.b ~mB/2 h`+FBM; mb a+?2`7 2i HX (NN- Ryy) FQK#BMB2`i 2BM2 "BH/b2;2KiB2`mM;- /B2 2BM2 H2p2H@b2i@J2i?Q/2 mM/ 2BM2 FiBp2 EQMim` Mmixi U*?M M/ o2b2 (RN)V- KBi 2BM2`
MB+?i@T`K2i`BbB2`i2M "BH/`2;Bbi`B2`mM; U>M/ 2i HX (9j)- hQFm?Bb M/ EM2FQ (RR8)VX
>B2`xm rB`/ 7Ƀ` xr2B m72BMM/2`7QH;2M/2 "BH/2` 2BM _B+?imM;b72H/ #2`2+?M2i- /bb 7Ƀ`
D2/2M SBt2H /B2 o2`b+?B2#mM; b2BM2` SQbBiBQM BK M +?bi2M "BH/ M;B#iX JBi /B2b2K 62H/
FMM MmM 2BM h`+FBM; /m`+?;27Ƀ?`i r2`/2M- BM/2K 2BM2 w2HHFQMim` pQM /2K 2`bi2M
"BH/ BM /b M+?7QH;2M/2 "BH/ i`Mb7Q`KB2`i rB`/X .B2 w2HHFQMim` rB`/ rB2/2`mK Hb T`K2i`BbB2`i2 Em`p2 BMi2`T`2iB2`i mM/ M+? /2K ~mB/2M JQ/2HH QTiBKB2`i r2`/2MX
.2` oQ`i2BH /B2b2` J2i?Q/2 HB2;i /`BM- /bb xr2B ;2M2`2HH2 Mb ix2 /2b w2HHi`+FBM;
FQK#BMB2`i r2`/2M- /B2 BK 6QH;2M/2M MQ+? 2BMKH 2tTHBxBi M;2;2#2M r2`/2M,
RX .2` 2`bi2 Mbix #2b+?`2B#i 2BM o2`7?`2M- BM /2K /B2 w2HH2M xm2`bi BM D2/2K "BH/
2BMx2HM /2i2FiB2`i r2`/2MX Mb+?HB2Ľ2M/ r2`/2M /B2 w2HHFQMim`2M BM 2BM2K xr2B@
i2M a+?`Bii Ƀ#2` /B2 w2Bi p2`FMɃT7iX .B2b2` Mbix Bbi BM /2K ɂ#2`HTTi`+FBM;
mb #b+?MBii kX9 BKTH2K2MiB2`iX .B2 b2T`i2M .2i2FiBQMb@ mM/ h`+FBM;b+?`Bi@
i2 7Ƀ?`2M /xm- /bb /B2 :2MmB;F2Bi pQM /2M 62?H2`M /2` a2;K2MiB2`mM; mM/
Rd8
M?M; X M?M;
/2` _2FQMbi`mFiBQM Ƀ#2` /B2 w2Bi #? M;iX .B2 pQ`;2bi2HHi2 62?H2`MHvb2 mb #@
b+?MBii jXR 2`Hm#i 2b xr`- /B2 62?H2` xmp2`H bbB; xm 2`F2MM2M mM/ Mb+?HB2Ľ2M/
mb /2` mbr2`imM; mbxmb+?HB2Ľ2M Q/2` /2M 62?H2` xm #2?2#2MX .b ;2M2`2HH2 S`Q#H2K /B2b2b Mbix2b HB2;i #2` BM /2` a2;K2MiB2`mM;X .B2b2 rB`/ BM D2/2K
"BH/ 2BMx2HM mb;27Ƀ?`i- Q?M2 /bb /B2 AM7Q`KiBQM2M /2` w2HH/2i2FiBQM mb /2K pQ`?2`B;2M "BH/ ;2Mmixi rB`/X AK :2;2Mbix ?B2`xm Mmixi /b ~mB/2 h`+FBM; 2B@
M2M ;HQ#H2M Mbix- /2` /B2 AM7Q`KiBQM2M #xrX /B2 "2r2;mM; /2` w2HH2M /2b pQ`?2`B;2M "BH/2b MmixiX
kX AM /2K xr2Bi2M Mbix rB`/ 2BM2 FiBp2 EQMim` p2`r2M/2i- mK /B2 w2HH2M xm }M/2M
#xrX B?`2M q2; xm `2FQMbi`mB2`2MX >B2`#2B rB`/ 2BM T`K2i`BbB2`i2b- Ki?2KiB@
b+?2b JQ/2HH /2` w2HH2M ;2Mmixi- mK /B2 "BH/b2;K2MiB2`mM; /m`+?xm7Ƀ?`2MX .B2b2b JQ/2HH 2`7ɃHHi bT2xB}b+?2- ;2;2#2M2 M7Q`/2`mM;2M M /B2 1HbiBxBi i- E`ɃKKmM;
/2` EQMim` 2i+X mM/ Bbi M /b o2`?Hi2M /2` w2HH2M /TiB2`iX 1BM2 w2HHFQMim`
rB`/ Mb+?HB2Ľ2M/ BM /b M+?7QH;2M/2 "BH/ Ƀ#2`i`;2M mM/ /B2Mi /Q`i Hb BMBiBH2 EQMim`- /B2 KBi /2K JQ/2HH M /b xmpQ` #2`2+?M2i2 _B+?imM;b72H/ M;2Tbbi rB`/X
.b ~mB/2 h`+FBM; Mmixi 2BM pBbFQ2HbiBb+?2b JQ/2HH- mK /B2 o2`7Q`KmM; mM/
.27Q`KiBQM /2` w2HH2M xm #2b+?`2B#2MX .B2b2b 2`Hm#i 2b- w2HH2M BM mMKBii2H#`2`
L ?2- /2`2M w2HHFQMim`2M QTiBb+? p2`b+?K2Hx2M- xm i`2MM2M mM/ /B2 A/2MiBi i D2/2`
2BMx2HM2M w2HH2 xm 2`?Hi2MX
1pHmiBQM /2b ~mB/2M h`+FBM;b
.b ~mB/2 w2HHi`+FBM; rm`/2 KBi /2K w2HHi`+FBM;@6`K2rQ`F mM/ /2M _272`2Mx/@
i2M *2h_2aX 2pHmB2`i- /X?X 2b rm`/2 2BM2 bvbi2KiBb+?2 62?H2`MHvb2 /m`+?;27Ƀ?`iX
>B2`xm rm`/2 /B2 oHB/B2`mM; mM/ /B2 AMi2;`Bi ibT`Ƀ7mM; ;2Mmixi- /B2 m7#m2M/ m7 /2K ;2M2HQ;Bb+?2M JQ/2HH mb #b+?MBii jXRXk pQ`;2bi2HHi rm`/2MX JBi /2` 62?H2`FHb@
bB}xB2`mM; mb h#X kXk m7 a2Bi2 je r` 2b r2Bi2`?BM Kƺ;HB+?- ;2xB2Hi HH2 72?H2`?7i2M w2HHT7/2 xm }M/2MX JBi /B2b2` MHvb2 rm`/2M /B2 7QH;2M/2M bvbi2KiBb+?2M 62?H2`
B/2MiB}xB2`i- /B2 Mb+?HB2Ľ2M/ BM /2` aQ7ir`2 #2?Q#2M r2`/2M FQMMi2M,
Ç AM 2BMB;2M 6 HH2M rm`/2 /B2 A/2MiBi i 2BM2` w2HH2 MB+?i m7 /B2 `B+?iB;2- M+?7QH@
;2M/2 w2HH2 Ƀ#2`i`;2M bQM/2`M m7 xr2B M+?7QH;2M/2 w2HH2M m7;2bTHi2MX 6QH;@
HB+? ?ii2M xr2B w2HH2M /B2b2H#2 "2x2B+?MmM; #xrX 2BM2 w2HH2 #2biM/ mb 2BM2`
xr2Bi2BHB;2M w2HHKbF2X .B2b2` 62?H2` rm`/2M pQM /2` AMi2;`Bi ibT`Ƀ7mM; mb #@
b+?MBii jXRXj ;27mM/2MX
Ç q2MM bB+? xr2B w2HH2M m72BMM/2` xm #2r2;2M- i2M/B2`i2 2BM2 /2` w2HHKbF2M /xm- B?`2 :`ƺĽ2 xm p2``BM;2`MX wmK h2BH rm`/2M /B2 w2HHFQMim`2M BKK2` FH2BM2`
mM/ r`2M 2BM T` w2BiTmMFi2 bT i2` MB+?i K2?` pQ`?M/2MX .B2b2` 62?H2` 7Ƀ?`i2 xm pB2H2M p2`HQ`2M2M 1M/2M- /B2 KBi 2BM2K HQbi 2M/@6H; mb h#X kXk m7 a2Bi2 je B/2MiB}xB2`i rm`/2MX
.B2 mbrB`FmM; /2` 1pHmiBQM bBM/ BM ##X 9XRe m7 a2Bi2 3d Hb o2`#2bb2`mM; /2`
:2MmB;F2Bi /2b w2HHi`+FBM; M;2;2#2MX
Rde
:`ƺĽ2 /2` >b?i#2HH2M mM/ "2biBKKmM; pQM d˜max
1b rB`/ /2` q2`i d˜max ;2bm+?i- KBi /2K BM 2BM2K ;2;2#2M2M "BH/ /2` :`ƺĽ2 S KBi M SmMFi2M /B2b2H#2 Mx?H M 6ɃM72+F2M mM/ .`2B2+F2M KBi /2`b2H#2M G M;2 d˜max
;2#BH/2i r2`/2M FMMX Hb mb;M;bTmMFi rB`/ /2` 6HH #2i`+?i2i- /bb xr2B SmMFi2 A, B KBi 2BM2` 1Mi72`MmM; pQM dmax ;2r ?Hi bBM/ mM/ /B2 :`mM/b2Bi2 2BM2` ;2QK2i`B@
b+?2M 6B;m` #BH/2MX lK 2BM ;ɃHiB;2b .`2B2+F xm #BH/2M- Kmbb 2BM r2Bi2`2` SmMFi ;2r ?Hi r2`/2M- /2` BM 2BM2K E`2Bb KBi /2K .m`+?K2bb2` dmax HB2;i- BM /2K m+? /B2 #2B/2M SmMFi2A, B HB2;2M Up;HX "2`2+?MmM; /2` >b?r2`i2 BM #b+?MBii eXRXRVX 6Ƀ` 2BM 6ɃM7@
2+F KɃbb2M /`2B r2Bi2`2 SmMFi2 ;2r ?Hi r2`/2M- /B2 2#2M7HHb BM /B2b2K E`2Bb HB2;2MX .B2 ;H2B+?2 Mx?H M .`2B@ mM/ 6ɃM72+F2M Bbi /?2` /m`+? /2M q2`i pQMdmax /2}MB2`i-M /2K-D1.=-D3.;BHiX D ;B#i /B2 Mx?H M SmMFi2M BM /2K #2b+?`B2#2M2M E`2Bb MX .2` 7QH;2M/2 "2r2Bb HB272`i /2M q2`i 7Ƀ` d˜max- #2B /2K ;2Mm /B2b2 "2/BM;mM; 2`7ɃHHi BbiX
.2` KtBKH2 "v2b@6FiQ` Kmax
JBi /2K @T`BQ`B qBbb2M /2` w2HH/2i2FiBQM- /X?X /2` Mx?H /2` w2HH2M BK h2bi#BH/
IT mM/ /2K ;2;2#2M2M σ2F FMM 2BM KtBKH2` q2`i 7Ƀ` /2M "v2b@6FiQ` #2biBKKi r2`/2MX >B2`xm rB`/ /2` "v2b@6FiQ` mb :HX UeXRyV mMi2` /2` MM?K2 #2i`+?i2i-/bb KBi Tk,l 2BM2 `B+?iB;2 h`Mb7Q`KiBQM ;2;2#2M BbiX .MM FMM /2` KtBKH2 q2`i Ƀ#2`
M?M; X M?M;
#2biBKKi r2`/2MX . H /B2 `B+?iB;2 h`Mb7Q`KiBQM #2b+?`2B#i- rB`/ D2/2 h2bix2HH2 pQM ;2Mm 2BM2` _272`2Mxx2HH2 2`x2m;i mM/ 2b ;BHi ν = 0X . Mm` /B2 _272`2Mxx2HH2M Ƀ#2`T`Ƀ7i r2`/2M- /B2 BM /2K i`Mb7Q`KB2`i2M "BH/ IT HB2;2M- ;BHi MR =MT mM/ /2`
q2Bi2`?BM ;BHi- /bb D2/2 h2bix2HH2 pQM ;2Mm 2BM2` _272`2Mxx2HH2 ;2M2`B2`i rB`/- /X?X /B2 amKK2 p2`2BM7+?i bB+? xm"Mm=1T N(cTm|cRn,σF) = 2πσ1
AK 6QH;2M/2M rB`/ 2BM2 .BbF`2iBbB2`mM; /2` >b?i#2HH2MHR, HT #2b+?`B2#2M- rQ#2B pQ`mb;2b2ixi rB`/- /bb /B2 >b?r2`i2 BM D2/2` .BK2MbBQM 2BM2M q2`i xrBb+?2M MmHH mM/
2BMb MM2?K2M- /X?X /2` q2`i2#2`2B+? /2` >b?r2`i2hTk HB2;i BK Qz2M2M AMi2`pHHhTk ∈ (0,1)d Up;HX ##X eX8VX .B2b2` q2`i2#2`2B+? rB`/ BM D2/2` .BK2MbBQM BM M AMi2`pHH2 mMi2`i2BHi- rQ#2B BK 6QH;2M/2MM = 10 #2i`+?i2i rB`/X 6QH;HB+? r2`/2M /B2 .i2M BM D2/2` .BK2MbBQM BM x2?M AMi2`pHH2 /2` G M;20.1mMi2`i2BHi- /B2 KBi1, . . . ,10MmKK2`B2`i r2`/2MX 6Ƀ` .`2B@- oB2`@ mM/ 6ɃM72+F2 2`;B#i bB+? 2MibT`2+?2M/ 2BM2 .BbF`2iBbB2`mM; BM 102,104 mM/ 106 h2BHK2M;2MX C2/2` >b?r2`i FMM MmM KBi /2` >b?7mMFiBQM
index = round
>b?r2`ihTk = [0.21,0.01,0.99,0.57]#2i`+?i2i- /2` 2BM2 EQMbi2HHiBQM mb pB2` w2HH2M
#2b+?`2B#i(d= 4)X .B2b2` rB`/ m7 /B2 AM/2tK2M;2{3,1,10,6} #;2#BH/2iX
.B2 BM :HX UX8V M;2;2#2M2 6mMFiBQM 2`Hm#i 2BM2 b+?M2HH2 mM/ 2{xB2Mi2 .BbF`2@
iBbB2`mM; /2` >b?i#2HH2 HR mM/ `2/mxB2`i /B2 Gm7x2Bi /2` am+?2 M+? ?MHB+?2M EQMbi2HHiBQM2M 2`?2#HB+?X 1BM Qz2MbB+?iHB+?2` L+?i2BH /B2b2` J2i?Q/2 HB2;i D2/Q+? BM /2` .BbF`2iBbB2`mM; b2H#biX aQ Bbi 2b MB+?i Kƺ;HB+?- ?MHB+?2 >b?r2`i2 xm }M/2M- /B2 BM mMi2`b+?B2/HB+?2 AMi2`pHH2 2BM;2i2BHi r2`/2MX qB`/ HbQ 2BM >b?r2`i [0.10,0.10] BM [0.10,0.09] p2``mb+?i- bQ M/2`i bB+? /B2 AM/2tK2M;2 pQM{2,2}BM{2,1}X
Rd3
.`2B2+F oB2`2+F 6ɃM72+F 0
500 1000 1500 2000 2500
Mx?H>b?r2`i2
##BH/mM; XRX, .B2 FɃMbiHB+? ;2M2`B2`i2M .i2M mb ##X eXRk rm`/2M p2`r2M/2i-mK /B2 Mx?H M ?MHB+?2M EQMbi2HHiBQM2M 7Ƀ` p2`b+?B2/2M2 ;2QK2i`Bb+?2 6B;m`2M xm
#2`2+?M2M U"BH/;`ƺĽ28×8mm2-2000w2HH2M- σ2= 16µm2VX .B2 >b?i#2HH2M HT, HR rm`/2M KBi 2BM2` EQMbi2HHiBQMb;`ƺĽ2 pQM dmax = ˜dmax = 403.7µm 2`bi2HHiX 6Ƀ` 9yyy
>b?r2`i2 mb /2K h2bi#BH/ #xrX HT rm`/2 /B2 Mx?H M ?MHB+?2M >b?r2`i2M BM /2K _272`2Mx?b?i#2HH2HR #2biBKKi- /X?X 7Ƀ` D2/2M >b?r2`ihTl ∈HT rm`/2M HH2
>b?r2`i2 mbhRk ∈HRKBi 2BM2` .BbiMx∥hTl −hRk∥2 <)= 0.1;2bm+?iX .B2 Mx?H /2`
?MHB+?2M >b?r2`i2 Bbi BK "HF2M/B;`KK Hb JBii2Hr2`i mM/ aiM/`/#r2B+?mM;
M;2;2#2MX .B2 JBii2Hr2`i2 H;2M #2B2037,91 mM/ 4X
RdN
M?M; X M?M;
SQbBiBQM .`2B2+F2 oB2`2+F2 6ɃM72+F2
MQ`KH 72?H2`?7i MQ`KH 72?H2`?7i MQ`KH 72?H2`?7i
R dNXy jkeXN kX8 eeXd yXe dXj
k RkkXy Rj9Xk kXy k3Xy yXd RyXk
j R83XR RkkX3 RXe kkX8 yXd kjXR
9 R3kXy kyeXe RjX8 R8dXy jXN R8Xy
8 8eXd 9e8Xe jXR kNXR yXe dXy
e ekXd kyyX9 jX3 dX9 yX8 9X8
d 83Xe jeXy RXe 8XR yXe jXk
3 Ry8XN kd3Xj 8X8 k9XR RXy kdXd
N Ry8X9 8e8XR jXk j9X9 yXe RNXd
Ry RR3X9 kkdXj kXk jkXR yX8 RjXd
RR 8yX9 R8eX3 9XR k9X3 yXe 8X9
Rk djXN RRyXe 8Xy NXd kXy dXd
Rj NdXy jdjX8 9Xd 9jXd RX9 RjXk
R9 8RXy 8R8X3 kX9 89Xd yX8 jX9
R8 RyyXe 9kNXN 9Xj RyX8 yXN jX8
Re j8Xk k9yXy jXe RyX3 RXy RNXk
Rd RNjXR 9N3NXd kdXd jRyXj 9Xj R89Xy
R3 RyyX8 9kjX3 eXj edXy yXN j9X3
RN 9dXy 9yeXy kX9 NjXk RXy 8Xk
ky j93Xk kyedXe 9Xy 3RX8 RX9 R8jXR
h#2HH2 XjX,am+?x2Bi /2` SQbBiBQMb#2biBKKmM; BM a2FmM/2MX .B2 SQbBiBQM /2` xrM@
xB; a+?` ;HB+?i#BH/2` /2` JQbBF/i2M mb #b+?MBii kXjXk rm`/2 KBi /2M pQ`;2bi2HHi2M H;Q`Bi?K2M BM /2K _272`2Mx@JQbBF#BH/ 2`KBii2HiX AM D2/2K a+?` ;HB+?i#BH/ rm`/2M /B2 w2HH2M /2i2FiB2`i mM/ /B2 a+?r2`TmMFi2 /2` w2HHKbF2M rm`/2M Hb w2HHTQbBiBQM ;2Mmixi Udmax = ˜dmax = 213.2µVX wmb ixHB+? rm`/2 /B2 SQbBiBQMbbm+?2 KBi 72?H2`?7i2M .i2M rB2/2`?QHi- BM /2M2M 50% /2` w2HH2M 2Mi72`Mi rm`/2M Udmax = ˜dmax = 301.5µmVX .B2 am+?2 /2` 72?H2`?7i2M "BH//i2M rm`/2 KBi 2BM2K MB2/`B;2`2M a+?r2HHr2`i #2`2+?M2i UθK = 14kmaxV mM/ #2MƺiB;i2 2BM oB2H7+?2b M am+?x2BiX .B2 SQbBiBQM pQM /2` xrMxB;b@
i2M m7M?K2TQbBiBQM rm`/2 BM /2` am+?2 KBi oB2`2+F2M Hb ;2QK2i`Bb+?2 6B;m` MB+?i rB2/2`;27mM/2MX 1b rm`/2 2BMσF = 8µm #xrXσF2 = 64;2r ?HiX
R3y
##BH/mM; XkX,JMm2HH 2`bi2HHi2b JQbBF#BH/ /2` a+?` ;HB+?i#BH/2`X .B2 /2i2FiB2`i2M w2HH2M bBM/ Hb r2BĽ2 EQMim`2M /`;2bi2HHiX
##BH/mM; XjX, 1BM ;`}b+?2b >BH7bT`Q;`KK 2`Hm#i /B2 mbr2`imM; mM/ oBbmHB@
bB2`mM; 2BM2` T`K2i`BbB2`i2M w2HHFmHim`X
R3R
M?M; X M?M;
##BH/mM; X9X,JBi >BH72 /2` SQbBiBQMbbm+?2 rm`/2 mb /2M xrMxB; _272`2Mx#BH/2`M 2BM ;`QĽ2b JQbBF#BH/ xmbKK2M;2b2ixiX >B2`xm rm`/2M /B2 i`Mb7Q`KB2`i2M mbb+?MBi@
i2 Ƀ#2`2BMM/2` ;2H2;i- bQ /bb /B2 _ M/2` /2` 2BMx2HM2M "BH/2` MQ+? Hb `i27Fi2 2`F2MM#` bBM/ mM/ B?`2 SQbBiBQM x2B;2MX
R3k
`#2Bi w2HHivT "BH/2` AMi2`pHH w2HH2M JBiQb2M "BH/b2`B2M
(N) Jmb- kRyy k JBMX Ikyy IRyy j
2K#`vQMH
(9k) >2G 9R e JBMX @ 8R 8
(Rkk) l3d@J: jje3 \ ee89 ke 8y
w2HHFQMim`2M
(k3) _ii2 kdj Ry JBMX @ @ jy
>BTTQFKTmb
(3R) Ga.*a jej @ @ @ R
.i2M
(ee) J:@ej R8y 9 JBMX @ @ 9
(e3) J:@ej R8y 9 JBMX @ 9eN j
(RkR) FɃMbiHB+?2 jyy @ Ryy R Ry
P#D2Fi2
(ky) >2G Ryy R8 KBMX 8y8 RNN 9
U;27 `#iV
(38) \ RRy R8 JBMX eR8d Iky 9
U;27 `#iV w2HHFQMim`2M
(Rk8) >2G RNy R8 JBMX jyy @ R
U;27 `#iV
(ke) ljdj Ry3y 9 JBMX R93y Rey R
*2h_2aX `Sa* kyN R8 JBMX 9e3N kyRN R
*2h_2aX" U_ii2V jNN Ry JBMX R9jR 8dj R h#2HH2 X9X, GBbi2 pQM .i2Mb ix2M- /B2 BM p2`b+?B2/2M2M Sm#HBFiBQM2M 7Ƀ` /B2 1p@
HmiBQM pQM w2HHi`+FBM;H;Q`Bi?K2M ;2Mmixi rm`/2MX Zm2HH2, _TQTQ`if"2+F2` 2i HX (3)- /QB, RyXRjdRfDQm`MHXTQM2XyykdjR8XbyyjX
R3j