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LL | Sipfeatction of tiptrt)
Diffraction 7 beveling Kpreading of Leg was ead Hay Coc AC
Chstalle
Didtewtin products iniofource paleo arith sueqiens of constrctn
Bdesbuctie Guscfouncs, deadig We formation of bmight &
Cork frvges Size of obstacte~J
Fresmet Dij}redion
_t! | r
1 L |<
Suaer
Pranrefer i frachen
f
Dubtance blw sovver &
obstocke and geutn Kebstacle
wd finite
5) Ture comen Lent #09t
© No sons yepeired
O) Wovepnerd > Cy fires pho (2) Warejscont > plow u /
@ Snitial phase of See wavelets (GH) dutta phase > Same oh plows Of cpevir
8 obiff. cd cliff pedxts hy
plane cf pest
Fraunhofer diffaodien at Aingts ster]
| Frounhotten cffredien af “get
i f
AL =A >] Ty constuction’ S) Ltr,
plane
@ Deane pw source & hStacls & rw
Sunn & abHacle cs pofiwte
Sow
fabh diffe b= BD= ABan 0
=agne i - \ yp Ortensit distnbudton 49 cloth
fimalyricol Touccctmand Oo \y .
dur Joa Ainglt aud
Let us contiole susult of Siconclasyy Usave ci ffracteol af \
an angle & fam mormat Ls cotiecttd by Lund UL freums
pont P an Roreen
; : istus boy.
For ths, Oct the colistusiboanes Ms ‘
pant stat of aut ak Cub giver by
Go = Aceswt
let @ be a point aba distance y prem C ter ere
dy aff agit at
ck P by Sec wave from
aaa
Re dubptacement ot Pub given by
ee
ae =Adycos(wt +o)
ushene d= DEK = nly 2en®)
dt = Ady cos + Qty e
The total dapat ee
= rn dy uss(wt + I ysin@)
A
YD
A/D yor
= Ad [cose costar zin t din & ‘nO
he de A wo n “3 an
2 . sin ,
a Ady coswt(sinan J gin wt ~ cern.) ang]
) 4 agains
g fy “ay,
L , +p t
— Aceswt sinh) aint Asin
ay ne _
y T=Acoswt uin(1L0 dino)
YA (o5ino)
& =f ° :
Aa sin(asind] corp
eane ‘
‘ (hose
ferop prude
Lee = ME &nG BA, = Ao S700. ainphitucle
A
G) Central Moxtma
Fos TMOAX Intkerarthy
&ma=G
2 &nG=0 . asx]
&=6=0°
Ae= A= Aa
Troy= Te = To= @ay
UO) Fee seendg Mining
ind = 6
OS cae
Usher N=1,2,3 Yeme gesmat ce wations t
* Cond” fer morime
at a8n@ = nor
i
a an@ and
© Cond fer Maxine
Ti @ gine =QntE
A
a gine = QntvuAa
2
Cryst Sec- ymarrma n=!
axrne = 34%
(Zora, Fela) > Fema. To(4eq2)
> AS ad incuase, Intensity dee
Ce Ot ey : jit
Poo divtonce bie by & dvecen/ Foca Cougs ef furs
x
oe
X= A (For n=! /contrat may.)
7
waa
Width 6+ contral maxima =2x= QAP
a
[Rewhete dHoechin at Sourte 81:4]
AB, cD Rag
8, C opacity
Dittrachon pattesin due to duso 8lt consist OL
Irtoyounc phinemenen due to gece waved coming fem
. Crusponching points Gf uso Slits.
i ) Pippa ction pottestn duc to Secondary waves qpeem howe
ALS vndividualty .
Theory
CD Sordestoun ce
Poth Ltt. = A=@+b) ging
For. moxima : (atb)ano= nJ
N= 0/12
Vy Fox minima, :
(2.46) eine = a (n7 Ay
N= 1,2
YN dy
SinGe dA | &nO= 24 /
b atb
at
uno3= 3A
ath
° . * & 8 On-
Ainb;-2ind,=A & BinDs-gnO, =A & *
aa. ath
=2 tingulan zep. bus any tue consecutive MAX. /mLn-
WA efuol & egual +0 A
4b
© Dittsoonen
Fath cif. = A= 0 ding
For minima +
O kn ¢ end on= 172,7
Fa may.
Gang Qn! Ej we ‘i
*For min: Ln
Irderfounn Ditts
gmo= nd Ung =hd 2 e dotterfouncg by tiso port Sounces
by dbtance d-
(PY Fox Minima :
Line
ae
Sepanaled
Te=-o
> AN L= 0 Or wosp=o
=+ .
a=ine p QneOn
N=1,2,3, N=O,1,
2 ainO= nA (a+h)din © = Gra
(1) For Maxima é
To = max.
eaivry= | on cos Bat
&=Qn+ Da peut
a :
( ushone = 0,12, ua ae
Ba almo = Qn4+Ay (ath 4'n@ = nA
m=0,1, 2, Masking Orelens ;-
é ; ys poth cone
8B = nj > Diff mm P
(a+b) gine = mA > Int. Max 9
Hee
ath ™
»Gse (ih a=b
m=on
n=l os
m= 2, 4,6,
? Case diy Boor
Renae
“pat y,
Sn n- ates 1 erly Limit chonge -orpd-a, £0 (n-00 />,
&) a= 6x10Sem , x= Simm, $=
2com , tind a=?
Bor: dmo= a agind =m m0 =r. :
whew Pinel, SoS. xed" 2 a= 2oobXWT aye oH
fee Ga 200 x0 Sx [oF = eee x
= 24gno%
78
=2-tmm
Go= A test
Le = : ;
d Adycos(wt 28 y sing
ale,
a ty WtO/y
oe Jae+ fact...
seca Ut i oes
Fe, fM4tere Sntegrating 1
Arnp plitude 1 Ag = Aon sing ) singin
A
Intensity 1 0 = ToWy(bivtec) in NB )
7 Nain’ fp
Uh c= Tadin9 bk p= Tat h)aind
A ie
Tosin2d Intenaliy déledbation duc sto dliffeectten diet
“xt do Ringte het
Lin NB — yak fence effect clue te &condas uy saves
sop peur N= Gulls
x Position 6 >
- Pudrmarey maw ime
Bin p= 0
= tn
21,2, -
tim ginNB = tim Nas = tN
pom ging point ces
Tp = To dine (mor intensity ) att
“
anax+ yr
(ath) sine =nA
n= l,2)
+ Becorclauy Minima
&mNB =o
Np=tmm
am = 1,2) 3) Hy--- NY N41, N42
om FO, nz (N, 21,3 N-- ~~)
N(v-!) 4 2Nt Necondatey Maxine
ol Ip
lps
Tie? i oat
To giniy | scxine oO
eC gor p
Toatnty }siorpbee aorm penn? sin’ wp ainposp)/ =o
- Sin? ps
To sin'x [tates Cainanp) sininpiach’p | So
x Ain’ fy
To gin'x | Nserowp - an’ NAsin2p J =e o
Ce Sin p
At lord,
Mon B= ton wp al
Nan Py
e NZ . Toasty
a ken? owe
I= 207 B4+N amp
Te), = FT Sint ol =e J
Gorse, = Fe ain Tae.
We ENO (To Vpym = Tosintg (n2)
> Tea t+WOI SI ps ne. of gichs NT
aad Intensity of sec mex: Tso cap:
SE (WI) = Mingma (W-2) > Levon
_aN\ \ Law
me Dan la VA
a Naw \nw Vall
3
Awa) cov i= Hesad\.
sip |
abtp a.
Z — frase
sowh /\y
Re >
20
inp
© Width ef Gntval Maxima
n/\
Wa,
un Sm 6n
/’ Nn
may. (@atb)smO= nA nel?
min. Nf =m
f “ap + AO
N(ath) &nO= MA, MFO, NN oe ere
Mom: wearb)ain@tde) = NADA
N Cath] cine cesdo + cose cindey= GrvtDA
Sf ce ws Smate , cesdo=| & SindOr de”
N(Ca+b)[ ainet cose do J = (nv tia
NCa+b) an + NAb) cos OAO =QntidA 4 4
NO) 4 Nath) cosodo = nWA+A
d@=/
N(ath)ces@
Width : fetes oa |
| N(a+bhcose
ado= gy = 6A
i nNCELO
oa "G4o) oe a
@ Absone Spectra with g
¥ Ptating
OLN = mm)
G+b)gmne- nA
(44h) = »
a on
ctt: min-
Int. max.
@) Overtapping of Bpectya
shappens Cf Source 1g poly che comatie
(Ci+b) wind = nA
MA, = 3XFe00=2}o00M 3 M2Ay= X56
O= 2looef 3 343 =5x42c0= Flocesy |
|
wD No- ef erdesi ef xpectsa wt th foting
(ce th) ating = nA :
Mmay =(Ath) doesn depend en no-of elite |
A }
[ Faawdrefpen Diklnocion by & Creatas, Apedune i) v
el ue conaiden co plone usavefeont us Jinciclent on @ clreciter
apedw fer ushich use usild use caylinelesetcal coordinates
be. Bez $e
ex = Frosh
= fain
veer wes
Because Of Uvelas eymmeby of the aystem, Hu diffraction
pattem will be af the foun of concenbuc clrcila sungs
Ut thein conser 0!
We witl collate intensity distoibution only along nL»
Fos aris,
g=0
ote tye
Pea
Yro means =O 8 ain gs we
Zz
O> angle OP makes ustth 2-arces
eee, U=sue co hate §=6| t= Se nee ®
Az Az
‘i “be (ote. t {+3 i sn) cls, Ay
EP = A. el eapf ikltey? exp Uccts Bt) erp (UaFEN
CP. Aoetve pew If ms
fer ciaculax apecturt of sadius “a, if wet ebsewe in?
co dimensions much real ee Shean fa?, they use moa neglect
dhe tuans trwetving (1+ oe)
= Boe ep ih? Co(us Pe
ieee cate Ser (44) dy dsr
= A_elk? exp tka? ff expf Ct ine Peesd) gol pg
Laz 2260
jet 9 = kPsin€
Be 4 ys 9
as a . Pe a
Sql De = Pdf kaine
dp = de —
a Kaend A —~
£
Ha Berl oop
a do
Sept eo} Bio Io
kasho 9 2n
os
2 )ckmer J gag foterita g
-" A elke eee kaun®
vale t's eo Gane und) °nJ 9 Teg og
Loire an
Ime) = TtlOmy +uces w)
i =| : races v),
ar
fer m=0 oF
Tew= 4 Je Seale
é
Klmilasdy .
Tots) = oa eee
Also, A Lu Inlw} = UTrn- ld
er um Trl) = fu" tml) due
Fox mel,
Url = =Sudwdu
New, kasin®
Ete Te? eae (ike s¢ ata
ca exep (ik x) ney fen],
A tk2 oftk 27,0
Ae nel) ne [ 30]
Ushou w=-Raatne Te(oj=)
TU) = Te [amy ]* ee
va
To Intensity at Hhr pent 0/,
Ths Bb Hy famous lay pattern. haacie
rie) | d Hea aio) 77
ha gino
NOVSo when V-= 3-83
ha gino = 3-94
2u Ha =3+83
Rati.
x) = 383C12) 122 (dz)
ela
Ta ws the sade Of but dash sung
& beng fpctiged on gesxceon, the fecal Jength -~2, %0
ys 122 fA bo ameter oy
Dd
Foor
apecure
wa 2 apprmaches Ay Ae Nowy disc can be very Large
Resolution ef Fmaging System |
Comstelesr dive poent anes folaceet vesuy Cheee sy toch
Ralls ef Aimy odse als given -by
X= 224A
D
Angudas: meagisee = AB = 1224,
If, crngutar, Stparncition Gf podrit gerwices= Ad
7 then domages sib
che distinct uf Aps> A6. ~
EE
(BO) no. = ap (224P
D
AL contece lo centre geparertion
BOmin = b22M =o,
dD
Revolving feuce /
i" (AW mine
Froumbogper Dapfuaction af scretangutar aperture |
Let us Congide a seectangetas apediore Cof Atmensiion Ax) the
brounhepben clifpeaction ®f @ plane wave fnetilent reranalthy
OM guch a rectangilase euperclesce weet be ceven be
yf
EGuy, 2) Ae esp Oe Pht” el Fes, oy
% bla
Fein - 4, fever Cae = asin’
Vy
origin cenber of sccctangulae apertiore
Ebay, 2) = Rab fk esc eh Gtr y2) 5 (sine ainy
912) = flab el erp the Gory’) § (Sink) (air)
whee B= ub = 21x b
2 i
Op eine
Om angle of chifpraction cdong x-direction .
& y=cvae 2 a
07 © UES <8 = aa. sing
4 angle of diffraction along y-dir”, Wpn, [LOP)= To ginty ginrB] To- Deudltance at p
ns (at y=2=0)
a
puiriras,
Along, %-098 *
Teo ushen p= vor
The =m, m=o,1,2
z
w= Az
b
Abong yaoi =
I=0 when ¥ =n
Tay =n
de
y= naz
J a
¥ Martimas,?—
Along %-a008 3— yoo or N=0 0% 720, dink =|
a)
uy
wadDace.
a
eg [J =-ceatgaae [Rexotving & Dispensire power of grating |
. at maxima Lies just above 1c: mini
Rayleigh Cscifercia > Princip
nd) Wr
adh ® ve
aren ment]
Max (a+b) grn@ = n/
Mov. N(arb) sen = mA
@th) &nO=nUtdA) —O
N(ath) &in® =(mn-4)4 —@
Resolving power =
Using OD & ©
Nn (A+dA)= nNA-A
Nn A+Nncda = nNA-A
Resolving pow: [A J=nN
Huspeute power = ae
& oid Leatbyamo]’=[na]’
(atb) cos Que nels :
dO - on & dP
OM Cath)c6es® a
Hipelve power=nsino - 4 °
nAces@ Acete@
