a?^ ;D ??c ;¥M??F
??c;¥M??F
o??ò??μ?? V[¨ˉ?? ?
í
?b??'
&
^B? ?D
'
^B?
O
*
1 ?T+
o bWM? 5
?B
o?|?B???? ?toM???¥
9¥????N? ?D¥e ?b
§ 3.1o¥?Fe ?
B=?
o¥? ? .l?
p
V?]?÷
??÷ ? ¥o bWM?
H ????
Es<
ò?o|?ò1
¥+??M??.lMo-W
àμ?Yb
o¥?F e ?
+
oM??¥???
^ò?o?1????¥
O
?Fb
? ?¥Hqoé1L?b???<
HL?oé?M1dL?¥b
?i1??
^<¥?F9?
^??¥e?MF7
^??
O
¥?Fb
31·¥
^
ù?
?o¥?Fe ??
?¥
^B??¥e ?
a¨??R¥f ? ?
^;D?aa¨ ?) ?s ?aμK¥+
oíK? V
?¥o
?F¥f ?b
=?FZE
]?
qa]??Z_¥??;b
}
?E
§
H′E
)cos(
111
tA ω?ψ ?= )cos(
222
tA ω?ψ ?=
??MFaˉ1e~??b5μ
)cos()cos(
2211
tAtA ω?ω?ψ ?+?=
tAtAtAtA ω?ω?ω?ω? sinsincoscossinsincoscos
22221111
+++=
tAAtAA ω??ω?? sin)sinsin(cos)coscos(
22112211
+++=
1
a?^ ;D ??c ;¥M??F
)sinsincos(cos ttA ω?ω? += )cos( tA ω? ?=
' )cos(
21
tA ω?ψψψ ?=+=
?
2
2211
2
2211
2211
)sinsin()coscos(
coscos
cos
????
??
?
AAAA
AA
+++
+
=
2
2211
2
2211
2211
)sinsin()coscos(
sinsin
sin
????
??
?
AAAA
AA
+++
+
=
2
2211
2
2211
)sinsin()coscos( ???? AAAAA +++=
)sinsincos(cos2)sin(cos)sin(cos
2121212
2
2
22
21
2
1
22
1
???????? +++++= AAAA
)cos(2
1221
2
2
2
1
?? ?++= AAAA
' )cos(2
1221
2
2
2
1
2
?? ?++= AAAAA
)coscos/()sinsin(
22112211
????? AAAAtg ++=
2ˉ
?E
1
11
~
?i
eAU =
2
2
~
?i
eU =
??? iii
AeeAeAUUU =+=+=
21
2121
~~~
V¤ #
2
A ?tg Vr
T]-b
3??
O
E
ˉ bW?p ? m
?
U
21
~~~
UUU +=
?
o¥?F V[?ò?
O
?Q?
náM¤C?1M?¥êMμ
2
a?^ ;D ??c ;¥M??F
??F¥<
;¥?
q
^ 10
14
HzM??ù1N¥Y?
HWl¤;<¥?
′o?
^?
@
áB?
HW=
'NY?
HW=¥ü (′b
43
HWNY?
HW τ= ()T>>τ
<
∫∫
?++== )cos(2[
11
1221
2
2
2
1
2
??
ττ
AAAAdtAI dt]
∫
++=
τ
1
2
21
2
2
2
1
AAAA dt)cos(
12
?? ?
12
??? ?=?
^
o??¥êMμb
1?
12
??? ?=? 43
HW=?
^ ×?′ 7
^
?
HW T í?a
? ?M??
??cos
-1 +1
?|′5μ
0cos
0
=?
∫
τ
?dt
'
^
;¥<e?MF
àμ?
C`b
21
2
2
2
1
IIAAI +=+=
2?
12
??? ?=? 43
HW=?
?
HW?M7
^B?×?¥
?′5μ
τ
1
??
τ
?=?
∫
coscos
0
dt
2121
2
21
cos2 IIAAAAI +≠?++= ?
o bW?]¥ 1 ?μ?] ¥ êMμ ? Faμ? ] ¥< ' C?
C` b
??cos2
21
AA $?1?
[b
9oD bWê?μ1 '?]¥ bW? μ?]¥êMμ y7μ?]¥?
[¥
?
′b
aa π? j2=?
H 1cos =??
2
2
2
1
AAI += +
21
2 AA
2
21
)( AA +=
21
II +> ?
M éb
ba π? )12( +=? j
H ??cos 1?=
2
2
2
1
AAI += -
21
2 AA
2
21
)( AA ?=
21
II +< ?
M h
o bWM? M??μ%?¥êMμ
P¤;¥?
×?s? ?1?
C` b
?á
3?
¥;?1M?;
3
a?^ ;D ??c ;¥M??F
1M?Hq
1a ?? ×?
2aωM]
3ai Moü?¥??s
b
???
21
~
,
~
ψψ
nullnull
<° 5°¤? ¨
O
?F ¥ZE? ??
O
ψ
null
~
=
21
~~
ψψ
nullnull
+ ]
Hμ
2
2
2
1
2
|
~
||
~
||
~
| ψψψ += '
21
III += í?
b
?
???ü? V|?B???s31?
6B?sYü?a <°¥s
é??
Fb?<°¥s
T1???D?
b
21
ΨΨΨ
nullnullnull
+=
xxyy
eΨeΨΨ
nullnull
221
)( ++=
?α? ?++=+?++= coscos2cos2
2121
2
221
2
2
2
1
AAIIAAAAAI
xyy
T?
1
ψ D
y2
ψ é?M??F 7
x2
ψ ¥< ??D?
T1?
?
;Cb
2
2x
A
4
a?^ ;D ??c ;¥M??F
??]?
q??o¥?F
V
?D
A ?
q?]¥
f
?MF 2T???e1B?e~o¥Vr
T
?[ b
Wò?¥;<D
HWμ1 y7¤??B?×?¥?
s?m"b /
?B?e?¥ è0 V[
a
ü?B?b
I
n??Z_M]a.lZ_M]a??M]?
q?]¥
o
ψ
1
=
0
A ?t
1
cos(ω )
1
zk =
2
ψ
0
A )cos(
22
zkt ?ω
???
=ψ ψ
1
+ =
2
ψ
2
)()(
cos
2
)()(
cos2
21212121
0
zkktzkkt
A
???+?+ ωωωω
)cos()cos(2
0
zktzktA
mm
??= ?ω
?
2
21
ωω
ω
+
=
2
21
ωω
ω
?
=
m
2
21
kk
k
+
=
2
21
kk
k
m
?
=
??
m
ω ?l
? ω ??T¨M???
q1 ω ¥o¥??[??¥?
q
?
HW
M??/m
Ub
)](2cos1[2)(cos4
2
0
22
0
zktAzktAI
mmmm
?+=?= ωω
??;D???1
m
ω2 <s?
?
HW? bWM?b
5
a?^ ;D ??c ;¥M??F
2
? 1a?]?
q ??;?F??;D?
2a?]?
q ¥?
?;o?F??d?
?;b
§ 3.2
??o¥?
?"
B
??;÷¥?
o
?o?? 1M ? 5μ
)
2
cos()cos(
01111011111
?ω
λ
π
?ωψ +?=+?= trnAtrkA
)
2
cos()cos(
02222022222
?ω
λ
π
?ωψ +?=+?= trnAtrkA
V
!êM (1
,5êMμ
?=?
22
(
2
rn
λ
π
? )
11
rn
;?μ
1122
rnrn ?=δ
? b? )(
2
12
rr ?=?
λ
π
?
?
Mé r(
2
λ
π
2
)
1
r? πj2= ' λδ jrr =?=
12
?
Mh
2
(
2
r
λ
π
)
1
r? π)12( += j ' =?=
12
rrδ
2
)12(
λ
+j
j=0 1 2 3 4ll$ ?S?
)
?b ± ± ± ±
H??àH? bW??B"
?=è
?w
?b ü
?¤
là
1BF
?wL
ü
à?ps?b?
H?1d?×¥ bWò) ( Vn?b
6
a?^ ;D ??c ;¥M??F
? ?1 d¥
??÷ ¥?
?Tt?????
?@íàHq 5
??¥;o
à
¥ˉ??sY1
)
2
exp(]}
2
)2/(
[exp{),(
~
222
1
x
D
ikd
D
yxd
Dik
D
A
yxU ′
?′+′+
+=′′
)
2
exp(]}
2
)2/(
[exp{),(
~
222
2
x
D
ikd
D
yxd
Dik
D
A
yxU ′
′+′+
+=′′
??¥ˉ??1
=′′+′′=′′ ),(
~
),(
~
),(
~
21
yxUyxUyxU
)]
2
exp()
2
]}[exp(
2
)2/(
[exp{
222
x
D
ikd
x
D
ikd
D
yxd
Dik
D
A
′
?
+′
?′+′+
+
)
2
cos(]}
2
)2/(
[exp{
2
222
x
D
kd
D
yxd
Dik
D
A
′
′+′+
+=
<s?1 )
2
(cos4)
2
(cos4)
2
(cos
2
2
0
2
2
2
2
x
D
kd
Ix
D
kd
D
A
x
D
kd
D
A
I ′=′
?
?
?
?
?
?
=′
?
?
?
?
?
?
=
2
0
)(
D
A
I = 1VB? d?
¥;oà
¥<b
^B"
?W?¥ü?°H?b
H?¥ê? πjx
D
kd
=′
2
' λ
d
D
jx
j
=′ bàH?¥ê?
π)
2
1
(
2
+=′ jx
D
kd
λ
d
D
jx )
2
1
( +=′ b?i
H?¥ 0) ??) 7àH?¥)
??
T91 ? s?¥? ??μ λ
d
D
jx )
2
1
( ?=′ null3,2,1=j λ
d
D
jx )
2
1
( +=′
7
a?^ ;D ??c ;¥M??F
null3,2,1 ???=j bW ? π=′?x
D
kd
2
%?1 λ
d
D
x =′? b
=
?L;÷¥?
???
¤
là
1Moü?¥°H?
üà?pb
?@íàHq
H
=?
12
rr θd θ
0
rx =
d
r
0
= )(
12
rr ?
5
H? λ
d
r
jx
0
= ) àH?
2
)12(
0
λ
d
r
jx += )
àH?W λ
d
r
x
0
=?
8
a?^ ;D ??c ;¥M??F
?
oêM?1
,5H???M?8 X_M?b
?;÷?¤
là-W
?oéy1
nd
D
j
kd
D
jx
λ
π ==′
2
5H?W 1
nd
r
x
λ
0
=? n1|
qb
?
H?1d?×¥¤
làò) ( V A?H?b
??
H?¥Qé
Vn
Qé¥?l¤
là
Bê?¥u×?|;<Kv′?Kl′μ
mM
mM
II
II
+
?
=γ
7
2
21
2
21
)(,)( AAIAAI
mM
?=+=
5μ
2
2
2
1
21
2
AA
AA
+
=γ
2
2
1
2
1
)(1
2
A
A
A
A
+
=
? A
1
=A
2
H' =1 ? A
1
<<A
2
A
1
>>A
2
H' A
1
aA
2
Mμ?
y
H' =0b
: I
0
=I
1
+I
2
5H?
VV
U1
)cos1(]cos
2
1)[(cos2
0
2
2
2
1
21
2
2
2
121
2
2
2
1
?γ?? ?+=?
+
++=?++= I
AA
AA
AAAAAAI
1
?ü?;¥?
]?
q??; b??sY1 A
1
A
2
êM1
10
?
20
? Z_???1
111
,, γβα
222
,, γβα
9
a?^ ;D ??c ;¥M??F
Z=0¥o -
¥êM1
101111
)0coscos(cos),( ?γβα? +?++= yxkyx
202222
)0coscos(cos),( ?γβα? +?++= yxkyx
êMμ )()cos(cos)cos(cos),(
10201211
??ββαα? ?+?+?=? ykxkyx
YZ) ¥<1
)],(cos1)[(cos2),(
2
2
2
121
2
2
2
1
yxAAAAAAyxI ?γ? ?++=?++=
V¤?
H?
)()cos(cos)cos(cos),(
10201211
??ββαα? ?+?+?=? ykxkyx
?
?
?
+ π
π
)12(
2
j
j
'
aàH??
^?W?¥ü?°L??ü?°LB|
q1
12
12
coscos
coscos
ββ
αα
?
?
?
H?W?1
?
?
?
?
?
?
?
?
=
?
=?
?
=
?
=?
1212
1212
coscos)cos(cos
2
coscos)cos(cos
2
ββ
λ
ββ
π
αα
λ
αα
π
k
y
k
x
H?¥ bW?
q1
?
?
?
?
?
?
?
?
=
?
=
y
f
x
f
y
x
1
1
10
a?^ ;D ??c ;¥M??F
^d?×¥b
§ 3.3 M?;¥¤
Be0?;¥+?
e0V?ú¥?
?M?
% ???¥?
?
H L?μ?¥?
V[[
ò??
T
db ?b ?T
?
-μ?
a 5[?;¥?
T
db?
b
?[ ?;
^e0
?]¥?
?-W%¥2Tb
;÷?9
^cv
¥e0 9
^μv
¥e0]
H?; ?]e0
??¥;o ?μ
?i¥.lZ_a ??Z_a êM??
qb
?[ ?]e0]B
H Y
??¥;o
^? M
?¥ ]Be0?]
H Y
??¥;o9
^?M?¥b '?Y;÷
??¥;?
^?M?¥b
?[ Yèf ?/ A??;¥?
b '?Y;÷
??¥;M?
H9
^<MF ??á
3?
C;<¥×?s?b
=M?;¥¤
??Y¥;÷ 1X¤?M?; oμB?ZE ü
^
!E|]B?e0]B
H Y
??¥B
;os1+?s?+?s;o?? ?1]B
;o
?[ μM]¥?
qa
%?¥êMμ 7OiMoü?¥??s
ü
^M?¥b ?ü
^?
¥t ?'éb
?[
9 V[
a?
^B
;o1-?1-¥?
9oμ1-?1--W?μ V??
3?
b
;÷
??¥v
;o ?¥
?B
?D1-?
??B??
?" μB?;<
s? ?]¥;o-W5
^?
?"¥<?Fb
11
a?^ ;D ??c ;¥M??F
V[¨
?DVr
TV
U?/
H Y t; ÷?? I?e 0%? ¥o:1 U
i
?
oü s;
?a s1
?s ?
?s
^ M ?¥b?
?s?r ? ? P
H ??1 êMμ 1
21
,
ii
AA
i
?? ?e0 ? ¥o
P?¥?
<1 ??;÷?M]¥?
?
?
μe0¥
iiiiii
AAAAI ??++= cos2
21
2
2
2
1
i
??
^M]¥b
? μe0 t
H Y?¥ o P?? ?¥9¥?
<1
∑∑
==
?++==
N
i
iiiii
N
i
i
AAAAII
1
21
2
2
2
1
1
cos2 ?
V[YVso-s??¥ZE¤?M?;b
?a
f?
B
;oüV
??
? ds?M?¥
;o
M?; bW P )M?êM
μ1 ?? á
3?
b
?=
;os?¥
M?; P)¥êMμD?B
;oM] g1 ?? á
3D
?B
M]¥?
<s? D?B
?á
3¥?
é?<?Fb GN ?w ¤?B?
?
?"b
t ?V?1?B?
^M??F?=?
^<?F
dM? b
;÷?¥?B
;oüV
??
? ds?M?¥
bWM?á
3?
b
;÷?¥?];oo
^?M?¥ò1?
aMo-Wo?é?<?Fb
?t ?V?1 ?B?
^]B
o¥M??F ?=?
^?]o
W¥<?F
d
M? b
1a?
¥+?
12
a?^ ;D ??c ;¥M??F
?
^B
B
s ?¥;o-W¥M??F
?
^B
;o1-?1-¥?
?
¥2T
P¤;¥?
bW×?s???B"
üà?p¥?
H?
?
-a¥;o?ˉ?
^?
?o?
§ 3.4ò÷
? —c\9e ?
B;¥
C`
o?Vp?t??.l9??
b
=Qo
;o bW.l
^??¥.l o bWò)???? o???B? 'o- ?
?B?? V
j1?¥?????t?????¥;o?1Qob
Qo? V[á
3?¥???? ???Qo ?N
P¤;o?_-.lb ?¥o
?
'
^?t?????¥ò?Qoo
?¥
?
?b
¨Qo¥? V[??^3
d;¥
C`b
13
a?^ ;D ??c ;¥M??F
o-
?B??
^B?Qo?? 'B??;÷ ?o
?o
?? '
P
^
#í¥
?¥Qo9
^?]¥b?ì1
a
^
àμo;Lpo;
?p- ?¥àQ¥b
?Qo¥?F ——ò÷
? —c\9e ?
1Qo¥M ??F
I3o-
?B
?í
¥B? Q'B?Qo??
??¥o
?Qo?? P)?¥
ˉ??±sí )(
~
PUd b
)(
~
)(
~
0
QUPUd ∝ Q?¥ˉ???1\f
?
r
e
PUd
ikr
∝)(
~
Q?1?;÷?o
?Qo
Σ∝ dPUd )(
~
Qo??
?í
?
),()(
~
0
θθFPUd ∝
0
θ aθsY
^÷????M?Qo
?í Σd ¥Zê?b
0
θ
?
íELD SQ ?LW¥C? θ
?íELD QP ?LW¥C? ),(
0
θθF ?1`|y0b
?òy
�iVr
T1 Σ= d
r
e
QUKFPUd
ikr
)(
~
),()(
~
00
θθ K11 èè
?b
|o-
?μQo???¥Qo P ?¥? ?M??F'¤??o-?¥Qo
.l? P ?
H
??¥???'?o-?¥Qo P ??¥??b?ü
^ ò÷
? —
c\9e ? b
2c\9 —: ?
s
T
?T|B?>¥ bWw
? 'B?>¥o- ??V;÷?¥
?μZ_¥o?
|YVNo-7OoYVNo-BQ
?[;÷?B?? P
?? ¥ˉ??D?o-
??¥??Qo??
??¥ˉ???Nb ??o-
^B ??s?¥w
?
?μQo?
??¥Qo P?¥ˉ??ü
^[/w
?s
Σ
14
a?^ ;D ??c ;¥M??F
∫∫
Σ
Σ= d
r
e
FQUKPU
ikr
),()(
~
)(
~
00
θθ '
∫∫
Σ
′?+′?+′?
′′
′?+?′+′?
′′= ydxd
zzyyxx
e
FyxUKyxU
zzyyxxi
222
)()()(
2
00
)()()(
),(),(
~
),(
~
222
λ
π
θθ
N'1 Fresnel
c\9
s
T b
üV Kirchhoff
: ? 1882M ?ì¥
?D
?£ Fresnel? °4
? y ?¥s
T'
^??¥b 31??¥o
^ o- V[1?i?¥>w
? 7O?
s
T?¥1 èè
??`|y0¥Vr
T?
λλ
π 2/i
ei
K
?
=?= )cos(cos
2
1
),(
00
θθθθ +=F b
1 èè
?? ¥êMy0 ?1 07
^μB? 2/π ¥ êM?-
a
ü?rQ o÷¥ ê M
???o-
Q ???¥êMb7`|y0¥Vr
T
a
ü_a?|¥Qo9 P ?¥ˉ?
?á
3T¨ oμo-|1o
?¥f ?/ 0
0
=θ )cos1(
2
1
),(
0
θθθ +=F N
H πθ =
?μ 0),(
0
=θθF b
üV Kirchhoff??¥
?s
T$?T 'SFTOFM,JSDIIPGG
s
T b) ?;
¥
ù5? V[B21p3 Fresnel-Kirchhoff
s
Tb
?o??μp?t
H '
à
H V[1?1|o-|
à¥ê? N
H>¥
bWw
????s?
à
¥i;?s
0
Σ ?i;¥;à?s
1
Σ [# bW ?Z
¥??w
? b V[-
{ D ¥Mo? Ya1 i;?s¥ \f
?
2
Σ
0
Σ
1
Σ )(
~
0
QU |T 1?
.l
H¥
?′7?i;?s¥\f
? )(
~
0
QU 1??? 0bM ?;¥oé
à ¥ ?
i;?s9 V[a1
^íKv¥
?[???s V[|B???íkv¥?o
? üV?ì
¥
?D£
üs
T?o
?
¥s′?? 0?A I
nb5p3 Fresnel-Kirchhoff
s
T
H o31
à¥; d?sTsü V[
'|w
?s¥S? K?
; d ' Vb??SE?T ,JSDIIPGGH?Hq b
0
Σ
s
T V[?1
15
a?^ ;D ??c ;¥M??F
∫∫
Σ
Σ+
?
=
0
)(
~
)cos(cos
2
)(
~
00
d
r
e
QU
i
PU
ikr
θθ
λ
+?¥
LHq/ ?¨íàHq?ù?Hq s
T V[¤?e? ió?z
¥2Tb
1
¥s ?
?
p?t
à?;÷?¤
lॠ?s ?b
?μK¥à
B?
^μK¥1 c\9
'SFTOF M
bN
H ¤
là
¥?
B? ?1?]Z_¥Qoé?M??Fb
?íK ¥ 'ü? ; ?
a
1 ? ° ? n
'SBVOIPGFS
bN
H M oü?
¥;íkù)M??Fb
Y
L
àa?Bji? Moü?¥;?
i??ü
?
¥]B?é?M??Fb
p3
ù5 üM?
3
?s
T¥ù5b ?
^ ? ?s9
?¥ˉ? v
?f ?/
?s
^íE?ìp3¥
?[9
^B?Hq/|c\: -: ?
s
Te?1 V[p3¥?
Tb
§ 3.5c\9
Fresnel
? da?à
B
C`
? d
à
Vn]??ìb d??M ?ì??
üàá
??9M? àà_M?
?ì??
üà?
¤?9M?b
?à
à
Vn]??ìbà°??Màà_M??ì??¥ù
^
?b
=?o{Esc\9? d
16
a?^ ;D ??c ;¥M??F
|c\9 —: ?
s
T?1p?í
?b
|o-
o
??s1B"
¥]??ì{
?B{¥??? P ?¥ ?GNMμ?
?oéb?t?ì{?1?o{b
o
?
òQoo÷êMM?bM
#?o{?¥Qo?r P ?
H;?μ1
??oéêMμ1 πêMMQ??Z_MQMo·hb
9
?ò??o{¥
? S
k
b
o3
? )cos1(22
2
?ππ ?== RRhS ??π dRdS sin2
2
=
)(2
)(
cos
0
2
0
2
rRR
rrRR
k
+
?++
=?
k
k
dr
rRR
r
d
)(
sin
0
+
=?? ?
2/λ=
k
dr
H
k
SdS =
λ
π
0
rR
R
r
S
k
k
+
=
∫∫
Σ
Σ= d
r
e
FQUKPU
ikr
),()(
~
)(
~
0
θθ =
∑
?
=
+
1
0
)
2
(
0
)()
~
(
n
k
k
k
krik
k
r
S
eFQUK
λ
θ
∑
?
=
+
+
=
1
0
)(
0
0
)(
~
n
k
ki
k
eF
rR
R
UK
π?
θ
λπ
∑
=
?
+
=
n
k
ki
k
i
eF
rR
R
eUK
1
)1(
0
)(
~
0
π?
θ
λπ
17
a?^ ;D ??c ;¥M??F
∑
=
?
?+
+
=
n
k
k
k
i
rR
R
eUK
1
1
0
)1)(cos1(
2
1~
0
θ
λπ
?
∑
=
?
?+=
n
k
k
k
A
1
1
)1)(cos1(
~
θ
?
0
0
~
2
1~
rR
R
eUKA
i
+
=
λπ
?
5
1
)1)(cos1(
~~
?
?+=
k
kk
AU θ 1? k??o {?¥Q
o P ?¥ ˉ??b??1 )cos1(
kk
AA θ+= êMy01 b VnM
#o{
Qo¥êMMQO kv¥o{??lb?
^9¥ˉ?? VV
U1
1
)1(
?
?
k
null?++?++?+=?=
∑
=
+
55433211
1
1
2
1
()
2
1
2
1
()
2
1
2
1
(
2
1~
)1()(
~
AAAAAAAAUPU
n
k
k
k
])1([
2
1
1
1 n
n
AA
=
?+=
3
do{
? n1
?
? n1 }
?à?b
1?.l ∞→n 0→
n
A
1
2
1
)( APA =
S?
?b
?à- n??o{${t
1
1
2
1
)(
+
∞
+
==
∑ n
n
AAPA 9
^
?b
?o{Z?
0
2
0
2
0
2
0
2
0
2
)
2
()
2
( rk
k
krrkrrr
k
λλλ
λ
≈+=?+=?
1
2
2
0
2
0
22
0
22
2)( hhrrrhrr
kkk
???=+?=ρ
2222
2)( hRhhRR
k
?=??=ρ
3
Rh2≈
?
2
3
2
0
2
0
2
2 hhrrr
k
???
2
2 hRh?=
V¤ λ
)(2)(2
0
0
0
2
0
2
rR
kr
rR
rr
h
k
+
=
+
?
=
?¨
1
T ¥2Ti I
n?
0
rh <<
2
T V[éB??1
2
00
2
2 hhrrk
k
??= λρ hrrk
00
2?≈ λ
18
a?^ ;D ??c ;¥M??F
|
4}?
T λ
λ
λρ
0
0
0
2
0
0
2
rR
Rkr
rR
rk
rk
k
+
=
+
?=
)
11
(
0
2
Rr
k +=
λ
ρ
k¥}? ? r
0
%?b
?B?f?/¥o{
?TéB?|
???o{?s1
? 5M
#o{?¥Qo P?êMμ14 /2
?¥ˉ??
O
??1B??o{¥??
O
b |
?B?éB?%s ?¤?¥
?o{
¥??
O
¥êMμ14 /4llb
V[|??B??o{éB?%s1 n? ¤? ÷¥o{ M
#o{W¥;?μ1/
/2n êMμ 14 /nbn? v
H êMμ?l ¨??
O
E e ?¥
???o{¥ˉ??o
OM1? n?lo
OF?¥??b ?m
?
Ub ?ì1
a ?? kv¥ o{¥;?1va ]
H
`|y01l
?[?t???
^?�?? 7
^?w
q???vhl¥?L?¥B
???b
1o{?
¨?o{|o
?sé ?ao??¥
?
}
? ?o{i; '???o{b i
V?o{¥;??êMM]??Z_M]
avv9<b
B?f ?/ V[a1-
?+??o{¥`|y0Mμ?v '
?@íàHq
?[
e
ì?¥Qo¥??í
?M?b?To{?μ 20??o {5 P?¥ˉ??1
19
a?^ ;D ??c ;¥M??F
119531
10)(
~
AAAAAPU ≈++++= null P ?;< 71?.l
H
2
1
100)( API =
10
2
1
)(
~
APU = ; <
2
10
4
1
)( API = M μ 400b Vno{? μ
P;?
¥T¨b V[
|?o{Z???/?
T
f
k
rR
k
111
2
0
==+
ρ
λ
]i?¥
Tb
λ
ρ
k
f
k
2
= 1? b
?Bo{??o
a¨?B?oéb?
^%?¥bü?;o{?1ü
?¥b
?"???-??μ?Q??b
ü?;?
∞=R μ
0
2
1
r
k
k
λ
ρ
= ' ? r
0
)??1
k
ρ ¥{
^? k??o{ b
?o{??M
H r
0
?M?? k¥ ?M' V?s¥?o{
?"?Mb
r
0
hl? r
0
/2
H k=2k à?
r
0
hl? r
0
/3
H k=3k
?Q??
r
0
hl? r
0
/4
H k=4k à?ll
μ
12
,,
5
,
3 +
=′
m
fff
f null llB"
Q??b
§ 3.6? °?n??? d
B
?
ü?;?
¨ji??`?^Z?ü
?b M??ò??¥Qo?
?íkù)b '
^ü?;¥M??Fb?T
d?'.?
^BHNQ
?f ?M]b
20
a?^ ;D ??c ;¥M??F
=
<s?
1a¨??
O
ZEp3
!?
;
0
θ Z_ θZ_¥Qo?
? P ? V.?
/
?Qo???
¥Qo;?μ?êMμsY1
)sin(sin
0
θθ ±=? aL )sin(sin
0
θθ ±=?Φ ka
?|.? (s1 N?ü??sM
#
?s¥;?μ?êMμsY1
N
a )sin(sin
0
θθ
δ
±
=
N
ka )sin(sin
0
θθ
?
±
=?
?T
0
θθ = 0=?? ò?Qo¥o
OMoü??
O
¥??1 A
0
b
0
θθ ≠ ò? Qo ¥o
O ?? M? M
# o
OW C? 1 ?? ?
O
¥?? 1 b
?
@íà Hq
H-
{` |y0 ¥? Y' ?] Z_¥ Qo o
Ov lM ?b 1
é1 ¥B
?? ¥?b? ??1
θ
A
∞→N
θ
A
0
A ?Φ
?Φ
=
0
A
R )2/sin(2 ?Φ= RA
θ
21
a?^ ;D ??c ;¥M??F
2
2
sin
0
?Φ
?Φ
= AA
θ
2
)sin(sin
2
)sin(sin
sin
0
0
0
θθ
θθ
θ
?
?
=
ka
ka
AA
λ
θθπ
λ
θθπ
)sin(sin
)sin(sin
sin
0
0
0
?
?
=
a
a
A
u
u
A
sin
0
=
λ
θθπ )sin(sin
0
?
=
a
u
0
A 1Qo??)???¥??
2a¨sZ E
P?; ?1]BZ_ `|y0M]b ?]Z_¥;
?@íàHq `|y01è
?
1'
?μ 1),(
0
≡θθF b
5
T?1
∫∫∫
?
Σ
=Σ=
2/
2/
00
)(
~
)(
~
a
a
ikrikr
dx
r
e
Kd
r
e
QUKPU )(
~
00
QUKK =
rrr ?+=
0
)sin(sin
0
θθ +?=? xr
u
u
U
ka
ka
ae
r
QUK
ik
ka
i
e
r
K
ee
ik
i
e
r
K
dxee
r
KPU
ikr
ikr
a
ik
a
ik
ikr
a
a
ikxikr
sin~
)sin(sin
2
1
)]sin(sin
2
1
sin[
1
)(
~
)sin(sin
)]sin(sin
2
sin[2
1
][
)sin(sin
1
1
)(
~
0
0
0
0
0
0
0
0
0
)sin(sin
2
)sin(sin
2
00
0
2/
2/
)sin(sin
0
0
0
0
00
0
00
=
+
+
=
+?
+?
=
?
+?
=
=
++?
?
+?
∫
θθ
θθ
θθ
θθ
θθ
θθθθ
θθ
22
a?^ ;D ??c ;¥M??F
?
0
0
0
1
)(
~
ikr
e
r
QUK 1 Q ??¥;àZ_¥Qo;à
¥ P ?
? ?¥ˉ?
?
0
)(
~1~
0
0
0
ikr
eQU
r
KbU = 1YV??.?¥;;àZ_.l
H;à
¥ P ?
??
¥??'ˉ??b5
*
000
~~
UUI = 1;à
P ?)¥;<b
)sin(sin)sin(sin
2
1
00
θθ
λ
π
θθ ±=±=
a
kau ?; àZ_?
¥; 0
0
=θ
θ
λ
π
sin
a
u = b
u
u
U
sin~
0
1??
?í
y0b
<s?
2
2
0
sin
)(
u
u
IPI =
1
a
?w?V?¥e± V[o)
??
;i?;à¥f? N
Hs¥o-'
^
?
;¥o
?9¥; ?μ?üo 19
?
à-a¥? s' V' θsinxr ?=?
θ
λ
π
θ sinsin
2
1 a
kau == b?T?
;¥`?1
0
θ 59?
à--¥;?μa μ
)sin(sinsinsin
00
θθθθ ?xxxr ?=?±=?
)sin(sin)sin(sin
2
1
00
θθ
λ
π
θθ ±=±=
a
kau
;EL]§| s§|b
?
?"¥+?
1′?
23
a?^ ;D ??c ;¥M??F
0)
sin
( =′
u
u
utgu
u
uuu
==
?
,0
sincos
2
v′?b
null,47.3,46.2,43.1sin
bbb
λλλ
θ ±±±=
l′? nullnull ,)1(,,,2,1sin
b
j
b
j
bb
λλλλ
θ +±±±±±=
2
H?? z
M
#àH?-W¥? ?
,)?v
b
λ
θ 2
0
=?
?ú)QH?
b
λ
θ =?
¥Q11"b
à
/M?
H
?"?Mby1
<s?oD
Z_μ1b
,)?v?+?^??
;Z_?M
?"?8üMb
? ?¨
Babinete ?
o?à i;?sMF??í
àb Σ=Σ+Σ
ba
∫∫
Σ
Σ=
a
d
r
e
FQUKPU
ikr
a
),()(
~
)(
~
00
θθ
∫∫
Σ
Σ=
b
d
r
e
FQUKPU
ikr
b
),()(
~
)(
~
00
θθ
=+ )(
~
)(
~
PUPU
ba
∫∫
Σ
Σ
a
d
r
e
FQUK
ikr
),()(
~
00
θθ +
∫∫
Σ
Σ
b
ikr
d
r
e
FQU ),()(
~
00
θθ
=
∫∫
Σ+Σ
Σ
ba
d
r
e
FQUK
ikr
),()(
~
00
θθ = )(
~
0
PU 1?.lb
ü?;?
?o?à
H?+?;De ??`"`?-?))??1
,b
5 )(
~
)(
~
PUPU
ba
?= )()( PIPI
ba
=
'%
′D.?¥
?""
,)??v?))M]b;??N¥e ?b
1 ? °?n d
24
a?^ ;D ??c ;¥M??F
d a?b
?B? ?),( yxQ ),,(
321
θθθk
null
Z_¥Qo ?
321
,, θθθ 1o
O
D YOZü
? XOZü
?? XOYü
? ¥C? '
2
1
π
θα =+
2
2
π
θβ =+ ? γβα ,,
^o
O ¥Z_??b5 d?¥Qo P?¥???1 k
null
∫∫
= dxdy
r
e
FyxUKPU
ikr
),(),(
~
)(
~
00
θθ
Q?? P?¥;?1 bV ??) O? ?BHD kr
null
]Z_°L ? P?¥;?1
D ¥;?μ'1
O
OQ
¥g?b'
0
r
r
0
r
0
r
null
)sinsin(sin)(
321
0
0
zyxyx
eeeeyex
r
r
OQr
nullnullnullnullnull
null
θθθ ++?+?=??=?
)sinsin(
21
θθ yx +?=
5 )sinsin(
2100
θθ yxrrrr +?=?+= b
?s? ]Z_¥
; `|y0M
]bíàHq/s?1
2
2
1
1
0
2/
2/
sin
2/
2/
sin
0
)sinsin(
00
sinsin
)0,0(
~
)0,0(
~
)0,0(
~
),()(
~
0
21
0
210
u
u
u
u
f
e
abUKF
dyedxe
f
e
UKF
dxdy
r
e
UKFPU
ikr
b
b
iky
a
a
ikx
ikr
yxikikr
=
=
=
∫∫
∫∫
?
?
?
?
Σ
+?
θθ
θθ
θθ
11
sinθ
λ
πa
u =
22
sinθ
λ
πb
u = <s?
2
2
22
1
1
0
)
sin
()
sin
()(
u
u
u
u
IPI =
25
a?^ ;D ??c ;¥M??F
2
00
|)0,0(
~
|
0
f
e
abUKFI
ikr
= 1 d ? ¥;o
0 0Z _r?? ? 'à
F
?¥;<b
μ=?
<s?b
§ 3.7? °?n? d
B
<
Q???iZ_;L r
null
D;àW¥C?1 θbV?? O?TD r
null
]Z_;L
0
r
null
|US"?/
0
r
null
?àL
?ü
?1 XOZü
? Z1;àbV QTD r
null
a
0
r
null
<°¥ü
?
D
0
r
null
? X àsY?? BaA ?b5 AB D
0
r
null
<°b
0
r
null
D YOZ ü
?¥C?1 θ A Q
?
?¥Qo
^?;?¥b 5?B? Q??¥QoD??? O?¥QoW¥;?μ1 OA
0
r
null
¥g?'
θ?ρθ?θ sincossincossin ?=?=?=? OQAOr bíàHq/?ü
?
P ?
¥ˉ??1
∫∫
∫∫
Σ
?
Σ
?
=
Σ=
ρ?ρ
θθ?ρ
θ?ρ
θ?ρ
dde
f
e
UK
d
r
e
FUKPU
ik
ikr
ikikr
sincos
0
sincos
00
0
0
)0,0(
~
),(),(
~
)(
~
|
L?
∫∫
=
π
?θ?ρ
λ
π
ρρ
2
00
0
)sincos
2
cos()0,0(
~
0
dd
f
e
UK
R
ikr
7 θλθπ sin/sin2 kRRm ==
26
a?^ ;D ??c ;¥M??F
T?1
∫∫
=
π
??ρρρ
2
00
0
)coscos()0,0(
~
)(
~
0
dmd
f
e
UKPU
R
ikr
=
m
mJ
f
e
RUK
ikr
)(2
)0,0(
~
12
0
0
×π b
J
1
mB ¨?:f
?
∑
∞
=′
′
′
′+′
?
=
0
2
!
1
)
2
(
!)!1(
)1()(2
k
k
k
m
kkm
mJ
}]
!3
)
2
(
[
4
1
]
!2
)
2
(
[
3
1
)
2
(
2
1
1{
2
2
4
2
3
2
null+?+?=
mm
mm
;<
21
0
]
)(2
[)(
m
mJ
IPI =
=
?"¥+?
1 ]??ì
üà?p?? b
2 ??v
,)ê Aivryê ]9<¥
?? z
DR
λλ
θ 22.161.0
0
==?
? d°?1)ü?;°¤YVi?5 Aivry ê??
D
ftgl
λ
θ 22.1
0
==? b1ü?;Y
Vi?a¥
êb
27
a?^ ;D ??c ;¥M??F
?a?ù?¥sO'
5
ü?;ü;D g??^ μB Aivryê 7?
^+?;D
?a1¥B?+??b '??
B?tü;D g??^a ??
r? 9μB? Aivryêb
?; 5μ
? Aivryêb
9ü
^
a
?
L=
bWs 7¥t ü;D"d?^a ??
??¥
?^ V ?
L=
íEs 7b
? Aivryê?T L¤?í 5íEsOb ?¨ Rayleigh?
;ê¥
? ???B?;�? z
H 1 V[sO¥KlKb ' V[sO¥t?W¥Kl
f?
j? 1
D
m
λ
θδθ 22.1
0
=?= λla )v VsO¥W?l sO'
5
vbN1?ù?¥sO'
5bDbv'
5?]b
1a+?;D
^
;D¥ví
?
???
¥??vμ
b
λ
θ =?
0
?? d
¥??vg μ
D
λ
θ 22.1
0
=? ? b? D
^
d?¥+?b '?
;�? z?D
d?¥?Q1b ?T
d?1;¥oév¤ 5 0
0
≈?θ
a
üN
H?
ê|
?
1B?+?? 7
eú)Q¥
¥? z9?? 0 '
àμ
b ?üM??+ ?
;D¥f ?b Vn o1
d?¥1;¥oév¤
¥rT|?A÷ +?;
D¥?
p|??T¨b'?T
àμji?¥?;|°L.lb
?T
d?
^B?Q
? ?
;¥Z_1
0
θ ?
à
?1 ¥
?Qo
??
x?
θ Z_¥
;;?μ1 )sin(sin
0
θθ ±?x 5M?1μ
)sin(sin)sin(sin
2
1
00
θθ
λ
π
θθ ±=±=
a
kau
¥? ?v¥ Z_1
0
θθ = b
?
@ λ>>a
HQ
?
p? ?b ?T
d ?
^B?|
q?]¥ i
oé 5
à
?1 ¥
?Qo??x? θZ_¥
;;?μ1 )sinsin(
022
θθ nnx ±? 5M
?1μ )sinsin()sinsin(
2
1
012012
θθ
λ
π
θθ nn
a
nnkau ±=±=
¥??v¥Z
_1
012
sinsin θθ nn = ]"+?;D¥|
?
p? ?b
28
a?^ ;D ??c ;¥M??F
8
?
?? λ>>a
H
;D V[M??¥¨+?;D9}b
?oD?
?
B
??o V[¨ˉ??V
U1 bd??;
'ˉ?;
^
oéμB?S?¥;o
L=
^oé?]¥B"
??o¥?F?F¥2T??o?b
' b? T oé
^ ? ?s? ¥ 5
? p?M 1 sμ
)(
),(),,(
~
tkzi
ekzatkzU
ω?
=
∑
=
k
tkzUtzU ),,(
~
),(
~
∫∫
∞
?
∞
==
0
)(
0
),(),,(
~
),(
~
dkekzatkzUtzU
tkzi ω
!o
O ¥s ?S? 1 19
? e? V[ L
! ò?? o¥ ??M ? '
b
2/
0
kk ?±
kAkza ?= /),(
)(kωω = ,? ? ?o ?? oé S? ?l V[ ¨ Taylor
TZ 7 μ
)()()(
00
0
kk
dk
d
kk
k
?
?
?
?
?
?
?
+=
ω
ωω :
g
k
dk
d
v
0
=
?
?
?
?
?
? ω
tkzktkkzkktkk
dk
d
kkztkz
g
k
)()()()]()([
000000
0
ω
ω
ωω ?+???=?
?
?
?
?
?
?
+?=? v
s
T1
∫
?
+
?
?
?
???
?
=
2
2
))((
)(v)[(0
0
00
00
),(
~
k
k
k
k
tkzki
tkkzkki
dkee
k
A
tzU
g ω
: kkk ′=?
0 00
)( ωω =k 5μ
29
a?^ ;D ??c ;¥M??F
)()(
)(
)v(
2
)v(
2
)(
2
2
)v(
0000
0000
)v(
2
)v(
2
sin
)v(
)v(
2
sin2
)v(
][),(
~
tzki
g
g
tzki
g
g
tzki
g
tz
k
itz
k
i
tzki
k
k
tzki
e
tz
k
tz
k
Ae
tzi
tz
k
i
k
A
e
tzi
ee
k
A
edke
k
A
tzU
gg
g
ωω
ωω
??
?
?
?
??
?
?
?
?
?
?′
?
?
?
?
=
?
?
?
?
=
?
?
?
=
?
=
∫
0
0
U(
z
)
z
?μB?oés?S?¥d??o?F¥2T
^
?s¥e ú??s¥??
q
1 )(
0
kω o
O1 ???s¥??
q1
0
k k
g
?v
2
1
o
O1
2
k?
b?????sM??
¤
V[| i??? ?sb5 9¥rT M??o
O1 ?
q1
0
k )(
0
kω ??1
)v(
2
)v(
2
sin
tz
k
tz
k
A
g
g
?
?
?
?
¥ob??
?B
H Y?? z Z_a' bW
^??
?h¥
v′¥ê?1 M
#l′¥ê?1tz
g0
v= π=?
?
±
)v(
2
1
tz
k
g
'
k
tz
g
?
±=
±
π2
v
1
b
μrs?u×1a '??v′s?u×¥B?1 b?
^B?ob λλπ ?=?=? //2
2
kZ
o
?ré ¨?
qV
Uλλ ?=?= /
2
0
ZL
νν
νλ
λ
λ
?
=
?
=
?
c
c
222
# ν?= /
0
cL b
?ú??s¥o
O1 ?
q1
0
k )(
0
kω o¥
?1
dk
d
g
ω
=v
^?t?]?
q
¥??o?F-a
???¥o?.l¥
??1?
?b
1o¥ M
? ' ?
?B? ?? s¥
? b ??
P
v
PP
kvv ===
λ
π
ν
π
ω
22
?[
30
a?^ ;D ??c ;¥M??F
μ
dk
d
k
dk
kd
dk
d
p
p
p
g
v
v
v
v +===
)(
ω
7 λ
λ
λ
λ
π
λ
π
d
k
dddk ?=?==
2
2
)
2
(
?[
λ
λ
d
d
p
pg
v
vv ?==
λd
d
p
v
Q?¥
^o ¥??1" '?]o é¥??o μ?]¥
? b? b ?
à μ ?
? 0
v
=
λd
d
p
pg
vv = o¥?
??M
??
^ boé?c 0
v
≠
λd
d
p
?T
pg
vv ≠
0
v
>
λd
d
p
pg
vv < ?T 0
v
<
λd
d
p
bYè f ?/? ?o¥|
q?
v
?[
pg
vv >
0
v
>
λd
d
p
'?
?l?M
?b
pg
vv <
31