NASA Technical Reports Server (NTRS) 20040120868: Information Content of the Near-Field I: Two-Dimensional Samples

0.47 MB·English

by  NASA Technical Reports Server (NTRS)

Tnfnrmation content of the near-field

two-dimensional samples

Richard A, Frazin

Deparunent of Klectrival and Computer Kayineccis

Univarsitg af Tinie at Ursa

tampaign, Urbs, H, 61621
Davie G. Biscber
NASA Gleam Research Center, MS110-8, 21000 Brookpark Rd
Clevelaad, OH Aa1%s
F. Seod Carney

Department of Electrical aud Computer Bnyinecring, The Becks

Institnte for Ackareca) Seienoe and Tecluvolugy, saul The Coordinated,
Science Lahorarory, University of nots 4 Urbana-Champaign, Ubana

IL o1ai

1

2 ou easton, bonte

iiccr roauo.
Limits in he ofuetioe rescintion af sweag oneal near fad esparimenta

ture inesligacod, The reales are apotisablo 20 variants of etal incerne’ rele:

‘om snieteseape {L123}, ploton eezoming optical -nisresccpy (SUM; and

seagy (NSOM: in which the s

ea:-ield epteal scom=ng 12 sple is woakly

swatting ard the direstian af iuminstion ray be cemeler, #nalylicad

psa far he ottanen of the we amie AE The semper smscepbiiry fem
lankewsen ssisdiewonienil jets os 4 faration oF spgeiel Pecan ane ob:
wel far Gavsvinn cul Poon anioe nce ed zd “lepondn, an
sure i oxcaniad, Tho msv.ts aro wat Loca lowe Une teasing Sous, moakesans

ty Tarsveue dotecliow. eb demusisteee thet the Tarihi meat Les

meseroneubls noo ob a ditoues of cven uu wuvslengtir uwuy Com Ube seat

Ble cay co reuch diferent son rhaefarnstisn nomntent of the Bei

1 IMO Oplivel Sasieky af Amesien

OCHS estan: TUO.M188, 180.5810, 29018200, 07,6620, 110.3000,

1. Introduction

Near

d eicenscozy™ iss emerged ss en increzsingly important imeging vechnol

ge the Da

tivo docedea, The principal advancage ef nent fiald aptical maschods

ss hse willy eprosaehe wmygese 1 resco am suse rie salar Ui hi

MeyiaighsAi resution “neil! Sug fal woerested tlhe bases wethice ia wich
olin fomple ie sedans Jurong w vibsvuvedengti, auesture ULat is uamie ey

close (less than @ wavelengtia away) to the sample while tho smnaum: ef transmitted
Sahe is eoverdsd as 4 Curtin of pation. Tl metbod is wen? hagson as wear

sens igcieal evcrompy (SIOMLES uel eaten poetical by iluminasing rhe

sanpl nl seMeteng she Feit wish a aieoneeenghis verte se the ead

lapsed
cstv bre: Photon avenging aewosceone PSM) i rand meee i
‘which tho snenpls ot lominateé yan exancannat wot create ye sat intemal =
ft pS ed Ue soy seabed gh «clad hy Lape
oc asia NSOML

Vill ese walling wierasvayy STURT ase Wolss sonunage of wap.

rmination by evauescent waves ot a prem face, Ulle NSOML oz PSTM, 's “IRM cao

salt

radiation is awasuevad ‘a Ub: Garlic, LHR YL ae ava eed ariaarily

fa inapaesion corinne haswever, racmuey there kar beon inert eabing

ecumtsge#f ube high patel “raquenes eee of Je moat seve! ba pean

tol imaging Eli tenance. ean he Ghee Abbe Hino?
usutative itexpeelation of NSOM, PSTM anc: TRA janes ts senuseaane

liu, Under cert sia

uusptious sue as bomoypaely 6 tbe mato

‘ial delectric suscepefiliey.$ the mosaurements way “so selated w Lepography Uncer

nore general amdiions, ¢ snlilion af iw Historians seotttringg sooblemt® wey 9

eupliyat! co rie enfield optinal reasuremene mo captor structure and empeet
‘Yon. Ar wnportant question remains: What is the :esolucion that a given experiment
se Ue wise?

his pau aebussue Uae questi of cecal cua a aalys uLae wick
snot in the Feusier companats ef the esticsace of Van saamps. “Ine impair inet
carving sul ico"® "*s ayyliod i tow ue os thin, seule sete ate val
av aly: express far Ube ertur eomamvense masters of “he estinant oF He same
le sie cil ie chlained tor Gaaanian end Potiton vise modes. Partinmagre,
ss ninecnedel iudepondens bound ou the cotiuaats crore bead, These Rrean’ae

are Ubon aypiied te PSTM fur increasing distances beeen Une anaple and measure

neat pane unti the cepoviment is essantial,

ve way kargase tho natal AEBmacron ‘init ith che kovueds ising act hy rhe signal
ote ribo, Twit Ua Us iaferev est eta i Tae glans Mk i oul
excelent ste Fea Ue sae strane amie salar bn char cP the fare H,

cae obtains the uous] Ell spLere of raver

Scattering muclel

‘Lousids an exusvizaeub ia oLil. # useuuelataustie Gel ie “anileut ow 9 2

-pedlime wich eusceptibiite nie} The fehl metdeat om the sarcpls is talen so be a

re wave. One half nace, talem ta be 2 2 fl, hat the vasinim née of raftweon

siile tte = =O hal! spate has an andes of refrcetiom a. Orly nonmagnetic anata
soe sonidos cn win ical so Ure sly Use belo ll "hs ike see

Hae eau

DFS orl ALAR HN = dadgotr bees, iT

us bn ab Tron spe wave muesbon an ule) i io 2 depen bebycanel ia
ct veraction ae cectibed aber

The

omple se ssmumed to he of ccustent thickness Az, waste Ac is mek: Jess

than.» wavelangrh, sna ta desend only on the transverse spatial coordinate p, were
uM ale fda Ae

Az

The Bed is abst. wo cuusind a Io pur sy HB BE eho BY i Lo ase

lid wativiving Ky. (1; wich g{r} 7 ‘Dip eestlones sll I ues ue «ems of

“Whe insicene teld 's a (24ssily ovamsceul! pay ware

Wir — ee ke

‘nie cs Unb Tenuseess wie veer of a i eden was and sh ples Hele
‘oot sud Ubu hay ls of enerey tiene areal. The eave cectr eis aycified

by tae Leusyures comport y such bat

Maj = (tal). and 2)

it 4

"The nodes for shicin q_< Ry are aosogencone, oF prapagating, plane waves, Waen

Ja] 2 to he plano wave ia exanosocat. cecaying cxtusa ay 1M unerraaeyg CHE

of 2, Toone sevens ave suseroselLatory in she transvotse plane ae tas panies &

eesti te pooh fhe High spare: fray ouch of ths

we. Kocping oly Ue

Se bere tine (Ram series? th

be Gf ee a

seucrr (isthe 12-pne Crer's terse ong pis equal te the waeverse ecu:veaonls
Thee micas roms ave sos ee plan 2 — 2g, whieh os Ahnmnales Syn

retiree was wih polaron

EF

of eap hia ici

Noe ule cu ttee NSORE ond 28031 ring mealies. Ue insider NE

pangs

lie i

Ue ele the reuenos Lield. Tas tot Lis

ploeber siaso fs gives by We

reference aud ecotcered telés, andl the remting imversing, called

Pipa = RS PL RR mS A fa

bore ube 9pa:ial acgucaas af the Qiks ase sea sppasased cal ba © we ejoa

inuliostes “hat a8» stan

fe eco fr taken The Soot tera

liad 2c Te sevviel (wet ‘2 uesoesily saat Liaw in Ube cusergtilils, Cuudes woh

seatraring cencitions, wy negligibe wamparad ty “he thd andl “aurea terra ane well
he diseypardad hereaher Tlesower, if ie selisenoe fl ie evaneacin bse arwstenie

enn bocumis mere irupovianh sud eventually dominates av ay iaesescs The end

fel Jou Leems 21 oa uyacos Ula cares imag inlueanstion, which tugeber sl Le

sical by a Uae laze se

He,

8)

Lu stecaal se uolesl not fp

vey be penitine ar usgatis
Devon mavign af a in Ute ay boing Ue 2D Gewumverse) Bouse rouse
cof tne aclag-azhic intensity £37, 20. be

ce! Pater. 2 o
heed = feteties o:

6
Srcaa ning Frgp. (8) 9d (81 mo (2) vields

FiQ.22 = [TOW

HOE ad HC Quit

vere sepuemaly cou plex eaiusats of Uke Rene kenastcrt

The expression for #10, 4

sVealae~ Q)
PRI =O,

Hed — esnvin, -Q)— Flaca 0

The tensor Ty contains tlhe buegrabion over <' axd i give i she cppenis, Je is

‘wurtnetals Le rete Uh fellse ng grog

at by 10h

Yeleu [de Q) fy eg] 2 fr, Loe wale of 71LQ, 29) dectesien exponentially

with ig Shnllrly, when ye Qo bye fay, 2 Rye doe walne of HPO 2

enseanen mattun iy UL

‘The arguimenss of 0.14% aul 3

ere Silla by yee. Thala Oe pense

forsnaee of lan: cupersnelacony corapanients cf #10} with Q_ > fn ea vecartied

is Uno fe Eu via Moraspetae wares.

Se this peont anc may gonoratiag the result of Ute 17, have Ue seatered lskls

im TIRM capevinnonts act reid toyed emseruee, 06 imolude the ettect or tae

nolugrapie mcaso-emien. Ts inderstend the reculte its helsSul first to sousiden a

snouriatie urguscoul. The ubjeaives #9 determine she maiemun velns of [Q] auch shat

the peine of A(Q) snay be detcrasined (ron. aaecsurcaun:s iu Un Zaman, Canecor

only the arse carm it Be, 220}, In erdar ce auuid uxpenontially decisesiny 110,

with

ae and Q rms eeiety tne conditions Qa] dna fae ~ Ay. Reculng
Tha for ki TIM and PSTN imeging moealines a

vi (where m ie the priema
ince of vatraction’, and setting Q ~ gp = Set where & is the uxt vector in the x

lcuclion, iL ng Le goor thnt [Qi qe = maamized when a, — abuse. Tams

Qa apm a = fo My Stuue Lies Caeion was cveou aebiceuriy, X seay be

replevee ty aay anct weetcr in Ue szansease plano. Lhceoioee, ia guiaciple, 920

snag deleminest shan [EQ] & ou = Yas Tie in

sgl indawrricas Wp eoreteuch
fs losepoae fored viesion of rhe abjert, Poe emnpariem, che Mower erannfeann af
the eewrenicn sive by So" for the peint sresed funtion cf a cemfpesl mierescone

Jost Wyn bandlimit of Q, 2 NAky, whens KA is tke anmeritad aperture ‘recall thee

NA sa

3. Statisties! model

Heal measuremerts ae made on & spaccimlsed arty. Ker Suuplic.g, assuo Ut
he deteetion sariars Fae an aven of Fox Ty Met fn the plein # — ay, ane het is hes

MAF pcs that. ge the Rotal ically ae pointe (fue) Sines he OF fi

srs papetional bo xp @ sah shen QL qe andl [>

ds the frtersing i the
ieee plows is die svely Gael mired, Tieafire Sherman's Rhearent apron nnd
ue iobvosiy ia Ue detechor slaw can Ye cepessunied by a disure.e el of enionaly

spaced senples"* ‘Ihe pixels axe assumed t9 be sms enough $0 1

ho intansity

1 in Bo, (7% is esseutial’y ecnstenr tronghcue caca sisal (20.. the doteeco:

eas not introdnes sige cent

sptsa spatinl Pssring} Wie alan avenmed Ahan the

lotcelee Ts eng sures awa se deal aly al’ Uw seater “ign # eo

lees

Houccfurtb, AF i vaca ty new oc Bileger taf large crags Loa alo fs
negigthlo. Ui Kees to te Ghose distebization ef ae spain “permet variable

Ube eisunete eal Crecwney is dein

Ga, why By i

Note that Sin

Tw lus ngeasein he sericeasicel motel tor phecoelectic detection !s 198. Le,
Le eecrorauguie hel ivient oy “he detcror wg treated claccicaLy, bue ce im
cosation wilh Ubo uelwioe ie quantised in univa of plotocwent.:! The intsmuties
Shp. 2 ane. f;p.2g) aks considered 4s be éolcemivisie qa auies, The mesa ue
Yor af sholons cvs ia Une

vot fermen. tren econdnnts fy)

Te mpeenrvond by +h cucuans variible Ny. ‘The sapected uonker of phccoos at

Sec" WH Wye tete hiss WE — (An Batty, ome the ox

ar sine expecta,

lium pperakir, Sa, Ag. avd fh are the effects pixel

ara Gizelwling the qnes.uie
sficeney, the mecmavemens time, el Plan's evnatant diviced ly 21, rojpuctvely

wih

soling. My = Ws. A whieh ig the expetced muaber ot reZererce

bbeaaa eousrs trea: Ube lies berm ie Hy. (5). Ta eanveriere to deine fhe “anda

eat

eu Luss Taz Hayy Whi! Ly He te Molageahie

swenniey ‘rom Ei. (81

Eiscear fem Es. (10 vith tha a

‘ina unsucbiguens Uowemisation 0 9

tage of puna sformvaion (ochew than Gnits supped eapiiess ob Seash Gy mauris

nals i.) Lure expuriuealad oncaree cnt. Let Howe vt naovarenuenit bs dee

uote (ey ated "Te eshianede af ie seprsenle by which bye oy ater

4
iy th sevens simon of Uke Hs RF he cd

vith 1{Qyg} om Ube

Taft are ele rapa he renee De Zag, Dine Un mised #9. Reunites of

the prodabulity densi-y fmuction mrsice consideratio:s, Eye — Tan { Ps otul Buy {10} for

ve waco the two measaremants takes the form:

Fda iQue La “|
WHQ.
dee Qon an — an?
BQ mar oa)
FETE Qe oo) 8)
F1Qes nat wd 4}
oot Oy wg a hae aed)
= WTI Qa
Tn eae | iQr nem ta2—ae) |
| FUQgrc rng teen 42 — Ga
FHT Qas atts ol '
PHOairangatteo tan — tal }

whore ube inegets (P+ AY — mi} aug (@-+ fF wh we co he leaned include

M. The integers 9 aud @ ers hone sy chat lie srammerte p* stud 97 iu Kats

UT} ave eal za within the dineetinataon of

van iu Ta. (19). Thaw Gael

fat Nove thn in uke eau: of PRTM y= qe und pa
U. In ordes empy sha nolan, he wembione {1} wil Ie ccwuictew a ldons, wth

Lae liu asim. relents

my