qudratic phase factor

Upload: maitham100

Post on 02-Jun-2018

222 views

Category:

Documents


0 download

TRANSCRIPT

  • 8/10/2019 Qudratic Phase Factor

    1/18

    !"#$ &'"($)*"+,

    -.,*"#* //0

    1233!456278 481 37&!29! 7-625:

    2; 2'+)#+"

  • 8/10/2019 Qudratic Phase Factor

    2/18

    "

    !" !$%&'()*%+'$

    #$ %&'( )*+),'-)$%. /01 2'33 4',(% )*5-'$) (0-) 04 %&) -5'$ 4)5%1,)( 04 %&) 61/7)$(89,)($)3

    (:535, %&)0,/ 04 0+%':53 ;'44,5:%'0$< =&'( %&)0,/ 5++,0*'-5%)( %&) >):%0, )3):%,': 5$; -57$)%':4')3;( 2'%& 5 ('$73) (:535, 41$:%'0$. 5$; 5;0+%( 5 ('-+3'4'); ,)+,)()$%5%'0$ 04 %&) '$%),5:%'0$ 04 5$

    )3):%,0-57$)%': 25>) 2'%& -5%%),< ?( /01 2'33 ()). %&) -0;)3 5::01$%( 40, 5 $1-@), 04 0+%':53

    +&)$0-)$5 ,5%&), 2)33) ;'(:1(('0$ 04

    5++3':5%'0$( 2'33 @) 401$; '$ %&) 3'%),5%1,) 0$ 0+%':53 ('7$53 +,0:)(('$7"(#$(?)6 +)9'* D$

    !! !!

    !!!""" "#$ !#$!"" #

    $!"

    %&'(#) %& >"?

    !

    " #

    $ #

    $%

    "%

    &%#

    K)+: E ;

  • 8/10/2019 Qudratic Phase Factor

    5/18

    "

    #$%& %'$ ())'&*+,%-). !! ,) /0$% 0120*+ 3,$02+45 607,-3 +70 (*0$+'$0. )% +70 )'$8(20 ,-+09$(4

    08802+,:045 $'-) %:0$ +70 (*0$+'$0 ,- +70 )2$00-;

    '0-+45 +70 2()0. +70 6($$,0$

    0,+70$ +%+(445 +$(-)&,+) %$ +%+(445 64%2I) +70 ,-2,30-+ 60(&. %!E1!.5!F 602%&0) ,30-+,2(445 J 8%$

    E"!#$!F B,+7,- +70 (*0$+'$0 (-3 /0$% %+70$B,)0;

    D70 %6C02+ (&*4,+'30 !!,) 8%'-3 65 &'4+,*45,-9 +70 ,-2,30-+ B(:0 65 %!E"!#$!F; D70 *$%3'2+

    ,) *($+,2'4($45 ),&*40 8%$ ( *%,-+A)%'$20 %- +70 2%%$3,-(+0 (1,) ( 3,)+(-20 &' 8$%& +70 (*0$+'$0.

    *$%:,303&',) 4($90 2%&*($03 +% +70 3,&0-),%-) %8 +70 (*0$+'$0; H- +7(+ 4,&,+ B0 2(- $0*4(20 (65

    &',- +70 30-%&,-(+%$ %8 =>; "; K0 &')+ 60 &%$0 2($08'4 B,+7 +70 ( ,- +70 01*%-0-+,(4. 602(')0 *(

    ,) 4,I045 +% 60 ( 6,9 -'&60$ B7,27 B0 &')+ 30+0$&,-0 +% ( 8$(2+,%- %8 L"; < ),&*40 01*(-),%- %8

    (9,:0)

    !! "# !!!

    "

    $%" $&"#

    #

    $% &

    '("

    !

    !

    "

    '% "'&"#

    #

    $% &

    '(")

    *+

    ,

    -. EMF

    B7,27 2(- 60 ,-)0$+03 ,-+% E"F +% 5,043

    ! !!

    "# !"#$$%"# % !"#

    $%

    &"# &'

    &"

    ('&

    # $

    !

    "#$

    %&)' &''('# $ ENF

    #'$+70$ ),&*4,8,2(+,%- ,) %6+(,-03 8%$ *4(-0 B(:0 ,44'&,-(+,%- -%$&(4 +% +70 (*0$+'$0. B7,27 ,)

    %6+(,-03 65 40++,-9 &' !" 7%43,-9 +,&' !+- 8,-,+0; D70 :($5,-9 *7()0 8(2+%$) +70- :(-,)7.

    40(:,-9 !!O+- %!E"!#$!F;

  • 8/10/2019 Qudratic Phase Factor

    6/18

    "

    #$ $%&' ()&*$+ ,)'$ )- $%. (%/'&0' &' 1)*. 2*1 $%. 0)*$.*$ )- $%. ,)1.3 %2' 4..* (5.'.*$.16

    7%. 5.,2&*1.5 )- )85 9)4 &' $) ,2:. '),. ;.),.$5&023 2((5)2382$.

    ?@A &* $%. 02'.' )- &*$.5.'$6

    !" $%&'(&) *(+ $%*,(-./&% +0//%*120.(

    B.-.55&*; 2;2&* $) C&;6 D+ =. '.. $%2$ ! &* EF6 @ &' 1.$.5,&*.1 4/ $%. 1&'$2*0. ! 4.$=..*

    2(.5$85. 2*1 &,2;. (32*.'+ 2*1 4/ $%. 1&'$2*0. -5), $%. &,2;. ()&*$ $) $%. )5&;&*6 G- =. 5.'$5&0$

    )85 2$$.*$&)* $) 2 -&*&$. 5.;&)* )- $%. &,2;. (32*.+ 0)55.'()*1&*; $) !3.'' $%2* 2 -.= 1.;5..'+ &$

    &' 21.F82$. $) $2:. 0)'!!D6

    E.3.*;$%+ 48$ *)$ *.0.''25&3/ ,80% 4&;;.5 $%2* $%. 3&*.25 1&,.*'&)*'

    )- $%. 2(.5$85.6 ?7%. .. 2*1 *.;2$&>. 0)*$5&48$&)*'6A

    # -85$%.5 5.2552*;.,.*$ )- $%. C5.'*.3 1&--520$&)* ..*&.*$6 E

  • 8/10/2019 Qudratic Phase Factor

    7/18

    "

    !!!!"#$!"#%

    !!#!"#

    !"

    $!

    &" %!

    $"#$%

    !&&& !"# '!"

    #$!$&" %!% $

    "#

    $%'$&'%& #$%&

    '()*( )+ +),-./ 0(1 2345)15 0567+835, 38 0(1 6-150451 )..4,)760)379 :1 ').. 4+46../ '670 03 ;73'

    0(1 3-0)*6. )7017+)0/< '()*( )+ -53-350)376. 03 =!=>< +3 0(1 -(6+1 86*035 )7 85370 )+ )551.1?6709

    !" $%&' ()'*)* +', *-+.&+( /&(.)0&'1

    @(1 A13,105)*6.B3-0)*+ 676./+)+ 38 .17+1+ )+ 6.516C/ 86,).)65 03 /349 D151 '1 651 *37*1571C

    ')0( 0(1 -(6+1 38 0(1 3-0)*6. '6?1+< )7 35C15 03 05160 )701581517*1 1881*0+ -53-15./< +3 '1 ,4+0

    511E6,)71 0(1 1881*0 38 6 .17+ 37 67 )7*3,)7A '6?19 :1 ').. 1?17046../ 8)7C 0(60 .17+1+ C3

    )7C11C 835, ),6A1+< F40 ')0( 6 -(6+1 +()80 '()*( C1-17C+ 37 -3+)0)379 235047601./< '1 651

    4+46../ *37*1571C ')0( )7017+)0/< 730 6,-.)04C1< +3 0(1 -(6+1 +()80 )+ 47),-350670< 67C '1 *67

    1E-1*0 03 4+1 .17+1+ 6+ 4+46. 03 835, ,6A7)8)1C ),6A1+ 38 3FG1*0+9 H351 +45-5)+)7A./< '1 ')..

    6.+3 8)7C 0(60 6 .17+ *67 F1 4+1C 6+ 67 3-0)*6. 2345)15 0567+835,159 @()+ ').. 6..3' 4+ 03 3F+15?1

    0(1 25647(3815 C)8856*0)37 -600157 60 6 8)7)01 C)+067*1 853, 0(1 C)8856*0)7A 3FG1*0< 67C 03 C3 0(1

    2345)15 0567+835, 51I4)51C 835 +-60)6. 8).015)7A 1E-15),170+9

    $9 J17+ A13,105/

    @(1 0/-1 38 .17+1+ '1 711C 03 47C15+067C *37+)+0 38 3-0)*6../ C17+1 ,6015)6. F347C1C F/

    +-(15)*6. +4586*1+< 6+ +(3'7 )7 2)A9 >69 :1 ').. 05160 37./ 0()7 .17+1+< )7 0(1 +17+1 0(60 6 56/

    17015)7A 60 #!"#& 37 371 86*1 1,15A1+ 60 7165./ 0(1 +6,1 *335C)7601 37 0(1 30(15 86*19 K 0()7 .17+

    0(1518351 +15?1+ 37./ 03 C1.6/ 0(1 )7*)C170 '6?185370 F/ 67 6,3470 -53-350)376. 03 0(1 0()*;71++

    38 0(1 .17+ 60 16*( -3)709 L17301 0(1 0()*;71++ 60 67/ -3)70 F/ !#!"#&< 67C 0(1 ,6E),4, 0()*;71++

    F/ !%9 @(1 0306. -(6+1 C1.6/ F10'117 0(1 )7-40 '6?1 !!67C 0(1 340-40 '6?1 !!$)+

    !!!""# !#$"!!""#"# "$ # "!!""## $ #$$&

    '(151 & )+ 0(1 )7C1E 38 51856*0)379 M165567A)7A< '1 A10

    ! !!

    "!! !"#!""$# $ !"# !"%# # &'"%$(%'# $ #$>&

    @3 *6.*4.601 !#!"#&< '1 ),6A)71 +-.)00)7A 0(1 .17+< 6+ +(3'7 )7 2)A9 >F< 67C '35; 340 0(1

    A13,105/ 03 3F06)7

  • 8/10/2019 Qudratic Phase Factor

    8/18

    "

    !! !! "!" "" "" "# "##

    !"#

    #

    $%

    &

    '("$#)

    *+

    ,

    -."!# "" ""

    "# "##

    !##

    #

    $%

    &

    '("$ #)

    *+

    ,

    -. #$%&

    '()* *)+,-).)/* /012+13*-4 ). 5/ *674 0/72 6(/ -/0* 78)*9 *)0:/ 6(/0 5/ :70 /8,70; 6(/ *

    !!!""#!!$"!% " "%

    %

    &

    #&"

    &

    #%

    #

    $% &

    '( #$?&

    @

  • 8/10/2019 Qudratic Phase Factor

    9/18

    "

    #$ %&'()&*&+ !"*,- !#

    ./ ,01 2*3/ *44 )2/ 5*62(,/&+ 1/ ,//- )0 2*,-4/ )2/ 7()8*)(0, 7201, (, 9(:$ ;$ %, 0'2/&(6*4 1*3/ 0= 7)&/,:)2 !"@$"%&"A$ ?2/

    78>/&>07()(0, 0= *44 )2/ 7>2/&(6*4 1*3/7 1(44 :(3/ *, /F>&/77(0, =0& !!0= )2/ =0&5 0= GH$ I$ ?2(7

    1*3/ (7 )&*,7=0&5/- )0 !!( '+ )2/ 4/,7 *660&-(,: )0 GH$ JK$ L= 1/ 60,7(-/& !!( )0 '/ * ,/1

    78>/&>07()(0, 1/ 6*, -/76&('/ !#(, )2/ =0&5 0= GH$ I *:*(,$

    .&()(,: 08) )2/7/ 7)/>7 (7 5/77+ '8) ,/6/77*&+$ 9&05 @IAC -&0>>(,: )2/ 60,7)*,) >2*7/

    /F>@#)*AC 1/ 2*3/

    !!!!

    !!"#!#"" "#$

    !$

    %"#%! #%#" #

    %$ &!# " #

    %% &$%&

    '()"%#" @JMA

    ./ )2/, :/) !!(=&05 @JKAC *,- >8) () (,)0 @IA *:*(, )0 :/)

    !!!!

    !!"!! "!## "#$

    !#

    %"!$ "! $ $!# $

    %% % "! $%!# $

    %& '%&'

    ()*"$ "!"% "! @JNA

    L) (7 60,3/,(/,) )0 (,)&0-86/ * ,/1 =8,6)(0, "@$#%+$"%&"A -/=(,/- '+

    !! ! "!"!!! "#! #"$"#$ $!$%"$%#$ @JIA

    ?2/ /F>4(6() =0&5 0= "(7 =08,- =&05 @JKAC @JMAC *,- @JNAO

    ! ! "

    #! #"

    #$

    ! !%

    9(:$ ; P'4*,/7 =0& * )2(, 4/,7$ % >0(,)E708&6/ (7 406*)/- 0, )2/ *F(7 *

    -(7)*,6/ !,=&05 )2/ 4/,7$

  • 8/10/2019 Qudratic Phase Factor

    10/18

    "#

    ! !!

    !"!"!#

    #$% #$

    "!#%#

    ""

    "# $"

    #$%

    &'#$%

    #$

    "!"%"

    ""&"

    "# $"

    #$%

    &'

    ( #$% #$

    "

    !

    !#"

    !

    !")!

    '

    *

    +, -

    ./(

    !

    ""

    #$

    %

    &'0 #$% )#$

    %"

    !""

    %#

    !#

    *

    +, -

    ./(

    !

    "

    #$

    %

    &'!(

    !

    ( #$% #$

    "

    !

    !#"

    !

    !")!

    '

    *

    +, -

    ./("

    ""

    #$

    %

    &'0 #$% )#$

    &"

    !""

    !#

    *

    +, -

    ./("

    "

    #$

    %

    &'!("

    $"%&

    '()*+(,- ./01 )23*.045 01 .44 6)11, .4 7) 31)83(- *59 :) 5))9 .4 1). *743. );*(3*.05< 146) 1=)>0*(

    >*1)1? $@)84+) =+4>))90543(9 /*;) .(, 7, 805905< ./) 06*) (4>*.)9 *. $!"#$"& 105>) ./) 9)8050.045 $"A& 01 B31. ./) C3,.0451? O371.0.3.05< 05.4 P2? "A :) )=. 84+ * =/*1) 1/08.- "&01 * 1>*()9 >4=, 48

    ""? R/) =/*1) 8*>.4+ :0(( ;*501/ :/)5 :) .*I) S"&SQ.4 4590.045 84+ 06*

  • 8/10/2019 Qudratic Phase Factor

    11/18

    ""

    !"!!"# $%! &" #

    "& $%! $!" #! "#$ !

    "'

    !&!

    $!! &" # $% ! &" #$%!$!" #

    ()!$*)

    !" ##

    $%

    &

    '(

    )+! (!%*!" # "#$ !"' $%! &" #& $%!$!" #

    (!()$*!*)" ##

    $%

    &

    '(

    #$"%

    &'()( #*!+,!% -)( .//)012-3(4 12 3'( 56-2( -3 0!7 8'14 14 -69/43 3'( 3)-24:/)9 /: 3'( -5()3;)(

    3)-2491441/2 :;2.31/27 8'( ' 3'( 3)-24:/)9 56-2( 14 )-3'() .6/4( 3/ 3'( /=C(.3+ - 5/3(231-6

    -0A-23->( 12 4(3312> ;5 (*5()19(2347 8'( 19->( 14 -64/ .6/4(6, )(6-3(0 3/ 3'( 45-31-6 :)(

  • 8/10/2019 Qudratic Phase Factor

    12/18

    "#

    $!"#$"% &' ()* +(,-'./0,1 23-'*+ &. 2,020,(&0'-3 (0 ()* .2*4(,-3 -123&(56* -( /,*75*'48 $!!#!$% 9

    $%!":#"%$":#"&%; 35, -33 .)-,2 *6=*. &' ()* /&'-3 &1-=*;

    G'/0,(5'-(*38? ()* 40'6&(&0' '(9 &? ,*75&,*6 (0 40123*(*38 *3&1&'-(* ()* 2)-.* /-4(0,. &' ()*

    (,-'./0,1 23-'*? 3*-6. (0 -' &1-=* -( &'/&'&(8; H)&. &. '0( A*,8 .-(&./-4(0,8 /0, *F2*,&1*'(.;

    I5220.* &'.(*-6 ()-( @* 40'.&6*, ()* 10,* =*'*,-3 4-.* 0/ '(J / (0 0>(-&' - /&3(*,*6 &1-=* -( -

    /&'&(* 6&.(-'4*; H-C&'= ()* 3&1&( ')!" &' $#"% ()*' 8&*36. -' *F2,*..&0' 3&C* $##% >5( @&() -

    153(&23&4-(&A* 2)-.* /-4(0, *F2KD$*%%:$#%$'(D&%$!"#L$"#%M; N /&3(*, &' ()* (,-'./0,1 23-'* " @&33

    106&/8 ()&. 40123*F -123&(56* -440,6&'= (0 !"+ 9 -&$!"#$"%!"; H)* 106&/&*6 @-A* ()*' 2,02-=-(*.

    (0 ()* /&'-3 &1-=* 23-'* -( '*-440,6&'= (0 O7; P? @&() ()* ,*.53(

    !!!!"

    "!$%

    "#$ !&%#!& '!

    !#(!

    !$ %!%

    #

    $%

    &

    '(

    ) )$** " )*& '"#$ +!&

    %'!'+#(!(+$ %

    #$

    &'

    ,'+,(+

    $#Q%

    @)*,*

    ! !"! " # !"!! !"# "#$

    %&"&%$'"'%% &

    #

    $%&

    '((&"('" $#R%

    &. ()* E05,&*, (,-'./0,1 0/ -(-'6.9 '*D&; S0(* ()-( ()* 75-6,-(&4 2)-.* /-4(0,. &' ()* (,-'./0,1

    23-'* )-A* A-'&.)*6? .0 @* 4-' ,*(-&' -33 0/ 05, 2,*A&05. 6&.45..&0' >-.*6 0' O7; ##; N3.0 '0(*

    ()-(? @)*' -/ 9 "? !* &. ()* E05,&*, (,-'./0,1 0/ ()* E05,&*, (,-'./0,1 0/ -(; T05>3*D

    (,-'./0,1&'= - /5'4(&0' ,*.53(. &' -' &'A*,(*6 A*,.&0' 0/ ()* 0,&=&'-3 /5'4(&0'? .0 @* ,*40A*, ()*

    =*01*(,&4 &1-=*? 40'.&.(*'( @&() O7; ""? -. @* 15.(;

  • 8/10/2019 Qudratic Phase Factor

    13/18

    "#

    !!!" $%&'()%*%+,'

    -" .%+%)&/ '%,(0

    $%& &'(&)*+&,- .*// 0& 12,& 2, 3, 2(-*43/ 0&,4% 52 -%3- 3// -%& 42+(2,&,-5 43, 0& 3446)3-&/73/*8,&19 $%& /*8%- 526)4& *5 3 5+3// /35&): 3,1 3 (%2-2+&-&) *5 ()2;*1&1 -2 +&356)& -%& /*8%-

    *,-&,5*-7 *, -%& ;3)*265 1*

  • 8/10/2019 Qudratic Phase Factor

    14/18

    "#

    $%& '()*'+' ,*-.(/ '($0%&, $%& "12 3(.-& 45 $%& *.$&35(0&6 &7&. *5 $%*, 3&,+/$, *. $%& 8(.&/

    '&$&3 -4*.- 455 ,0(/&9

    : '&0%(.*0(/ ,/*;& *, +,&; $4 84,*$*4. $%& /*-%$ -+*;& (/4.- ( /*.& 8&38&.;*0+/(3 $4 $%& ()*, 45

    $%& 48$*0(/ %*0%

    *, 04..&0$&; $4 !"#$%45 $%& *.$&35(0& ;&7*0&9=%& ,$(3$+8 5*/& &'()*+,-.,/01 >*// 8347*;& ( -44; ,$(3$*.- 84*.$ 543 4*;& %(, $%&3&543& %*0% *, ,&&.

  • 8/10/2019 Qudratic Phase Factor

    15/18

    "#

    $%&'()(*+ ,*%- ($%&* .'/. /0* 10./.$*/*, 23,**'4 50* 3.,,*21.'+('& .67*3/ )., /0(2 ($%&* 8(--

    6* /0* .1/(3%- +(2/9,6%'3* !!1,*2*'/ %/ /0* 1.2(/(.' &(:*' 6; /0* -*'2 -%84

  • 8/10/2019 Qudratic Phase Factor

    16/18

    "#

    $%&'()) '*+ , -. )+%& (' (/01' '*+ &(.+ 20&3'30% (& 401 535 607 '*+ 87+&%+) 2(''+7%&9 (%5 )0-: 3'

    '0 '*+ /+%-*;

  • 8/10/2019 Qudratic Phase Factor

    17/18

    "#

    !"# %&'()*+*

    $% &'(%)(&*+, -%+ )-.*/ %.0+'()1**2 3(4 45+ 0-/+* +6.14(-%7 4- 45+ (%4+%7(42 /1418 95(7 (7 1

    '145+' /(33().*4 417: ;+)1.7+ -3 45+ 10-.%4 -3 )-0&.414(-% %++/+/ 1%/ ;+)1.7+ -3 (0&+'3+)4(-%7(% 45+ *17+' 1%/ *+%7+7 '++

    '107 .7+ 45+ E174 E-.'(+' 9'1%73-'0 1*>-'(450 IEE9J 4-

    )-0&.4+ 1 !"#$%&'&1&&'-D(014(-% 4- 45+ E-.'(+' 4'1%73-'08 95+ /(7)'+4+ EE9 -3 1% (B&-(%4 1''12

    )*(7 /+3(%+/ 4- ;+

    !"! #$

    $!!

    %!"

    " #$% !&$"

    %

    $%

    &'

    IKLJ

    3-' +M N, ", 888, (B"8 95+ 1*>-'(450 '+6.('+7 4514 (;+ 1 &- 45+ -.4&.4 7&+)4'.0 1;-.4 (PK8 95+ 3-*/(%> )1%

    ;+ '+0-=+/ '10 45+ %+)+771'2

    -&+'14(-%78 R+ '+&'+7+%4 45+ 7*(4I7J ;2 1 -%+B/(0+%7(-%1* 1''12 )-%41(%(%> -%+7 -.I/.01.J ;2 -.I/.J,

  • 8/10/2019 Qudratic Phase Factor

    18/18

    "#

    $%& '()*+%,-&( .)/& 0/ 1%& /0234&/15 /0+.& 6& ,+47 +&&8 1, .)4.*4)1& 1%& 0+1&+/017 9!!9:-(,2

    ;