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Статистические оценки фундаментальных ограничений на применение типовых ПЗС-камер в составе тв-под смотров больших оптических телескопов

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¯ ¨?œ.š2œE¬.£?›E£¡ß¼\¨©e¸E£¹›E™U›ž¨§˜ Ÿ¤£ µ ™ "!$#&%!$')(ºÊi’Ë *¼
B‘’
•
S/N = hnm i/
p
p
hnm i
var(nm ) = p
= hnm i = σm .
hnm i
ºT´?´?¼
Ä £iš ¯Uµ Ÿ?¨?œE¨aº ´´?¼r¨>º ´‘¼ ¸ £¹ ­.¾Eœ ¡
“
p
ºT´b¼
σm = 10−0.4m · αη · I0 · ∆λAT D2 /d2 .
Ý ŸšŒŸ¨ µ œ ¸EœE¾E›E©e™§ B› Ÿ¾E™U› œ'¦6œ ¯ °£iš2›E©°ž¸Ÿ˜ Ÿ¡™ µ ®
˜E£¨Ô¨G› Ÿ?¤¹ ¿gš2™U›EœEœ ¯ ¶ÃÄ › ŸGÅ ¶"Æ Ç
α¡=¡ 0.05 “ η ‘=‘0.5
d
‘ ´ fR
´Xg “
∆λ = 3 · 103 c “ θ = 200 “ d e
•
“ T e
•
“
hhTi
jlkmn$okqpDrstkqmCu)v&wDk
AT ≈ 2 · 10−7 xzy
 |„‘6
2
· x{|}~&€\‚$ƒ&„D‚†…ˆ‡‰Š‹D~D‚$Œ~&€Ž$‚zy
“… ‡q”•Š
– €  „&y—Œ~&€Ž$Œy˜{™D„&xOš6‚$ƒDƒD}‚›ŒœD‚zƒ  „‘&š&ž Ÿ‚¡š&‚z‹DŒT‘&¢
x$yŒŸ~DŒ|=£¥¤¤§¦¢¨yŒT‘6„&©t„  €œ&„D„ª|"‹&‚$~D|„D™DƒDŒ•y«©tŒ  x$‚
¬˜–­ $‘•Ÿ®x¡š&‚O‘6¯°l„&y„/±
‘&šDž m = 15 ‹DŒš&™D„6y σ15 ≈ 3e’ „ hn15 i ≈ 9e’ {
‘&šDž m = 20 ‹DŒš&™D„6y σ20 ≈ 0.3e’ , hn20 i ≈ 0.1e’²
³ }~&€qU‚$ƒD„D‚\…ˆ‡‡ŠX‹DŒ  €Ž$}|•€‚zŸT{™DŸŒ´‘6šDžµ~&€x$‹DŒŽzƒ&€q¢
|€ƒD„8ž«x¡š6€Œ  Œƒ&Ÿ~&€x$ŸƒD}˜¶·‘6‚zŸ^€š&‚$¸«|›„&Ž$Œ~&€qU‚$ƒD„&„
ƒD‚zŒ^¶ŒT‘„&yŒ¹Œ‚zx$‹D‚$™&„D|€ŸºyX€  x¡„&yX€š&ºƒ&Œ‚ Ž$ƒ&€^™&‚$ƒD„D‚
hnm i ‘&šDžEŸŒ»zŒ&{a™DŸŒ} ŒŸƒDŒ¼\‚$ƒD„&‚Ux$„D»$ƒ&€ša½^¼\8y¾}˜¢
š&Œ·yX€  x¡„&yX€š&ºƒ&}y ²X¿ šDž
„DŽzŒ~&€qU‚$ƒD„D¸¾ƒ6€ ¬˜–­ x¡Œ
x¡~&‚O‘6ƒD„6y  €^™D‚Tx¡Ÿ|Œy
… θ = 200 ŠO±
‘&šDž m = 15 (S/N )15 ≈ 3 {
€‹D~D„
(S/N )20 ≈ 0.3 ²
À ~D„=|}x$Œ  Œmy = €^20
™D‚Tx¡Ÿ|‚t„DŽ$Œ~&€\‚$ƒ&„D¸ª… θ = 100 ŠO±
‘&šDž m = 15 (S/N )15 ≈ 6 {
€‹D~D„ m = 20 (S/N )20 ≈ 0.6 ²
³ Ÿq€  ŒyÁ
~D‚$„6y‚Â~6€ŒŸ}߂¡š6‚$‹DŒT‘xzyŒŸ~6€ƒ&€
Ä  ~&€ƒD‚ ³˜ÅtÆ ƒ&€š&¯§‘€‚zŸxǞȩtŒŸŒƒDƒ&}¸È¼\yÉ|Ê|„8¢
‘6‚®ŒŸ$‘‚¡š&ºƒD}˜¶ª|•x¡‹D}¼\‚  …Ëx¡Œ}Ÿ„&¸6ŠO{?~&€xzx¡‚¡žDƒ&ƒD}˜¶¹‹DŒ
„DŽzŒ~6€q\‚zƒD„D¯ÌŽ$|‚$Ž¡‘6}È|•y‚zx$Ÿ‚µxŸq€  „&y„́U‚®|x$‹D}¼Î¢
 €y„Ï„DŽ$¢“ŽT€©tŒƒ&€EƒD‚z€Í„¾Ÿ‚z~&yŒ Ä š&‚  Ÿ~DŒƒDƒ&Œ¸ Ä y„6xO¢
x¡„&„"‹D‚$~D|Œ»zŒµ©tŒŸŒ  €ŸŒT‘€ –˜³˜À ² À Œ Ä ŸŒy=‹D~D„&|‚O‘‚$ƒ8¢
ƒD}‚ÐŒœD‚zƒ  „ (S/N )m žD|šDžD¯ŸxǞlyX€  x¡„6yX€qš&ºƒD}y„/{$‘6Œ¢
x¡Ÿ„D»¡€¯ŸxǞ¹|=ŒŸx$•Ÿx¡Ÿ|„D‚\‘6~D»$„8¶ª¼l8yŒ|фª‹D~&„&x¡°l„
ŸŒš&º  Œ·„‘6‚z€š&ºƒ&Œy
©tŒŸŒT‘6‚$Ÿ‚  Ÿ„D~&Œ|€ƒD„D¯ ²§Ò ¯Œ¸
€^‘&‘6„DŸ„D|ƒD}¸ ¼l8y·x¡ƒD„8€‚zŸUŒŸƒDŒ¼l‚$ƒ&„D‚ S/N |Žz€|„8¢
x¡„6yŒx¡Ÿ„=ŒŸ\‚z»$Œ„DƒDŸ‚$ƒ&x$„D|ƒDŒ•x¡Ÿ„ ²
σm ≈ 3 · 10−m/5 · 103 e’ .
ÓÔTÕ¹Õ6֡סصÙZÚU֨ەܴÔ$Ý)ÞaÖ¡ßÚÛaÔ^Õ&Õ&àXá"âUãTÜåäÔ^Ú\Ô^ßØÚ\Ôqæ^Ø
ç 8y茟®©tŒƒ&€\ƒD‚$•€
é ~D‚¡‘6ƒD‚$‚l™D„&xOš6Œ®‹D‚$~D|„D™DƒD}˜¶"©tŒŸŒ Ä š6‚  Ÿ~&ŒƒDŒ|UŒŸµ©tŒ¢
ƒ&€´ƒ&‚$€&{‹DŒ‹&€^‘€¯°\„8¶Uƒ6€ h ‹D„  x$‚¡š&ºÎ‹Dš&Œ°U€^‘6º¯ A Žz€
|~&‚zy9žÏƒ&€  Œ‹Dš&‚$ƒD„Dž·„DŽzŒ~&€qU‚$ƒD„8ž T {~6€|ƒ&Œ
…Ëêt~D„8¢
š&Œ|x  „D¸/{ hzëìì ŠO±
hns i = ηSEs AT = ηSBHAT /e,
…ˆ‡íŠ
»Ç‘6‚ Es î Œx¡|‚$°\‚$ƒDƒDŒ•x¡ŸºÑ©tŒŸŒ  €ŸŒT‘€|†š /ï S î „Dƒ8¢
Ÿ‚z»$~&€š&ºƒ&€ž¹™D|x$Ÿ|„&Ÿ‚¡š&ºƒDŒx$Ÿº ©tŒŸŒ  €ŸŒT‘€®| |„‘6„8¢
yŒ¸›Œš6€x$Ÿ„›x$‹D‚  Ÿ~&€E|Ey &ð ½Tš6yñ…ò‘&š&ž·©tŒŸŒ  €ŸŒT‘a€
ó ¢‡ i
ii y  ­ ½^š6yŠ ï
2
S ô ‡
B ≈ 2 · 10−8 š6yC½x¡Ÿ‚z~½qxzy =

2 · 10−4 ƒD„DŸ î x$~D‚O‘6ƒDž8ž
žD~ Œx$Ÿºè‚$Ž¡š6•ƒ&ƒDŒ»zŒõƒD‚$•€ ï
π D 2 ö x$|‚$ŸŒx¡„Dš6€lŸ‚¡š&‚Tx  Œ‹&€ ï
H=
4 f
Å
À
e = 1.6 · 10−19 š î Žz€~•ž‘ Ä š6‚  Ÿ~&Œƒ&€ ² Œx¡š&‚®‹DŒT‘&¢
x¡Ÿq€ƒDŒ|  „ H ||}~&€\‚zƒD„D‚…ˆ‡íŠ§‹DŒš6•™&„&y˜±
hns i =
π D 2
SBAT /e
4 f
…ˆ‡ ì Š
¿ „&x$‹D‚$~&x$„8ž™D„&x¡š6€ñ‹D‚$~D|„D™DƒD}˜¶É©tŒŸŒ Ä š&‚  Ÿ~DŒƒ&Œ|÷|
‹D„  x$‚¡š&‚
øqùúT… ns Š ô hns i {UŸ ² ‚ ² ¼\8yûŒŸ ©tŒƒ&€Êƒ&‚$€
p
σs = hns i ²
¬˜–­
¿ šDžüƒ&€š&¯§‘6‚$ƒ&„D¸û|—i‹Di ‚z~D|­ „&™DƒDŒyý©tŒ  •x¡‚
… B = 2 · 10−4 ƒD„DŸ^{ S ô ‡ y  ½Tš6yŠ‹DŒš&™&€‚zy¾x¡š&‚¡¢
‘6¯°\„D‚´Œœ&‚$ƒ  „±
σs ≈ 0.3 e’¥²
s i ≈ 0.1 e’ ,
À ~Dhn
„=„DŽ$Œ~&€\‚zƒD„8ž8¶µ|}x$Œ  Œ»zŒ  €^™D‚Tx¡Ÿ|•€
… θ = 100 ô 5 · 10−6 ~6€^‘aŠ hns i x¡ŒŒŸ|‚zŸx¡Ÿ|‚zŸ
ms ∼ 21m ½  | ² »)š ² x ²
ç 8y蟂$~&yŒ Ä š&‚  Ÿ~DŒƒDƒDŒ¸ Ä y„&x$x$„D„
ó ¢‡ i ‹D~D„
Ÿ‚z~8¢
t = 10◦ ¤
¿ šDžþ©tŒŸŒ  €ŸŒT‘€
yŒŸŒ 
‹&‚$~D|„D™DƒDŒ»$Œ
©tŒŸŒ  €ŸŒT‘€
x$Œx¡Ÿq€|šDžD‚zŸ
Œ  Œš&Œ 1000 e’ x$y −2 x −1 ² À ~D„ Œÿ/‚Ty‚ |}Œ~  „
‹DŒš&™D„&y
|‚$š&„D™D„&ƒD ¼\yX€
AT = 2 · 10−7 xzy 2 · x
Ÿ‚z~&yŒ Ä š&‚  Ÿ~DŒƒDƒ&Œ¸ Ä y„&xzx¡„D„±
hnt i ≈ 2 · 10−4 e’ ,
σt ≈ 1.4 · 10−2 e’ .
ç y·x¡™&„DŸ}|€ƒD„8ž | À é
À é ¢ Ÿ‚¡š6‚  €y‚z~¹xU|„‘6‚zŒ•x¡„8š&„&Ÿ‚¡š&‚Ty
¿ šDžªx$‚$~D„&¸DƒD}˜¶
xè‘6|Œ¸DƒDŒ¸  Œ~D~&‚¡š&„D~&Œ|€ƒDƒDŒ¸ |}Œ~  Œ¸È„DŽ$»zŒŸŒ|„8¢
À é
Ÿ‚$š&ºÑ  €Žz}|€‚$Ÿ®¼l8y
x$™D„DŸ}|•€ƒD„DžZ| σ ∼ 50e’ {
é
ŒŸƒD‚zx$‚$ƒDƒD}¸  ŒT‘ƒDŒy"‹D„  x$‚¡š&¯ ² ŒŒŸ|‚zŸx¡Ÿ|¯°l„&¸
Ä  |„D|•€qš&‚zƒDŸƒD}¸Ì¼l8yû‹D‚$~&|„D™Dƒ&}˜¶ ©tŒŸŒ Ä š6‚  Ÿ~&ŒƒDŒ|
z‘6‚zŸŒ‹D~D‚¡‘6‚¡š&žDŸºxǞ  € 
σr ≈ σ/G ≈ 5 · 10−3 e’ .
ç 8y  |•€ƒDŸŒ|€ƒD„8ž†|•x¡Ÿ~DŒ¸&x¡Ÿ|€q¶ÑŒœD„&©t~&Œ|  „
­ ƒ6€qš&Œ»$Œ¢ œD„&©t~&Œ|Œ¸®‹D~D‚zŒ~6€Ž$Œ|€Ÿ‚¡š&º=… ­ ´À Š˜x¡ŒŽ¡‘€q¢
‚$Ÿå‘6Œ‹DŒš&ƒD„DŸ‚¡š&ºƒD}¸¼l8y  |•€ƒDŸŒ|€ƒD„8ž ²®¿ š&ž—Ÿ‚¡¢
š&‚z‹DŒT‘x$yŒŸ~DŒ| £¥¤¤§¦¢ yŒT‘6„6©t„  €œD„D„ÈyX€  x¡„&yX€š&ºƒ6€qž
‚zy  Œ•x¡ŸºÈ‹D„  x¡‚$šDž ≈ 2.5 · 104 e’ ² x¡‹DŒš&ºŽzžå¼l„&~DŒ¢
 Œt~&€x$‹D~DŒx$Ÿ~&€ƒD‚$ƒDƒ&}¸l‘6šDž®ŒœD„&©t~&Œ|  „\™D‚z~DƒDŒ¢“‚¡š&}˜¶
­ ´À {ŒœD‚zƒD„&yè|‚¡š6„D™D„8¢
|„8‘6‚$Œ•x¡„D»zƒ&€qš&Œ|q¢ ~&€Ž$~•ž‘6ƒD}¸ ƒD‘6šDž=„&ƒDŸ‚$~&|€qš€  |€ƒ&ŸŒ|•€ƒD„8ž q = C/256 ≈ 102 e’¥²
Å |€ƒDŸŒ|•€ƒD„&‚†| ­ ´À x†š6„DƒD‚$¸&ƒDŒ¸·¼  €qš6Œ¸è‹&~D„8¢
|ŒT‘„DŸ  |ŒŽzƒD„  ƒ&Œ|‚zƒD„D¯—¼l8yX€  |€ƒ&ŸŒ|•€ƒD„8ž σk ≈
√
hzë Š – Œ»Ç‘€È¼l8y  |•€ƒDŸŒ¢
q/ 12 … ŒƒDŒ~DŒ|x  „D¸/{
²
|€ƒD„8ž/{§ŒŸƒ&‚zx¡‚zƒDƒD}¸  ©tŒŸŒ  €ŸŒT‘6{Cx¡Œ•x¡Ÿq€|„DŸ σk ≈
√
–
(q/ 12)/G ≈ 3·10−3e’Dz €  „6yZŒ~&€ŽzŒy˜{z‹8žDŸº1¼l8yŒ¢
|}˜¶Íx¡Œ•x¡Ÿq€|šDžD¯°\„8¶¹|"ƒ&€¼l„8¶Íx¡š&Œ|„8ž8¶¹„&y‚z¯Ÿ¹x¡š&‚¡¢
‘6¯°\„D‚´Ž$ƒ6€^™D‚$ƒD„Dž/±
ŒŸŒƒDƒD}¸ ¼l8y
ç 8y·ŒŸ©tŒƒ6€\ƒ&‚$€
– T‚ yƒDŒ|Œ¸ ¼l8y
©tŒŸŒ  €ŸŒT‘€
ç 8y·|„8‘6‚$Œx¡„Dš&„DŸ‚$šDž
ç 8y  |•€ƒDŸŒ|€ƒD„8ž
σm ≈ 3 · 10−m/5 · 103 e’
hnm i ≈ 9 · 10−0.4m · 106 e’
σs ≈ 0.3e’
hns i ≈ 0.1e’
σt ≈ 1.4 · 10−2 e’
hnt i ≈ 2 · 10−4 e’
σr ≈ 5 · 10−3 e’
σk ≈ 3 · 10−3 e’
!#" %$&('*)$+,-%$/.0$1*23!546#$7%$89$:<;=6>:,-%$ ?$ #@A@A@
CDFEGEGH/IJKMLON<DEQPRS&TU&HVWXP=YV[ZF\W/]3NDFE_^=PK*`
Ya^YaW#H/PS\Tb<cF`dcX^ZI&V?e:VS\VWY\9PKMI&H/f<VJcVE
σ=
p
σ g2 + σ h 2 + σi 2 + σ j2 + σ k2 ,
lnm=o/p
Hq^W/J&^NVJcVrYac&sJ&H/S>t5N<DE
lumv=p
e H/VWy^W/J^=NVJcVzYcsa{
S/N = hnm i/σ,
UW/^wYxDUVW/^E
J&H/S>t5N<DE
hnm i =
2
σm
p
hnm i
«2 „
«2 „
«2 „
«2 .
„
σ
σ
σ
σ
+
+
+
1+
σm
σm
σm
σm
S/N = s
|
}
~

€
‚5ƒ
„ I^e:^/S&fqH#\…e:VaS H/W/]†U&c&Y?S&VJJKMV3^=‡VJR&cˆe&S\xW/VaS:Va{
Z ^e YE_^W/I&^PX‰‹ŠMŠŒŽ{E_^e:c&‘c&RH‡ccOP3ZVIPcU&J^=E’‘^/{
RDYaVr“*”•–e&S\9—™˜šB5›<c σ ∼ 3eœ Z^S&DUc&E
15
2 i 2 2 k 2
σh
σ
σj
σ
σm
+
σm
+
σm
+
σm
Z^=W/^E_D[e&S\3YaDFEGEGH/I&J^s^<N<DEGH[^=W/J^=NVJ&cV
(S/N )15 ≈
p
1,
hn15 i ≈ 3.
” HRc&EQ^ž=I&H/Ÿ^=E*–>VYaS&c ^=W/J^YacW/VS&]J&KMV[¡S:DR&W/D=H‡cc7–
^Z&IV?e:VS\Tb<cVrW/^=UJ^=YW/]cŸE_VIVJcF\ 1/(S/N ) –&Y^/{
YaW#HP/S\TW¢^=R^/S&^¤£=£¥¦–dW/^§P¤c&Ÿ^ž=I&H#fqVJc&c¨15\IR&cF`
ŸP=VŸae3Y¡—ª©wB›e:^E_cJcID=VW‘^W^JJKML9NDFE*«
¬ Ÿ lumo/p ^=ZIV?e VaS&c&E E_cJc:EGH#S&]=JKML YacsJ&H#S
–QR^=W/^I&KML­E_^5fJ^®^=žJ&HIDf[c&W/]®J&H¯‘^JV
hn
YaDFmin
EGEGHiIJ^s^°NDFEGH σ –ˆVYaS&c±ZIVae:Z^S&^5fcW/]&–²UW/^
Yac&sJ&H/S³^UVJ]¦EGH#S´– H¦Vs^µ‘^W/^=JJKML3NDFE
E_J&^s^
E_VJ&]NV‘^YaW#H#S&]=JK*`dNDFE_^=P&«¶xW/^=EˆY?S&DU&HV σm
σ=
p
σh2 + σi2 + σj2 + σk2 ≈ 0.37eœ .
· ^r‘c‡cVJWr^Z&IV?e:VS&VJ&J^=YW/cd¸<e&S\¦^=žJ&HIDf<VJcF\
ZIVae:VaS:]J^¹Y?S:Hž^=s^…c&Ÿ^ž=I&H#fqVJc\zŸP=VŸ?e KºJ&H¹‘^JV
JVž=HI:H/PVJµ› l “*H5DE*–>B»¼ op «F½W/^<^=ŸJ&H5U:H/VW5–UW/^qD=YaS&^/{
Pc&V
hn i = 5 · σ ≈ 5 · 0.37eœ ≈ 1.85eœ
YDUVW/^E lnm/min
^Z&IV?e:VS\VW‘ZI&V?e:VS&]JDT¹ŸP=VŸae:JDT²P=Va{
S&cU&cJD–J&H/¾=žS&p Te HVE_DT¿YOZ^=E_^=b]=T°W/VaS&VPcŸc^J&J^/{
s^ Z^e YE_^W/I&H&«7ÀS&\†I&H/ŸS&cUJK*`ÁŸJ&H5UVJ&cL…RFH5UVYaW/PH
cŸ^žI:H#f<VJcF\[^‡VJRcdZ&IV?e:VS&]J&^LdŸPVŸae:J^=LPVaS:cUcF{
JK†e&S\[W/VaS&VZ^e YE_^W/I^=P‘‰‹ŠMŠŒŽ{E_^e:c&‘cRFH‡ccP‘ZVIF{
Pc&UJ^=E²‘^RDYaV‘“*”•ÂY^=YaW#HP/\WÃ
e&S\µYIV?e JcF`dD=YaS&^P=cLdJ&Hž/S&Te VJcF\
mlim ≈ 16.9 Ä
l θ ≈ 200 p?Å
≈ 18.4
Ä e&S&\†^WS&cUJ&K*`ÆDY?S&^=PcLOJ&Hž/S&Te:V{
JcF\ ml lim
«
00
Ç W/θ^≈ž=K¤1 Zp ^S&DUcW/]Ož^S&]N<VVµ^W/J^=NVJcV³È&t#ɨe&S&\
ž^S&VVY?S:HžK*`‘ŸPVŸ?e l —§ÊxB› p –WIVž=DVW=Y\¡S:cž^D=YaI&V?e&{
JVJcVqZ^µž=^/S&]=N^E_DµUc:Y?S&D³RFH#e:I^P · –:S:cž^9JV^=ž5`=^{
e:c&E_^ÁDP=VaS&cU&cP=HW/]OPIVEË\ˆJ&HR^ZFS&VJcF\ˆP†‘^W/^=ZIcF{
VE_J&cRV–Ëc&YaZ^S&]ŸD/\OJ&H/R^=ZcW/VS&]JKMVµYaP^=L&YaWP=H „Ì C-{
EGH/WIc‡7«
BB=B
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P „Ì C-{ RFHE_VIV–ÙW^…ZIcQYaUcWKMP=H/J&ccxJ&H/R^=ZFS&VJ&J^s^
cŸ^žI:H#f<VJcF\qŸH‘PI&VEË\ KT N<DFE(ZI&cž=HPcWY\[W/^S&]/{
R^…^e:c&J I&H/Ÿ=« „ ^=W/^E_D²P=KMKcsI&KMN P…P=VaS&c&UcJVOÈ&t#É
žDe:VWI&HPVJdJV √K –H α · K > √K –se:V α ≈ 0.5 − 0.8
YODUVW^=E J&H/R^ZS&VJc\’H5e&e:cW/cP=JK*`QN<DFE_^P&« Že J&H#{
R^µe&S&cW/VS&]J&^=E_D³J&HR^ZFS&VJcTšP „Ì CÜZ&IVZF\W=YaW/P=DVW
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W/VE_ZVI&HW/DIKrÃ
qt = q293 · 122 · exp(−6400/t),
l £ ¾=p
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RDJe:D p P=IVEË\‘RFYZ^Ÿc‡cc‘žVŸGJ&H/R^=ZFS&VJ&cF\‘Y^=YW5HP/S\F{
VW T = T ˜ ¾ « ¾=m Y–FUW/^dYa^=^W/P=VWYW/PD=VW 40eœ t#ZcRFYaVS
YGN<DE_^E Kσ ≈ √40 ≈ 6.3 eœ cFS&c σ/G ≈ 6.3 · 10−4 eœ J&H
‘^W^RFH/W/^e V¡”*¶ „ «
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e HVWŽYaDb<VYaWPVJ&J^s^MPRFS:H#e HMPŽ^=žb<cL‘NDFE3”*¶ „ #« Že&{
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I\eÁY^=YW5HPcW 2000 · 2/3 ≈ 1300Keœ t#ZcRFYaVSOYqNDFE_^E
√
– UW/^9YaI&HPJc&E_^µYNDFE_^EˆYUcW/KMPH/Jc\
1300
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50 eœ Ic¯J&HR^=ZFS&VJcc®ŸHI=\e>H P
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W $ à Bˆe ^ £¼ ÃAB–VY?S&c¤J&VzPKMU&cW#H/W/]ÂWVEË{
„Ì C ^"
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T
J^≈YaW/]=20000/2000
T’c:YaUVIZ&H/J:=H<10ŸH[YaUVWqWVE_J^=P^s^[W/^RFH „Ì C«
%&%('
)+*#,.-0/1*3254167*3,98;:<5*
=>?5@0A5>BDC"E5AF&G5?5HJI#KLNM0OQP0E5FRP0F&SRG5FRP0T#? T#MVUJMVW
E5FYXZP[\F&T#AF&C"T&?5EI^]`__abPcG5M0F(dUJI#eNXfI#M[\FROQg
h1i9W
[I#T&A5?5H5MO E5A5? S&F&Uj&BNFR[ CRA5M[\MG5? GI#kFREUM0G?l
E5FP0AI#CRG5M0G5?KQPm]`__anPVFoPVT3I&GXZI#AT#G5F&O
(T = KT )
p=qWrAI&s0CRM0A5T#kFRO
[\F(etGFuF&H5MG5?5T#jE5A5?
FYXZG5FR[v?
T#Fw[veNM
s0GJI(x5M0G5??zy{#|
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K
(S/N)m1 = (S/N)m2 .
00
=FRPVEF#UjRs0F&CwI#CRB+?P0j€ '&R‚ }?J[\M0M[
p
hnm1 i ≈ TK ,
p
p
= hnm2 i ≈ KTK ,
√
≈ K ≈ 10−0.4∆m.
(S/N)m1 =
(S/N)m2
(S/N)m1
(S/N)m2
p
hƒI(XfI#CRI#l€C&AM[„l…GJI#kF&EUJM0G5?lvGItg
h1i9W[I#T#A5?H5M
† ‡ ' {3‰.PtŠp‹‡"‰ ' T }ZŒ‡"‰ 'R‚ }5EF#UŽx5?[CR>?5@0A5>B
ˆ
‡ % ~  ~qT3I‘C&MVUJ?5x5?5GI“’0kPVEM0A5?[\MGW
∆m = m − m
T3I3UjRG5FˆE5FYXJT&C&M0Awe”XJMGI•CˆGI#S&UKXJMG5?ld–GJI‹—7M0OPP˜W
%™R™&™ Šš5›Rœt0ž5ŸR›”0 ¡#¢r~} '&™&™ ‰ ‚ ~
£"Ž[ F&Tb¤7FRGI¥G5M0SwI¦CbEM0A5CR?5x5G5Fw[ ¤7FRk5ŽRP0M
—7M0OJP0P˜W %™R™&™ FRH5M0G5?J[§E5FD '#¨w‚ }•E5A5?5G5l5C¦sGI(x5M0G?l
}N©r‡ %Y' [}Nª† ≈ 0.8 · 10 P0[ · P , B ≈
T = 32 T
J
U
9
[
N
{
PVT#MA ./P[ } S = 2 · 10 « {(UJ[~ƒp¬FR@­XZIvE5F#W
2 · 10
UŽxI&M[
K
1
2
K
2
®
σ =
T(~ MR~
2
−6
−8
r
¯
¯
σ ® σ ° + σ ± + σ² + σ ³ .
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XZI#MTzGI&[µC&FRs[\F(emG5FRP0T#jvF&H5MG5?5T#j
hn i = 5σ ≈ 2.5e
E5A5MVXJMVUJj&G5ŽK s0CRM0s˜XZG5ŽK CRMVU?5x?5G5Ž¶XUl GI&kwFRE5?W
T#M0Uj&G5>d T#M0UM0E5FYXfP0[\F&T&A5F&C ]`__aW·[\FYXZ?¤7?5kI#H5??
C¸EM0A5CR?5x5G5Fw[b¤7F&k5ŽwPVM¹—7M0OJP0P˜W %™R™&™ ~g7A5?ºP0A5M˜XJG?d
ŽRPVUF&CR?ld»GJI#S#UJKXJM0G5?O¼ θ = 2 }¾½ ≈ ™ ~ %Y' [[ ‚
E5F&UŽxI#MY[oXJU5l…—7M0OJP0P˜W %™R™&™¿ mÀ Á ° ∼ 17.5 XUlÂGI#kF&E?W
T#M0Uj&G5FRO“]`__aÊE5A5?C&A5MY[\M0G5?‘GI#kF&E5UM0G5?5l“GIÄg
h1i
' {#‰.P ‚ ~
T = 32T =
=E5M0A5CR?5x5G5Fw[Ť7F&k5ŽwPVMÆp « E5A?ÂT#MVdme”MŽwP˜UFRC&?ld
 ‡ ' {3‰RP ‚ GI#kF&E?5T#MVUJj&GI#lÂ]`__ac[\F(e”M0TNF&S&MYPVE5Mx5?5T#j
E5TA5MVXJMVU ¿
2
2
2
2
−
m
00
K
mlim ∼ 18.3
mlim ∼ 19.8
c
c
T
A
(θ = 200 ),
(θ = 100 ).
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UMYPVkF&EI#dcP“E5FR[\FRL+j&KºT#MVUMC&?5s?5F&GG5>dcEFYXZP0[\FRT#A5F&C
CRI#emG5F•s0GI&T#j}ÏkI#k P0F&F&T&G5FRP0?5T&P­l^P0A5M˜XZG5?5O^XJ?IR[\M0T#A
s0CRM0sVXJ>Q½•ÐA5?JP#~ ‰ ‚ GI¾¤7F&T&F&kI#T#FYXZM…PzAI&s[\M0AFR[‹E?5kW
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dwI#AJI#k5T#MA¤7F#W
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0
1
1
2
0
2
−4
π D 2 SBAT
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η
4
f
e
2
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ž]–9œŸ˜. %™¡¡º…¤¢ EC –%œ¡ C œ¤‰£W¿
C
¯
C
Cµ ¡9«.š.–9—´ª«.œ¤¥º µ
• ª «§%«.¬™¡ ½ « %«.Ÿ%˜.œ ¬¢—l›
C ¡˜œ •«"–'¬•œ¬]ª9¡º ¯ •œ– C­C ¡
C{À‘C Ÿ EC ™•«.¡°
∆» §% F
C
C
¡™¤£‡•W™ª¡™¤u˜.œ]–%œ• ¬ ™¡%¡™¤u§™.–%œ
Áàœ¡Ÿ C ª9•¢ ¯ ª C ¡%«¤ C­ œ E Ÿ C¯ ª C «.§%«¬™¡%™•f•ºn§%™.–%¡ C ¤
ª%–”b˜.œ–%œ§™ª E ¤¥™˜ ™•©¤¥™ª C9À‘C Ÿ«  CCbÄrÅnÅ´ÆÇE ¡œ§ %œ]°
ºn•¡™ µ %«¬•œ ˜.Ÿ™ µ ¹ T = T ¼ •·§œ • C%­ ¡™¤ À ™Ÿ¢ E œ
È ±É F ¨¡%« ­ «.–9«W %« EE ¤¥™˜. C ¤K•« C «.¡%˜W 9«.š™˜.ºËÊ Á ³f«
§ C ¤ C ¡ C ¤ˆ«"–%¦¡™¤hž]–%œŸ˜. ™¡¡™.°s™§%˜ C­ œ E Ÿ™¤h¢ E]C –%œ]°
¡ CC G F
min
Ì –”
œ¤¥Ÿ™ E ˜ C
Ÿ«.¡%«.–9« ½ š.– C ¬Ÿ™¸™
Ÿ
¡%« E º)°
C
C
C
C
C
›œ¡ — ½
§ ¤ ¡ ¤ˆ«"–9¦¡™¤
C≈
20000eÍν
C Â «
¢ EC –%œ¡ CC
Ê Á ³f«
¸
%
.
«
¡
ª C ¡%«¤ C °
Gmin ≈ 10
­ œ E Ÿ™¸™
C
C
¯
E ™ E ˜"«"°
ª «§%«.¬™¡%«
ª%–”
” %Ÿ
¬•œ¬]ª
C• ˜
™˜.Ÿ¢ª«
hnm i = C/Gmin = 9 · 106 · 10−0.4m ½
F
mmax ≈ 9
³‘ œ=ªœ]–%¦¡%«"”2¬•œ¬]ª9¡%«"”©•œ]– C%­C ¡%«Ï¡%« µ ªœ¡%«Ï %«.¡œœ I
C
C%µ ª C ¡%«¤ C­ œ E Ÿ Cµ
mmin ≈ 17 ½ ˜4«Ÿ ¤Ð™š %«.¬™¤ ½ ™š›
C
E
E
ª «§%«.¬™¡ ∆m ™ ˜"«.•–”œ˜^ÑW¬•œ¬=ª9¡%º ¯ •œ– C­C ¡ F
Áàœ¡ C ¤8ª C ¡9«¤ C­ œ E Ÿ C%µ ª C «§%«.¬™¡f¡%«l¸ %«¡ C  œ,” °
Ÿ C¯ ¬•œ¬]ª•u™ª9¡%™¤p˜.œ]–9œ• C ¬ C ™¡¡™¤Ò§%™.–%œ F ±H«.ŸŸ«Ÿ
§ C ¡%«š.–%—´ªœ¡ CC ” Ÿ C¯ ¬•œ¬]ª|§ %œ™š–9«4ª<«.—l˜ À ™˜™¡°
¡º µbÓ ¢¤ CbÓ ¢¤ E­C ˜.ºn•«.¡ C ”b³ Ô¨ ½ ˜™Õ¹×Ö.Ø ¼ § œ™š.°
%«¬¢œ˜ E ”ÏŸ|• C ª9¢
™˜Ÿ¢ª«
S/N = p
hnm i
,
hnm i + σÙ2 ,
¹ AA ¼
p
A G
1
(S/N )2 = 1 + 1 + 4σÙ2 /(S/N )2 . ¹ ¼
2
³‘ C ¢•œ œ¡¡%™¤Ú™š¡%«. ¢ÛWœ¡ CC •Ü˜.œ–%œ• C ¬ C ™¡¡™¤
@á
§™–%œ E –9«š™ µ ¬•œ¬=ªº E ™˜.¡%™ Ó œ¡ C œ¤ÚÝ%Þ.ß
à
¹ σÙ ∼ 50eÍâ¼ C ¬^¹ A G ¼ §™.–%¢ ­C ¤
hnm i =
hnm i ≈ 550 eÍ = 9 · 106 · 10−0.4m ,
™˜Ÿ¢ª« m
¬• F •œ– C­C ¡%º F ±«.Ÿ C ¤Ò™š %«.¬™¤ ½
min ≈ 10.5
C
C
­
E
%
C
µ
C
ª ¡9«¤
œ Ÿ
ª «.§%«¬™¡•‰™ª9¡™¤ã§™–%œ ∆m ≈ @ F ä
F
%
C
­
C
F
¬• •œ]–
¡º
B « EE ¤¥™˜. C ¤u•«. C «.¡˜W %«.š™˜.ºåÊ Á ³f«§ C ¤ˆ«Ÿ E]C °
F ²
¤ˆ«"–9¦¡™¤Ïž–%œŸ˜ ™¡¡%™.°s™§˜ C%­ œ E Ÿ™¤Ï¢ E]C –9œ¡ CC £
max
Â
E
­
C
C
C
E
¯
ž˜™¤ –%¢ «œ ¬™š 9«"Û;œ¡ œ)¡%«f¸ %«.¡
œ –9«.šº
¬•œ¬]ª
E
À ™˜.™Ÿ«.˜.™ª9œ
C
ª
«
œ
˜
%
¡

«
œ
¸
™
mlim ≈ 17
hn17 i ≈ 2eÍ § Ó
™š›œ¤
¢¤¥œ
p
σ ≈ (2 + 0.37) ≈ 1.54e−.
¨,–%œ=ª™•«˜.œ]–9¦¡™ ½ ª9–”;˜"«.Ÿ C¯ ¬•œ¬]ª^˜.™ ­ ¡™ E ˜.¦‘™š¡%«"°
¢Û;œ¡ C ” E ™ E ˜"«.• C ˜ (S/N) ≈ 1.2 F,æ «{žŸ% %«.¡œ©²)ç‘è
C ¬™š 9«"Û;œ¡ C œ©§% œ=ª9œ–%¦¡%º ¯ 17 ¬•œ¬=ª E
À
mlim ≈ 17 ™ °
C
E
E
C
b
C
E
E
µ
¤ ¢œ˜ ”©ª9•¢¤”é˜ œ¤” ™šºn˜ ”%¤
™ œ=ª¡œ «¤°
§– C ˜.¢ª9™ µ ∼ 10000 eÍ F ³‘™ž˜.™¤¥¢¬•œ¬]ª9º E –9«šœœ 17m
§ %«Ÿ˜ C­ œ E Ÿ C ¡%œfš¢ª9¢˜;¡9«.š.–9—´ª«.˜.¦ E ” F
³‘ C ™š %«.š™˜.ŸœS• C ª9œ™ C ¬™š %«"ÛWœ¡ Cµ ¢ E œ=ª9¡%œ¡ C œ
çcŸ«"ª9 ™•©ª«.œ˜{•º C ¸ %º Ó √K •b˜.™ ­ ¡™ E ˜ C ™š¡%«. ¢°
Û;œ¡ C ”Õ¬•œ¬]ª9º F ±«.Ÿ ½ §% C çêàëÖ äì ™˜¡™ Ó œ¡ C œ8Ý%Þ"ß
ííî
ïð.ñDòóð"ôõö‘ð"ñ,÷$ø%ùð
úDû%üýþÿ
!#"%$'&!()+*-,/.-102435.56879():3;.</
5=.10+:3#.>6@?(9.<=,A
<-.B36DCE(GFH.I,J#.-=.IK%2=L!-;,/.MN5=!+.M
6POQ(G!>.-*-..>.,/,5R/.-*2#+=L!!-;,.>M
6PS(NTUTWVYX'A4.>;Z2+!*6[%(!\]@^@A_%-W3/`6Ha)(!\]@^@A4#43b+c
dfe+gh û
i û
jü<k e √256 = 16 lm2n+o j m2p û/qsr+t
v r ü=j2wGr+t v m2l d#x!gv ûbkNy l g{zg=h w v
|U} n eg n z
ü=
r ü=j e û
j
ý
~ m j2r#(S/N)
q ü h/17/256
id g€≈e 19r zv rq y/r h/g
t h‚z j2w ü<k d#xgƒem í5„
tr h/g5g ü h
m
l/m+n
û
ü
z| (∆m = 2.5)
mlim ≈ 19.5
l/ü m2n
rq
o
j2r+ibu
mlim ≈ 17
q@r+ d j v u
mu
t
m j+r+|1i g rü=n j2+e w g n
v
‚
√
ý
(S/N)19.5/256 ≈ 0.2 2 + 0.37 · 16 ≈ 4.2
… /û qRr+t
rq r+t†û
‡ z û v q¥û
i g ü û/‡ z û y r v
m
p
m m+n
…U~Uˆ m+e p r
=ü j l/g m2j n z r o
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iû vŠ‰ í>„+„+„„ ÿ í>‹ ý
n
l
m
∆m
∼
n
Œ i ge û zv r i/j2rj2r z rüj.û
 v
d j2rŽy d j g q d y e u
o
l/m
û y
q g j q¥‘
û j g=hg y
r z ü5q@r+j r e
h/g5v bû kj m+p /û q¥
2
m
l
m
/
l
m
l
1
o
 hg j r v
v r gWd üû h/g5v û gY’ û e g qk d ü g{zv/gv ûbk pbm+p ý
p l
l
l
KTK
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r z u
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b
p
m
l
f
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p
l
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p m l
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pfm
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r
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r ü5q@r+j m rq ‹ y û
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nû/j2w lm xg5v gڇ v m q
m l
o
m
e
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v
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n
m
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û g q ü j t v r+l‡ ü g j û î y û/q g v Ñ
r m e í>„ n
l/û m xr gv ¥
m
Ñ
m
p
l
l
l/m2n
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q g rqRy
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hnm i = αη · 10−0.4m · I0 · AT∆λ[(πD2 /4)/(πd2 /4)].
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¸,õ _ ð 4 · 10−2  ¿²¸ _ ðá³
² ∆λ2/∆λ1 ≈ 2
rAacGeAdGn hn i ≈ 4e , σ ≈ 2e –
hnm i ≈ αη · 10−0.4m · I0 · T∆λ(πD2 /4).
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v,wm8dGnvcGt
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Gr dAwm1f1c /c, σ283 ≈ 36e ,
eAb,am8{Gv,i
gAdGnam’na
nm1eAdGb,ji
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rAacGtz:,}"¤&³
ñ
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hnm i ∼ 105 · 10−0.4m .
— j{Gv|“f8gAdGfy¤ç³ í ´ZrAa
z8i
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hn283 i ≈ 1300e /
hn2.5 i ∼ 104 e ,
hn5 i ∼ 10 e ,
3
hn7.5 i ∼ 10 e ,
2
hn10 i ∼ 10e ,
σ2.5 ≈ 100e ,
σ5 ≈ 32e ,
σ7.5 ≈ 10e ,
σ10 ≈ 3.2e ,
(S/N)2.5 ≈ 85;
(S/N)5 ≈ 14;
(S/N)7.5 ≈ 1.6;
(S/N)10 ≈ 0.16.
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f1x
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(S/N)2.5 ≈ 1360, (S/N)5 ≈ 224,
(S/N)7.5 ≈ 26, (S/N)10 ≈ 2.6.
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