A- 34125 REAL TIME OPTICAL INTERFEROMETRIC IMAGE ADDITION AND 1/1

TUCLOA O MISUBTRACTO OBY WAVE OARZATIONIU LUMN INC

UNCLASSIFIED DAAHOI-81C-B 20 F/G 20/6 N

EshhEEEEomEEmmhmhmiihmhhihl

ELIaII~aaIII~a

-a--

LoU 1112.2

gill EL1.8

1111.25 1111.4 1.6

MICROCOPY RESOLUTION TEST CHART

NATIONAL. BUREAU OF STANARS-93 -A

Mim

UMII

I I I P i -

U. S.Ar HO'i-31-c-!Iz()

Addtio aan w utact by T Wav oarzto

J o'y

P.O.S BOX 562 TUCLOOA, AAM LECT401

83 08 3, 009

DISCLAIMER NOTICE

THIS DOCUMENT IS BEST QUALITYPRACTICABLE. THE COPY FURNISHEDTO DTIC CONTAINED A SIGNIFICANTNUMBER OF PAGES WHICH DO NOTREPRODUCE LEGIBLY.

I2

A>YI 5 OPTI CAL1 INTLFRTEPI !AG \>

ASD UBTRACTION BY WAVE Pl.RZTO

ABSTRACT

real -time coh% rent ontical i nterferornetric imnage addition

ond utrctonsvsty,, :xic on a technique simr-Ia to an earl er

wor b' Ys - in d S,:i scl~han- is extensi vel.. i nycstig.ited.ThecrrI. s A - s,.,ster has beenc'paeiwtoeer-

tin I. , t~*'i on and r-esol ution rpov.er of theo

~'st~.-'it re; ,l oa : and j-siti ns C-f the npt

YDitributiOn/

S.e" I -dO

I. Inroucio

3. fltr 7 i o f ~ ' t221 .1. .~r . .ki.. .

C. ',',Sult' of s '.c t L.! ' tAO ',i I

~.t

APpend ix D .17 . . .. . . .

Appendi ;. C . . ' . . . . . .

Append ix D0 19

References .. . . . . . . . . . . . . . . . . . . . . . . . 6

T ab le I ... . . . . . . . . . . . . . . . . . . . . . .

Ta bl1e I I. . . . . . . . . . . . . . . . . . . . . . . . .

P ciure C t)t i o.................. .. .. .. . . . ..

. . .. . .' . . C

lilt

On ica 1.e Adt on and 1ii> race jwU: ho] w!"aa m

er'K. K. a)en i nov ;t i (atcd :va Vd uc rt- ea rche rs i

Lhe n ntri rff ri c wetra,ot , cenipi e~ irw i tides of ' wo i iaco f roi d

ci 1 (h t i tti, o of -in i nottrf ero;irter iare recom!bi ned [,-, a qrat; r) or

o rd in ii . 2ra:,hi c lbuii: ia;) i t te r. i'y i n troduc i non ahasu difeer 7

1it t ofW t h e pat h, t he S Ubt ra ctCion be tween the two ir aeos can

ahiovel. ,iver, in the '';cthod u tiy Kurstlinn and i t; 'a

in;I ~d 10np;ioPhase; for thle tlw: ;atal o ao

aM dKa~ on',~l H sn a ;od for the recoirbi nati on of the i.; ra1ct

Otn .1: t t va VL1 e le a nd_ ) ffors t he f o 11 owi ri~ advar.tmes.

- i liodi f 0000n(: hove tho UifJ(; 3 '

I I I b a o Achieod I-), siiralv,, rotatinti the anal, 7C-r.

nt a' L, o ic li S d r' re It eo I I o er to Cach ete han- 7 wsa

co F!: a 7 (c'-/htie r 1 nttr rcN ieteor. Hence the th 11

V!ArercIa _ t CH 1,'.1 IIfO vi trations . F'urthermore , no holctirav hic I-,,

5151 t~: 0 V~t~iV :>requi red. The Lirefrincent Wol laston ori s.

C nll~~ r 1 ' va a I iabhic: . ilow.-eve r al thoiojh Kuns tmann and So i ts char 5 : a*

,hat, subt onot i n has Leen performed in an area of 3mml by 3 miii in thei r exivr-

iion et , aloo rti a anal' vs is of thei r experimental res u Its w-,i th reg: od to

th)e var-ious opti cal components such as the lens and 1Wol lastor nri sm,. havo

been ivn.For example. they have not taken the aberratioins of thle <.-

1 sto r i w alnd the( pro:-i sir n of the co ficdence of the two i manes in0to

t , Lu f itr i r t I ition a-nd :i : II-' aim........ . n;

a~ i "'iuu I S o o f the tehiu of nefric real St~r 1 ;

u t 'ito LS usi'g pol ari zation modulation can o iI II It(,?2 '

with the. iI un C )f F i . I. BeSide s o rd in ary o oI ar'iz ers . is noc i

r i e 1 v'e t u sd i s ca l I I 'e d i . ',o,11 s'to n pri..

I a oho-ent p(. 'in.t I i'ht sou-ce. Cis a c-I a ,

,I ,,Ir~ r ; , t.. .ransp r"en ie wi.th ! ht.i r ' r. 1 i p I tude tr',ins ri-)4 I tt in .

,eT, ,ie '1 rue ei the vc v the two nrfo; sin r t2-e

.Kubt G Ko caaf , d ts olrization modula t C Il t.

rtl; i , , lt.I ; t <a s.. t o t) a le re 1 u 1 , l t J t 1 2 13 L'

Le -a iIi. e j.., ne iu t: lI soun ce 4 1 at t tn,.

4,p: h. n wthe '! irat O:flituof the S, Ste i i .I

Jc k fo a i an :.I, P j s .-, P01 ; izp~r ard AN i s an ana .VZer .

and t, iPC ,O i:'C~d~lu J;) -n ul an z'I l ocated in front Cf the i ,Lt tI,

IT,' : !. ' , . ii, ' Sf., i :' ' ! c t : i , . _-:0'"

;3 ci S1 a -e ,~ Ie),c t i velIy. The uni t-vectcrs along the di recC

the prn i ,al traSifli Ltau.e of P, P .P2 ' ,nd AN, represented u y P. C

and .A ren.civ ioy. are -,hown in Fig. 2. W is a W ollaston tri s-i which

located at the vicini-ty of the back focal plane of and the front ,J, I

r~~ine of L 2 and has its two optical axes parallel to P1 and P2 resectively.

an 5A' sir plicity we snai l assume that the tio lenses L anid , t,..

the savi' foi l 1 enth f and have per f n:dt image formation prc erti w, it ,;

" . ' ' s

the input plane I and output plane I., a . a pair of conjugate p1 ane.

Since the spheri cA waves radiated by the points at the plane I1 re

transformed into plane waves by lens L1, the Wollaston prisi' thouqh 1 r,

introduce i.tortions but will not induce any other monochro:ati c a!'or-

rations fcr :h.jects at plane 1l.

,, ,,ip ex. vectorial amplitude distributior of the ill u: inat41,

i ,;t: at 1 :'o be 50 rcoresented by P. A,; a rcsult of the poianizatic,,

.v ,a i m .f ! !( t he ampl it ud di str I buti : 1 i t, ' i

''pI

' - . , ,, , te lr is: .11 tiw sys,,te!:. t')e dilf r-ent i t ,

I i'. o ; uld not: aifect their" ii i:ii lc:ciu:. ar-,

I..

i' L.. . (' ',,t.1 t i] he -,eparated at the outilut :,lane P, ...r

.,.:.:,,~ ~ hl, , i , ; , <,c te s it 'I'at ion i; diffornlit. The I.. I, s t-

"i .,'i i . ,' .: te ] iit beams :lassinq through it accordi,.l to t" ..,

ic, l -, :t n ; t , As .,n !:e seen I) Ap em-,r ix A, the vaue Iti tie

jrii ot ,lec in 1 ,- [ , S V olarized along jnd P, are both ,* I"i i''.' 0 '

: tanA ,n e

1et, e t. e au j anle of the Wol las toron srisn defined in the Acnendi x

, 0P ,- t refractive indexes, of the prism correspondinoi to the

;r! ..... i i) U,,, r ~nv beans resne(rti vely. However, the d ccti o" s

of the deflecti ,u; of th'se wo e:;s are opposite to each other. Thu;, ,

we adju- t,', ,i:,ti-ne x (:) ;'l ,ke h anale of inclination c be ep',cal

to the anle , the centers of the io'iages of S| and S., can both be shifted

to be on the z-,:I II the output plane and hence the two inages will

____ .--- -

._ i | .. . . ..... .. . . .. .'-.."'

Cv.~c.fIk " 1; itd by I,(-) trt i Or!~ ill Ih ~ Ot ohe (se A-,-:ndi x A).

f ro , *; ol I r t i, o On :n c o' t, -iY

I<c S is 1 alcc in (I n I I9 I-a LoI (s s hown i n F ig.1 d G t- tr

F ~ ,~)2 ~x 2 2 ] A

'h- swU!'r( t ior, L" n dt' S n 2 can thus bw acbi eyed.

wicv.''.~-C ;t n ~ t h rpSd st can beseeri K'

be- a;..:n' ,. *. Secondr~

tmef the two ii!agtes is5 do' iired, -w-e can simply rotate AN (or P) i.c

ob)tain the ft 11 tting output,

0--2 LS1(x2, y,2)1 cosj; x y 2 sii;'.] A

viho-re is the infl e between A and P1I and the -"and +'Si qns cori-c puricA

) h .)* & e r 1. , . ( -n .o., . t i V. tr 1 .

sI' s.1' le an1 corven it tec:hnique :,r th. I 'i, r " CIV' nfl na.

' , ,, , td pr -ctical iiir.,r nce. For aO!d I , in Xirane cIc

traction, the two trans ,a lercies y do not hav the sail .e tranwi

ta,-io eve; tho ,uoposed-to-bLe identical portion of "he two ilr-aoces ,

the differences in emul i errs or the exposure and r.viri nIvia ot ccndit.

hlu;. .)rr to .C rrv out I truo .,!tractiorn, - "v.eighted" subtra t

or a i un I r,1.r)- i olt on reluir 'ek for the removal " the psendo-

ai Ii Lr'L " .ir'c 0,

I; , s I Z 1)1 'i' s -d i th rpa; s. .:n C t 1i ''iu; ijt paCe, the ,a P is 'Ad in the ra1 146-.,

,ri,( t1 .rorciq. iin-ho~ spatial tilter, was cell :a.otd Ly :i 6-irs 'e,

tu r, inch fc :a l-Inth telescoi c lens C. It was found that the ;.O

iznrs F. ind P,, ...ore no! required. In that case, each input irane I

t'V,( .) 1Vll v seurated images at the output plane, and the use les s crc >

be c;js y blocked. The rest of the system remained the same except t :ait

the imaging 1,ns L2 was inserted between the analyzer AN and the fina! c'ut-

:-ut image 1,. Five different len: es have been used at the position ef L

1or the ;urpe of finoin. out the influence of the Fourier transforr: rn

th:e ftect f ,uhtraction. The important characteristics of the le!,-- :ire

i-sted in ahie 1. l.e Il laston orisim is made of calcite, with its f-on'

f,! a !..(a of 1: ', by I,;, , , total thickness of 6 mr, and the s!lit tnole

,b5 ' " r,,, A= .>,5rad.

~' ~ i

Jn~u'f~ ~1(: i ~;~esil t~i the .ubtractian of

- I ~isteci in Jl1

UU~'i 01 pu ofaIpr stK

n:~~~~.~ f~ t ~cn ~1

-. L'o 0.if~', r:e r.u ni n ie-, i I~ 1e arnalyzed

twio Ij,- a lr i n' I the I ht Oucc(ay *rttc: )brco: r'.t-

*~~ ~ o h fi I~: i fle~t nd thao w'hen t he SUrf ict.1C2(~ faci

fr() iI ii ht .or'c Ori urta t i u ?) . The phencA' r1ion , Coi:)on to

thie er~ :~o nTat, I I , i s f urthe r I Iustrated i1n F -,s. 4 -Q. n e;

A. *;:~~i~v- ~crit tir hot )orhi c -p-rio of the 4interference frini.

V j! ' traroform lens I was -)laced alonr Orientation I

pai~ [r ts i jC r, Vs e iu res n d ic ate t iferf

* ~~~~ t '' c] * n~n r lo h a a x is. vih'en Y'

(2 ' I d iition a, the c~ar;, frnrce has it wii:i -rea i~ '.

in ' ~** * n: '~V'' t-'' sec"' teaIt tlii i s t' V....

s of, 'L t' f if 3: 1- r

L .:t .

t - I v tn,

it Ij r1 ti )11~ t s Lta i ted J t h !Ie n sr 1orc 'e I-; i.. '

S i't 'It to lnot,. trldt I.ne I I, fi n ,,e~ L, c SC c Ib the e-,

c, c d* *~w 1 im~I i i k Yr-i neo's i n the we -

smtteoo;~~~~~~~ CPJ tre' (OIh a Iono the two oi 1 2

c I In t. 11~. hi r f c~~f. aw t in rI fC th I) ''1a x i I'!c x - ..r v -

of thc !I' :?,S rnw ci.e of the- p 2teero:s of Fi :te thr;h

d;;~ tCI.. i. ro a tcte oc 1>,' Th M.':h t.121

*V I' ;. ',Y-e 2 f the, cases 1 i ted I 1; T L '?iO

til

It. f ct i o. be ty.een wnii'::fi Ii,, t n.-C --

L~ T; L !A aced I .inq Or-ertati on 1 has yi de the ma i iiu a'"(,I

o f ''I t rk fr r , ei t w i c hos en fo I the Fo urierI t rants fornl en S . T.

II

* . ii . '.'v .::J ' C: tt i .. ' S IL:', . '" ' .'- C 2,'!e..? ., 4, 4

..... ].Vi , , _.o . n ' n,' i.as ' r.4 . 4.,:,

.. h. '.. ' ,a te (' tc l t T. . T - e "

ire S-t",, ed t. 1h i, . .lte ,. di it-'t'.ck . i .i trh d tr.t? 2n . .o 1 2C CIt(

d7t , . ,t .7 ( /16 . ThC .. / )hoto d s

the 'L, :r -tio1n re-ult. I re prese:,.ed in Fi 1. ". T : );l.:i"ato' c r ,..-

t>"c ,nu'r ! t -inlr'Q; r(2,,...Xr the i " y and a t,her - 70 , .

£3. ;n .f 'c. 1'" , .. ., . 3/3' fri. a K and c ::rt

2' I "!" *.j ra

tt- ! .: 1 . ,;' I " ' 4.4. ,lc". <t .? e t,.4 t.. 4.r, ".,4,

. , ' :.: .v .. *2ll I.I ' v an , nch t 2 ' c-. th e ' (4 . . :, * 4-,. ",4 'r-, e r,_- o, u r).4 4

r !-e I I I' r1 4C1I ra1 c c i s o S tJ, 4, - , r mt i r

Iii~~~' I tL'II L'' .2 , C 4.

,: , : :. ; t o 2222'. iin £1i1L,',' 1 that the re*,iou 01 CC :ld ," 'd,

i ... ...'. , ', ti1 .4 'i th . I "IY was Fil'd. . e glue ;rarik is also an ,1' . t.

o tho r's olt ion of t Ve syste:.

* V . 4.44 t,_ 4411,1 '/ ,i i

I rt,r wl , U nerstand the ibtraction system thoro,,,in,-, the 4,.,

t ,...r.t2, fl' ,1 C i2t.t('4fls as s '..'r in Fias. .1-10 require a th oc ti al i te-

i .. 1l2 ,:l'C til d.i,,',,,' (Jt ,1.4 .,I a of the ;ubtraction results n,,e.';

.4 . ,211 ,jj,2::,,. trI s t;.o 1, .cts of the sys te as I .

A~ Intrp'-oatio: of Lio i!torference ine

Ke Pal o'~t'o me pff ropec~e ta interrpret ti~ ter

fri l&qe c't.: :Uij tit a ~ m o1 C itS ; ' in

171 ~' 1 1 .7 2 t , t u ~ ' uo i t K I

c f 1Itr 1" ti oo e'ii1 . t! prvsorl .s Jc,)r

t 1~ t K~hl ;etOLSS1 n1 I SvS toC cf K. 1'dli

t( I 11 K.V Po in r i S cer(,t'tai r f ni nt t th cot rJi ; a~

''e L (I Ot;L i,; . sdont ini of qern etn 2t zs

t, t J i 1*T iJ . i 1i (1 t'to 1 L cLti oi. of t1he *wo inp ,- !, oe .. t

th c rr r I I the . I ' pc i !I t .;'I rC ce r- t h (2 1coal'.e Ca 3ii K w tIst-o; is u of he V1-a t i 1) .. nddifct

or, . c c, CCTT' tec 0 ' ec ' ilia~] t r t S T!t c 0

Cn I ca ',,1 ,vCO il luated .lor iny aravn. '~;~t

:.L :t;r u 'sp fic.. we '. oonf tle rags )r-I in ati n Ior

1 1 t o wi oupti C~i 1 .1i S "C fore ttne re'ach t110 FOU-i er

if tY1 low- 0er . 1no t wa ray wou)ld intercept (it the back feco .Ir

k21

I'

*.li ~ ~ ~ ~ 'I~ !~ o (tI-ij ,nIV ) K;do toi ~ tli O

e'W, V. Co Vc C~ Iu 2a ted on !: d i yi taI c cn;-)uter tne iriterferc-

.thi or t in e nt -j ti u sd n t - r a 7C I Ia t -!On ,

h2 6nIf 32 .3 nmii; t he i (-k tie s s o ft the i-e 1as t o 1 1;1

1110 ~ mjlfe cf the Wol laston nri-mi ...................................... .... '5 -aia

0] et act' Ve 110n td2 the extraornir e' ti

ii, *, > cal I t~jis of the Fowri( r leli jIl,

f~ 7* ,' thi, rangces rf t h r i

7, We JCC X - 50Q :11 15/

ti, t~~~cj:. ron ~~ t lit, o \~ c1

~ o ou ri er t iarf : 1 r. 1 era:.

4- a .. . w to 2.0) 1 *.i i t i ti c s r ' i r a t 7

*- i adj t Irot o f t !lv N I1 ac, toll n'~ .'

j t n!cul ,-o : or i-e j ted K'y Lno cc;: r i

~'n f * . h 1 he i nterference fri nges are represer ted ~vn'A

d!dhe dot, jeiot-e that the absol ute val ue cf a fraction of' thr.

*~!:W ~ Ic .. jth dl fferenc.i introduced by the Wol laston pfS a

th /4 ,): qrea ter th-n 2.,/4 and the letter B denotes that tho athsc IL.C

* ~ ifidei ccn tre frir viavolength X = 589. 3 nit); for x 632.0 m - "t-tc i.: a cd pa LI (Wfl A..otl d ho sli ghtly different.

i d

I L' I . he da. ''u a ri, r , .c.

Li~~~~~ het ro t C.> h t i c a I jrea,,i c te d rhra'F

v .. ,. tile OX!, l rta I i'eSIIts t ,2 ':li :

r, "il Iu ) w d xid t: ::i:'oit~i diita ,I S- *uC,

0;t~ *ollaston )risri and the ! ertici. :,

'T hi I (. i FCle 1" t.' T- a' rc it' 1~ f r, Cr c~ 0 1.F1

.. : '~' r lent 110 K' et o

t a1 n' t~ tC t~ . t,!j. V

r(, D ilpw o* t'' th r:, Cc'n i'i2' tc hn i

he s i, I r cef01 "i it C. c !a ( h1

toir" i (-r .and tr. t o f r out the pt ilii pos i t4o s of 1 1acin t

irom; -ra:es ,-nhro the t6i ,Irtions can be riniciW zed. For s i mn1i ici ty L th

ca u t ~ i () r, .i 'a on 1 vFor onie-di rens iona 1 case. We assurre tha t the

a 0 n, r i ,I. hv trf'.' ''airo aramretei's as those in thle A parf- rf thi F

c~~~~ .' r .Io s J n t ~ n Ki ti!- shi i

1':t 1. *..12 .~ifl t C (~i tt, 1 '1> a~r t CC'1 trat-e C.> '2

th ' L2.'i, " : a f' I , t ths to :[- . . . ". +i d n i.nts d C

L; ! '.e i Ut S a I(. 'r r' shi . "'1 I I the .,in C -. ., fn " nd

the ce ,i (', n~u. i sp t' .VQ,. maI ", L l i ti " t +r' S',','rt[iF"

t i2 c 1t n s , . k o In tijii . i . . t n t ira - .1 ,7 :

ro 1) !~ J I )ud 0

.,) P., H< ~

r I

ra',. +e + tf; a i > . t + (+,N C, :C.. + .rl t .-. l'rd n 0+i t un

I an- . . . .S ,,C ,'t laI2 sr, r C:, . nO s " , I l t h ,' 1,i ti-'J , C1 , ; n

I .- ,.-., ... CP I. an.

2la

a r -1 2C I ;1 hl .hrea al I ~ (i ,onsidered to e th f" ~

.1. t,. t t.," , i, . ' r t I = " .

1, .0.,n P ii the ., i 0I 1

t, ti ilia x h i. a -, aond 0.1 o. Tho vei . T F 0--

j u Tll s le~ U rt~C 1 two a ddi tioni I i qr, F i (p;re 16( i s a

h - .: .J f .'r . iiw l n :cated On the i, .. - ocon e s ' , "

a . r I % ' w ).f i d !11r 0.01. the jit ference H - H

eJ,, : -! ,+ f'ot (.l thn f. ri H,. ihus, i n o rde er t o r i n = . i .

ii 7 d i1 AIt,.iWO ;O-I',V 'a i re t.h o s i7e o 17L~ t i :iide to be SG,

t 6: 1 o a 1) tho c L f st n ter of ima 0 s ,.

' 1 _ _,_ .. L' : c f er ,, : H .

F '2 iL' f tti hO a,i'iwil foA1 C A (I (ilf trunce (H 2 fl H I

;iu le e thcuppeyCr end point of -a ch of the input images .7:K'o*

CL e the total 11iu-ht (" the iwaqc can he suhtractej c

0.t ~ l nstea:. no the iniddle noint 1:, S

Ilu It t h 0 etO I' t he t o ta d C 1 e t ciF the irlane that can t,,,2 :

t i2tu 1 hjTe:lr 11 ce is, tht- reduced to 0. 04 -0 1'.4 0.

il:jr .~ A ft c as e ';r .h i ch th ( r t C 3 is rot lorate: at

tfl 7''.i1 : at. Ck .A'.Ter it cii br, seen, 0hat The !'.

of ':7r' but ej .iti 1 iin he Ccelter

.. . , '* ~ . r'.o ters !IA C,

C' :. It J d ,) !" U,.(. . W

?. irtl CO ),I~ tA the0,. 1h 0l'~ vii

0 &rlhO1 - 0. Two ,:d' o!o:i

1 t,~ t ' I t 'el I y o * t , l' :t for thI fi -It cac

iSC~~td C h r tv~dstortior. i qroate r it the vicinity' f

c.' tor ' it J., lw,,r p 5jr' of the iniacoc. For- te sec)r'd ca-o (,__ Lit

a. t ir f 'itm rltvE dIi st ort iont ar;ei rs a t thie vCirni t y

t'. c -1 r. t total I t f cr '_1)e f irs t c as e %.wi thin+ th c tale r -, r c I

iI )jsabot ,-r).4) - (-01) 01 whil the total he4,:tnt

fla '0 soow 0.6 00 .4 The coini oter ; j'ro 'l

for- toi' juan r Ir Vted it- 'a.e)ndix C and D n-spectivel y.

tt t I to r t-l f rI, 1 t, hodu d :o rodu,-nCl i n !.re ,Ys te7 an -Ii

I' -h. 1.., 113 CCC fit lil' 01W h 4ar

.n'tr.I d i o ~c..?

t 1 cr

ad c uat i n (if p

itI' Ir enris vi th thIe is.,llest sF tid te t

T c c~ sh r e q e~t nn ei Icc ;e 'IIt S ne 0

4: ~ F 1 aberrations

Ii .; ~ !.. TIC s ~ncoporate tile subtra ti tcC(:e . II :ir ok tSesthtt.ofail iyi i-1 n

- uwlti.-OI 1: '.;tc Lt iTI'C1UC, the LiSe of a Hugjhes 1liquid cr

:,I v. v' P u rt -i imIaqe' "Su)tract ion I n a cant i nuot1,.s

h V vhe 140 1 't ur r 1i sfil f or pe rf o rc:ing reaI- t i! e

sr 0 ;trai t I a (Iit Li Po>fWh of them, ideas could lin tc

1 111

APPENDIX A

iriP FUNCi iON OF A k'OH-ASTON PRISM

(;11 the natmure of a Wo] 1 a- ton ri51 'g ht bcu~'i t rdXC n:

tH'ULfd IhC ' ~ rmWill c I an d!1ount of th-ericthi accor'd'n, 'c

'e;s iv1to af p1 t ]UL ,T ( i IIu st r.dt o the cf f e t X- Z

i 1.~IK. 1 raq na~, hoarex A~ tan- /vv.n*

*i.t :K;, J~ a;isI the heir; 4 of- the pic.The ~~ Kai

Jo fthe _1 e 01-4 cf )I ref r-,n :ent cry'stal hut Lv

fe~i.~ ID C dXI. Kr' ' P4IPF% , 1 p fr,'ta I a'.

rj*A. irll t.,- aIxi S C Y P a1 ) ad toit of "he riq (h l;

P.,, Ithu K:tj ip) s9O'~ )ppr \\ i r15

1 ~ .t~~i - )+ 71.tn).n -1

41.S i., Leo. 21 P thie incre-ent.*K

[),Id oI t!e :,,,Awiptiln, rprV(sefted. by equations (Al )and (A:

two jr!, no-Imt o-nci usim(I can be de(duced. First, any plane wave after

24,

\~

trOU~ji a Wol ]dston prisl1i wil I he deflected by dr,

.hi ierox imatoly emial to (n0- n tar-A. Because w have ,

o fur' uri16tivye crv-stal , .x has a pusi tive value, ie. ill plave

W, V e S ('kl W ' frin tle -oints of wil1l bo deflected downwm-d tby an1

anclIe ' >wC they, me"( f'e'eli~ed al,)1l' P.1 The iinncc of S, -it thle e

pijt lar . ~ii tior, il o e.,ovnd .eei. t ll -en'cred 'i t'

*~~~~~~~ -x, f .' k .'r-e cl 1i~lt WdVe'src 'ri" 1) 2 ori pOIlri :Cc

a i en; tt i:rl JP 4 S- wi 1 r vi VIA rd wid c cc nc i doi-, withl t he i i,,

r h C . tucle 01 St, ci IJ e tev. ld, tnT r' U

f e.- t the c a? 1 ted pa th 1 enatth d i tfn're yt due to t-,

f co- __ 'r,-, ~ t I , h aston pr isl of rel J veiv S: i I r t I

c a r u~ urd

x C) 1 0 4

1. it 11 It .2

14 1.

If it 14 -- 2 -

I .7

vAL L t~ 1 H

. I L.

f.5~

Si, *

i, , .. . ,

Io, ,', J Ji )

: i , L( ~'; ?i "' r~ ~~ Mt ?' A { '

I / 1 '

. • -~'1 . L , 'L " l : , : . ' ,') , , ' . 'J ¢ f , ,

.- , , ,,- LF *,.1'

, 51L ... ti ! " - * t " At : * { I[ I c) " I I } - F

,. t "'i >) . 1

* i. . J .- 11] , l

, 1 *i, .-

.. .. ' )

.1' :". ...

* *2 ,, .?- *' f , , .I/ . *F * i r

t _. . I . t~ t t

Ar <.i ] t, ''

(

i r. , 1) C P: -iu H.TkI 7

I. .

t

L TV . U. D~ iw 1~ Vt U

*"'*~i.~ n'l pQ rt LI IC2

*1 9.525 2 ]07

Vj 1'-.

[I

I; .2 '. ).* .

* i

4

.,,-usrRlP - *tj.t, *t~$/ "~" ~;k7.< *

ii

18.. ii

'4' II% )I

I&

C, c

ti i. 1

*~~~~ 1. t 1 t : I d e ;

4. hu r~.s u'l~eeto f(ringes w-)th L1'e a1in Orenaio

on ' t. .... - i fl ac d l. u i -e ,

the-.:r :.tmc of .serto :c-et -en th two imge re. L :1ce WC:.

1 - 1 d i thp st K Vi alnOintatin I nd th four dahecii

I*Lc' ptositici a showvn in Fiq. 10.

rlic i t)Ij frol!m nilltS 1 alnd p2 at the input plane

2K ; 1 'i ' t the oijtput rnlane through theC WO1lastcn

7? t' i fiae'. rr ci 2 a 1iils ssi n t i io rh t e W o 1 a st cn

r2 I'-m v cow'{u Led i riterf e r nc(, nri ' ' c'n r ..ni; - iai L, oi t io o lf the Wo 1 a st O rl *1 .

15. K'Li '/0Osi tiof;':. of and 11 at t C infri;t p n nI a

OLI ;)11 [11 f,( for_ thU COMIDutItiol Of ir ul iSte."tionl.

iV AvIoL f H, ~ver;us H3 wi th C 3 locatec nn-aixi S.

7 . 1 r*4 u s~ ! i h C' (-,,Cal.4 off -axi S-

E. o,) Nv thC ot v n-a. i

19. . f, 1 ot I 1o'; [I i H3) '0rth C3 located off-axis.

*A...'.Lm c "cs-s'ciona] view of a W11 s 1k o ris:.

Mir, __'9

04-

211

SIL

'04

JL

~2 > T

ii tcL

.;-.q~;,;~* '~ - .We

_______________--I

~1

______________ p

I I... I

*1/

b

~;4P~ *-~"~*~ ... ~ .. -x **

1

I.

i I4.. .4

LL.h -'2 b

C-..

&

I' :1V 1~

I

I*1 ] .,,.,~

-~ I - - J

(-I

.1

-- 177.

I'~A .,, ..

p ~ .. ,

~-- 4,- .4"

.. ..~ -.. ~- . 4

I -~. -.- -- I'I,

a

71

b

KQ ~ K777~<~'~ . .. -~~-------~-~-.

4 *n

t I t

llt Sl i *

Ni1

,~ Ir 4 r'~~' -,

*1I

r ILx. ~i~L..

a

K4-,.

')~ r~

t ~.'?:'

b

-p .p~t.,t.0O*.. 4,.- ,C*fl.*UMS - I

1:~ :..~ I

~1

I41'

I l.p'

__ . ~

~'P~s..J~L...-27~d'i*.. ,

i ''1

.. m_ N : .. - .,

I

i

(i

* V.

L. .

* U

*1V

~ 'Nj~.

.~s -. 1*

14* I*~. . ~ = -.--

* - ~ J777A;;~ * 77. * -**~ .7

.10

* I I

ii ~~i:>

0

I> 0Ir I I

LL L9

. . ... . . . V.

.. . .. . .

. . . . .... ........ ..

. . .

. ..

.I .. . . . . ... ..

.4 ......

I .. .. . .

.4 .. .. .. ..

.I .. . . . . . . . . . . . .

.- ... . . . . e .

.$ .5l5454 .S ... .. . ~ .S .. .5 . ... . . . . . . .

.5 . ... .. . .. . . S..

. . . . .

.. . .. . . .. .. .. 1

S.. . . . . . . . .

r. . .. .... . .. .. . . . . .

.. . . . . .... . . . .

. ...........

I.. ..............~~ ~ .. ... .. . . . . . .

. . . . . . . . . . . . . . . . . . . . . . .. .

.......... . . . . .. . . . . .. .. . . . .. . . . . . .

. . . ... . . ... .. .. .. .

. . . .. . . . . . . . . .

. . .. . .. .- . . . . . . .. .... .. . . . . .

444..............f .. .. . . . ..

. ~ ~ ~ ~ ~ ~ 4 ..* ....- . .. . .' . .i . .-~tb .4 . . . . . . . .

. .~ . .i .. .P ~ .~ ....... . . . . . ..

.~ . .. .. ...4

P .4.4...

. .. .4.9L. .4

. .

. . .. . . .. ...... . ..4.

. ...................................... .4. . .'. . .4......................... .. . . . . ..... . . . . . . . .

.... ... ... ... ... .. .. . . .... ...... 4',, . .4.9.. .. .. . .

.......... ......... ................I.t.' .... .. .. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . .-... t.

. ~ ~ 4~ .... .. .. ..

.~L ............ .. ....... . ,.,.

.. . .. . . . . . . . . . . . . . . . . . . . . . . .. .

. . . . ................................. . . .. . ... .

.................... .............

.. .. .. . ..... . . . . .. . . ...........

................ .. .. .. .. .. .. .. .. .. ..................... . . . . . .. .

. . .~ ..L . . . .

. ... . . . . . . . .E. . ... . . . . .

.. :.*4h.. ..!: .." 9 ' .'~. .~ .

.... .... ... ........... ... ... ... .... .I.

.EJ~~~ . .. a .I~ . .'.t.I...P.

.t " E i . . . . . . . . t I E I ' I . i E f , I j . l

.~tI.t .,"E .E .' .. ...

I ..

4. . . .

....

. .

*. .. . . . . .

. .. . . . . . . . . . ..

.t . . . .

. .. .. ..

I..... ....2I .. 1i'$ ... .44 '.... .. ..... .. .I' . . . .. . . . ..~~~~~~ ~ .. .1 1 ... . ..

4 . . nhr...........N

.. .. ...............

. . .4 .. 4.. .. . .ii.t'.:I.,e. .i.1.P4..I . .1 .

44~ .tt'' . .f . 4..4 . . 4

.H .';': .J. .'~ . .

.4444 ... t4ftI .... .b .4"! ... ...

. ..

. .'!r: 4.4 R ... q. .... 4.'...... ~ ~ ~ ~ ~ ~ ~ I~ 4~ . .44 .44..1l4 . ...... fl ......

. . . . ..

.......................... . .. . . . . . . . . . .

. .. . . .. ... .. . . . . . . . . .

W .. .. . .. . .. . . .........

51 .. Hi.............LI...

.. . . . . . . . . . . . .

.. . . .. . .

. . . . . . . . . . . . . . . ... .......

...................... ... ....................................... .......... ................

...................................... . fLI'IIII. n.6

I ~ ... ~I. . . . . . . . . . . R HI Ph$.... I%~ ~......

.~ .............

.... . . . . . . . . . . . .

. . . . . .. . .

................. . . . . ............ .. ..

. . . . . . . . . . . . . . . . . . . . . . ..

.. .......... . . . . . . . . . .

. . .*, ..t .S.... .

.' .. .

........... . ....

.~~ ~ ~ .. .,. . t.g .. . .. .. . . . . ..'

. .M ~ b ' .M. .-. .. .f. ... ... n.

... . . . . . ... . . .4

. . .f. . . . . . . .4...-

s5~t. . . .. . 4, . .. 4 .~ . .. .....

............. ... ...... ............ ..... . ..... .. .. .. .. .. . .4 0

....... . . . . .... . ..... i . .

. . . .4 .4~

.41 . . ... .. . . . . . . . . . .... ..

.49 . . . . . . . . . .... 45 . .. 44..44..

. . . . . . . . . . .. . . . . . . . . . . . . . . . . . .

. . .. ......

............................................. .

. . ... . . . . . . .

vt.. . . . . . . . .. .... . . . .

........................................

. . . . . . . . . . . . . . . . . . . . . . . . I . . . . . . . . . . . . . ... . . .~ .

t,. I .

. .. .~ .. .I .I~ r . .~.P .Mi i ~ t'~ ..'' .. ... ... ...!if..i ... ... r.....: ..t ....... . ... .np.U.-. ..~i':I~:it' ' . . . . . . . . .. .

Mi,~~~~~~~~ .l'~ .t .. ..~i ' .i .''~ .UI '''F c 8....

. ....... .. ..

- ! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.................................................. .................................................................... .............. . . . . . . . . . . . . .. . .. . .. . . . . . . .

. . . . . . .... . . . . .... . . . . .. . . . . . . . .... . . . . . . .

. . . .. . . . . . . . . . . . . ... . ...

........................................

. . . . . . . . . . . . . ... . . .

............................

.. .... .. ... .... ..... ...... ., .. .4.- . ............... ........... .........

. ....................... ..

. . . . . . . . . . . . . . . . . . . . . . . . . .

............................................ ... .

.4..............

...................................... ...

'........ ....4.44' ........... .

... ......... '4 4. .44..... . . . . . . . . . . . . . .. . . ....................

. . . . . . . . ................ . . . ........... . .

v t . . . . . . . . .. . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.............................

. . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .............. .

........... ........... ................. ....... ..

.......... ...h~.............. .... . .~ u:L- 4................. . . . .

...............................................4k,.'''9....... ....... ........... . .

.............. .......................... ... . .

7l, ..... ~.. t '' ........... . ......... . . . .

* '4.',. 4.444~'''.' 2'3 ii H,'3491'4444''.............................................................

* 44'4' 4*..4'4"' t: '' r~~b~M4tk........................................................

............ ......................

.. . . . . . . . . . . . . . . . . . . . . . . . . . .

.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .

...... .. ... . ....4...................4 . ................ .. .

4~~. .. .. . . . . .. . . . . . . . . . ..... 4: ~:4 . .. '4 4 4 . ~ - 'F Q ".

I ~~ .. . . . . . . . . . . . . . . . . . . . . .Ih : t~

4~~~~~. .. . . . . .,..................j. 4.1': t't,~9 t~'t'4442 ,*~............................4'

t. . . . . . . . . . . . . . . . . . . . . . . ..t' . . . . . . . . . .

I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ..

. . . . . . . . . . . . . . .

...................................................................... ....... ........ 4r ........

.. . . . ................... ...... . . . . . . . . . . .

. . . . . . . .. . . . . . .

. .. ..... . .. ...

I.. ........ ................ . . . . . . ....

.. . . . . . . . . . . .. .

. .L' . . I .. h . ... f.... r....t

.* . ... . .*. ... . . .... . . . . . . . . . . . . . . . . .

..... ..... ..... ........, ........................... .. ..

.IL . .n .' .1 .

.11 .

..... . .............. ................. .. . . . .. . .. .. .. . ...... ........ ...... .... ... .... . .. ............ ........ . ...... .... .... .... . ... ............... ........ . ..... .... .... .... . .. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 .

. . . .. . . . . . . . . . .~~ ~ ~ ~~ I . .. . . . . . . . ... .. . . . .. . . . . . . . . .

.. .. .. ............. .. I... ............................. . . .

...... . . ...~. ...... . . ....... . ....

*~ ~ ..t........::*~~~~ .. ...2~ :,~i u!d! f.i.... . .. . ....... ..... ..

....... ......... .. .... ..................... ..... .

. . .. . . . . . . . . . . .. ! . :. . . . . . . .... :r' , **j .... . . . . . .

............. ... ... . ..:: tt ..... - :i .. . .. . .. .

. . ...~ .. . . . . . . . . .

........................................................................................... ........

.............................................. ...... ..

.. . . . . . . . . . ............................... .......... .

. -................ .... . .. . . . .. . . . . .

t t:- L uv t1 11 "i:111 .. .... ...... ... .... ... ... ....... .. .... . . . . . .. . . . .. . . . . .

.' . '. ... ..... . . ..... . . ... . . ..... .. .. .I. .. .. .. .. . .............

.......................................... . ... ... ... .. ... ........... .... ..... . . ... . . . .. . .. .. .. .. .. .. .. .. .. ....

. .

-~~~ .. .~ . .J. . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . ... ... .... .... .. .. . . ... . . . . . . . .. . . . .. . . ...

-' C - ...... .. ..!,C. !... . . . . . . . . . . . . .

.. . . .2 . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .

. .. ... ... ... .. ... . . . . .. ...

H . . . . .. .. .. . . .. . . . . . . . . . .... . . . .. . . . . . . . . . . .

1... ... ... .. ......... ......... . . . ........ . . ..... . . . .. . .. .. .. .. .. .. .. .. ............................................................ ........... ..... . . ... . .. . .. .. .. .. .. .. .. .. .. .. .. .. .. . .

................................................................. ..... .. .. .. .. .. .. .. .. .. .. ..............

. . . . .. . . .. .. . . . . . . . . . . . . . . . . . . . . . . . . .

... ... ... . . .. .. ... ... .. .. ... ... .. .. ... . ... . . . . . . . .. . .. . .. . . . .

. . .. .. .. .... . . ... .... . . .. .. ... . . . .. .... .. . .

.... . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . .. . . . . . . . . . . . . . . . . . . . .. 4. . .. . . . . . .. . . . . . . . . . . . . . . . .

0 C L'd OU

. .. .. . . I . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ...I

. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .. .. a.

... ....... . ...... . .. ... .... ... I... .... . . . . . .... ... . ... . . .. .. . . .;.

. .......I.I...............1. ..............I I . : I . : ..

...... ...... ............ .L .t~...I......I....I........................... . . I . . I . . . . . . . . . . . . . . . . . . ...

. .. I I. .. ...... ... .... ... ....... ... ..... . . ....... j.. .. . ... ... ....... ... . ... . .. ..I ... . ....... ... ....

~~~~. . . . . . . I. .......I. .................. I... .... ... . ... .: .. . ... . .. . . . . . . . . . . .

. . . .. . . . . . . . . . . . . . . . . . I . . . . . .. . . . . . . .

... 1 .... ......... . ... ............ .... .. . ................

:1.. .. .. ... . .. : , * : . . . . .. . I

. .. .. . . . .. . . .. a , . .* , , . . , , . ,. . I I . . . . .. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

I~~~~ ~ ~ ~ I .I .......... I....

. . . .. .I . . . ... ... .. ... ... .... .. . . . . . . . .

I .. .. .. .. I. . .. .. .. .. . .. ~ i tf .9 i~ ."'...-..M '..t

... ~ ~ ~ ft,~C tP~ .S . .t S ' I .. ...... I.....

.f .~ . ... ... ... . .... . .... ... .. ... .

. ~ ~ ~ ~ ~ ~ ~ .. . . I.:.... .....

rt,.. .. ......~rt ..... . . . ......

. . . . . . . .2.. . .. .. . . . . . .

. . . . . .. . . . . . . . .. . . .

. .. .. .~ . 4........... .. I..

.~~~~ ~ ~ . .... .......

. . . . . . . . . . . . .~~ . . .. . . . . . . . . . . . . . . . . . .

. . . . .

. .. . . . . ............................................ . . . .. ..

. . . . . . . ..

I ~ ~ ~ ~2 . .... ....

.... . .. . .. . .. .. . ............ .. .. . . . .. . .. . ..I .22 .24.

......... ...... . .................... ... . ...............

.~~iF .J . .. . . . . . ...I. :....

.... ..... . ... ...... ... ...............................2

2ti ~ ... .. .... f2!I.l4, .

. . . . . . . . . .I. IJ . . . . .. . .

tW :b U~d~ fr-i' . .. .... ... .P .. H.... .. S.i .. .. A. .. P.. .'.; .. rp( .Oe;,lpf.,..t . ..I . .. . ... . . . . . .. . .............. I-1

.5. . ... .. ......... . . .

.1 ..

I ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ f. .. . ... ...... .........

.i, ..r . .j .i 4* f .4f .- rs . . . .. . .. .. . ... ..

U,',~~~~ . .p aJ .'h'F Li"h ~ P: .Sl .S .9.5 . .S

at,.~ ~~~ .'B .L i....I .... . P'b ... 4 .n .4B rt~ .S.I4 .... .j. . .

.5~ ~~~~~~~~ . .. .... . .1.U. . . . ijSr 1 .4 .' 4f'" 3P A 'l 4 "

ncr . ~~ . .. . . P .'tb 4 .'B'.t't..9!.-'.-'f..4JI:..."

.~t ( 'f . ', . . .4t .................. . .41

4 4H . f . H 1 M ' I'F P'i . ........ '~fl

.~? .s . . . ........................ . . . ', u I ..4Ag. .. ttfl. n.ss .lt .. .. .. . . . ... .. ... ... ... .. ..'

....................... f pil

. . . . . . . . . . . . . ... . . . . . . . . .

. ~ ~ ~ ~ ~ ~ ~ ~ .... . . . . .. . . . . .

.... ~ ~ ~ ~ . . . .. . . I. . . . ..... . . . . . . . . . . .

. .............................................

j .. . ...... I..... .. ....... ..

..................................... . . . . . . . . ...

;:............................t~t.~,-

. . . . . . . . . . . . . . .. . . . . I... . . . . .

. . . . . .. . . . . . . . . .... . . .

FL . .. ....................... .. . . ...

. . . . . . . . .. . . . . . . . . .r4

F. . .

1~1... ...... ................ ~ ,....

F:................. ..... . F11R''% 2

............ P . . .. .. ...... ..

. . . . . . .. I. . . . . . . . . . . . . . . . . . . . . . . ..

S,. ............. .................. 8I 9 3s~IfFM.fi'' .F I.

, t~ 1................................. . ................... P i. .'F1 S F.~t1:F." FF C

. .. .............................. t..!~ t1

F.F.(P'. ... ,nF.~F. ~ .

. . .. .. . . . . . . . . . . . . . . . .. . . . . . . . .. . . . . . . . . .F 'F;t:5 . . ..

.................................. P5:t ........ tFFftki< ~.:F~~rrFt.....................................................F3.Hr

.t FF 1................. ........................ ........... U11I 3 'r~iM bIM b~l3Il......... .................................. ~ 1t'~1SiAIF j COt~F

........................................... -B1lP.IF[F.r~l.F FFF"

. . . . . .................................... Ft.3FP I*i~~~ FE~f.Flt.................. ....................... I.........l5.. F fhl~~.H 8 FFP

........... . ................... 33 1!~.0bFM~i~l13~tRT....... ...... I......I.................[.. 1. -~h!~tRH. 3K1N

.......... I:..........................Ie F .. I..l~btFIE[ tFF.I!

:. .. . . . . . . . . . . . . . ............ I....... *.......'. P~e~l~ej~h PF.iK.2:1 . . ........................... 98 F ~ fb.R~~[IPf1.&AF

F *' ~ ~ ................FF..................b.FejIP. jtiRbS ~ PI........

~~1F F . .............................. FF .11111 .O"1t8I.PFLIRP'$........

.. . .. . .. . .. . .. .. . .. . ........................ 2'&31( 311R!b r'3i'i.........

. ... ......... . ... ... .................. P1 F~l~lI1FID-f 331F13.................. .... . ...... I........ ..... F~.~.!cEf.FtA. ~''1fli3'............

I: - . . . .................................... ......... ~FMI-l itPIiFF4Itr- R~'....................

. ..... .. . . . . . .. . . . . . .. . . . .....'UF~ FI ......... 3t 1 t. IF B ~.. . . .. . . .. . .

F .* . P~b~rFF.......................iF.cr fI#!lI:kPPPIfhiL..........

. .. . . ..-- - - - - . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .

.. ..# ... . .. 4 . . .. . . ... ... . . .. . . . . .. .. ..F. . . . . . . . . . . . ... . . . . . . . . . . . ..

.; . . . ...

... ~ ..

... ..

.... ... ... .... ... ... .... .. ...............

.......... ...... . . . . . . . . . . ...

...... ..... ..... ......... ........

.. .. .. .. .. .. .. ...... .. .. .

........ ....... ............... .. .

. . . . .. . . . . . . . . . . . . . . . . .

. . . . . . . . . .

. . . . . .. . . .. . . . . . . . .j . ...t. . ..f

4; ,. ... . ..... .............. ~ 4~.~ p4 .~4

. . . . . .:. , .4 4 . . ..4 . . . . .. 4. . . .. f..l4..4

.~ ~ ~ ~ ~ i''"tl .l :P '~4 '"r . . .... [ .... .... ....

. .fE ri r [. .i5fv .',,4 .hIM I.......I...

....... . . . . .... . .... . .... .. .. .. I.. . .. . . '.[i'I4 Il .b1t.~~ " . .r. .. . . . . .

.~~~~~~~~ ~ ~~ . .. .l .........................................

.1 ........................................................................... ............ ....... ..... . . .. . .. . 9'N'84 . ~ .4tMf,,: I 'Il............ . . . . .. . . . . . . . . . . . .. . . .u ' r . .. ' 1 U 41 . . . . . . . .

........................ ..... .. . . . . 1M. . . . .

.~~~~ ~ ~ .eMiH eIr . .i.. .. .'4.. .. QI. . .. .. 4..( . .. ...

.1* * ..

4. . . ........... . . . ...... . .. . . . r- .n~ .s .ll r~h ' I. ....... . .. . .. .

. . . . . . . . . . . . . . . .

. . .. . . . . . . . . . . . .. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ * .1" .

* .. . ... .. . .. .. .4. ........

. . . . . . . . .

.4 . .. . . .

t . . . .4 .~ .

. . . . .. . . .. ... .. .... .. .

. !4. . 4 .i

.4. .. . . . ..... . . . . . . . . . .

. ....: ...... . . . . ... .. ....... ........ . . . .. .. . . .

.4 : .: .. ..

. . . . . . . . . . . . .. . . . . .. . ......... .. .. ........................... .

.4. . .. ... . .. . . .$ i

. . .'t .... 4 . .4.4 .4 .M4 ..

~~~~~.~ .. . . .l. .~ ..44 .... 4 .41.4 .. 4 .

. ... . ... . . .L.t.. . .. 4. . .. I.f. . .

. .f .~~i . .949 .H . . ....... ........ .. .. .. .. .. .. .. ....4 . .. .'I .*. . .. .. ..

.. .9..... .... . ..... . . ... . .. . . .. . . . . . . . . . . . . . .:4 ....~ - '...... .. .. .. .. .. .. .. .. ....t .4 . . .:: .4.4. .~b~ 4 H .fl.b.L .S.f.t ......................

Ut. ~~ ~ ~ ......... .49.... . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ~9~bi............~........ .. ~. . . . . . H e .bt9' .H e"'r . ....... .. .. .. .. .. .. .. .

~~~~~~~~~~1~~~~~~~~~ . .'94 .?4.1 .UC .4.4. . . . .. t!~~p .ri .' .4 ........... .. ..

. . .4 . .4 ..41 4S'. . . . . .94r9"~3.~P~dPr ....... .. .. .. .. .. .4. ..:1 1.. .. . .. . . . . . . . . . . . . . . . . . . . . .b 9-n .4. ~..... .. ... .. . .. .P.

: u9 1. .. . .. 4 9.. .. . .. . . . . . . . . . . . . . . . . . . . .b~Jt P9. .... . ..... .. .. . ....~~~~~~. . ."~~b

4' ....... .. .. .. .. .. .. .. .. ... 4I1'FH ' ~e9b'E '..... . ...... .. . ...

. ... .44. 9tv:4 . It. . . . . . . . . . . . . . . . . . . . . . . . . . . tr..... . . .. . . . . . . .. ., *: . . .FL.t '. ....... .*4.944. . . . .. . ts PPFHB . .431 4 "........ .. .. .. . . . . .' ..

.49 .4'44 .s4 " ... ..... . . ... . .. . .. . . . . . . . . . . . .,t .. .t . ........................ .9 4 .9 Md. 5.. . .4..... . .. . . . . . . . . . . . . . . . . . . .19 .9.9.9.....4..... . . . . .

... ... . . .

.. . .> .

'.. . . .I*I*II. ... . . . ..~: .*" '.. . . . . .. . . . . .. . . . .

. . 4.......

.4 .. .. .q . . . . . . . .

a .11 . .i~ .- W [.4 .. 4 .. H 1............................ . . .. . .. 4..Z.44...4 ..

.L . .. . . . .. b c .

.4,.~~ .p4.-. .. . .... .................. .'4.4't. .4. . . .....4. .

~~~~~~~ .. ..f.J., . .4

4-f~ .~- .. . . . .

: ~ ~~ . .............f. . . . . .4l . .44.,.

.~~~~~~ ~ ~ ~ ~ .~9 . .... .. ... .. ' ... .. ... .... .... ....

., .44. .%' . .r.I .q . . .........................

. . H. . . .. . .,. . .f.'.(... ......................... .I'4... .' ... . . . . ....

. . . . . . . . . .. .. . . .. . . .fs . . . . . ................................................. .............. .. . . ....... . . ... .4 .. -e(b r. .. .. ... ... . ..... I

4~~~~ . . .. . t!' .h~h . .''1'4 . . .1

.1 : .. . .c": . .b 8"tFA .w EH .. .1'H . ii ........

. . .I... ... . . . . . .

Cl~~ ~ ~~~~~~~~~~ . .. .-' .. . 4 . M~4:fb .,31i'S . U'4 :4.''.

. ,. . . .... i ..... . ltPtU .14 .9 .FH ... 'l9fi'''~

.~~~~ ~ ~ ~ .. 4 .. ,4i .f4' .

. . . .. . . . . . . . . . . . .t .. .......... .......... ........ ............

. . . . . . . .~. . . . .. . . . .

.. .... . . ...

............... ...

.~~ .. 4. . . . .. ..

. .. . .4 .4 .

.. . . . . . .. . .

...... ... .. .. .. It .. .. .. .. . .. .. . .. .

.. ....... .............. ...... .............. .4 ~QJ

..... .... ................ ................

.. .. .. .. .. ... ...Nt~r fi ' H s~~ ... . . . . .

.4 .~ .................... ..................t'iP p (,- B( ib............................................. ..................... :I...........!tPeris fI4Ftf r

44!........................(4~ u.........~%4 ........ 4,4..,4

4 ! ".:!:n. & H~eten~...,ru!.......... ................ ,

41~ ~~~~ .414 .3 .be.r.i .S.e'.j.E'.. . 4

.......... .. 41 I u. r ............ .. . . 1' ........................... . .f..H~.L13 !'H..FbF'

': i;1 1.4.............. ............. 3.~i!FF''4'B!........ ............... .. . .. . .. .. ....4 ' tfH li~1 tfR4.d R t

........... II.H......... ...............

4).........N E ~ ~ ~ ...' r ... ... .. ... ..

"~,PM .~i 144$............ ................... 4f............. ........... PIMA341n Hl~t....................

. . . . . . . . . ..... . . . . . .4.44. M etr4b'~"..................... ........ K4

!14. . .. . . . . . . .~...... I .4..4. . . . . . )b~e M . . ...............

4.:. . ..I. ... *. . I 4 .. C'4 . . . . . 3 i4 b .i '% ..... .. .I. .. . . . . . . . .E..

. . ... . . .. . .! .M. .t:.i. . .' .......... . . 34 ~II*~~..... . .. . .44 . . .. .>L

4414..4 . . . . . .$Ph 'hb h ... .. .. .. .. .. . ...

.r .. . . . .. . ...

41 ~ ~ ~ -2 t 4 4..444 f... ....... 4.* .....

.......... . . . . . . . ....... . . . .. . .. . .. . I

tit- .............. I. . . .. . . .................. ... ..... .. .. .. :,.."' ' -t. . .. . . . .. ..

. . . . . . . . . . . .. ..* .! ' ' . . . . . . . . . . ' . . I.... ... ... ... ........ ....... ..... . . . . . . . . . . . . . ........ . ........

............... ..................... C- I........ .. ...... ..

......... : , ......

. . . . . . . . . .. . . . . . . . . . . .. . .... . . . . . . . . .

t 4- .. . . .. . . . . . . . . . .. . ... .. . . . ... .. .

. . . . . . . . . . .. . . . .. . . .. . . . ... . . .. . . .

.. .. .. .. .. .. .. . . . .. . . . . . . . . .

4. . ... ... . . . .. . . . . . . . .

........ . . . . . . . ...............

I. . .................. ~ ............. . . . 4

i t . r.~~ :1... , ............... t N.'4Fo

................... .~: ...................... . . . 4 4 . .

7 .. 2I Ft'CMU9.............. . . . . . . t ~ ~ 4~. . . . . . . ... . ... . . . . . . . . ... . . . . . . . . .. . Ii ~ . j ( * . 4 . ~ . . 4 $ ,

... .. ... .. .. 17 -9 ' ' t 't i d t -4 4 .4 * .-0I...

I. t t:~ .. . .. . .. . !'~4

U . ..... .... .... .... '. .... ..... . . . ' ,.

..... .... .... .... .... .... ....

. . . . . . . . . . . .'0 ~ 4 ; .4 t tf . . . . . . . . . . . . . . . ... . . . . . . . . . . . . . . ..*

a .............. ii: 'tH i ................ .. ''M n iitl ~. ..................... M'I H,Irt . . . . . . . . . . . 1 .. .. . . . ..e' f i . (.. . . . . . . . . PtI . . . . . . . . . . . .O

lit: ... .. . I p : I . ., 1:: .. . . . . .. . ... . * ..q :~.h ~ I 5 ~ .. .. . I ... ... f' tf f~ t.d . . . . . . .l i F ....

4 I . .. * . .... . . . . . . . .Ii. . . . . . . . . . . . l & 7 f

i ........... ......... .... . . .......... 'PU~rt'tW~.................~

..t..........t.' I"r'4~rt .. . . . . h ti~ t~tH f~ .... .0 1PPC 17rr~it I~'~',. . .. . . 7..44.,.4..9, . . . .~ l'.f~b'..............it.. 444

..............

.r 7

.......... ........ .. ......... .... ....

.. . . . . .. .. . .. .... .

..............

........ .. ..... .. . .. ...............

. ..... . . . . . .... .... . . . .

*~~~~ ... ... ... ... .....

.. .. .. . . ...... .. . . .

:1. . C~~.............. ........ ''~ t4F U 1

.. . . . .. . . . . . . . . . i . . . . . . . . .. . . .

...... t.~. ........ ................ . . . . . . . . . .y f 4I.

. . . . . . . . . ..4 i~it . . . . . . . . . . . . . . . . . ...

i... N......

. . . . . . . . ... .. . . . . . . . . . . .. I . . . . . ..

. .. . ... I ~ l.it t * :4f. .. . . .. . . . '"4 : F4 .... ... ... ... A l, ... 2

.. ... . .. . ..............,', L'* ' ... I9 t.J ' . .

tn . ........... 4P-~: .. . .. . ..... 4 4 " .. . .. .

. . .f4

. i. . . . . . . . z .4. ..4 .J.4 .44 4 l 4 i . . 4 I. . . r

.. . .. 1 ..! .. . "4 . 4 . . .. . .. . .1 $.n.P.<.. ~r~r . .ij ....... ..... . . . U' . iF

.1 ti t :.. . ...... ..... ..,, .'f4 r .'4f 44f.

t . 4 4 4 '

. * . .i ib. .. . . . . . . I. . ...... ... .*~w4t ~ . . . . . . . .~%

.... ... . .4 . . .tt .I 44 .Mi . .t.. .I .. fb. .. ... .bb..t . .. .l .p41~M ..

.7z z r .1 2. ...

... . .. . . ... . . .. .ri # .4 3 . . . . . ..

. . . . . . . . . . . . . . ....... . . ........... .

.4 .... ... ..

. . . . . . . . . . .. . ...... . . ......... .. .. . ....

.. .. .. .........

. . . . . . . . .

..........*............ . . .... . . . . . . . . . ... ...

. . . .. ......... . ..... :...

-~~ .. . . . .. . .

. ...................... . . . ... .. . .

t.. . ............................ j. . . ... .I...k. .

222.202~. .. ... . . . 'vt . . .~22.~. . .. ..

. . .... . . . .. . . 2. ........ . ... ... 22 ... . . . . . .....

. . . . . . . . . . . . . . .. ... .. . . . . ..... . . .C.1.1. .'.. . . . . . .... ,.2.-

. . . .. .. .. . . . . . 2 . Iq2 2 . .22 . . . . .

. .. .. .. .. .~A 2V tO~ . .. .... I................ .

. .2222: .(:'2 ..... .....

. . . .WC~ . .3 . .. f . "1itk t . . .. 2 .....

. .. .2..~~f : : . . . . . .. .b. .. .. .. .. ..

. .....21 2.2L.2. .p1

2.3,,0. .22 .2

. . . . . . . . . . . . . . .: .2. U . . . . .... . Hb~ . .... ... .... ....3

.~- . ... ...it.... .. . ... . . . 'i ' ~ '"~ .. . .........

2i:,:L202~~~~~~ .,: . . . ..~ .2. . .2. . . . ..... trP l6 24. . . . : ~ .2 ......2 . . . .

2r. t2 223P 2 .:12 ......

. ....... . . . . . . .~.. M *231 ..'. .~r . . . . . 5 . t .

.2.~~~~~~~~ .92: . .. . . . . .23

.2.W2- 2 . . . ... 2.. .2...

.2 . . . ... . ... I.2 .d .1. . . tV~tV 4 1... . . . j ui .. .. . .

.2 ... ... ... .j .. . . . . Ml2tt1:&. .2 .222.312~.

..2. ..... ... . . . . . 1. ..2. . . . . 1. .11 ,.22 ~ . . . . . f.. . . . .

2. . .. ..... .. . . . ... t t22. 222 ..I, . .2. . . . 3 22.... .22, . .2t .i. . ..

~~~~~~~~. . ..2 ., ., . .23 . . .. 2. .I2 F 22 . . *1

. ... . . . . . . . . . . 2 b.. . ..2.:..2. 1.

. ..... .. . .1. . . . . .22:. . IU.12 22.....22. .22.1.2.2... . .

~~~~...... . . .'2~ .. .2. . .. 2 ... . HP.21 . . . . . ... . . . . .' .. t I . .

. 2 . ... 22.. . . . .. '. 2.2................ t.tI . .22Y . . . . ...

.,. .... , . ...... .. 2 2... . . .2 . .. .. .. .. ..

V0-

INI

"I

~ 'I

4

d

j I . .

A'.

{L 4

I

ii

I,

4. ,-x,'-,

'% t U-

; It

II

I

II II

-______________ ''I

- ~

I

I

I

I

.1Li

.2 -t

- ~ -'-1~ - -- .- - a- a

-----Ti ~~ui41 *V~,. *

b .1 x

K. d1:[ + A

Iz

----- I ~--~--------

A 0

*.1 _________________

Isw

~*; 1'

-- - - - ----- ~. *. ~*..a''.