϕ 4πl ϕ 4π sin ϑ ( ϑ β) l cos( ϑ β) sin ϑ ϕ 4πl 37

In ode to compute the intefeometic phse the following steps must e implemented () A couple of SLC imges must e geneted 38

39 () The two imges must e egisteed fo infinite ndwidth SAR ( ) ( ) ( ) [ ] ( ) [ ] ( ) ( ) ( ) ( ) [ ] ( ) [ ] j dd j dd δ + δ π γ γ π γ γ sinc sinc 4 ep ˆ sinc sinc 4 ep ˆ 1 ( ) ( ) ( ) ( ) π δ γ γ π γ γ j j 4 ep ˆ 4 ep ˆ 1 nd egisttion is equied ( ) ( ) ( ) ( ) + δ π γ + δ γ γ j 4 ep ˆ ˆ

Intefeometic finges 4

II Decoeltion effects 1. Misegisttion ccucy of 1/ of piel is equied. Sptil decoeltion The sme cell is imged fom two diffeent looking diections l c cotnϑ l l c 41

3. Dopple centoid decoeltion The sme cell is imged fom two diffeent squint ngles 4

4. Tempol decoeltion Pesent only in dul pss systems 5. Ovell decoeltion estimte Coss-coeltion fcto χ * E[ ~ γ ~ 1γ ] p k ep ~ ~ E[ γ ] E[ γ ] q q 1 1 ( jϕ ) coheency mp 43

III. Topogphic mpping 1. Idel Phse Unwpping (PhU)pocedue ϕ m π s π π π ϕ m ϕ π π π π π π 44

. Discontinuities pesence () Non-miguous phse jump () Amiguous phse jump 45

IV. Phse unwpping techniques 1. Locl pocedue. Glol pocedues: Lest men sque method L [ ϕ] ds[ ( ϕ s) ( ϕ s) ] min S 46

3. Glol pocedue: Geen s identity method S ds [ ϕ g + ϕ g] c g dcϕ n ϕ g ( ) δ ( ) ( ) ds g( ) ϕ( ) + dc ϕ( ) S S c g ( ) n 47

48 4. Locl nd glol PhU techniques ( ) ( ) ( ) ( ) ( ) ( ) + + s n n s ˆ 1 ˆ ˆ ˆ ˆ ˆ M M M M M M d d d d d θ θ ϕ θ π ϕ π θ ϕ θ θ π θ ϕ π π π

V. Emples: Sdini Itly DEM Intefeometic SAR Dt Amplitude Phse Coheence Rw dt ESA copyight 49

This shot couse is ove: I do hope ll of you enjoyed it. 5