DTIC ADA432042: Numerical Studies of Low Grazing Angle Microwave Scattering from Breaking Water Waves

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by  Defense Technical Information Center

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exer CHES ‘Youn FORM To THE ACOVE ADDRESS,

RESORT BATE GEUNEWPOY) 1 REPORT TYPE 5: BATES COVERED Frama
18-04-2005 Final Technical Wav, 7002 -- Jan. 2003
Suterical Studies of Lox Grazing angle

Wicrovave Scattering from Hrookieg Water fac gsarmme————
Waves Nooet4—-n3-1--0134

Janes C., pest [se Ta NORE —— —

7 PERF GRR ORGANIZATION WARTS) AND ROGRESTERT F-PEFORTING ORGANIZER
Orlahona state University ‘PORT NUMBER
Biec=rical aad Conputer Enginccring
202. BS
Stillwater, Ox 74973

fo sronsommanvontTaRBe AaPNY RATRTEY ANE ROGRESSST 1 FESSOR OAS RCRORTINET
Office of Naval Rescarea on
hellalor Ceatre Tower Oae, Code 334
800 N. Quincy Strost TSS ORS TORT
Arlington, VA 22217-5660 suas

APPROVED fUL PUBLIC RELEASY

the alezowave backesazzering from broseing uncer waves at seal] illends
tion gvazicg argues (0h! tae been lavectisosad sine cerpveation=) clectronsgnetics
(eno ‘tecunlyies. Good agueenent 12 aosieved batweon tee fumorscstly ca:sucatea ane

Siperinescelly neasured backscattering from a wave tank Fl)
aasurec 30/7" polaviza

fea catze ie dae to the shape of tha wave cross ead che culti—

Fete sssttering srom she wave crest ana froct face. tho KAW ratio (o mdniacmed woe
Ene wave crest nar mocified scmuniformitiss in azauth, asthough it 2¢ affecc= by
Lasqus variations, The tro-scale adel Zlle to predict the Lie sentrerseg. rom =

ihe gently apllling oveaker even afta: ths stespess wave features hoor tars remove

Sea surface ia scattecing
kough surface Ra geaktering
Compulakional elcotromagnetics

Fiz SECURITY CRASSTATION OF FPERTARON OF 8 PRET TS AE OF ERPORTTE SOW
REPORT [ABSTRACT [2THIEFAGE) ABSTRACT eg |__oaues C. Wen!
v o D oo PAOES Tp TELHONE NOMEN acs”
19 440517246096

sega Fag Bey eH
DISTRIBUTION STATEMENT A,
Approved or Public Release
Distribution Unlimited

Numerical Studies of Low Grazing Angle Microwave
Scattering from Broaking Water Waves

James ©, West
Peiucips! Investigator

ONR Contract NOOOLENS-1-0134

oajoet period: 1 Nowereber 2002 ~ 81 lununry 2005

1 Introduction

‘Receord efforts have been perforin’ to fellate ihe audsrmtanding alent modeug oie
xoatse sualtering ftom snp al reetrontfestines on the aaa suite al how erezing angle (TGA)
Sluminetion. TGA a sumface tealtecing is characovial ls bef bates f yen RQoNn 22 “eek
spies". Sen spibes ace can estate ly brizntaly frac eeanest/tersivel (LL) 2a4er
‘vesoting thet ot vieica polarization (VV) ly mete than 10 dB (Lewis and Gila, 85 eae,
1901), (Lvencs vl HH exoasca VW ane ennotings also relent to a Seuper tc.) “ale
beclevior is at prodited by troditonal rough sucfceaetterng eadkla sock ante, Rize ap
peonimecion {KA} ar twuscala model (T8V) that have proven etal st modanajnidenea, Se
2plkes have been eotelatnd with braking ewes fa eperimaninl sili in both labnesbry abe
taka nnd the open ea (Kalinghuy ane Pastosoylo, 1970, Lat w aly W005; Sots et 1200,
Lee etal. 1990; Ties et ol, 1998), wih mnsions eine OoeaT}A Aly wear tho tbe of ripe
imum steepness ofthe breaking waer. Proriouny, the os euseasful raods bo expla ae oi
responses ure fir sirple optical aprons ta dao Ie ltipat ccaicriny fra the ean,

rest (Weel, 198 Triznny 007). ‘Phe ving saliech nayonary 3 the he lecantane ee
AN iaterterence,lenlng co tha ou spike In previous wath, we tocorpoveest un fats af te
sseve ett abage ait if regtace on ce fx of the beak Inn Fru diseacenal ceeomagnice
seattering wodels thas deuanvteted » sing’ entering eauroe of wopor evets (Kel. 202). Tae
{sof Ih project was uly validate thar lnwliarasinal tandleIivough ezect voor af
‘aodsled ater with wavetank experimoaral eile, nd to apalyAdwenerd amsrcal sc(oag
‘algerithins I more complatelyeneral thren-diaracid wae cana tll addional sal ering
schon thal re got avid ledinenions ia

2 Approach

‘lormomegseir wottering motels wre vault freslaed using eppuusinations to Mons oun
tions tha ali fhe deefratione of cvs) form elutons bur go Bade it range of appleblte fo
‘ie curbs conTniout, The rongh wn surface quite complica, wilh features angina
‘vive eral toile Igo compared WU esetromagante savelngeh, Tel Heefareimpresve to
havouteize the arateriog vith arate, unfcral setter made. Lani Ue appraaah Fonsi
fol in this monk is to bret pci seater mothandans wilh nique made tht are frail
for ut pucicular extn. The "global" wll is fred by wrcbining the efi of the inde
rns ia 8 physivaly consistant mame. Th eheae pebnairy mechs neice. are qui
specie reRostion Som steep wove ses, Oshutod atu cattring Bow reeduta roughoeet om

20050419 016

1
‘the even, sd uultipathrwlerton between Ha eres and other poiuts on the surface, The vai
of the miosis under spel: conditions ws leled through enrapwccen with boferencaaeaerg
ccna wie cuuputationaly expensive ramen wcthode: Where onptepdsin eristiog oltre
secandel 10 yield more areurste results at tor calito afar ples xe ooneere, A the
sulte sue onfy us valid at che unelvng ate repnenentartny aged inte calculiogs,the on is
foeneed on diosty meancel profs of hreskingwavee when poral, oro tumerically gover
sualnce thot are thoaghs tr provide realli epressrals of tho deaunar! necting ales

‘The peajeer was ciel into to distinc, luk ralated, Fires ‘he frm, ees cue appletan
of s nueecal scattering apnrthm tea svi uf azeznured woe prodlee mrwsned ft a wate ua
by James Donen of the University of Mrvioud under ORR. lvnding Flimuing beatae Wav
‘were melonically generated hn the Univats of Maryland ww taak, ha lieve evolatien of the
‘upwind /dowsind erose-actln of Cac bali ieee ran contin moasired iy deo eater:
‘mounted tn netrumant careingo thse tactlst with che wave exc A over she Unita
Buorescens ie withix the ster to peosde 8 aga in the reo Stam thot wes digitally deta
tc veld the saw profile, The fol meneacemeat techuiqne wo shown ts Dunsan et a (1990)
A summa cersomagnetis code was apulis co the dececlel sare profs ot Oblatoun Site,
vig & tise hisbory of the vaso radar cnny-wctons, Siwoltonoooe baie mcamoebeal of ts
baehsceLletiry was ponevinel by Mark Beer uf tho Naval Ressch Laboralony (MBL), ala wider
(OU funding: he simutaneons rperimentsl rahe measurtienln provide around treth to whieh
fc numerical ss may be enorsred co tly widens “be tartniguc of epplylng tho aera
swooning reniinns ly mecaure] was. Rafinemnots over previons, sinilat eaperimeatal ara
‘aclu movement of the eatennas Tarr faa lin wow eat tn ern eboe they were operating
in se far Bel, as wel npraved opti maazureannt of ott thes mi under Ube jo tad the
region in font of che eval. Infrared (TR? phctographa che wave nels (lahea by el Sith of
the Nao! Taconteh Laluraturs urder ONR, finding) were ake masse die the Breskiny enge
revealing Uv seimahal vation of the pntbreaking worl eanank be masstced bythe ase
Inoes shove. The RRL manatnnotcuts are deserved i Sletcen (2004)

“The set ering Eom the succes eavecane create waa everett Ed sing & Ayr teh
igue that ponds the monet mothod (WIM) ving the gSvtcrialthosry of idkaction (G20)
(Wis ofa, 1806). MM/CTD ie ivw-dimans.otnapitational encod thar nme te wate
evil daly mhiforn in the celta directing, mtn all ul Rr appelion tothe mee,
ura wn dowosave co-aeccienet wase-toak wave pres, ‘Tbe tehaigae allt te wodled
oatbering exe to be numerically exande? I innit with Wille editions ewapacatentl ec
Joo, theta coating the ext edge ditartion fein euncned surface eyes thnk an Mas
the seattring ealeasties Thain unre alla ele teal nifocm phone wave iannintion ots
alc ontermp pabeci Wo ured i te watering elise, ing a realistic reperrination oF Ce
coulis af lfrsok ave feature ty the total alluring arom on, lmpetane Doundesy
cdi ane applied ia te eurface 20 2eprevent€38 fils onduatvly of mata ae mierorone Be
quencies. Thi tecbniqne hn been used estraerey by sw Pl in peeviton sve avatering seadeo
(Wet et wl, 1998 West and Milne, 1997: Wis! 2000, 00)

“Tae meconl major effort. of the projck was 20 chazacery Lue seater, bom fully Ure de
mcnsicnal wave crest (this i, woves that ae not ridin in ove dimavsion), Direct muplnotion
of sevacard mnriealelatromegnetic algortha to gaara! Ihveodmencnval tating pelle
i: for move eranyutationally een tha the poviounlypetlosned txo-dinenetnal sien ie
eatoring clowlalsn.s ers tere pexfouant urive oa atalraid taller! ft natpole Sle,
‘chun (BILPMA) cat we implateatl mv hows (Zh nd ese, TURD). The Ceca te decal
‘tea, grasralseattevng tga: georotcce, a5 Wally sued ta pplication to the rattan ft
‘uve seit with beeing wacer waves tha patrol implementation, esl loodng of
‘he edge nf the modeled nsf is ud lo vale the aveaco cxeroats le ety sal alone Fhote
‘appienting tbe edge cist that would ke t insranateeetterng croseanctions. Plane pave
Suminaton run ugaim be une to give realltiy Humana of She scaeriy, Raautes. The Dato

2
ovluctviy of che snrfaos it ele acing impedes bounty wnlitiogs. The leslie ylation
Df the MLPA aystert is partored ing the gnszatbel imam veal (GMRES) mporthua
fotiemtion wih & Khrsholded incomphte LU dacomtion (LAT) neanditiores. Th areca.
‘loner reduces the nuuiber of MRF tyeations vd for convene om seater Hn IUD to
Sonrarimataly 15 tn moet soass. The vlidig of the MTS cchutywe wus contre npr som
festion ofthe aeueriug fram imple +1 shopea with coulytical aad 2D based nomatial cles
ve tothnique ie fills donrived in Zao oad West (2481).

ue dificunty in yrrforsiag the enocanensioaal slicing sbudien that dzeetly wenurcd
8.7 woe profiles are not redity wade. Ina, we ve reed igen apathenaing 4D est
fro existing mnversally yonsrate! or mnced 2D ces rafle, ‘The nls press allows the
fnewteity 3 che wave harect tobe cacflly enameled, with now selterng entra merbnlealy
introduced, “The tealive eunteibatinn a cach foture tyae eam tbeceline Uv Hearied, and ap-
Imac bo accunately proce cha backascnring without rumaeialyaoleeg tefl 20 probe
a be formulated al detod. SD tose phoning breshat vaste were generate om the Wiser
feally qrncrabed LONGTANK pron (Wang ota, 1995} thet reper de Lnae evecntnn hi
Anterrafiate sale (appnaciustely Ew wave'ength) plunging tna Chee ees have Beene
extensively iu 2D electroncypetie astunng tndins (Holic ct af, 199A. Wists 2002: Feta an
ebacoo, 2002) amd have lncuno a standard ese eos fer LGA rip seating rem breablag
raves, Ad hily.s sample SD sping besser erat ae syshstod by satel ining
he 2D upmevefdonnave censssectins of x geull piling teal mesma
‘Maryland wave tare

8 Results

3.1 Wave Tank Results

iy. 1 shows tha Une listory of the langag brake eve! mcasared to ths Univesity of Maryland
bine tak. The iacidual rsdmsnsiona cfce protease inthe podem
238 the cenle of the tare tank are stacked verily, ‘The veri dimeasina Creve chow to
rolation of the uve with mcrening time, Sika tbo ietsamact cocrage “aal eu the optical
‘scurencant sxicon was non with he ene Lhe we, fetes Tht oppest to ent th et
in the faure arth “wereciag tine ore moving fete van cho ve rest, we Heal res Wie oH
‘>the night nee anng lower uit tho cnet. Thy wave stoepens ml aot nua vs U co 180 coe
‘Tho je impacta he wrfae st epprosiestaly EN a, ner tic theres "plea sense hoy
20 mato A00 ma, Aer that, rude cll ours firme the inst at ate lek Debod oe
se wee ropa

ig. ¥ shovs the geriry uscd Sn ube wprmtiel ealeualins of che herkenttoring fom he
ani wrests, Additional pli meosaretss performed by th Urey of Mocplaad showed
‘thar che ewrace Weplocemane etre alzely to vero the saglon fn Lunt ofthe wove. A splise
Interpolation was Usmufore ure jee the Bout a i aeasund css too et dager poi
placed approwlrely 1.25 ma in Front ofthe ext. Tho sunfae win Unen scoot Jone! bo Bate
‘rtenscos chat wee ged at 3° t horizonal, Ths any eteraon lw tho uzbef eyed 2D
YAM/CID mumme.cal nthod. The emplote radled afew the exon aan ig 2,
‘Te large dot in Fig. 2 rs the appreslnute phase cer vf tho wide ancl horn antatana wedi
fhe Naval Resecth Laboratory mearnectnts, ‘The dati Hoe shows ue wulhipts bastion
paths Fro the erat tthe anvunas wich ts ur foe extension. "Uo itsnution erating abe st
he wave peaks ypprenimalely 6° (the incor ange i") Merouredanteuna pbteraa peor
by che nnufactuser wore wiataally diz ard ineladed 4) Vas autpetiead cautions, Aateen
beams erat last 20° ut the bequenciny conan, su tho featiees mire approniattly
nil naato

Fg. 3 chow 9 compan botmean the 7 Gi

seateetng mans by cbe NRT. radar an chaz

Fy
igure 1: ‘Tins hiery of che wynseo/domanare c-section ofa pling Ezeakar wave seat
pty -maszmed ina wave ean.

Ea
> oo ee
at
2 2 4 3
xb)

Fire 2: Hitensiont of w single 2-D wwasineé ereta vied in 2D MM/CTD WeaBscaterig aa
suleiors. ‘The dash line sure the extennion uo eo awl ultipath vellelinn, he colt! Use

‘thao the font tes eadewion uscd ea give wltipoch relia, ‘The dotted lie sere aka
elleriuea whoa tho aneaioe tcl atthe ch

Joe cumieally. The oooluta Ivey of che sedar cease shot ihe direct compart
Suor the measures yield tue -D cree ia JB tlalive o Lane Alc the 2D manerat
results yieM 2D oreazarelions ia a salatie to L mk, Th crusescctionsahow tr crane ea:
spike superar respae with, HH backeeasieriny exceeding VV by upto 25 dB. Overall eels,
SNgreement Ss ublined during the jetting and aylisieup stages of breaking fom O tit ea. Te
pestcuar ie HIT backs, es rail rig the ering sage in boc, th The eam
Yeachad jure aller 10D ms. HE ladlsxotering toy aichty afer Ia, but than ren again dig
ho splaab-ap with soon vent wim appearing jst beta sl na, VW barks 00
Ure otber hand reins very low fr tho Sst 10D wre, after NLICh rie quickly to 20s, A
tH the Level oeciates, Bt che numer VY level alin apeoxdmote eomevat tacugh 4
et sma, Aft 400 ms th agree ie not aa gone AB II pats loaligy Unis is doen Inge rare
{2 the uote fev of the radar menursseats, whlch ajpecea at -I8 dar, However, i ro the
TET backaestarog Muga deamdlale ater the epleki opion, whic i consent wither
‘nfenlatoon. The measured VV barke-Ulur dees lawl fnr 100m. Tl mneiel VF ens

4
uwnwieal

ROS tan

Po)

Tigun % Comporion of manares! ans ewmnwental ? GF. haskecotering fm tho wave tale
reals ut ig

tectiera alo chnw a yeowral downward tread during thie tine bur woes anc ama copy
"The IN metauretente choved that The su Taos Inarme very noruifere in te wlzanthal dss
doring this ime, ‘Theis uot rllectt in ihe 2D ergreocionnl meaeucaairs ad tetas ak
‘he sorveriealseeeringealelelora,

Tig: 4 shove o widsband compasison (f GH to 12 GH) of do NIL exporimantal remake ad
‘the wuineriel eelealtions, Overall the agreement Ss yind. The VV baclzertaring baa a majo
rosuiwe centered at 11 Ole/60 ma Sa bot, wleh rower steoog vale ding at omer feo
From 100 ste 00 mak LM reponse ts Goushated by the lag rxponve during ee eting at 1M
se ab all Lexuencho, eit wonter eeponzcs at 276m,

Fig. 5 abies Une Seyeifers of thy Doppler shift found at 7 GHs ae Inieion uf tine. (Ihe
Doppler shite ae cancer a0 Hu in the fen of ference moved with the ware] RU po
Toreotioncgeia shows cele ante, with Use jet dovinating wad a later Vee sent
<aving th: eploshan. "Ube jercg aespanoe ie easter we appraimptey 16 He ance the ee tine
Taxi Man The ware phuse seen. The VV Dopplee vente aunce ie roones atending out
1thAN He ducing The jag round 200 me, Soonge nespoove cure st Dg/2U0 ma str that the
i respons ireroase in equency, aca 20 Hel Ao AM aie the agrasme
‘sansathat nave yan eat eeiutk nou-uniemmity ofthe win inthis tw: pera. lower,
signin Doypler syrals appear Kem -20 lz 0-420 He i lk the mera wad aac
seater thelighont this Fre

Aa. Gna tt the mumeleal stern from tho monsured eave cent wd Roun itn Be
fro ee extensions thor ite che lip buderefltion, An erazaple of the reeohng urs
le ahuven a Thndasled hao in Pig. 1 Tea tne Rtery of the rurneally found beekeattarlaz
fEom hie wave Wnty i shin i fg 6, The VW backacatening is ay slightly cbonged tom the
comsepoadhng snmenes! emits in Fig, &, Tha confine thal milli eRection ab westial poly
lassen is damped tur to tie ewer yng fects of the fnite convey ha wate. The bk
low level of tbe VY backirsering is duc to the shape of the eves fate Hersch wet ack
seftions from the ron vl coneove envi ragiona descrutiely Sueforing. At herzoxal
Polatisation, howaver, tne backeclicrvg, dori jetting hos despped dramas, cuufcing that
he stang eroeeeactionsabaerve ain pet cv to co multipaets. Theor, bat Khe eresi feats,
fond amitiath eBesteconttbute to Ihe expel bred stroagnuper evant
3
g
a

eso (OHe} Freaund tt
[gure ds Widchond eompavean of the baskactteting fam tb rar of Fig. 1. Ths unr pos
08 the eapevinwalt myles aad che lower are oierioal Aaa atime fa) wetaus keueney (Ga.

3.2 3D Plunging Crest Results

-Al134> erteulstons shows were penformed at 19 GH using the MLEMA scattering code derbi
‘dune.

B22 Uniforus jots

ig. 7 alow Une 2D LONGTANK wast: rete that mate tl fo aynthesize che phingingbaakse
Dest gw bies, AD ora avllnved from LONGTANK ws through 13 em in Big. Ba
re pile was farmed by aligning the eres ofthe LONGTANK waves i the eve: wave dirsan
wih ave FY iw the centr, Proles 12 to T wero chen glanal on bot iden seventy with the
spacing Tetweey he: profiln decreasing tho ditengenicted Irom the canta. Snr polation
fn the scoes wove diection gave a ctatinmoae nutes sn, Prof 1 wo a0 reat ote
Gem ot Une extruur edge tn ge + ten for eho recite Inn neadad te ave eye doco,
‘ho eading sl tating edges of the wares ene aso extn! by Dea for therein Icing.
‘The back culeing froma the eave corso Pig eben aking dicey pave shown in Fi
‘Uho HE bactealtcring fnuad using the MUFMA momeranl rte excavls that at VY at nels
Exptimental

° 30 0
Dopplor Shit Ha}

9
Dopplor Shit)

‘Figure 5: Comparison of Doppler shit of? CHL Tos beattnring fxn the plunging bres of 5g
‘The once ore tase (2) voraus Deppler a (2)

RCS (¢6-n)

oo aid” staaoa sta c00 750 bo
Tene tn)

Figuie 3: Nonoasiealtiumestal 7 GHs Dackaatiering fam mre wn eeaty wh Sout ae
xtom)

Figute 7: LONGTANK yosee wed tu spathesige -D wre ene,

(QS imo a meta a9 Rin pei an oy

Figuy & 4D wavn crs ayethesind from LONGTANK wanes J abnough 12,

sll insdeaco angles etiong wil occ in the WW Tuslaralering ot 5” ieidene (18° gran
‘Vhs tohavios scenester with that obser pretouay wilh 2D wom problem sad appends othe
sinall VV erosesostions during eting fa fig. The onlin Ue 27 foarte me som
a he due lo inerlernara in the Iovkereeeio From apetilar pointe ot the wre untae Fri,
Jot nd wl the cavity bel the jt. ‘The orroqpondingreeston pnts for ue 3D? we ant
sha in Fig. Sb, The sane a entatore of the anfoe at the rection pois bz aller Than ts
Cleotremamnetia warelangt, #0 the eeetion rom theve points didi at the tro palate. Tis
ses myodeled in che 2-D case by mullpylng tho elton from cooh pol pradctad by greeted
optics by the correction factor

Le Smgas + tier BH,

‘ware & i che eletramagretie wave runber «By the rodiua of curvature at the tellin mint,
andj Ths ayrare roc ol. This “extde yurateea epee (GO) toednereoppast fs
tii the releied Mlle al VY wel HH, iving devrueive intertnence a VV wd center
iwulerusa: al HE, Pig. 8 ube stuns tie BGO prediction ofthe backscattered fled wan aed

8

(ae ate os »
igero B10 Gis beskocatering fom the cess uf Fig. 8. Shona ave the scattering exvesestinos
Forel wing MLPKIA snd the 3D extended gcomediriad option face ave radar eroce-seetion (2
urs tsideney augh (),

to cho reflection points of Fig. Sb. The cureeshi Forte was anplind to the auntie cotvabie
the oft print in boch the upmave/dowtavacn aul rrowmenee rection, 3 direc application
PPGO to the rection pois found Ly an auarnc poustue gave 9 reesonable petition at
the HRL-VV tiv ovvoll but manval adja of Ui surface curvature ae the ralerlon
finns terol to ily represent the deep wll In the VV beckeentering, A fly automated
feet) of piling, the sp VY mol ont the wate yropentn nt tho rection pots as not
fue,

Tig. 10 sucus the dependenv of ths sackwottering from che erat of Fig. a0 ainnth sre
"indicate dzeetiy upwave IUwlnavon. ‘The bigs HIL'VY ratio sem la Py. 9b austivod out
8 srimnt, besoad whlch the VV Taclewatoriog inereee, Pg. LL ame te Deletion pits on
ho sae cost at 6 and 10" aimuth. AL 5° rf pote eeu Beth on te fl Ue wave
fa tho ent, giving detruccv laste Tntacrn fs vmeave cad eoute pelottefetion, AE
1 Taoxewor ths eeflceton poze bave tooved cif Ue wnin poet cf the ame ost the ald, wl he
cunceve acy engi e not a defied athlete.

Fig. Zebown a 3.D sue cnt formed tom LONGTANK veaves1 dhrough 16; This ware has a
sunk score davelped jt. ALO" gear the erty a felyebedowtt fon ss ov Mapenecion
ty the jet co chae ie na concave stim poiat Ubi ratlsted J Uhr haclonwtcring shor in
Fg. 18, No VW cancellation spam at O° asimuth, However az the aint sensi to
‘acho VW nll opponre, Tia explained Wy uw: rf pots ied st 6 alr son a
Fig. 12. As the osimuth angle inreare, the cavity xederuct tho et bernie slinging He
‘aneeva -sectinn jvnt woud for the V¥ eanealation. Oval we have cemsitenly observed VV
cesnosEtlon wheurver Uns ue beth zonsave aad caves back-cRevion pinta dient Sire
‘hen the rad of emeatnen al Hse man points exe oa the cde uf an lf th electromagnetic
woveleagth,

82.2 Nomuniforn jets

Adttinal esta wene prvi to determine the eact ote otn-unllrntics onthe beceratering,
Fig. 1d chavs tove pies formed from LONGTANK waver 11 rough 1d th ripples of iasteanig,
ride iteoued ino tho eaves, ‘The 0 asiawt: harkncaring re hse waren i abr In
pat d ofthe gue. The buedscatering is very sia te lat ie Fig. when sal nd moderate

9