The Wavenumber Shift in SAR InterferometryFabio Galelli, Andrea Monti Guarnieri. Francesco Parizzl, Paolo Pasquali, Claudio Prati, and Fabio Rocca

Abstrac/-SAR surveys from separate passes show relativeshifts of the ground wavcnu mber spectra thaI depend on thelocal slope and the off-nadir angle. We discuss the exploitationof this spectral sllift for different app] ications: I) generation of"low noise" intcrferograms benefiting phase unwrapping, 2)generation of quick-look interferograms, 3) decorrelation re­dllction by means of tunable SAl{ systems (TINSAR), 1 4) rangeresolution enhancement, and 5) the combination of SAR datagathered by different platforms (airborne and satell ite) for a"long-lime coherence" sludy.

1. INTRODUCTION

SAR interferomelry was introduced 20 years ago byGraham I II, However, only afcer recent studie~ in Eu­

rope ano at the Jet Propulsion Laboratory, has its poten­tial becll fully demonstrated. The growing interest in SARinterferomelry is also due to the impressive amount of datasuitable for interferometry from the firSt European remotesensing satellite (ERS-I) and (he many airborne systemsavailable.

The information added by inlerferometry 10 delectedSAR images is clearly shown in the example of Fig. 1 and2. In Fig. 1, the ERS-l detected image of the area of Na­ples, It<tly is shown. In the upper part, Vesuvius (the largeVOlC3110 that dominCltes the area of Naples) i~ imaged.From this imClge it is difficull to get an idea of the topog­raphy. Fig. 2 shows the interferogram (phase fringes)generated from two repeated ERS-l surveys. The topog­raphy is now evident, since th~ imaged phase fringes are.strictly related to the elevation cootour lines.

The relalion between the phase of SAR interferogramsand ground elevation is usually explained by means ofgeometri co. I approac heg 12J, (3]. They <l re based on theassumplion Ihal the RF bandwidth is so small (and thisis the case with most sntellite systems, induding ERS-l)to be negligible. Thus, the system is considered monO­chromatic.

This approximation, however. hides an important as­pect of the interferogram-generat ion mechanism. [n fact.if the finite system bandwidth is considered, a relative shiftof the ground wavenumber spectra dependenl on the base-

Manuscripl receIved June 28" lY93; revised Fehruary 8. 1994. ThiS work,was ~upponcd In pan by the' European Space 1\gen<;'y and by [he ESRJNunclcr the FRINGE ProJ<:CI.•

The ~lUthol'~ IIrc wJlh [he Di f'iln inlcnW dl Elcllron iL·a. Pol "cc nico d L Mi1­ano. 20133 Milun. !laly

IEEE Log Nlllllber 940268 J.lPalenl pendmg,

line and the local ~Iope is recognl.!:ecl. Important conse­quences are revealed from this result,

1) It can be shown thal as the b:Jseline increas s and inthe absence of volumetric elfects, to be discussed latcr,only the spalial resolulion of the interl"erogralll ic: reducedsince the "geometrical decorrd:J{ion" [4J can be re­moved. Thus, teclllliqucs for improving ime rf~rograJ)1

quality (j.e .. yielding a higher SNR) can be found (witha considerable benefit for phase unwrappin2.l. Moreover.this effect could be completely avoided by means of tun­able systems.

2) Rules for the design of presummin.~ filters for quick.­look interferometric processing can be JaivcJ.

3) Repealed satellite surveys can be combined in orderto improve the slant range image resolution 171.

In this paper lhe emphasis is on intcrferograms gener­ation, quick-look interferometric processing. and tunahleinterferometric satellite SAR systems. Symbols that willbe used throughoul the paper are summarized in Table .land Fig, 3.

SI II

(I)411"

q, = T .1r(l.

h Int ~ metn pha e tb i u uall den ed from thepha e of Ih produ t "l": \1 here lh * r pn cnl a com­pie njugal. In facl. t lilt i I mple imag (Ihei.nl ~ r gram) lhat ha a pha equal I tb. The quality rLh inlener metric pha e d p nd n the am un of phasen i~ Ihat. in general, com from di tin I source r 1.

tion"; lhe relativ y. t m band idlh i 0 mall i.e.. inlhe ERS-l a e it valu i 3 . JO-3) to be negl I d.

hus lhe pha e di~ ren e q, b tween the IT. pond ntcomple pi el in "1 and 1'2 i proportional to lh Ira elpalh diffi ren .1ro:

- -SYIlIh-,1 ~t""lIll1. I R<; I

\ W'I\I·I"llpt" ... It I _lit

r. = '1\ "'1111 •.111"'11 11 '111"1 :\ I C:H.

I '·Iflil'. 11'111 fn'i[III·IW.\ ~lJjfl - --II ~y' kill 1o"II.\wid I, 1, Mllz

ulf'lI",llf ilJl~I,· :t.I·- -

::'11 ~1t'1"" II";' "1I~1I1;u PIMr,Llulh- ,. 1111 t11 f'~n-.ilU I"." I' II~'"

1/ 1'1.11 (111m. 11111111. 'i 0 knl

I'. .lll.i1t t.UIj(" 10·,,,11,111111 ll.li''im

H h..nzOJul ill lulo-,fNulllr\t', I, dill<'

IJ.. H pro).'" 1)"1111..1 ,,11, I""k dn....lloll

--- 11... nlll".II .., ,·Jllio - llfllhll fll' n =11

H.1 I ft ... 11.... ·1111.·1,,1 TI .Ak

, \1....1 , ..u~. ,.1

". ,\11 t I dr'Ctf'l \~ht1lI"·"

IJ ~"Ililld rWl,l(t' I,

~. llflllliid liUItV" 'Way nllllll"l

. "'''lli ... I.l,\lf-----

"f \'1~rt"4\l W Vf1 111111111".

~ IIlII·rio·rulll'· n' ph'L'"

I h1';1I1 n·l....,t\' :1 . 10"1Il1

I /II u. I l:fIllll\ll' II... i\'iw

R Inlcrfc:rometnc fringe: N plc~ .lnd Ihec no

A. far a, Ihe la'l. urc f n j e i on med it hab en 'ald 14J Ihal il in rease' ith Ihe ba. line. Tn ra I.

Fig , I' R gl:MI 'Il') I cc Tuble I),

U. INll'R

Mo

Lel u con. idt:r lw omple image t I and I'. r m tweparate pa:, e' and I I u uppo e mal the t mIn ba k­caner did not change.

Let u. no ploll the "monochromatl' appr ima-

141'J)

-)3)4)5)

ytmnlerrain d rr I tl n (n nsimuJtaneouima e mi Iegi lrali nappro imale u'in"geOID Inc de rrelalion...

urve

'"

We would like to stress agam that (6) docs not st:ne thatby changing the looking angle of the SAR survey the m-

this source of phase error is also referred as the "baselincdecorrelation error." It has also been shown (2J, IJ]thatthe total baseline decom:lation is reached in correspon­dence with lhe critical baseline:

(8)

(7)aj= _ cBn2ruA tan (8 0:)

dar bandWidth is ~h,fted hy tJ.j. It JUSt S:'lys thaI by chang·ing the SAR loolmg angle. the backscauercd signal can­talOs different spectml components of the groundreflectivity spectrum. In other wordll. if we look at the~ignals n~ccived by two 5ARs sepamtcd by an angle aO.(6) states that the same spectral components of the firstsignal are found in the ..econd !lpcctrum shifted by af. Insubstance, II is the optical diffmc1ion gmtings idea. onethnt goes back to the eighteenth cemury.

A similar l'C!>ull can be demonMr.l(ed for the blslaticSAR case (bul nOI the ER5-1 case), Inlhat case. a stereopair is acquired simultaneously by lwa senson;: the firstis equipped with a transmitter and a receiver. whereas thesecond is equipped with a receiver only. It can be shownthat the spectral shirt induced by a baseline On is half thatobtained in lhe nlonostatic case:

A. lmprowmerlt of the lmer!erogrlllll SNR

If the signals "~I (,,) and "1 (n) are sampled correctly. the1I1terfcrogram's ~pectrum R(k) is the lincur cross-corre­lution of the two llpcctrn VI (k) and V1 (k). Let Ull considerthat the rellecton; are located on a conMllnt slope Q. forlhe sake of llimplicity. In the following. wc ~hilll refer tothe reflectivity's spectrum common to both SAR spectrdas the "common band." The linear cro~~-correlation ofthe spectra shows three distinct contnbutlQns:

I) a peak at the frequency shift 111. for which thecommon bands coincide (thc "signal"). Note that ajfrom(6) is identical 10 the inlcrferogram fnnge frequency:

2) a rnndom sequence coming from the cross-corre~

lation of the common bands other than 111 the peak posi­tion. This sequence is conjugate symmetric around thcpe:tk position and the phase of its 1I1ven;e Fourier trans­fonn is linear. This lem\ is responSIble for the magOltudefluc1uatlon of the intcrferogram, but does not create phasedi~turbances unJess the symmetry is not broken by filter­ing the interferogmm:

)) a llecond random sequence coming from the cross­correlation of the disjoint pans of the spectra ("noise").

A!. suited in 171-(91. it is clear that the noi~c contribu­tion 3) can be easily avoided by prcfiltering the compo­nents of the two signal~ l'l and ,!~. The following expres­sions of thc filter bandwidth Uj and ccmral frequencies!1

Then, slfIce W = cI{2PJ)' the expression of the cmicalbaselines (8) is idcntical to that of (2). The spectml shiftequatIon (6) (;an be u~ed for difrerent applic<ltions.

Finally. note that m the mono!,latic case the two SARspectra become totally diSjoint liS the frequency shift AIequal~ the system bandwidth IV. Fram (6) the criticalbascline can be computed a~

(5)

(6)

(2)

~M ~ _ /""0

tan (6 - a)

Thus, in general, a looklflg-angle difference ae gener­ates a shift and a stretch of the imaged terrain llpectra.However, if the relative system bandwidth is small. thefrequency I in the sccond tenn of (4) can be substllutcdwith the cefllral frequency.fo. The stretch can be neglectedand the following equation hold~:

4</""0t:J: y = -- cos (8 - a).e

Finally. since the mdar is not monochromatic (we have abandwidth W cefllered around the centrdl frequency 10).we can conclude that by changing the looking angle of the5AR survey. we get a different band of the ground reftec­trvity spectrum.

Now. in order to compare the shift of the ground re­fleclivity spectrum to the SAR bandwidth W. it is wonhexpressing the ground wavenumber shift of (5) as anequivalent frequency shift af. The following expressionof af for an angular scparntion 118 can be obtained bydifferentiation of (3) directly:

III. INTERFEI(OGRAM GI:.NERATlON: TilE SPECTRAl

ApPROACH

In [71, It has been shown that the spectra of the signalstil and 112 correspond to different bands of the ground re­ftectivi1y's spectrum.

That point can be easily demonstrated stanlng from theapproximated relation between the frequency I and theground range wavenumber k.:

4~ . 4~1k, = X SlfI (8 - 0:) = --;- sin (8 - 0). (3)

Here, for the sake of simplicity, we have considered II

constafll uniforn) slope a of the terrain, t:Jc~. i.e., the var­iation of k~ generatcd by a slight change of the lookjng·angle a8, follows:

41f"la8ak, = -- cos (8 - a). (4)

e

I I _I~ .'0 - {an (0 - allB._ 2 .

p,

In the next seellon it will be shown that lhe geometricdecorrelalion concept without reference to volumetricscatter phenomena is in some ways misleading; we shallsee that the deeorrelulion noise of flat scatterers can easilybe avoided with a suitable ifllerferogram fonnation tech­nique.

"•..i

. I

Volume'nc \Callcrlng lal Lefl-hand \,Ik gcomc'l'). 11ll1l.11/hl-h;Hm".k waH'IlUnl!1oer I'l'prc""ntahlln

•FIg 6

.,,,. ,

\

. ,

hS ~ Cuhctl:n.ce h,slogl'1lm of the two SAR lmll'C\ u'cd llillelle1'llit .hcInferfeml:!I11m or hll ~ Ld,hand 'Ilk hc:lorc tihcnnl! R,glllhand 'Ide:ufler fillenng

Fill 4 tnlerferognm SNR cnrn.Ill~r~nllhm " ..htailled in Ihe ERS ll:ll>("wnh II baselmc uf I)()lJ m Blinn ~Il:~

,'.I

•

Thus. the received !llgnal can be regarded as the 2-DFourier tmn::.fonn of the ground reflectivity measured atIhe wavenumbcrs given by (13).

Two SAR surveys from different an~les (0 nnd 8 + .6.8)represent different bands of the complcx reflectivity spec·trum. From Fig. 6(b). it is clenr that in order to observeIhe same k, from lhe tWO surveys (i.e .. the condition Ihatallows: coherent interferomell)' in Ihe case of sulface scat­tering). the looklllg·angic change :18 should be compen­sated by the spectral .lohifl .6.w = -w.6.lJllan (IJ) thai iseqUivalent to the follOWing k: wavenumber shifl: .6.l( ==- 2J.wl(c co!> 0) = 2w~91(c sin 8)_

The coherence of the interferometric surveys depend!>on Ihe degree of speclral correlation between the mea·~urements in k: and k~ + J.k:. If we con.loider. as a specialcasco the flm box (.6.:. = 0). Ihc signlll is impublve In the

: \.·os 8) 1dy d=..

( 12)

'",Ik,1 = =- sin 8c

Iq2",

= -cos 8. ( 13)c

Lla(\.:)

. c'p IA Cw. 8) =

and 12 hold;

W/ I = 1Vr- = W - 6.1 (9)

j, =6.1

( 10)2

I, =_ 6.1

(II)2 .

We con:-ider the me(llum as semitmnsparent. in theu~ual firsl·Bom approximation. so thai Ihe scattered sig­nal is a Imear supcrpo:-ition of "ffects. Wavenumhcrs inthe I,:round mnge k, and now in elevation k: as well. havethe following fann:

As for pl1lctical cases. the constunt slope assumption isgenerally not respected and rnnge varying fillers have 10be used. Their bandwidths and cenlml frequencies can bee!lllmated from the fringes of il noisier intcrfcmgrum gen­cmted withoUl filtering.

The example of Fig. 4 Jihows the fringe's (interfero·grnm phase) SNR enhancement that i.s obwined in theERS-I case with a ba..clinc of 600 m (the noise that is stillpresent is commg mOlnly from thc image's decorrelationin time\. Therefore. the spectral band .... idth of the inter­ferogram is reduced (with no loss of spatial resolution).and the geometric decorrclalion is: removed. A quantna·live measurement of the enhancement is shown in Fig. 5.where lhe coherence hi!>togram is shown.

The following expression of the received signal holds:

A{lo y • k~) = )) a( y.:) exp l-j(k\y + k::l1 dy d=..

( 14)

B. £jJe('/ of VOIIlIllt' Scaf(eri"g: nit! Baseline lIS allAddiliOlwl Diml.'lIsitm

Up to now. we have considered only ::.urface sc:mcring.neglecting the effect of volume ::.cauering 141. [51. How­ever. when bacbcallering come!> from targets with n dif­thent clevauon : within the resolution cell. volume ef·fects cannot be ignored.

This c::Ise IS shown in Fig. 6(:1): the scallercrs are con­wined In a box with the dimemiom. (.0. .... Az). (lhe prob­lem can be as~umed to be invanant with respect to theawnuth direction). The mdar return is a function of thecomplex reflectivny a( y. :). the mdio frequency w = 21rf.and the lool.mg-anglc 8.

;; domain and we hove IOtal ~'orrclull('ln nf the different.!.pectl'3l componenh and unitary coherence. In general."lIh a finne volume and a nQnl.cm valu~ of .1;;. \lie shallha\(:~ the follo\liing e'pre\loltln of the "pc:ctrul correlationfunction·

"In (.14 .1;:/1)- --

.14. .1.::/1

ThcrdoR:' ..... c can llue thaI \0\ henelier .1;:l «2... .ll .d1C' \olulTh:lnc effect!> can be nej,!leclcd A u-w:tul eApres­slon C3n be found II II luoctlon oflr.Ifl.!lml1led .... 3\c1cngm.normal bJ~llnc. <too \ateUne altuude:

;lJI tan 81.l: « =

!8

Here. VeA,. 1..) llo the re'\uh 01' Ihe double IOtegral. Thus.If we ha\'c ro.my Inlcrfemmelfl( llh~cnallan!> with differ­ent baselines. we can l.plll cach ob..cn'3I1nn A,O:, . .t:l mton "l>urfacc contribution" A (A,. A) :lnu U "volumelriccontribution" proportional III lhe hu..cllllc; lhis lenn isproportional to the moment of the rcfiCCllVHy along the ..::axi ..

If .... e conMder Ihe ca>e of .l:: ~ .1~, ..... e have ~pectral

dccomlauon and luw coherence In the ERS·I case .... lIha baloCllne of 250 m. dc\.'tlrrelatlon I" expected for ..1;;1 ~

38 m On the olher hand. one might claim thai Ihl.!l llo notdecorrclalion but .!ligna!. One wuld rca.!tOnably considerlhe change of lhe t.... u SAR Inlage.. u!>Uble a.!l a function ofthe 00 line Hhc difference 01 Ihe (omple, samples) aslolgnal

For the saL:e of l.lmphmy lei us u..e the folio.... 10& ap­pro'lm:'!lun

F" ' \"hllnc ~!flk"nl ~I. US I lrna,." larel col Bo>flIl'Iu"c~J"'I"1"C"'loCd I" IIoCPIr»IC cmwtnPft~" Pd voJlvrntllX C1lc..:n T,"P ~ 01llle .rma.,,, L,c,h "aIoiJ.... ~~ put" Roll_ I\Itld Udot .otuJlll:lfll.rofttrn.l'_ lma,c.&«; UlJIII;dll tkJrU-.11 • ~ Lilli QJI1C' ncr11",1,

Image) Thl (eallut: comel. fmm !>Idelo~of "'mng POint"C3uerers la) Ing on adJacenl range billS Due to me lopeC­Inti ..hilt compeno;atlon. the \Idelobc.. arc ph~ ~hl(ted

.... lIh rt pC':et to (he maIO lobe. proponJonal both to theb.u.ellne .nd to Iheir dl'\UIOC'C' lrom the milln lobe. Hence.the) lend 10 be canceled from the "urfa(c comnbulJon•but leM"o from lhe volumetnc conlnbullon.:b far as thelinear dcpha.. ing approAlmale.. a linear eh.mge propor·Ilonal to the baseline Different re,ulh (uuld N: obtuincdby rc~rcs"JOg wllh Ihe baselme pha ..e anl.! modulus JOsteadof real lind IInagllllJry pam.. a.. ha~ been done JO lhis ex­ample. The concepti> have been checked wilh "ynlhclicl:xllmple.. that for hrc"ily arC' nOI reponed here and couldbe fUllher te"lcd by mean.!. of controlled c:<pcnlllcllb (e, g •b) el(plolllOg lile nc"" anechoic chamber available a1 JRC­EMSL 161)

(\61

J·h8~- - .- VII,. II (111In.. (an 0

e'(p I-J (J; , + k:.::>1 J\ d..::

J.hoB.• n -8 VII. l,).nl\ tan

- A(k A.J

al·~ - .14.a

_ .JUk • J; ) _ J !w:.18 r\ ;;of _' • .::)c: 108 J~

1C!.J. +.141 = :1(1..1.1 +

AI1,.11 • All .. I)

Fmm mo\(' obs.ervatlon~. It Il. then p.l\\lblc to dcri\'ean LM c\llmate of the ..urface and (he \'olumetr1\.' con­tribullOIb Juo;t IUo an eumple. \IX ERS-I un'e)" of meBonn arca h.1\e been e,plolted for thl" i!( I afler n=g~lra­

lion tn pace and trequenC) The C'!>lU1lllIIed urf<lce and..olumeln!,; I,:ontnbUllt>Os art' hmlon In Fig 7. The) arenot reprc-.enled .... 11h" (he Qme '\Cale. 1Iince the a\crAge3mpll1ud~ of the urf;l!,;e ronlnbutton IS roughl) 20 urnesthat of the \olumetnL cuntnbuu n. A~ of )et. no delinl·tlve L"OflI:lu",on ha\C' bttn demed from thiS example. Forooe. II can be noted thJlthe \olumetnc conlribullon sho\loSloldelobe, nlended 10 the r.J.nge dlrectlon (\'ertlc:.l In the

C. Mpr1fatlUlI ofW'QI'er Art'aJ

The \pcctnd "hlft bc::ty,ecn the ''''0 p3MeS ~llien in (61Sho\H .a dependen(e upon the local temlln 1I10pe alongrange a. A the h;M;31 )Iope appmache<o. the off-nadir an­gie. the spe..:lra become dl"Joinl (bhnJ anglol and final!).the specmll shift goes to Inliml) If the local slope In·crea'e agam C1a)o\Crl th~ abwlule \aJue 01 me ~peC1raJ

hit! decrea :-. t'out the Ign I" ..:hangel.!. AfJ. a COIlSe­quen..:~. negatl\ e and po)lll\ e freqtk:ncic.. uf the ,ntencr·ogl'llm 'ipe...:uum refer to areal, 01 la)'O\er and nonlayO'\cr.respecmel) Therefore. they \,;an he ..er.n'lIed. pro\-Idedthat the lime !>paR of Ihe Iot)ovcr "lope 1\ lung enough

blind 8"511a

IraJ . hlft :iIi mailer lhnn ~ • the IW trnn-

~~+-~-~-=-------------

4"10'

2

3

·3

...L-.L----'--'-_-'"__"-_-'-_---'-L-L-''-_-'--_-'--'~ ~ ~ ~ 0 W 00 00

LOCAL SlOPE (dag'-l

FIt! pcclral shlfl aJi lun<:llon olth· local ,lure III lhe II t: of ERS I"'Jlh b ~ellne 01 -f>()(l m Jntl nommaloff-nadlr n It I B Bhntlanllie f"'ln Q 7 III 36:! The C " b n 111III III cnnunuou hoe limll theu5ubh: ~pc Il'lIl tuft I ... 10 tHz!

2

i,t:z

i otIow

U~-1

en

-2

R would alllimitation tnR survey : the

D. A Tunable Interferomt'tric R \'. ( 111

tunable inl rferometncon I ercomc on f the m .. t seri ugenerating interfe grams from multiple10 of coherence due to large ba eline·.

I) MOIlOWflC. T \' Pa.\.\ s: In eeLion ill. II ha. beenh wn th t b changing lh 10 king angle of th R ur­e • a differ nl band of the round reflectJ\ it. p CU1.1m

is re v red Thus. as an e amp! • H.ehne lar er than• I m. would n I be u bl r R -I inlcr~ rom try

On the Iher h nd. a. u gested by ( ). [he eqUl alenlfrequency Iu I Indu ed b. a I km bu, ellne could b c m­p n. Sled by hiflln the eentrallransmll frequ ney dunngth e nd urv b 15 MHz. hi ould be don bm an fa lunabl In!n. miller with the c nl I requencyhi h:d proponi nal I Ih estlmaled a. ,110 • ~ lIowing

(6 . In Ihi w y, ba 'clin larg r lhan Ih I allowed by aIi d fr quency radar . uld b e plaited and. onse­qu nlly. Ie s Lrin eDt requlr' m nl on lh sal IIlte rna­neu er ae urne' would b reqUired

(i.e. . n ugh lant mog am available ~ r r­quen timali n nd fill rin ) In Fi . 8 lhe . P clrnlhift a a fun li n f lhe I . I I pi.. hown in the ca.f ERS-I wllh n ba. eline of m and a nommal off-

nadir angle of .. n ample e layover epararioD lthR -I data of mOunlaln u area in willerland i, . ho\ n

In Fig. 9 11 I W nh n ting Lh.at there r a'e whereonl a pama! :ep raIl n an be chle cd t. plcal ex-

mple I repre em d by a lep fuo ti n al ng Ih rangedue 'lion. In uch a a e. \ e uld ha e thre c ntribu­LieD from differenL regions ummcd at the !lam im rfer­ogram po. ilion: the first f1aL l. n al the lever I vaLlon.the second flal lOne at the hIgher elevatIOn. and th 'leptransiuon. The ·tep lran.-iUon can be eparated from the

th r LWO IOC 1\ h w a dilli r nl frequenc I Ihfnnge!>. H \ e r. lh' Iw f1al .lone h the same sp c­troJ shift and cannol bt:panned th r Ihan u ing a cend­10 and de e ndin p e The lep ar'a w uld in ahadow.

If In ov r area euld b eparat d fr m Ih re t f theima e. I pe in the range dIre ClOll from 0 10 9 0 (lO-

th r Ilh th e from -67 0 \0 .7 0 could bby ER -) in[erfer m \ with roundpend nL nlope. a u uaJ M re r. b. e pI iting b thascendin and de. ending ER -I pa.. e. ,almost 11:1 pcfrom - 0 t +9 0 with hat cr azimuth orienLUti nare re vercd: lhi ilUa[ioD I ho n in Figure I . Thdifferent urv f Fi . 10 Identify the .. I pe areca ereable fr m ER - I ( e ig 8) a. a unction IIf their azi­muth ori nlalion ( e the I wer pan of I. 10). Thicknd thlD lin refer I a: ending and de. endin pa e.

re pe II ely.Here. th ~ w comb," 11 n

entati n Ihal c uld n I rh wn (bl ck areas . On th th r hand. if we

able t d al With lao ver ar a', the n n b ervbination' would be more (the haded areas)

• 4.5 S2 Z5

I • II

"f

pi It

ld band

<_I

n in Fig. I

d t

ffereJ b)

== -----=~

I fun lion

I )B" _'0 Ulan (8 - 0').-(

thra-

_1 )

..0)

(l

limil d I

III tJ,8) 2 L n (0)

Itan (8 - (\0) l.an-------

B T-:-------B

- ...!b--'n

In !hi ca e. th ba line B

In lh u . (7) i m difi d In ord rIc m-p n at Lh P lOll shirl in 'al> r flal t miln (In pra liceil n a hleved b han in the frequenc tmnmiLlcdb . lh . c and radar

with u re luti n of 50 50 m bl med with a ba' lint:f 200 mi.. hnwn In Fig 1:\

1-1 14 R,m~e ~ olllll"n 11111'." ~n clII .1,llIn~ll IIh I R I n:~Jl ...surv~y, ut Booo l.dl h~oll jLl~ slOg I . unc) Righi h.111I1 lile ,nullll'I'ur. \ .: mbJnullllll The 1'1 el ,limen,,,m I _ _ m

. Combllld(lOlI oj .iR Data}1 om Diffi n'lI( Pfarjim,/\

The. pcctrJI shift (; n -cpt I' th ' .•mph: I \\Illy 10 und~r·

tand h w LO l;omhinc . R d t dcnved m differ III

AR '. stem In luder 10 g 'nernle In!'rt rogr:lln!\. anC ample_It IS 01 Int re.t to g~n~rJIc lllt'rterogram. b.

mblnln> EA T (1979) Jnd alrbl m~ L·band Rdata.. inc u h n e p 'nment wlluld allo\\ IUd} )1 th'L-band c h renee alh:r a I -year 11m mlenal

Th m Iry f Ihe pcrimcnl I hown m fig. 17Here. c have indie led Wilh llnd'" Iht: 'I::. A rand31rb me p ilion. repcl:lI ely: with and 0" the

AS nd airborne. h nl..mg angle • re~pel'lI el}.Moreover uncurl fial area such a Dealh alley ha hccnh Ihe lZed. lhe pe'lr:.1I hI h c ncepl will I,. ad )pledin urder to den e the expected re ull Illd lhe aJIh m .AR1m k and ,llulude l:lln traml

E en II It I nOt tnetl} requIred. lei u.... upposc: fIr theke of implicit}. Ihm the t 0 .~ hllve Illl: ame 'cn-

tn.1 frequ n} rom thl: rclalil n. h1r bel .... cen Ihe .tnglliar

10'

la'

110'

I~ 10'Ji'!:

10'

lI)

10'

10'2010 30 50

Ot!·N d" an60

(cleOl

FIt! I. . peelrul hill miluccll by I m cline' J' a Iun lion of the (IffnaJlranole//"'uhj, = 1,~.and~OGHl nJH= to m Th., kS Ic eI ho\\ n h r, mpanllull

F. Impmw!nlefll of (Il(' WII( Rallge R W/WIOII

cro.:.-Ira k re olution of. pacebome R ...y.-tem islimited b} po er and dala rate con traint . II could bimpn "ed If a lurger band r (he rcOcclI it' pc "(fUm I

re red. s h1l ... h en dcmODStr31ed In l7]. lhlS an bed ne b pr p rl' 11mblning R u yt- 0 n rI nalrea derived fmm . pamle pa SCI>. In fa·l. due I thepeclfa! hlft cquatll n ( l. th rdleclIvil)' •p 'ctrum band

!> n cd in s pa Ie Urvl' i' larg'r than that l r in Ieurvc . Then...rl)r " act S. -tra k resolullon \,;.In b im­

pm ed b hifllng to frequ"n'y and In phase ne SI nalwith respect to til lher and then adding the two. It the. pectnl (the diffi nI .urveys pantaUy overlap. Lhl.: phaser the iot r1' r meln' ign I can be U ed r e limallnu

Lhe «meel pha e nd r qu n y hift It i ., ar thai lh~

I rgcr the fre un' ·hlft. th greater Ihe r ' lullOn 101­

pro\eml:nl: meanwh,l , the pill! e timati nil r­hu t. san e ample. fi e r pc"l dR-I sune • dunn J

Ih Ihree-da r lilionc cle rom arcb:?to 14. of Bonnhave b en I: plotled 10 double Ihe reolution al ng lhrang . The compan n etween the mgle 'lIrve nd themuhlp ss C mbm 11 n i' hown In Pig. 14. From Ihl fig­ure, two clT<.: t arc vi. ible'

11 the range resolulion enhnn cment )f fixed 1 r I(s C Ihe map rLhe 1m Jcd area in Fig 15 and the pI I r1\ p in! caller .• ef r and after image C mhmuti nIn Fi . I ):

21 Ih re1ali e r. duclioo of Ih Image im nil nareas Ihul c.Jecorr~lale fmm one urvey to another.

inally, 1\ I. W nh mentioning Ihat a pe Ira! hill can1 () Ol.:cur 10 the azimuth dire '(i n du 1 different

Doppler nw id rrequcnclc•. [n u h I cas . r. lUll nimprovement an be applied in Lhe Ullmuth d,r ell n a.... ell (Ih ell-no n pI-light effe I r10J)

FIg I r "r tlk Irna:~cJ ar ,If Bunn

....

11

T

Fig 17. Geomelry of the propo~.:d expenment

pamllon and the spectral shift equation (6) it I clearlhal for 00 = B, the lW ground reflecti il •peclra (de­rived rom A AT and the airbome SAR) are cenleredUllh~ 'ame wavenumber (gr und frequ ncy). In th lea. e.in the irb rne R ha a larger bandwidth (100Hz)

with rc!>r I lO lhal of E AT (20 MHz). Ih gr undrcnl.:cllvily sp elrum collecled b. E SAT i. totall. on­lained in lhal colll:clcJ b the airborne Thu . if \ C ha eoheren e a fter I yea . an illl rferogram can be gener­

aledH w vcr. dut:' l lh !>rnaJi r .Ihitude of the ai m

with re pe I t I:. AT. the airborne R I king-an}­8" hange more r.lpldl' han (J \ ilh the ground range \(al< a uS! apr im Ii n 8, 'an ben Id rcd con. lam in:J few-hundred meter ulh). tn ther word. the bandthe ground Rectl\ II} pe trum c llected bEAT isaim I conslanl ith the ground range. wherea it rno eqUlle rapidI In Ih 81 muse.

h lar t ground-ran e. ath ~\ lhat all w a partIalcrlap of Ih I g und n livil.:p ctm can be c m­

pUI d from (6) In facI, the large. I .1110 cd °pectral hiftI ~ Hz (in lhat c w h uld h n 10Hz fre-quem: rlap), r m I (With ex = 0). the angular ep-aratt n thaI rre ponL! I( _ 5 H.l spectral hi fl canb mputed':::'O = 017 rad. The correspondingg und-rung ulh is

2IJaO.l~' =-­

c . 0,

\ here H IS lh' irb m altitude. If lh r II wing valu sre u. ed:

pi Is at Ihe air ome

Omo

H=

0.• =

fl' Itt PIUl lIf 1\"" p<llnl " Il.:ren. The hilnLt.lnl..ll .. 1\ I range s~ e I• n t lIn~ "If til t1c:tenl a710l1l1h rl(l\ltllln~ art' plllllCcJ Left hand ~Idc: ~in-

~l 'unn R ,hi h.lOtI Ide ",uttarlr ,ur\ e)' cnmhl11atll1n \'c

curacy III requested for the polnlln!; angle (a couple ofdegrees around the nominal value of 23") and the trackposition (some Kilometers around the SEASAT·beam cen­tcr trnck). Moreover, also 3 slight deviauon of the centralfrequenc)' would automuucally be compensated by a ..lightchange of the lOOKing angle (see agam, (6))

II iJ. ea:.y 10 appreciate the IOfonn.:J.uon gi\-en by thiS

e'l:penment. if posill\e, in de:sen area.. , mdt-oed after mul­tiple :urbome su~'eY's and .... Ilh considernble computerwort., one might be able to check the Intcg.roned tectonicmotlonll of the last decade

I V C()'l:CLt.iStO....~

The rel3t10nshlp be(\\een angular separation and spec­tral !lhifl hal> been dbcu-llsed for the monostauc and bl­static SAR inlerferometer. Thl" relation has been ex·ploned to Improve well· known SAR Inlerferometry tech­nlquell and 10 Inlroduce the idea of the tunable interfero·metric SAR

ACKNOWLrDG\lENT

The authon. would like to than I. the reyie"'e~ for theiruseful ~ugge~tlons.

Andrei MOllll GlIllrnlerl "'Il~ horn '" !t.lllIR. 11II)', on Februlf)' 9, 1962 He n:,cl.cd the "Iftu·n:1-' ill c:1Cl:lron,c c:RI,lIttlln. fm", Pnhternleo dlMIlano In 191111. "'l1h • lhc30l~ on lite pll1,pltueOf-, hIler ban1. ,U'II(\II\1: Il'phcli IU l)'ntheur Ipcnllll' I'Id:u dill foclI\""

He tau b«n .... lIlt Ihe Depannlenl of ElCl:uumeEng,nccnng. Puht«lIllX1 d, MIlI.lln ~I",e 199B. D

I member mille- SAil n:$ol'Ilth lei'" wllh Prul FRo«a and Prof C Prah

Fnlnc~o Plrlal Ina.lUllled III e1ectn..I' enll'II«n", frum lite Unl'enll" de,h itud, dl Gc:no"1In 1990 lie I~ 11o"" wllh Pt11uecn,to dl Mllaoo.""hen: he Iii "oBlnr 10"" ..nb hI' PI'a 0 decree

HIt rllmnl relCuro;h ",l.l're"b ronrem SAil InIc:rlemmelf) t«hnll,tuc. fOf OEM ,1enenuon.~ml1l1 cru~1I1 mOllon nhmallon. and Image tCifI­lllllon ImptD\'emcnl

II] R CrlIhm 'i)nltk'lk; ,nll~r1em"""cr ...lb, ' ...r "'POIrlIph...· m.pPIn• .' P,., .. Il:.tl:.. \01 (l,~. pp 16)-768. JIIM l'n4

I~l A Gal>(1ellnJ R GfoldRell. ··Cm<..ed (lrbll~ 1",erlernfDefl) Tlle<\r)­Ind upenllll'n~J 1'l'~lb 'rom SIR B_ bit J Rr_ rr MfU .ut ".lllI ,. J'fl "7 172. 19118

1~1 C l"rIll. F R(l(~", A Monti ~mltn, af\d E Darr'l('lnfi. "$c:,ytlteml'f1I11I" fOf SAlt 1000000~ln" Inl(t1el"\ll'M~--aJ Ipph~llIonl.. IEC£TN'H G,-."n R".."u Soon. .ut 28. rp 621 640. hll) 1990

14J ~ Jh>d(1'lIel lraJ J \1 Mamn "Tllwn- urad 1k~I.n 01 lnltrlCI\'rr\C',n, S)nlhl.lte lpenul'l' nda". IFF P".. PI F .J>] I \9. no 2,flP 1-11 I~q ICl9~

151 P Piau, IC Cue!. M !k)<;hall.... 10.1 A LOJlu. 'Anal)'s,~ 0' lheI'l'M)IIlI"m ul mulhlemponl SAR ~)ile"". In Pm" IG,-tRSS '9J. To.1.)11. Jaf'~n. All'. l~H, f'p Il%~ 119'Jl

Ihl A J S,chcr. "The: I:umpcln MI~m""ne Sllnlllu~ l..lIbonllol).I:.ARs..I.~,lt, Hr"''''r JIm . •ul :l, no \, pp J~~ 2ij.1. Jwn 1993

171 C. rnll alliJ r Roc:u.·· hnpm~'mg \111111 ntnl.le rcwlUlltln uf ~lutiOll'

ary obl(e,~ wlllt mulllple SAlt ,urve)'~. ' "·"F rrUn{ ArroJp6cr1'/r"I<In ,"\11, .1I! ~y. flP 1~5 144. Jln 19111

1111 Rlnlt( l'uoh.IlHln enltancement WIlIt llIulhplc SAlt .Ul'\'t)'~

t'umbl"lllOn,' In Pr(H; IGARSSV2, Itou~l"n T.... \1.)' 19'J2 pr1~76-1~111

I"J f Vutelh, "I:,pcruncnllt 1t'1L.,lle, on l-Itll I I'l'fereJk:e dltll >,c'" InP".. }u j,~H Itllrr/o"",rl lfurb1wp. ~A ~RI/IoI_ l-IU':ltl, Itll}(),;l 12 .• 9Q2

1101 C Pnh Ind f Ruo.:u, "F"cu"nr. SAlt lIlil. ""Ith lime _lll)lnlOopJIll:I «ntrohJ. 1£££ TroltS_ GrUln R~""'I~ ,Sr'u \01 30. pp'~j.,~~. Ma) 1992

.....ID Puo.tI1.II ...~ bom ,n VerbanUl. NO'lfll.ll­Ih. on 'u\cmbcr 10. 1965 He ftttC..ed lhe'-burel" III detll'Olll( en'lKena, from IhcPUhl«!l>':o iii f-hluo. \tdu_ lilly. 1ft 1990. "nlba tbc:s, ... blOn:ll'thcal llUlI,e pI'OCl'~,ng lIc uflO'II" "'<l1I lhe _ 1I1I1\("nll) .. hen:- tat II ...od­me ..,...lnU 1m Ptt 0 de.tCol'

HIJo INIII rnearrh ,nlCl'l'Sb t'Ol:ltC'm oJ.Jel-llll pro­cc;.s,1I11 Ipphed ~ ~)nlhetlC apenlln: radM dati..... here'" be hu ",udK'tlIIlta'fervmclneallpplia­llf1nli Ind d'Jlil4' de\lllOfl ITUpt ientnlKMI

Clillldill I'rlll 1I~,elved lite ·tallre." tn el«"lmn ..; engmeenns m 1913.lind lite Ph D uel!'l't' In 1987. hath fmm Ihe Polltetnicn dl M,llno. ~1IIa".

11.1)'In I'J1l1 he Jo,nc:d lhe Ce"tru SILJ<t, TelceommlllllculOnl Spu.IIh of lhe

Nau{lfuII Re~4lth COtIII('II In ~1lI1111O He \ 1~lled the Depanme,,' of Gco­phy.Il:\. Sunford t nl"er.lll). Sianford. CA, u a VIsiting ScM1ar dunneltall' all'urnn qllancrnf .987 Since .99. he Mi bct:n.n MSOCUltc Pm(euorof I)'iletm l(lr 1l',",'IC' 1oC",,,n« II lhe f'ohlec"k:O dl M,llno

Prul PrlIll \fib • .."rdcd tbc: S}mptb,um Pnzc Piper A..~rd II theICiARSS'lIlJ

tabla Cllelll ...., bura III Bn:M:La. Ital}. on Au(1"14_ .1161 II, t'CCeIH'U Ihc' 'llUn:a" ,n cl~,

'mell( englne~n.J f",," 1M Prlluc,ntal dl Mu..1Il)Mllul. 1111,. III 199\. ","t1I lhe'I' OIl ",noYlll\ea"phnUllft.~(II SAil h)nlhc'l" apenun: Ddlrl,nl.l'n~romelf)

f-.blD KllCCI I'«e,\ed the Oot:lore In Inf.cJllltttl EkunxtlCI from thePllluCl:"'':o dl M,l.illn ,n 1962,

He It;&~ ""nrkt:d In Itle Depanment of El«lron" En~lIIet:n"s IIf lhePuluerm.:o "he~ he I~ now Pmfowr or OI¥11I1 Signal Proen.limS Hc:\I~lle" the S)"em So;,cncel Depanment al UCLA 'mm 196110 11168. alii!ltk'n the: Department ofGe\Jph)'~iCl of Stlnford Unl'Cnll)' " V'\Il"'1 Pm­{c.......r III 1918, 1979. 1981. 1912. 19111. 1l,1llti. I"d, n:.:e"tl¥. In 1987-