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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
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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
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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
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