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40 .
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. , . , . . .: , 1998. 575 .
8 25142-82. .
[]. . 1983 01 - 01 - .: - , 1991. - 21 .
9 . ., -
, [] /
. . // :
- , . , 20 - 22
2004 . : - . . . -, 2004. - C. 118 -
120.
10 .
[] :
.013-00. . 2000 06 01 ; 2007 01
01. .: , 2000. 15 .
11 520-2002. .
[]. . 2003 01 01. .: - , 2003. 67 .
12 -, . . ,
[] / . . -
, . . . - .: , 1978. 232 .
13 17353-89 -
. .
[] . 1991 01 01; 11-12 94; 2 96. .: -
, 1999. 8 .
14 Atsushi, S. Maxim 3D-5700 / Atsushi
Sato // . = Instruments and Automation. 1991. Vol. 19,
No. 2. P. 54 58. (.).
15 , . .
[]
83
/ . . , . . // . . . . -. .
. 1999. . 3. . 65 75, 128.
16 , . . [] /
. . , . . . .: . . . .-. ., 1996.
320 . ( ).
17 , . . - [] /
. . . .: , 1982. 160 .
18 , . . -
, -
[ ] /
. . // . 2004.
187. . 1992 2001. URL: http://zhurnal.ape.relarn.ru/articles/2004/
187.pdf ( : 06.06.2013).
19 , . .
[] / . . , . . //
. - 2012. - 3. - . 34 - 40.
20 , . .
[ ] / . . , . . , . .
. . , . . //
, :
- ,
40-
: , 18 - 20 2012 .: . . . - : -
. . , 2012. - . 10 - 13. - URL:
http://window.edu.ru/resource/337/78337/files/PIT_2012.pdf ( -
10 2013 .). - ISBN 978-5-93424-627-4.
21 - [
]. . URL: http://www.videoscan.ru (
11 2013 .).
84
22 [ ]. URL:
http://www.astek-npo.ru ( 11 2013 .).
23 TRINAMIK motion control [ ].
URL: http:// www.trinamic.com ( 11
2013 .).
24 , . [] / . , . ; . . - 2-.
. - .: , 1973. 720 .
25 , . . : . [] / . . ;
. . . . .: . ., 1986. 512 .
26 , . . : . [] / . . . 2- .,
. .: , 1985. 752 . (. ).
27 , . [] / . ; . .; .
. . . 2- . .: . , 1980. 488 . (. .
Yariv A. Quantum electronics, , 1975).
28 Velichanskii, V. L. Method of measuring the astigmatic distance of laser
diodes [Text] / V. L. Velichanskii, A. S. Zibrov, S. P. Kotova, G. T. Pak,
A. K. Chernyshov // Journal of soviet laser research. 1991. Vol. 12, No. 4.
P. 341 352.
29 24643-81. .
[] . 1981 07 01. .: -
, 2004. 10 . ( ).
30 02068410-009-2007.
[]. - . 2007-11-01. - : - , 2007. - IV;
33 . - ( ).
31 , . . -
[] :
. . . . : 05.11.16 / . . ; . .
. -. , 2005. 20 .
85
[5].
:
( , , ) ( ) ( , )F z R z H z = , (.1) , , z - ; ( )R z - ; ( , )H z - . R H . { , , z } .
.
: -
, -
- , ,
:
,, N ba Na b
=GGGGGG , ( ) ( ),, b Na Na b
=G GGGGG , (.2)
, ;
, .
(.2) :
86
= , (.3)
: , R , Rz , , ; Rz - OZ;
R - OZ. :
( ), , ,c c R R z z = ( ) ( )( ) ( )
2
2
cos cos sin sin tg sinsin sin sin sin tg cos
c c c c
c c c c
A B AB A
+ = + + ,
(.4)
cAL= , sin c
c
d = , tgcz
L = ,
( )2 21 2 cos tgcB A A = + + ; (.5)
, cz - ,
- (XYZ . 2).
:
= , constc R= + , c Rz z z= = , (.6)
, B L b= G . , - . - R
Rz , ,
. d L [18],
.
87
( ), z (.3) - z
( ) ( )0, 2 ,R R R k R R R kz z z z = = = = = , (.7) k ,
.
. ,
,
.
(.7)
(.3)
,
, . (.3) :
( ) ( ) ( ) ( )0 0 00 0 0 00
, ,1 , , , ,approx R
R RR
= = + +
( ) ( ) ( ) ( )0 0 0 0 0 00 0, , , , R R + + ,
(.8)
( )0 0 0, , R
, ( )0 0 0, , R
( )0 0 0, , R
, 0R = , 0 = 0 = ; 0R , 0 0 - ,
. , , ,
.
.
, (.8).
88
, (.8) , , , . Rz .
(.8) ,
.
, (.3) (.8)
(.3) 0R . , (.8), .
(.8)
.
(.3) 0 0 . 0R ,
, :
0 0 0( , , ) 0 R = . (.9) ,
.
(.8) :
0
1 dH a H b cR d
= + , (.10)
( )0 0 00
, ,d Ra R
d = ,
( )0 0 0, ,d Rbd = ,
( )0 0 0, ,d Rd = ,
0 = , 0 = , ( ), z = , ( ), z = . (.10)
( ) ( )0, 2 ,k kH z z H z z = = = = = , (.11) k .
89
kz (.10),
a , b , c .
( ) ( ) ( )W b c = + (.12) .
(.10)
.
[7].
, (.10),
.
.
( )W ( )iW ; 0,1, 2, ... 1i N= ; 0 0 = ;
2N = . :
( ) ( ) ( )[ ]21
cos sinN
i j i j ij
W j j =
= + , (.13) 2i
iN
= , [ ]... - . :
( ) ( )10
2 cosN
j i ii
W jN
=
= , ( ) ( )10
2 sinN
j i ii
W jN
=
= , ( ) ( )12
0
1 1N
iN i
iW
N
== ,
(.14)
2/Nji
90
( )iH N i , ( )iW : ( ) 0iH R =
( ) ( ) ( ) ( )[ ]2 2 21
1 sin cosN
n n i n n in
n a n a n na n
=
+ + (.15)
0,1, 2, ... 1i N= . ,
- (.12) (
, ) -
.
(.4) (.6), (.9), (.10), (.12) (.15)
.
91
,
.
[24],
. ,
. , ,
, .
. ,
:
1 1 1's s f
= , (.1)
s - , ,
;
's - ;
f - .
,
.
, ,
, .
.
, .
.
[25]. ,
92
, . ,
, ,
. . ,
, , ,
,
. , ,
v .
, 0>v , 0
93
,
, 10 .
,
, . ,
,
, , ,
. ,
(. ).
.
, .
,
. ,
, ,
, .
,
,
.
,
.
, , . ,
, ()
,
.
,
94
[21].
.
:
''
v A B vu C D u = .
(.2)
(.2)
.
.
:
, , ,
(. [25]).
,
:
=
101
1'
100
101 a
f
bM , (.3)
a - ;
b - ;
'f - .
,
, ,
:
vua
= , '' vub
= .
95
a b
. a b
(. . .1)
.
H - a , 'H - b .
H 'H .
,
, . , ,
, 'f f= . (.3) :
1' '
1 1' '
b a ba bf f
Ma
f f
+ = . (.4)
(.4) (.2), 'v :
' 1' '
b a bv v a b uf f
= + + . (.5)
. .1 : )'(VV -
; H , 'H - , ,
( );
96
v
,
, ,
,
.
(.5) .
, h
v
cosh v = , (.6) - .
, ,
, , a b
(.1), (.5) .
a
0,1. (.5) ,
, .
,
. ,
.
,
.
.
97
.
.
, ,
. ,
. .
, ,
,
[26], [27].
[28].
.
{ x , y , z }. OZ
.
.
,
.
I x , y , z
[28]:
2 2
2 222
0 0
2 exp 2
1 1x y
x y
P x yIw wz z z
z z
= + + +
, (.1)
P - ;
98
0xz , 0 yz -
- XOZ YOZ ;
xw , yw - XOZ
YOZ , ,
z ;
z - OZ ; - ,
.
(.1) :
1 220
0
1x xx
z zw wz
= + , (.2)
1 22
00
1x yy
zw wz
= + , (.3)
0xw , 0 yw -
- XOZ YOZ ,
(. . ) .
(.1) (.3) , ,
.
.
XOZ YOZ ,
.
. xR yR
z :
( ) 201 xx zR z z z z = +
, (.4)
99
201 yy
zR z
z
= + , (.5)
. (.4) (.5) ,
OZ
z ,
XOZ
YOZ .
. .1
.
. ,
, , w , 0w , . -
, 0z = , O .
. .1
, (.5),
. .2.
100
(.4), (.5)
.
, -
.
.
. .2
: 1
; 2 ;
-
( );
,
0z = (.1) (.5) - . , , - .
.
, , .
,
,
.
101
. ,
,
-.
, ,
-.
, .
.
[24],
, , ,
.
.
.
.
, , .
,
. , ,
.
,
, ,
90 .
, , .
,
.
102
,
,
. .
, .
(. . .3).
.3
: XOY -
COD -
(), A; GH
CD -
A;
XOY G, O, H, K, B, M;
OZ C, A, D, F,
B, E; A B
; . 1
. ,
.
103
,
A.
, ,
201 8,34 .
2,86 . , ,
, .
,
.
.
, .
. .
. ,
. (
, ,
, )
.
(.1) [24].
, ,
, ,
. , -
.
104
- ,
0z 0w
:
0 2z
= , (.6)
0w
= , (.7)
- . 0z z= . (.6), (.7) , ,
21 e
.
.
0z 0w
20
0wz = . (.8)
. , 02 w - , ;
02 z - . , .
2GD w= ,
z , 0w
:
2 42 2 44
G
G
k Dz RR k D
= + , (.9)
105
22 20 2 4
2
4
G
G
Dw Rk DR
= +,
(.10)
2k = , (.11)
k - ;
- ; R - z .
(9) - (.11)
, , , 0 3z z . .
, , z R= , 0w 0z (.6) (.7), .
( , ) ,
, , , ,
,
2GDf
= , (.12)
f -
.
,
, , ,
.
, f ,
.
,
.
106
(.12) (.6) (.7). :
20 2
4
G
fzD
= , (.13)
0
2
G
fwD
= . (.14)
,
. ,
GD .
,
( ).
,
.
, , .
.
, ,
, .
, . ,
.
.
,
.
( .4) [24]
,
22
2UDu zf
= , (.15)
107
22
UDv rf
= , (.16)
r - ;
UD - ,
.
. .4
. .4 .
u .
, .
.
.
.
.
.
. .1, ,
.
XOZ .
, . .4.
108
( ) 2sin 44foc
uII u
= , (.17)
focI - . u , v
(.15), (.16).
, 0u = :
( ) 212foc
J vII v
= , (.18)
1J - 1- . (.18)
. (.18)
min 1min1
1,22
U U
f frD D
= = , (.19)
min1 3,85 - .
, ,
, ,
.
,
,
, . ,
,
min10,5 = . 0,36455. 1 0,36788e .
min 10 2
rw . (.20)
109
,
1/ 2min 1
4 ln 2 0,87G U UD D D , (.21)
1/min 1
4 0,742 UG e
D D , (.22)
1/min 1
4 1,04G e UD D , (.23)
21/min 1
4 2 1,48 UG eD D , (.24)
1/ 2 , 1 e .
.
.
21 e .
.
, ,
, .
0w , w . , 0z , , ,
.
, ,
.
:
0,405 = - ; , 10f = ;
110
201; , ,
, .
[6],
2 500 .
M .
N
4N M= . (.25) Sd
. Sd
.
( )minl . ,
( )min 2 RS Rd l N = = , (.26)
RR -
.
Sd ,
, ,
. ,
Sd , ,
(.26).
Td
:
cosT Sd d = . (.27)
111
, , z .
z , .
-
. (.5). ,
arcsin
T
dR
= , (.28)
d . . , Sd
Td .
d .
045 135 < < , (.29)
- . -
90 100.
0 L .
d L , :
0 d L< < , (.30) Rd R< . (.31)
d L , -
:
0 20d < < , (.32) 20 150 L < < . (.33)
,
. ,
, :
112
min 1 0,5 Tr d= . (.34)
(.16) (.34) UD :
min 1
min 1 min 1
1,22Uf fDr r
= = . (.35)
,
,
-
.
,
. ,
.
. .
, (.20).
.
.
,
.
, .
,
. -
,
.
113
, -
, .
1,
- 2.
:
, .
1 2 .
,
. ,
. , ,
21R ,
,
.
,
21 2
SRR = , (.36)
SR -
, .
(.1)
.
.
, . V H
. (.36),
21 2
S HH
RR = , (.37)
21 2
S VV
RR = , (.38)
114
S HR , S VR - SR
;
21 HR , 21VR - 21R
, ,
.
RR -
201 8,34 . TR
2,86 . , (. . 13),
:
S H RR R= , (.39)
S V TR R= . (.40) (.37) (.38) ,
, . ,
,
,
.
.
(.20) 10w
. 0 ,
.
, ,
, , . ,
,
:
115
21 21 10H Vw w w= = . (.41)
, (.37), (.38) (.41),
(.9), 21 Hz 21Vz
:
( )21 21 21,H G H Hz f D w R R= = = , (.42) ( )21 21 21,V G V Vz f D w R R= = = , (.43) f - , (.9).
, (.10), 2 0 Hw
20Vw
:
( )2 0 21 21,H G H Hw f D w R R= = = , (.44) ( )2 0 21 21,V G V Vw f D w R R= = = , (.45) f - , (.10).
(.5) d L
, | |bG
.
, (.28), bG
OZ
(. . .3) :
0b B L= G
, (.46)
( )20 0 0 01 2 cosB A A = + , (.47)
0TRA
L= , (.48)
0 2 arcsin
dL
= , (.49)
116
(.28). , (.42), (.43), (.46) (.49),
2 2 Hz 2 2Vz
:
2 2 21 | |H Hz z b= +
G, (.50)
2 2 21 | |V Vz z b= +
G. (.51)
, (.44) (.45), (.8).
2 0 Hz 2 0Vz . , ,
(.50) (.51), (.2) (.3).
2 2 Hw 2 2Vw :
( )2 2 0 21 0 2 0 2 2, ,H x H x H Hw f w w z z z z= = = = , (.52) ( )2 2 0 21 0 2 0 2 2, ,V x V x V Vw f w w z z z z= = = = , (.53) f - , (.2) (.3)
. , 0z = , (.50), (.51).
, 2 HD 2VD
:
2 2 22H HD w= , (.54)
2 2 22V VD w= . (.55) ,
. .
-
.
2 HD 2VD .
117
, ,
.
.
(. .5 .6).
405 . 13 .
. .6
:
,
;
- 256 256
. .7 -
:
1 , 2
,
,
,
,
, .
- , , ,
MathCad. .
118
.
,
, -
, ,
.
.
.
,
.
. ,
(
), ,
, (
). ,
.
. ,
, -
.
-
.
:
119
. ,
, .
.
.
,
.
, .
.
.
.
" " ,
, " ".
.
.
. . .
.
.
, .
. ,
. .
- ,
, .
120
.
:
L - , ;
a0, b - ;
K -
.
:
2N+1 - .
L.
:
x0 - ,
;
X0 - . .
K ;
delta0 - . . .
.
:
x -
;
delta -
, x;
delta1, delta2, delta3 - -
a1, a2, a3
;
a1 - ;
121
a2 - x;
a3 - .
:
fi(n)=exp(-2*x^2/L^2),
L exp(-2)
( , , x=0);
, (,
).
:
FI(n)=[1- a0/2 + a0*hi]*fi(n) - b*ksi.
( -), -
( - ); hi ksi -
, ; ksi hi.
(.
"\ "):
ORIGIN=1;
TOL=0.001;
CTOL=0.001.
1.
PRN , . . .
122
(. "\
"):
15;
:
8;
, ;
15.
(.
"\ "):
- "";
;
- "".
_______________
: L=4, N=9
: 0=0.04, b=0.005, K=10.
L 4
a0 0.04
b 0.005
_______________
fi i( ) exp2 i2.L2
-
123
=====================
,
, ,
. :
N if b 1 10 4.> floor 1.52 L. log b( )., 2 L.,
floor 1.52 L. log b( ). 9= 2 L. 8= N 9= 2 N. 1 19=
exp(-2*n^2/L^2) = b.
, FI(n)>0.
=====================
Randomise
-
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
,
hi n( ) rnd 1( )
ksi n( ) rnd 1( )
FI n( ) 1a02
a0 hi n( ). fi n( ). b ksi n( ).
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
---------------------------------------------------
.
-
, . :
124
K 10
i 1 K..
x0iN
N
n
FI n( ) n.=
N
N
n
FI n( )
=
x0
0.010328021454549
0.003823718097664
0.004867901455201
0.022579293397763
0.014733108369996
0.004856599190031
0.010226805242807
0.016014689371322
0.014696550760882
0.002709759887558
=
X01K
1
K
i
x0i=
.
delta01
K 11
K
i
x0i X02
=
.
- . :
X0 0.005974011251468= - . . .:
delta0 0.011170208193789= , .
--------------------------------------
::::::::::::::::::::::::::::::::::::::::::::::::::::
FI(n)
t N N.. FI0t N 1 FI t( )
FI n( ) FI0n N 1
:
FI010 0.992299690600485= FI 0( ) 0.992299690600485= FI 0( ) 0.992299690600485= FI 1( ) 0.870607734956855= FI 1( ) 0.895537190214928= FI 2( ) 0.615547715398837= FI 2( ) 0.595748567421512=
125
FI 3( ) 0.318127011568241= FI 3( ) 0.32736013530844= FI 4( ) 0.13258726353539= FI 4( ) 0.136198129810425= FI
::::::::::::::::::::::::::::::::::::::::::::::::::
++++++++++++++++++++++
( ).
a1, a2 a3
F1=0
F2=0 (1)
F3=0
(. ).
F1 a( )
N
N
n
FI n( ) a1 expn a2
2
a3. exp
n a22
a3.
=
F2 a( )
N
N
n
FI n( ) a1 expn a2
2
a3. exp
n a22
a3. n.
=
F3 a( )
N
N
n
FI n( ) a1 expn a2
2
a3. exp
n a22
a3. n2.
=
,
a1=q1,1, a2=q2,1, a3=q3,1 (. ).
max FI0( ) 0.992299690600485=
126
q1 1, max FI0( )
q2 1,N
N
n
FI n( ) n.=
N
N
n
FI n( )
=
q2 1, 0.005847372242777=
q3 1,
4
N
N
n
FI n( ) n q2 1,2.
=
.
N
N
n
FI n( )
=
q3 1, 15.2794399434495=
2 q3 1,. 5.52800867283138= - L.
a1=a1+EPS1, a2=a2+EPS2, a3=a3+EPS3, (2)
(1)
F1+(dF1/da1)*EPS1+(dF1/da2)*EPS2+(dF1/da3)*EPS3 = 0
F2+(dF2/da1)*EPS1+(dF2/da2)*EPS2+(dF2/da3)*EPS3 = 0 (3)
F3+(dF3/da1)*EPS1+(dF3/da2)*EPS2+(dF3/da3)*EPS3 = 0
(. ).
a1, a2 a3 :
(3), EPS. a1, a2 a3
(3).
(3) .
127
EPS1=D1/D, EPS2=D2/D, EPS3= D3/D,
D, D1, D2, D3 - (3) (
. ). : D
(3), D1, D2, D3 D ,
, , F1,
F2, F3.
dF1_da1 a( )
N
N
n
expn a2
2
a3
2
=
dF1_da2_1 a( )
N
N
n
2a1 n a2
.a3
. expn a2
2
a3
2
.=
dF1_da2_2 a( )
N
N
n
FI n( ) a1 expn a2
2
a3. 2.
n a2a3
. expn a2
2
a3.
=
dF1_da2 a( ) dF1_da2_1 a( ) dF1_da2_2 a( )
dF1_da3_1 a( )
N
N
n
a1a1 n a2
2.
a32
. expn a2
2
a3
2
.=
dF1_da3_2 a( )
N
N
n
FI n( ) a1 expn a2
2
a3. n a2
2
a32
. expn a2
2
a3.
=
dF1_da3 a( ) dF1_da3_1 a( ) dF1_da3_2 a( )
dF2_da1 a( )
N
N
n
expn a2
2
a3
2
n.=
dF2_da2_1 a( )
N
N
n
2a1 n a2
.a3
. expn a2
2
a3
2
. n.=
128
dF2_da2_2 a( )
N
N
n
FI n( ) a1 expn a2
2
a3. 2.
n a2a3
. n. expn a2
2
a3.
=
dF2_da2 a( ) dF2_da2_1 a( ) dF2_da2_2 a( )
dF2_da3_1 a( )
N
N
n
a1 n a22. n.
a32
expn a2
2
a3
2
.=
dF2_da3_2 a( )
N
N
n
FI n( ) a1 expn a2
2
a3. n a2
2 n.
a32
. expn a2
2
a3.
=
dF2_da3 a( ) dF2_da3_1 a( ) dF2_da3_2 a( )
dF3_da1 a( )
N
N
n
expn a2
2
a3
2
n2.=
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N
N
n
2a1 n a2
.a3
. expn a2
2
a3
2
. n2.=
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N
n
FI n( ) a1 expn a2
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n a2a3
. n2. expn a2
2
a3.
=
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dF3_da3_1 a( )
N
N
n
a1 n a22. n2.
a32
expn a2
2
a3
2
.=
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N
n
FI n( ) a1 expn a2
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a3. n a2
2 n2.
a32
. expn a2
2
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=
dF3_da3 a( ) dF3_da3_1 a( ) dF3_da3_2 a( )
D 1 a( ) dF1_da1 a( ) dF2_da2 a( ). dF3_da3 a( ). D 2 a( ) dF1_da1 a( ) dF2_da3 a( ). dF3_da2 a( ). D 3 a( ) dF1_da2 a( ) dF2_da3 a( ). dF3_da1 a( ).
129
D 4 a( ) dF1_da2 a( ) dF2_da1 a( ). dF3_da3 a( ). D 5 a( ) dF1_da3 a( ) dF2_da1 a( ). dF3_da2 a( ). D 6 a( ) dF1_da3 a( ) dF2_da2 a( ). dF3_da1 a( ).
D S a( )
D 1 a( )
D 2 a( )
D 3 a( )
D 4 a( )
D 5 a( )
D 6 a( )
D a( )
1
6
l
D S a( )l=
D1 1 a( ) F1 a( ) dF2_da2 a( ). dF3_da3 a( ). D1 2 a( ) F1 a( ) dF2_da3 a( ). dF3_da3 a( ). D1 3 a( ) F3 a( ) dF1_da2 a( ). dF2_da3 a( ). D1 4 a( ) F2 a( ) dF1_da2 a( ). dF3_da3 a( ). D1 5 a( ) F2 a( ) dF1_da3 a( ). dF3_da2 a( ). D1 6 a( ) F3 a( ) dF1_da3 a( ). dF2_da2 a( ).
D1 S a( )
D1 1 a( )
D1 2 a( )
D1 3 a( )
D1 4 a( )
D1 5 a( )
D1 6 a( )
D1 a( )
1
6
l
D1 S a( )l=
D2 1 a( ) F2 a( ) dF1_da1 a( ). dF3_da3 a( ). D2 2 a( ) F3 a( ) dF1_da1 a( ). dF2_da3 a( ). D2 3 a( ) F1 a( ) dF2_da3 a( ). dF3_da1 a( ). D2 4 a( ) F1 a( ) dF2_da1 a( ). dF3_da3 a( ). D2 5 a( ) F3 a( ) dF1_da3 a( ). dF2_da1 a( ). D2 6 a( ) F2 a( ) dF1_da3 a( ). dF3_da1 a( ).
130
D2 S a( )
D2 1 a( )
D2 2 a( )
D2 3 a( )
D2 4 a( )
D2 5 a( )
D2 6 a( )
D2 a( )
1
6
l
D2 S a( )l=
D3 1 a( ) F3 a( ) dF1_da1 a( ). dF2_da2 a( ). D3 2 a( ) F2 a( ) dF1_da1 a( ). dF3_da2 a( ). D3 3 a( ) F2 a( ) dF1_da2 a( ). dF3_da1 a( ). D3 4 a( ) F3 a( ) dF1_da2 a( ). dF2_da1 a( ). D3 5 a( ) F1 a( ) dF2_da1 a( ). dF3_da2 a( ). D3 6 a( ) F1 a( ) dF2_da2 a( ). dF3_da1 a( ).
D3 S a( )
D3 1 a( )
D3 2 a( )
D3 3 a( )
D3 4 a( )
D3 5 a( )
D3 6 a( )
D3 a( )
1
6
l
D3 S a( )l=
EPS 1 a( )D1 a( )D a( )
EPS 2 a( )D2 a( )D a( )
EPS 3 a( )D3 a( )D a( )
ERR1 3 102. ERR2 5 10
4. deltaL 1 10
1. -
L, .
ERR3 2 q3 1,. deltaL. ERR3 0.552800867283138= Jmax 15 q3 Jmax, 0 j 1 Jmax..
131
V001 a( ) a1 EPS 1
a1
a2
a3
V002 a( ) a2 EPS 2
a1
a2
a3
V003 a( ) a3 EPS 3
a1
a2
a3
V00 a( )
V001 a( )
V002 a( )
V003 a( )
COND1 a( ) if EPS 1 a( ) ERR1> 1, 0, COND2 a( ) if EPS 2 a( ) ERR2> 1, 0, COND3 a( ) if EPS 3 a( ) ERR3> 1, 0, COND a( ) COND1 a( ) COND2 a( )( ) COND3 a( ) 0.5( ) 0.5 (x) , x>0
x
132
0 2 4 60.94
0.96
0.98
1 0.99
q1 j,
j
count
1
2
3
4
5
6
0
=
0 2 4 60.006
0.0055
0.005
q2 j,
j
0 2 4 64
5
6
sign q3 j, 2 q3 j,..
j
133
q1 j,0.9922996906004850.9610608868757160.9590100479314060.9686501609820720.979433713790602
= q2 j,-0.005847372242777-0.005586503293125-0.005372187167343-0.005239087518193-0.005182679554685
= sign q3 j, 2 q3 j,..5.528008672831385.042529177990614.653195801995864.378773725735424.20611018404365
= j12345
=
x q2 Jmax2, delta x
^^^^^^^^^^^^^^^^^^^^^^^^^
j 2 Jmax2.. FE1 j, q1 j, q1 j 1, FE2 j, q2 j, q2 j 1,
FE3 j, sign q3 j 1, 2 q3 j 1,.. sign q3 j, 2 q3 j,..
2 3 4 50.04
0.02
0
0.02
FE1 j,
j
FE1 Jmax2, 0.01078355280853=
134
2 3 4 50
1 .10 42 .10 43 .10 4
FE2 j,
j
FE2 Jmax2, 0.000056407963508=
delta1 FE1 Jmax2, delta2 FE2 Jmax2, delta3 FE3 Jmax2,
2 3 4 50.6
0.4
0.2
0
FE3 j,
j
FE3 Jmax2, 0.172663541691769=
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
:
x 0.005182679554685= delta 0.005182679554685= delta1 0.01078355280853= delta2 0.000056407963508= delta3 0.172663541691769= Jmax2 1 4= X0 0.005974011251468= delta0 0.011170208193789= N 9= .
++++++++++++++++++++++++
.
:
L:=4; a0:=0.04; b:=0.005; K:=10; ERR1=3*10-2; ERR2=5*10-4; deltaL=1*10-1.
:
( - Randomise -
)
X0=0.002227014697664; delta0=0.010215078861837;
135
x=-0.005762041563924; delta=-0.005762041563924;
delta1=0.007762513035773; delta2=0.000657878240668;
delta3=0.095227900657006; Jmax2-1=5; N=9;
(- randomise,
Mathcad
)
X0=-0.005974011251468; delta0=0.011170208193789;
x=-0.005182679554685; delta=-0.005182679554685;
delta1=0.01078355280853; delta2=0.000056407963508;
delta3=0.172663541691769; Jmax2-1=4; N=9.
-
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.1 DLT.dpr
program DLT; uses Forms, Unit1 in 'Unit1.pas' {Form1}, Unit2 in 'Unit2.pas', Unit3 in 'Dop\Unit3.pas' {AboutBox}, Unit4 in 'Unit4.pas' {Form4}; {$R *.res} begin Application.Initialize; Application.CreateForm(TForm1, Form1); Application.CreateForm(TAboutBox, AboutBox); Application.CreateForm(TForm4, Form4); Application.Run; end.
.2 Unit1.pas
unit Unit1; interface uses Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms, Dialogs, Menus, CustomizeDlg, ErrorMsgs, AppEvnts, ExtCtrls, StdCtrls, Grids, ImgList, ToolWin, ComCtrls, ShellApi,Math, TeEngine, Series, TeeProcs, Chart, Buttons, OleCtrls, Unit3, Unit4; type TForm1 = class(TForm) MainMenu1: TMainMenu; N3: TMenuItem; N1: TMenuItem; N11: TMenuItem; N12: TMenuItem; N5: TMenuItem; N13: TMenuItem; SaveDialog1: TSaveDialog; PageControl1: TPageControl; Tab1: TTabSheet; GroupBox1: TGroupBox;
167
List1: TListBox; Label1: TLabel; Label2: TLabel; Label3: TLabel; Label4: TLabel; Label5: TLabel; GroupBox2: TGroupBox; Label6: TLabel; Label7: TLabel; Label8: TLabel; Label9: TLabel; Label10: TLabel; Label11: TLabel; Label12: TLabel; Label13: TLabel; Label14: TLabel; Label15: TLabel; Label16: TLabel; Label17: TLabel; Chart2: TChart; OpenDialog1: TOpenDialog; Label18: TLabel; RadioButton1: TRadioButton; RadioButton2: TRadioButton; RadioButton4: TRadioButton; N4: TMenuItem; N6: TMenuItem; GroupBox3: TGroupBox; Edit4: TEdit; Button1: TButton; Button2: TButton; Label19: TLabel; GroupBox4: TGroupBox; GRmin: TLabeledEdit; Grmax: TLabeledEdit; N7: TMenuItem; Button4: TButton; Series3: TLineSeries; Series2: TLineSeries; List2: TListBox; Label23: TLabel; Series5: TPointSeries; Label24: TLabel; Label25: TLabel; Button12: TButton; Button13: TButton; Label21: TLabel; Label22: TLabel; GroupBox5: TGroupBox; Wmin: TLabeledEdit; Wmax: TLabeledEdit; Series7: TLineSeries; Series8: TLineSeries;
168
Label26: TLabel; Label27: TLabel; Label28: TLabel; Label29: TLabel; Series4: TLineSeries; GroupBox6: TGroupBox; TrackBar1: TTrackBar; GroupBox7: TGroupBox; GroupBox8: TGroupBox; procedure N11Click(Sender: TObject); procedure N4Click(Sender: TObject); procedure N6Click(Sender: TObject); procedure Button1Click(Sender: TObject); procedure Button2Click(Sender: TObject); // procedure Button3Click(Sender: TObject); procedure RadioButton2Click(Sender: TObject); procedure Button4Click(Sender: TObject); procedure RadioButton4Click(Sender: TObject); procedure List2Click(Sender: TObject); procedure Button12Click(Sender: TObject); procedure Button13Click(Sender: TObject); procedure Button14Click(Sender: TObject); procedure List2KeyDown(Sender: TObject; var Key: Word; Shift: TShiftState); procedure GRminKeyUp(Sender: TObject; var Key: Word; Shift: TShiftState); procedure GrmaxKeyUp(Sender: TObject; var Key: Word; Shift: TShiftState); procedure WminKeyUp(Sender: TObject; var Key: Word; Shift: TShiftState); procedure WmaxKeyUp(Sender: TObject; var Key: Word; Shift: TShiftState); procedure N12Click(Sender: TObject); procedure N13Click(Sender: TObject); procedure TrackBar1Change(Sender: TObject); procedure RadioGroup1Click(Sender: TObject); private { Private declarations } public { Public declarations } end; const pi2=2*pi;eps =0.0001; XG0= 0 ; YG0 = 20 ; NKDR= 500 ; SGY = 500 ; XG1 = XG0+NKDR ; YG1 = YG0+SGY ;
169
maxscale = 20; maxp = 2000; // var Form1: TForm1; // LFP,Y0:real; zmin,lkaz,lt,zt:real; Nfi,NSmax,delz:integer; dps,dtt: array [1..maxp] of real; Se4:byte;// Aver,aver2,max:real; z:array [1..100]of real; C,c2:array [1..round(maxp/4)]of real; IndGr,IndBar,tmpGr:integer; ER:real; psi0, teta0, rsred:real; rz, au, bu, cu:real; Npol:integer; NP, np0, ns0,SC_Z:integer; stet:integer; Scale:byte;scale2:byte; Fmax,Nf:integer; //gadosti fiy, fi2, v, w:array [1..20] of double; fi:array [1..100,1..20] of double; c1:array [1..20,1..20] of double; A, B, E, T2:real; sn, cs, sinp, cosp, sind, cosd:real; PSI, XPZS:array [1..maxp] of real; // H:array [1..360] of real; // AP, BP, AT, BT:array [1..round(maxp/4)] of real; H_W,H_G, V_WAVINESS:real;// N_G, N_W:integer; fnt:integer; hf,Inter,wav:boolean; // grminv,grmaxv,wminv,wmaxv:integer;// implementation var F_data,F_rez:text;tmpstr:string; {$R *.dfm} // , Procedure GetNumber(var s:string; var s2,s3:string); var i:byte;
170
begin i:=1; s2:=''; while (not(s[i] in ['0'..'9','-'])) do inc(i); while (s[i] in ['0'..'9','.','-']) and (i
171
if nsmax=1 then begin Groupbox3.Visible:=false; Radiobutton1.Enabled:=false; end else GroupBox3.Visible:=true; Button4.Click; list2.Selected[0]:=true; end; end; // procedure TForm1.N11Click(Sender: TObject); var FNameTmp,s,sq,s2,s3:string; i,j:integer; begin If not OpenDialog1.Execute then Exit; FNameTmp:=OpenDialog1.FileName; AssignFile(F_Data,FNameTmp); try Reset(F_Data); except MessageDlg(error_load+FNameTmp,mtError,[mbOK],0); { } exit; end; i:=1; List1.Clear; if not SeekEOF(F_Data) then begin while i
172
GetNumber(s2,sq,s2); nsmax:=strtoint(sq); Label19.Caption:=' : '+sq; Edit4.Text:='1'; se4:=1; j:=1; i:=0; aver2:=0; aver:=0; while not(EOF(F_Data)) do begin readln(F_Data,S); GetNumber(s,sq,s2); GetNumber(s2,sq,s3); dps[j]:=strtofloat(sq); Aver:=aver + dps[j]; GetNumber(s3,sq,s3); dtt[j]:=strtofloat(sq); Aver2:=aver2 + (dtt[j]); inc(j); end; aver:=aver/(j-1); aver2:=aver2/(j-1); CloseFile(F_Data); RepaintList; grminv:=0; wminv:=0; FMAX:=round(NFI/4); nF:=round( FMAX/2); Label27.Caption:=' : '+inttostr(fmax); Label29.Caption:=' : '+inttostr(fmax); grmaxv:=fmax; Wmaxv:=fmax; grmax.Text:=inttostr(grmaxv); wmax.Text:=inttostr(grmaxv); wav:=false; rest; end; end; // procedure TForm1.N12Click(Sender: TObject); var FNameTmp,s:string; i:integer; begin if inter then begin If not SaveDialog1.Execute then Exit; FNameTmp:=SaveDialog1.FileName; AssignFile(F_Data,FNameTmp); if copy(SaveDialog1.FileName,length(SaveDialog1.FileName)-3,4)'.rez' then SaveDialog1.FileName:=SaveDialog1.FileName+'.rez'; if (SaveDialog1.FileNameFNameTmp)and FileExists(SaveDialog1.FileName) then begin i:=application.MessageBox(' ! ?','',mb_YesNoCancel+mb_iconexclamation);
173
case i of IDNo: begin Form1.N12Click(Form1); exit; end; IDCancel:exit; end; end; AssignFile(F_rez,SaveDialog1.FileName); try Rewrite(F_rez); except ShowMessage(' '+SaveDialog1.FileName); exit; end; writeln(F_rez,' : '+tmpstr); if nsmax>1 then writeln(F_rez,' : '+inttostr(se4)); if not(wav) then begin writeln(F_rez,' : '+inttostr(grminv)+ ' '+inttostr(grmaxv)); writeln(F_rez,': '+floattostrf(H_g,ffFixed ,10,4) +' ' +inttostr(n_g)) end else begin writeln(F_rez,' : '+inttostr(wminv)+ ' '+inttostr(wmaxv)); writeln(F_rez,': '+floattostrf(H_w,ffFixed ,10,4) +' ' +inttostr(n_w)) end; for i:=1 to 360 do begin s:=inttostr(i)+' '+floattostrf(h[i],ffFixed ,10,4)+ ' '+floattostrf(psi[i],ffFixed ,10,4)+ ' '+floattostrf(XPZS[i],ffFixed ,10,4); writeln(F_rez,s); end; FNameTmp:=SaveDialog1.FileName; CloseFile(F_rez); end; end; // Procedure RepaintBar(); var i:integer; begin For i:=0 to form4.Series1.Count-1 do form4.Series1.ValueColor[i]:=clBlue; if not(wav) then begin if grminv>0 then for i:=0 to grminv-1 do form4.Series1.ValueColor[i]:=clRed; if grmaxv
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if wminv>0 then for i:=0 to wminv-1 do form4.Series1.ValueColor[i]:=clRed; if wmaxv eps) do begin
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y1:= Hl_R (y0, L, psi, teta, r1); y2:= Hl_R (y0, L, psi, teta, r2); ys:= Hl_R (y0, L, psi, teta, rs); if ((y1*ys) < 0.0 ) then r2:= rs; if ((ys*y2) < 0.0 ) then r1:= rs; rs:= (r1 + r2)/2.0; err:= abs (r2 - r1); end; sr_radius:=rs; end; Function dR_dz (y0, L, psi_gr, teta_gr, R0:real):real; var x, d, f, psi, teta, rad:real; begin rad:= PI2/360.0; psi:= rad * psi_gr; teta:= tan (rad * teta_gr); table (y0, L, psi, teta, R0); d:= B - cosp + A*cs; f:= sind + B*sn; x:= -teta * d / (f * E + cs * T2); dR_dz:=x; end; Function dH_dl ( y0, L, psi_gr, teta_gr, R0, H:real): real; var x, d, f, psi, teta, rad:real; begin rad:= PI2/360.0; psi:= rad * psi_gr; teta:= tan (rad * teta_gr); A:= R0/L; T2:= teta * teta; sn:= y0/R0; cs:= sqrt (1.0 - sn*sn); sinp:= sin (psi); cosp:= cos (psi); sind:= sinp * cs - cosp * sn; cosd:= cosp * cs + sinp * sn; B:= sqrt (1.0 + A*A - 2.0*A*cosd + T2); E:= sinp - A*sn; d:= cosd - A - B * cs; f:= sind + B * sn; x:= (d * E + sn * T2) / (f * E + cs * T2); dH_dl:=x; end; Function dH_dz (y0, L, psi_gr, teta_gr, R0, Rz, H:real):real; var x, d, f, psi, teta, rad:real; begin rad:= PI2/360.0; psi:= rad * psi_gr; teta:= tan (rad * teta_gr); table (y0, L, psi, teta,R0+H); d:= B - cosp + A*cs; f:= sind + B*sn; x:= -teta * d / (f * E + T2 * cs) - Rz; dH_dz:=x; end;
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//- - Function coef_A (y0, L, psi_gr, teta_gr, R0:real):real; var f, f1, f2, dx:real; begin dx:= 0.0001; f1:= dH_dl (y0, L, psi_gr, teta_gr, R0-dx, 0.0); f2:= dH_dl (y0, L, psi_gr, teta_gr, R0+dx, 0.0); f:= R0*(f2 - f1)/(dx+dx); coef_A:=f; end; Function coef_B (y0, L, psi_gr, teta_gr, R0:real):real; var f, f1, f2, dx:real; begin dx:= 0.0001; f1:= dH_dl (y0, L, psi_gr-dx, teta_gr, R0, 0.0); f2:= dH_dl (y0, L, psi_gr+dx, teta_gr, R0, 0.0); f:= R0*(f2 - f1)/((dx+dx)*PI2/360.0); coef_B:=f; end; Function coef_C (y0, L, psi_gr, teta_gr, R0:real):real; var f, f1, f2, dx:real; begin dx:= 0.0001; f1:= dH_dl (y0, L, psi_gr, teta_gr-dx, R0, 0.0); f2:= dH_dl (y0, L, psi_gr, teta_gr+dx, R0, 0.0); f:= R0 * (f2 - f1)/((dx+dx)*PI2/360.0); coef_C:=f; end; Function coefft (N:integer; y:array of real; k:integer;var a:real; var b:real):real; var i:integer; t, x, ak, bk:real; begin ak:= 0; bk:= 0; t:= PI2*k/N; for i:= 0 to N-1 do begin x:= t * i; ak:=ak + y[i]*cos (x); bk:=bk + y[i]*sin (x); end; ak:= ak * 2.0/n; bk:= bk * 2.0/n; x:= sqrt (ak*ak + bk*bk); a:=ak; b:=bk; coefft:=x; end; // Procedure pol_fft (N:integer;var H:array of real; M1,M2:integer; a:array of real; b:array of real); var i, k:integer;
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dx, t, x:real; begin dx:= PI2/N; for i:=0 to N-1 do begin x:= dx * i; H[i]:=0; for k:= M1 to M2-1 do begin t:= (k+1) * x; H[i]:=H[i] + a[k]*cos(t) + b[k]*sin(t); end; end; end; // Function vol_fft (M:integer;var a:array of real; var b:array of real;AU:real;var c:array of real):real; var k:integer; dk, ak, bk, s:real; begin for k:= 0 to m-1 do begin dk:= (k+1); s:= 1.0/(AU*AU + dk*dk); ak:= a[k]; bk:= b[k]; b[k]:= s * (dk*ak - AU*bk); a[k]:= - s * (AU*ak + dk*bk); c[k]:=sqrt(a[k]*a[k]+b[k]*b[k]); end; s:=0.0001; for k:= 0 to m-1 do if (c[k] > s) then s:= c[k]; for k:= 0 to m-1 do c[k]:=c[k]/s; vol_fft:=s; end; Procedure Interpol (ns:integer; mf:integer); var i,j, m1, m2:integer; ck:real; begin m1:= NFI * ns; PSI0:= 0; TETA0:=0; for i:=1 to NFI do begin m2:= m1 + i; PSI[i]:= dps[m2]; PSI0:=PSI0 + PSI[i]; XPZS[i]:= dtt[m2]; TETA0:=TETA0 + XPZS[i]; end; ck:=NFI; PSI0:=PSI0/ck; TETA0:=TETA0/ck; for i:= 1 to NFI do begin PSI[i]:=PSI[i] - PSI0; XPZS[i]:=XPZS[i] - TETA0; end; RSRED:= sr_radius (Y0, LFP, PSI0, TETA0); RZ:= dR_dz (1000.0*Y0,1000.0* LFP, PSI0, TETA0, 1000.0*RSRED); AU:= coef_A (1000.0*Y0,1000.0*LFP, PSI0, TETA0, 1000.0*RSRED); BU:= coef_B (1000.0*Y0, 1000.0*LFP, PSI0, TETA0, 1000.0*RSRED);
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CU:= coef_C (1000.0*Y0,1000.0* LFP, PSI0, TETA0, 1000.0*RSRED); end; Procedure interpol_dat(); var ck:real; i,j:longint; begin i:=0; for j:= 1 to NFI do PSI[j]:=(BU*PSI[j] + CU*XPZS[j])*6.28/360.0; for j:= 1 to fmax do ck:= coefft (NFI, PSI, j, AP[j], BP[j]); ck:= vol_fft (fmax, AP, BP, AU, C); end; // Function hgr (n:integer; y:array of real):real; var i:integer;min,max,s:real; begin min:= 1e6; max:=-1e6; for i:=0 to n do begin if (y[i] > max) then max:= y[i]; if (y[i] < min) then min:= y[i]; end; s:= max - min; hgr:=s; end; Function ngr (n:integer; y:array of real):integer; var i,k,s:integer; begin s:=0; if y[0]>0 then for i:=0 to n-2 do if (y[i]>0) and (y[i+1]
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hw:=s; end; Function nw (n:integer; y:array of real):integer; var i,k,s:integer; begin s:=0; if y[0]>0 then for i:=0 to n-2 do if (y[i]>0) and (y[i+1]
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form1.Series2.AddXY(r * cos(i*pi2/360),r * sin(i*pi2/360),'') end; // form1.Series3.AddXY(r * cos(180*pi2/360),r * sin(180*pi2/360),''); end; end; // scale1,2 - Procedure pict_vol(n:integer;H:array of real); var i, xs, ys:integer; r1, ix, iy:real; begin with form1 do begin Series4.Clear; xs:= round((XG0 + XG1)/2); ys:= round((YG0 + YG1)/2); pict_vol2(scale2); Series4.XValues.Order:=loNone; for i:= 0 to 359 do begin r1:= scale2+ H[i]*scale; if r1> scale2*1.5 then r1:=scale2*1.5; if r1< scale2/2 then r1:=scale2/2; ix:=r1 * cos(i*pi2/360); iy:=r1 * sin(i*pi2/360); form1.Series4.AddXY(ix,-iy); end; r1:= scale2+ H[0]*scale; if r1> scale2*2 then r1:=scale2*2; if r1< scale2/2 then r1:=scale2/2; ix:=r1 * cos(0); iy:=r1 * sin(0); form1.Series4.AddXY(ix,-iy); Chart2.MaxYValue(Chart2.LeftAxis); Chart2.LeftAxis.Minimum:=-(scale2*1.6);//Chart2.MinYValue(Chart2.LeftAxis)-10; Chart2.LeftAxis.Maximum:=scale2*1.6; //Chart2.MaxYValue(Chart2.LeftAxis)+10; Chart2.MaxYValue(Chart2.BottomAxis); Chart2.BottomAxis.Minimum:=-(scale2*1.6);//Chart2.MinXValue(Chart2.LeftAxis)-10; Chart2.BottomAxis.Maximum:=(scale2*1.6); //Chart2.MaxXValue(Chart2.LeftAxis)+10; end; end; // Procedure Show_spectr(); var i:integer;MFM:integer; begin form4.Series1.Clear; //Form1.Series1. if form1.radiobutton2.Checked then for i:= 1 to fmax do Form4.Series1.Addbar(0.015+abs(2*scale*c[i]), '' , clBlue ) else if form4.Button14.Caption='Teta' then
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for i:= 1 to fmax do Form4.Series1.Add(0.015+2*scale*c[i], Inttostr(i) , clBlue )
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