Desktop virtual reality in the enchancement of digital elevation models

Texto

(1)! $. ! %. &. &. Universidade Federal de Pernambuco [email protected] www.cin.ufpe.br/~posgraduacao. RECIFE, FEVEREIRO/2004. "# '.

(2) ! "#. $. % &. '. (. - .. %. )* +. /001. ! "# ,.

(3) 2! 3 34# 5 2 !:! 5 3. 739!:. # ! # !6! 5 3. 2!8 758 3 5. # !: 5" : 83 2! 95 5 2! 95 5 "! 5 3 5 9# !73 !9 9 !# !. 3 5 !# # 5. 758 "! 739!:!9 2# 3 42 5 9 4 5:. 6! !# 5: !# # 3# 6. ;2 2. 5 6!. !#5. !: 5":! 6! 3 !:! 5 3 95 5 # !< # !6 25. !9 3#5 9 25. !#5. 2! !# # 3# 6# !6 3 6 ":! 3# 2 6. 3;! !# . 5 # 5: # 3":!7 6 2! 5. 8 5"3. 85663 5 !9 ; 2. !#5. 8"! 9!. !# 89. :. ! !# 5: 6 9 !6 25 ! # 3 36!9 7! 2393:34!6 3 9! !. 5 9 5:63 3 # !73 ! 9 !# ! 25 5# ! 6 ! 5: = !9 3 :8;2!. + 96 3 !# # 3# 6. 9! !. 3;! !# . 2!6! # 3 !9 # !6 5. 4!# # 3# 6 ; 2 5#. :5# 25# 5 !#6. 2! 739!: 3 5 6 # !937 5 :8 2!6! 6 !. 7! 2393:34!6 3#9!. 8 45 9 3# # !. 5# ! 3 ;!:: !6 5": 62!9 5 9 !. !9. 25 2!6! !# # 3# 6 5 "! 5 6!9 "875 8. # !563 6 3#!5 2 4! !# 5 !9 9 4 5: !:! 5 3 739!:. 75+ 4 2! #9!. 3# # ! 3. 2!. 5 9 <5. 8 .. :85:43# 276. 6. # 39. 44339 # !6 : 6. 8 !6 3 !# # 3# 6. 4; 9! # 5 4 4!# # 3# 6. 5 3 5 9. 3;5958 6. 2!. 9 4 5: !:! 5 3 739!:6. ! . 5 9 33:6 5# ! 3 # !59 :85 5 :5":! 3 9 4 5: !:! 5 3. 739!: 6!# 6 2 6 2!6 6 599# !66!6 2! !:! 5 3. !!9 3 9!. 739!:6 4! !# 5 !9 2# 3 42. ! 25. ! 7! 2396 25 9!5: ; 2 !# # 3# 6. !#!# 37! # 8 2! . 5 7! 2393:3485 9 5 33: 3#. 49 4 5: !:! 5 3 739!:6 25 ! "!! 9! 2! 7! 2393:348 6 "56!9 3. # ! # !6! 5 3 3 25 ! !5 # !6 6 6! 3. 5 9 59!< 5 !. !9 5 9 7 :!7! !9. # 5: # !5: 8. 37 :!> 95 5. # !5: 6 !# 5. 3 5 9 5 45 3. 3# 75. :5. !#5 !6. ;2 2 5::3;. 6 5: = 5 3 3 3"* ! 6 ; 2 63 2 6. 2 56 2! 42 5 9 9! 2. 5 9 5# ! 2 42:8. 6 5: = 5 3 .. 4 !# # 5. !# 5. ! 2 < !6 "56!9 3. 739!:6 256 "!!. # 3 7!. # !6!. !9. 8 45 9 # !73. 739!:. 6 5: = 5 3 5 9 !> :3# 5 3 . 6 5:. 4!# # 3# 6 !## !5 3. !3. 2!6! 2# !! 5. 3# 9!#3 3" 5 5 9 !# 5 3. 5. 3 ! 25. 8 6 2! !9. 5. #36!. 2! 95 5 25. 3. 3 2!#5. 2! 739!:. 43 !# # 3#5# !56 3. 9. 5 "! 86 3. 5: !5 # !6. 8!# # 3#5# !56. 2! 95 56! .. 3# 9!#. ! 2! 9 4 5: !:! 5 3 739!: 68 6 !7. 5::!9. 9 3# . 256 "!! 9! !:3 !9 "56!9 3. 6!9 "8!> !# 9 4 5: !:! 5 3 739!: 6!# 6 739!:6 "56!9 3 2!. !6. + 3;:!94! 5"3. 5 9# ! # !6! 5 3 6 5 "! 6!9 3 !#3# 7 95 5 < 5: 8 3 # 3: 5 9 9! 5::8 .5 2# 95. 2!. !6 37 #6!6 9 4 5: !:! 5 3. 5 5:8 = ! 2! 9 4 5: !:! 5 3 739!: 6 46 ! 5: = !9 5 5:8 6 6 33:6. 63 25 6 5 6 2! 739!:. !#5 !6. 3# 9 4 3. 45 2# !! 9 7! 6 3 5: 9 4 5: !:! 5 3 739!:. 3# 2!. 3 9!. 6!9 3 75+! 5. 3# 75 3. # 5: # !5: 8. 9!. # ! 6!. 5 !9 625 ! 25. ! 3 !> :3# !. 7! 2393:348 . !> !# 9 4 5: !:! 5 3 739!: 6!# 6 25 ! 3 !#3# 7 2# !! "56 # 5: !. 9 4 5:. !#!# 37! # 68 2!. 2!. 2 6 7! 2393:348 3 "!. 9 3#" :96 9!6+3. # 5: # !5: 8. 5 !# # !# 595#9 4 5: !:! 5 3 739!:6. 5 9 5::3;6. 6 5: = 5 3 . !> :3# 5 3 . 5 5:8 6 6 5 9 !9. 43 2!6! 739!:6. !6+3. # 5: # !5: 8 6.

(4) # !56 4:8"! 37 45 5 # 5 # !5: 6. 5 9. !# 5. !!. !# 8 2! 95 5 3# # ! 2!. 3. 6 5" : 8 3 " :9 :3; 36 !> # !7!:8. 5 "! 9! :38 !9 5 # 366 ! !# 83. !66 5 9 !# # 3# 6 5 "! 9! 6!9 3 # !9. !9 5 9 3# # ! !9 3 ! 25. ! 2! # 3":!76 3. 3# 9!# 3. !. # # !9 9 # 4 2! 4! !# 5 3. !#!# 37! # 8 56! 6 9 !6 25 ! "!!. 739!:6 4! !# 5 !9 # 37 # !5: ;3# :9 95 5. 9!!9.. 6!# 6 3. !#3# 7!9 ; 2 2 6 5# !5 25 !. ! !66 3 2! 68 6 !7. 9 3# 3. := 593 5# 57. 739!:3 9 4 5: 9! !:! 5A B3. 3#. 7= 5#36 # 3":!756 9! #@ 93 5 4!# 5A B3 9! 7. !#!# 37! #5. 3# 57 # !5: = 5936 !6 936 9! 563 37. 739!:36 9 4 5 6 9! !:! 5A B3 4!# 5936 5 5# #9! 95936 # !5 6 3. 2! 68 6 !7. 3 5 9 4 5: !:! 5 3 739!:. 2 6 739!: 5 "! 5 5:8 = !9. 9 3#256 "!!. # 7!9 2! ! !. !. 3 4! !# 5 ! 2 42 # ! 6 3 9 4 5: !:! 5 3 739!:6? 5 !# 2!. 3 5 9 4 5: !:! 5 3 739!: 2# 3 42 9 4 5: !:! 5 3. 3 "! 5 6! 3. # 3 7! 6 25. 7 # 3 !6 2! # 3 !66 4 25 # 3 !66 43 # 5; 95 5. !3. ! 5 3. 5 !. C 5 93 6 6 !75 3. # 7595 3# 6 C#36 9!6 5 C# !5 6 5:. + 3;:!94! 5"3. !## !5 3. :58 6 5. 2! 95 5. 9! !. 4 2!. 4!# # 3# 6 ; 2 5#. !# 5. 3 . !9. 2! "5 +4# 3. 93. !!9 3#5 375. :5# 25# 5 !#6. 9!6+3 6 5: = 5 3 .. # 3:!. 2 6 ;3# +. ;2 2 !> :3 6. 2! 9! 6 3 75+ 4 # 3 !66 5"3. 2! 9 4 5: !:! 5 3 739!: 8 ! 3 !# # 3# . # !: !. 7 3#5. )!# # 3# , 5# !56 3 "! ! 25. 2! 6!#5::3;6 2! 9! 9! !. 3. 6!# D 6 !9. 5 3 3 5 8. 5:43# 276 25 6 ! 5: = !. 6. # 5: # !5: 8 . # !73 ! 6! 6 4. 9 4 5: !:! 5 3 4.!# # 3# 3# # ! 3. 739!:6..

(5) # ! # !6! 5A B3 3 34# C 5 9! 7 !# # ! 3 39! 6!#739!:595 5 5# #9! 7 739!:3 9 4 5: 9! !:! 5A B 3 3. 6 !6 739!:36 39!7 3 !#9 !# 636 !# # 36. 3 < ! 5 65. 5" : 959! 936 95936. C!: 9! 95936 9! !:! 5A B3 # !< !#< ! 5. !#!= 5. 5663 595 536 95936 6!* 5 :! 595 !7 3 6 9!# 5A B3 ! < ! 36 !# # 36 # !6 3 6C! 6. 3#!6 5. !#!= 5 6!* 57 9!. 63 3. !#!= 5 63"# !5. 5936 ! # !73 936. 3# E 7. 7 # 3":!75 # @ 3 E3 5 3 9! < ! !6 !6. !# # 36 39!7 6!# 5 65936 3# C#56 # 5= F!6 9 !# ! !6 !7 595 739!:3 9 4 5: 9! !:! 5A B3 4!# 593. 3 < ! 3#5 5 6 5 9! # 3. 6!# 57 7! 393:3456. 36 9! !# # 36. 3. 5A B3 ! 5 6 5 3# # !A B3 7. 5# 5 9! ! 5#! < 5. 5# . ! 57"E 7. C#36 !6 936. 5# 5 # !73 !#9 !# ! !6. 93. !6 !6 # 3 !9 7! 36 5 : 57 5:43# 736 !6 ! 5: = 5936 !7 9! ! 5#. !# # 36 37 5# 5 !# @ 6 56 5#. :5# !6. # 39 = 93 "3 6 # !6 : 5936 5 ! 56 < 5 93 3 739!:3. 3 E 7 # !937 5 !7! ! !6 !6 9!. 3 9 @! 6. 36 !6 ! @ 36 9! !# # 36. 5A B 3 ! 9! 3# # !A B3 9! !# # 36 9! 9 !# ! !6. !6 B3 3 63: 95956 !. B3 6B3 !. ! !6. !. 5:7! !. 56 7! 393:3456 9!. 36 !7 739!:36 9 4 5 6 9! !:! 5A B3 B3. B3 !> 6 !7 !# # 57! 56 9 6 3 @! 6. 5# 5 36. 6 C#36 9! 739!:36 9 4 5 6 9! !:! 5A B3 6 5 !6! 6. # ! 5 ! !66 959! 9! 9!. #7E3936 5# 5 5 5 5#5 # 3":!7C 5 9! !# # 36. !7 739!:36 9 4 5 6 9! !:! 5A B3 4!# 5936 5 7! 393:345 3 9!. 5# # 9!. !#!# 37! #5. 5# 5 663.. 75. 95 ! 75 !# # 57! 5 3 7 :!7! 595 5# 5 7!:23# 5#5 < 5: 959! 9!. 739!:36 9 4 5 6 9! !:! 5A B3 7! 393:345 E "56!595 !7 # ! # !6! 5A B 3 63 6. # ! 65 9! 95936 37 :!>36. 5. 5956 < !. !# 5. !#5 !6 9! # !5: 959!. 5 !45A B3. "56!5956 !7 9! !# # ! 3. 3 9!. 93. # 3. 7 3 * 3 9! E. !#5 !6 9! # !5: 959!. 9 959!. ! < ! 6B3 "56 5 ! 56 9!. 959!6 "C6 56 !7. :5#739!:36. 7 57" ! !. # 5:. 5#! # !73 !#!# # 36. 959!6 E 6 5: = 5#! !> :3# 5#3 739!:3 9 4 5: 9! !:! 5A B3. 5 7 9! 3" !#. 3 2! 7! 3 63"# ! 36 95936 < ! 39! 6!# 6593 5# 5 739!:3. !# 5A B 3!. 6 C#36 !> !#! !6 9! 739!:36. 5 # !6! 5 93 7 739!:3 9 4 5: 9! !:! 5A B3 #9 7! 6 3 5:. 5# 5 9! 75 9!6 56 # G 65. 6 5: = 5A B3.. # 5: ! 59!< 5956 5# 5 75. ! 5 3# 93 37 5 7! 393:345.. 9 4 5 6 9! !:! 5A B3 9! !7 # !5: = 5# # G 6 5. !# 7 !7 5. 6 5: = 5A B3 # !5: 6 5 9! 3"* ! 36 37 3# 756. 366 !7 5# 5 !# @ 6 56 373 5: # 5 !. 56 5# 5 !> :3# 5# 3# 75A F!6. # 5:. < !. !## ! 5#! !# 5# 6 5:7! ! 3. 5: 65#3 739!:3 9 4 5: 9! !:! 5A B3 65 93 !# # 57! 56 9! 5 C: 6! !6 ! 5: = 5956.. 9! 3# 75 < ! 5# 5 !# @ 6 56 ! # ! # !6! 5A F!6 !6 5 @ 6 56 39!7 6!# 65956 5# 5# !5: = 5#3 3 # 3:! 9! < 5: 959! 936 95936 ! 9! # !5: = 595 !. !:3. 6 C#3. 5:7! !.. 5#C# !56 9! !# # 3 3 739!:3. E3 # 55 75 !#! # 5 5. 959! 5 6!#. 959! E5 !9 A B3 9! C# !56 9! !# # 3. 3 # 5956 3 3 * 3 9! 95936. 9! 3# 75 5 7!:23# 5#3 739!:3 9 4 5: 9! !:! 5A B3 6 6 !75. 257593. 9 3# . 3 9!6!. 3: 93 37 "56! !6 5 7! 393:345. 5# 5.

(6) 6 C#36 !> !#! !6 9! 739!:36 9 4 5 6 9! !:! 5A B3 # !5: 959!. # 5:. 6. !#!# 37E# 3. !. E 5. 739!:36. 9 3# 3 6 # H 739!:36 9!. "56!5936 !7 739!:36 9 4 5 6 9! !:! 5A B3 9! # 595#9! 5"!# # 5. # !5: 959!. !# 7 ! 5. # 5:. 6 5: = 5A B3. !> :3# 5A B3. 5 C: 6! ! !9 A B3 9!6 !6. !6 C 595 !=75 6 6! 3#5 93 75 3 A B3 5 # 5. 5 65 95 6 5 25" : 959! !7 3 6 # #57" ! !6 "56 5 ! # !5: 6 56 ! 6 3. < ! 39!7 6!# : = 5936 3#< 5:< !#3# 45 = 5A B3 # 3 !6657! 3. !# 5. 5 3#. 36 9! "5 >3. 6 6 !75 5 !#! A 35 5 59! 5 9!. 5# 5 4!# 5# 739!:36 9 4 5 6 9! !:! 5A B3 9! 5: 5. # ! 6B3? 5 H6 3. # 3 !6657! 3 936 95936 "# 36 !7 7 739!:3 9 4 5: 9! !:! 5A B3. !6 ! 739!:3 39! 6!# 5 5: 6593 9! 3# 75 5 !# 5#6! 36 95936 !6 B 3 3# # ! 36 ! !# # 36 39!7 6!# 9!. 5936 !. 3# #4936 5# 5 7!:23# C:3 9 3# 3. := 593 5# 57. 739!:3 9 4 5: 9! !:! 5A B3. 3#. 7= 5#36 # 3":!756 9! #@ 93 5 4!# 5A B3 9! 7. !#!# 37! #5. 3# 57 # !5: = 5936 !6 936 9! 563 37. 739!:36 9 4 5 6 9! !:! 5A B3 4!# 5936 5 5# #9! 95936 # !5 6 3. ! 5 3. 5 !. C 5 93 6 6 !75 3. # 7595 3# 6 C#36 9!6 5 C# !5 !## ! 5A B3. 6 5: !7. 7. 5 !: 7 3#5 !. !6 ! # 5"5:23.. 3 6 !7 # !45 3. 3 2! 7! 3 93 6 C#3 63"# ! 36 95936 3 # 3 !663 9! 37595 9! 9! 6B3 63"# ! C# !56 )9! !# # 3, 5 6!# !7 7!:23# 5956 3 739!:3 9 4 5: 9! !:! 5A B3 !# 7 ! 5 9!. 5A B3 9! < 5:< !#. 3 9! !# # 3.. 3 2! 7! 3 # E 3 93 6 C#3. B3 25 ! 93 5. ! !66 959! 9!. 5:43# 736 9! 9! ! A B3 5 37C 5 !6 ! 5: = 5936 !7 9! ! 5#!# # 36 37 5#. := 5#. 5# 5 !# @ 6 56. :5# !6 # !5: 959!. 9! !:! 5A B3.. 6 5: = 5A B3.. # 5:. . 6! 63#57! 3 # !73 3. 739!:36 9 4 5 6. !# 5A B3. !9 A B3. 3# # !A B3 9! !# # 36.

(7) 3. 39. ;237 2! 73# !. :!5#. 2! 73# !. 5. # ! 5!. 84# 5. 9! 3# 2! 75 8. ":!66 46 25 ! # ! ! !9 5 2 6 25 9 3 78 57 :8 . 25 +6 8 3. 3# 2! 6. 2!: !9 7! $ # ! 25# 4! 78"5 !#!6& ;2! ; 62 3 25 + #6 6. 3# 5 9 5 !. ! 3; 5 9. # !. 2!8# 5 :3; "85:;58 6 "! 4 2!# ! ;2!. 3# ! 25 5 6 4:! !# 63 . 2! 256 "!! 5. 3# 2# 3 42 2 6 :3 4 # 3 !66. 2!. 6 5:7 !66. # ! :!. 3 .5 9!. 2!8. 5::!9. ::5#3 6 # ! 42 5 9. 3 # 54!7!. 25 ! ! 5":!9. 7! 3 6!! 78;3# + 2# 3 42 3 2! ! 9 # 3 * +. 789!5#6 5 9 4 95. !. 23 !. !# 63# # ( 9 2 %!: !# . ; 62 6. 5 # ! 588 3. 3#8 3 #6. ; 62 3 25 + # :!* 5 9# 3 ;3# :9 3. # !# 8 . ;23. 637! ;58. 2!. 3756. # !. # 6 3 ! !9 78!8 !6 3 2! 5 # 5. 573 6!5 >.. !# 3 ! 6 4 !57.. 9# !56 %! 7. 5 9. 9# !5. : !# # 6 2. 3:= .. 65. !. 2.. ;56 5 4# !5 !> !#! (3B 3. 3# !# 55 9. 2!. 9 3#. ! 3 ;3# +; 2 2!6! ! * 38 5":! !3 :! 2#6 5 I 77!# 3#. !6!5#2. # 3. !#57". 3. ). , 3. 2!. 37. # 5. 56 6.. 95 :8: !. 6 ! 5::8 . ;3 :9 : +! 3 25 +. 5: 5":! 6 44!6 3 6 3# 2! 7 :!7! 5 3 3. ; 62 3 25 + 5:63 78 3::!54 !6 !#. 2! !. ! ;3# + 45 9. !. ! !#3. 3 78 #! 96. 5:;58 6# !7!7"!#5 9 2 +5"3. 8 3. 2!. !:! 377 !9!# 5:. 3# 4 ! 7!. 5 3 6 !# 6 83. 93 D+!!. 2 56 ;!:: 56 623 :9 3 2! 7!7"!# 6 3 2! 377 !!. 25 +8 3 25 +6 3. 3. !. ;3 :9 : +! 3 25 + 2!7 3# 2! #. 3#5 9 #! 962 . 56 ;!:: 56 3 2!# 6 5 2 6 37 5 8 3#2! #+ 9!6 2!:. 3. !. # 5: # !5: 8 . 3#2! 5:+6 5 9 2 6 # 5: 377! 6 ; 62 3 25 + 2!. 6. 3#. !# !:8 3 25 + 2! 59. 9!9 2 6 # !6!5#2. .. <.. 3#2! !!9"5 +. 5 9 !# 3 ! 6 4 595# 68 6 !7! 7". 25. 5# 5::8.

(8) LIST OF FIGURES ____________________________________________________________XIII LIST OF TABLES _____________________________________________________________ XVI ACRONYMS AND ABBREVIATIONS ___________________________________________ XVII CHAPTER 1. INTRODUCTION _________________________________________________ 18. 1.1. STATEMENT OF THE PROBLEM ________________________________________________ 18. 1.2. RESEARCH OBJECTIVES ______________________________________________________ 19. 1.3. RELEVANCY _______________________________________________________________ 19. 1.4. THESIS OUTLINE ____________________________________________________________ 20. CHAPTER 2. REMOTE SENSING: CONCEPTS AND ISSUES _______________________ 23. 2.1. INTRODUCTION TO THE CHAPTER______________________________________________ 23. 2.2. REMOTE SENSING CONCEPTS _________________________________________________ 23. 2.2.1. INTERACTION BETWEEN RADIATION AND TARGET ________________________________ 27. 2.2.2. REMOTE SENSING SENSORS __________________________________________________ 32. 2.2.2.1. The Radar_______________________________________________________________ 33. 2.2.2.2. The Synthetic Aperture Radar _______________________________________________ 38. 2.2.2.3. The Interferometric Synthetic Aperture Radar __________________________________ 40. 2.2.3 2.3. INTERFEROMETRIC SYNTHETIC APERTURE RADAR PROCESSING ______________________ 44 FINAL REMARKS ____________________________________________________________ 48. CHAPTER 3. DIGITAL ELEVATION MODELS ___________________________________ 49. 3.1. INTRODUCTION TO THE CHAPTER______________________________________________ 49. 3.2. CONCEPTS OF DIGITAL ELEVATION MODELS ____________________________________ 49. 3.3. CHARACTERIZING A DIGITAL ELEVATION MODEL ________________________________ 50. 3.3.1. NON-SPATIAL DIGITAL ELEVATION MODEL CHARACTERIZATION ____________________ 50. 3.3.1.1. Moment Statistics_________________________________________________________ 50. 3.3.1.2. Accuracy Statistics________________________________________________________ 51. 3.3.2. SPATIAL DIGITAL ELEVATION MODEL CHARACTERIZATION _________________________ 52.

(9) 3.3.2.1. The Variogram ___________________________________________________________ 52. 3.3.2.2. Spatial Autocorrelation ____________________________________________________ 52. 3.4. ERRORS IN DIGITAL ELEVATION MODELS ______________________________________ 52. 3.4.1. GEOMETRIC DISTORTIONS ___________________________________________________ 54. 3.4.1.1. Slant Range Scale Distortion ________________________________________________ 54. 3.4.1.2. Relief Displacement_______________________________________________________ 55. 3.4.1.3. Foreshortening ___________________________________________________________ 55. 3.4.1.4. Layover ________________________________________________________________ 56. 3.4.1.5. Shadow_________________________________________________________________ 57. 3.4.2. IDENTIFYING AND REDUCING ERRORS IN DIGITAL ELEVATION MODELS _______________ 57. 3.4.3. QUANTIFYING ERRORS IN DIGITAL ELEVATION MODELS ___________________________ 59. 3.4.3.1. Root Mean Squared Error __________________________________________________ 59. 3.4.3.2. Error Maps ______________________________________________________________ 60. 3.4.3.3. Simulation Methods _______________________________________________________ 60. 3.4.3.4. Visualization Techniques___________________________________________________ 60. 3.4.3.5. Random Fields ___________________________________________________________ 61. 3.5. FINAL REMARKS ____________________________________________________________ 62. CHAPTER 4. VISUALIZATION, INTERACTION AND EDITING ____________________ 64. 4.1. INTRODUCTION TO THE CHAPTER______________________________________________ 64. 4.2. VISUALIZING DIGITAL ELEVATION MODELS _____________________________________ 64. 4.2.1. TWO-DIMENSIONAL INTERFACES ______________________________________________ 64. 4.2.2. THREE-DIMENSIONAL INTERFACES ____________________________________________ 68. 4.3. INTERACTION IN THREE-DIMENSIONAL INTERFACES ______________________________ 70. 4.4. EDITING METHODS __________________________________________________________ 72. 4.4.1. SELECTION METHODS _______________________________________________________ 72. 4.4.2. EDITING METHODS _________________________________________________________ 73. 4.4.2.1. Cut And Paste Editing of Multiresolution Surfaces_______________________________ 73. 4.4.2.2. Point-Based Surface Editing ________________________________________________ 74. 4.4.2.3. Image Editing Methods ____________________________________________________ 75. 4.5. FINAL REMARKS ____________________________________________________________ 76. CHAPTER 5. VIRTUAL REALITY INTERFACES APPLIED TO ENHANCE DIGITAL. ELEVATION MODELS__________________________________________________________ 78 5.1. INTRODUCTION TO THE CHAPTER______________________________________________ 78 >.

(10) 5.2. PROBLEM STATEMENT _______________________________________________________ 78. 5.3. METHODOLOGY: VIRTUAL REALITY INTERFACES APPLIED TO CORRECT ELEVATION. ERRORS IN INSAR DIGITAL ELEVATION MODELS _____________________________________ 79 5.3.1. VISUALIZATION OF DIGITAL ELEVATION MODELS _________________________________ 80. 5.3.2. INTERACTION IN THE VIRTUAL ENVIRONMENT ___________________________________ 80. 5.3.2.1. Two-Dimensional Interaction _______________________________________________ 81. 5.3.2.2. Navigation ______________________________________________________________ 81. 5.3.2.3. Object Manipulation ______________________________________________________ 82. 5.3.2.4. System Control___________________________________________________________ 82. 5.3.3. ANALYSIS OF DIGITAL ELEVATION MODELS _____________________________________ 82. 5.3.3.1. Histogram_______________________________________________________________ 83. 5.3.3.2. Profile__________________________________________________________________ 84. 5.3.3.3. Statistical Information _____________________________________________________ 84. 5.3.3.4. Position and Height _______________________________________________________ 85. 5.3.3.5. Minimum and Maximum Values _____________________________________________ 85. 5.3.4. EDITING OF DIGITAL ELEVATION MODELS _______________________________________ 86. 5.3.4.1. Selecting Regions Of Interest _______________________________________________ 86. 5.3.4.2. Removing Dummy Values__________________________________________________ 86. 5.3.4.3. Removing Error Values ____________________________________________________ 87. 5.3.4.4. Interpolating Holes________________________________________________________ 87. 5.3.4.5. Smoothing ______________________________________________________________ 87. 5.3.4.6. Modifying Minimum and Maximum Height Values ______________________________ 90. 5.4. SOME CONSIDERATIONS _____________________________________________________ 91. 5.5. FINAL REMARKS ____________________________________________________________ 91. CHAPTER 6. DEMEDITOR: A VIRTUAL REALITY BASED SYSTEM TO VISUALIZE,. ANALYZE AND EDIT DEMS ____________________________________________________ 93 6.1. INTRODUCTION TO THE CHAPTER______________________________________________ 93. 6.2. INTRODUCING THE DEMEDITOR ______________________________________________ 93. 6.3. SYSTEM ARCHITECTURE _____________________________________________________ 96. 6.3.1. PRESENTATION MODULE ____________________________________________________ 96. 6.3.2. REPRESENTATION MODULE __________________________________________________ 99. 6.3.2.1. Digital Elevation Model Representation _______________________________________ 99. 6.3.2.2. Icons __________________________________________________________________ 103. 6.3.2.3. Interaction Components ___________________________________________________ 105. 6.3.2.4. Navigation Components___________________________________________________ 108 >.

(11) 6.3.3. ANALYSIS MODULE _______________________________________________________ 109. 6.3.3.1. Histogram______________________________________________________________ 110. 6.3.3.2. Profile_________________________________________________________________ 111. 6.3.3.3. Statistical Information ____________________________________________________ 113. 6.3.3.4. Position and Height ______________________________________________________ 114. 6.3.3.5. Minimum and Maximum Values ____________________________________________ 114. 6.3.4. EDITING MODULE _________________________________________________________ 115. 6.3.4.1. Selection_______________________________________________________________ 115. 6.3.4.2. Interpolation____________________________________________________________ 116. 6.3.4.3. Cut ___________________________________________________________________ 117. 6.3.4.4. Smooth ________________________________________________________________ 118. 6.3.4.5. Definition of Minimum and Maximum Height Values ___________________________ 119. 6.4. IMPLEMENTATION ISSUES ___________________________________________________ 120. 6.4.1. A HIGH-RESOLUTION VIRTUAL ENVIRONMENT __________________________________ 120. 6.4.2. PERFORMANCE ___________________________________________________________ 120. 6.4.3. REALISM ________________________________________________________________ 121. 6.4.4. INTERACTION IN THE VIRTUAL ENVIRONMENT __________________________________ 121. 6.4.4.1. Navigation Strategies _____________________________________________________ 121. 6.4.4.2. Object Manipulation _____________________________________________________ 122. 6.4.4.3. Interaction Icons_________________________________________________________ 122. 6.5. FINAL REMARKS ___________________________________________________________ 123. CHAPTER 7. USING THE DEMEDITOR ________________________________________ 124. 7.1. INTRODUCTION TO THE CHAPTER_____________________________________________ 124. 7.2. DATA DESCRIPTION ________________________________________________________ 124. 7.3. EXAMPLES OF USE _________________________________________________________ 124. 7.3.1. REALISTIC DIGITAL ELEVATION MODEL VISUALIZATION __________________________ 125. 7.3.2. USER X DIGITAL ELEVATION MODEL: INTUITIVE AND EFFECTIVE INTERACTION ________ 126. 7.3.3. DIGITAL ELEVATION MODEL EXPLORATION THROUGH NAVIGATION _________________ 126. 7.3.4. 2D EDITING METHODS APPLIED IN A 3D ENVIRONMENT___________________________ 127. 7.4. THE DEMEDITOR SYSTEM: EFFECTIVE OR NOT? _______________________________ 128. 7.5. FINAL REMARKS ___________________________________________________________ 130. CHAPTER 8 8.1. CONCLUSION ___________________________________________________ 131. CONTRIBUTIONS ___________________________________________________________ 131 >.

(12) 8.1.1. A METHODOLOGY TO ENHANCE DIGITAL ELEVATION MODELS _____________________ 131. 8.1.2. THE DEMEDITOR SYSTEM __________________________________________________ 132. 8.1.3. THREE-DIMENSIONAL INTERFACES ___________________________________________ 133. 8.2. FUTURE WORKS ___________________________________________________________ 133. 8.2.1. IMMERSIVE AND AUGMENTED VIRTUAL REALITY INTERFACES _____________________ 133. 8.2.2. EVALUATION OF INTERFACES AND INTERACTION TECHNIQUES______________________ 134. 8.2.3. AUTOMATIC ERROR IDENTIFICATION __________________________________________ 134. 8.2.4. REPRESENTATION OF DIGITAL ELEVATION MODEL ERRORS ________________________ 134. 8.2.5. QUANTIFICATION OF DIGITAL ELEVATION MODEL ERRORS ________________________ 134. 8.2.6. EDITING METHODS ________________________________________________________ 134. 8.2.7. COLLABORATIVE EDITING OF DIGITAL ELEVATION MODELS _______________________ 135. 8.2.8. SCENE MODELING IN THE DEMEDITOR ________________________________________ 135. 8.2.9. OTHER APPLICATION AREAS ________________________________________________ 135. 8.3. CLOSING THOUGHTS _______________________________________________________ 136. REFERENCES ________________________________________________________________ 137 BIBLIOGRAPHY _________________________________________________________________ 137 ADDITIONAL REFERENCES _______________________________________________________ 142 APPENDIX CLASS DIAGRAM __________________________________________________ 147. >.

(13) !! FIGURE 1: THE SEVEN ELEMENTS THAT COMPRISE THE REMOTE SENSING PROCESS. _____________ 24 FIGURE 2: WAVELENGTHS. _________________________________________________________ 25 FIGURE 3: THE ELECTROMAGNETIC SPECTRUM. _________________________________________ 26 FIGURE 4: THE MICROWAVE REGION. _________________________________________________ 26 FIGURE 5: ENERGY INTERACTING WITH THE ATMOSPHERE: A) SCATTERING; B) ABSORPTION. _____ 27 FIGURE 6: FORMS OF INTERACTION BETWEEN RADIATION AND TARGET.______________________ 28 FIGURE 7: SURFACE REFLECTION: A) SPECULAR REFLECTION; B) DIFFUSE REFLECTION. _________ 28 FIGURE 8: LOOK DIRECTION OF THE SENSOR: A) WEST-EAST DIRECTION; B) EAST-WEST DIRECTION. 30 FIGURE 9: A TYPICAL SENSOR SYSTEM. _______________________________________________ 31 FIGURE 10: REMOTE SENSING SENSORS: A) PASSIVE SENSOR; B) ACTIVE SENSOR. ______________ 32 FIGURE 11: SCENES IMAGED WITH DIFFERENT WAVELENGTHS: A) X-BAND; B) P-BAND. _________ 34 FIGURE 12: IMAGING GEOMETRY OF A RADAR SYSTEM.___________________________________ 36 FIGURE 13: RESOLUTION: A) RANGE RESOLUTION; B) AZIMUTH RESOLUTION. _________________ 37 FIGURE 14: THE SAR METHOD. _____________________________________________________ 38 FIGURE 15: IMAGING GEOMETRY OF A SAR SYSTEM. ____________________________________ 39 FIGURE 16: REFLECTIVITY OF A RESOLUTION CELL.______________________________________ 39 FIGURE 17: IMAGING PRINCIPLE OF A SAR SYSTEM. _____________________________________ 40 FIGURE 18: IMAGING PRINCIPLE OF AN INSAR SYSTEM. __________________________________ 41 FIGURE 19: PHASE DIFFERENCE OF TWO ELECTROMAGNETIC WAVES. ________________________ 41 FIGURE 20: AN INTERFEROGRAM.____________________________________________________ 42 FIGURE 21: COHERENCE OF AN IMAGED SURFACE: A) COHERENCE SCENE; B) X-BAND SAR SCENE. 43 FIGURE 22: 2D AND 3D VIEWS OF THE TERRAIN HEIGHT.__________________________________ 43 FIGURE 23: MEASURE PRINCIPLE OF AN INSAR SYSTEM. _________________________________ 44 FIGURE 24: INSAR PROCESSING CHAIN. _______________________________________________ 45 FIGURE 25: RESULTS PRODUCED BY DIFFERENT STEPS OF AN INSAR PROCESSING CHAIN.________ 47 FIGURE 26: SLANT RANGE SCALE DISTORTION. _________________________________________ 54 FIGURE 27: SLANT RANGE SCALE DISTORTION: A) SLANT RANGE IMAGE; B) GROUND RANGE IMAGE. 55 FIGURE 28: FORESHORTENING. ______________________________________________________ 55 FIGURE 29: RADAR IMAGE WITH FORESHORTENING EFFECTS. ______________________________ 56 FIGURE 30: LAYOVER._____________________________________________________________ 56 FIGURE 31: RADAR IMAGE WITH LAYOVER EFFECTS. _____________________________________ 57 FIGURE 32: RADAR IMAGE WITH SHADOW EFFECTS. _____________________________________ 57 TABLE 1: SYNTHESIS OF ERROR IDENTIFICATION, QUANTIFICATION AND REMOVAL METHODS. ____ 63 FIGURE 33: AN EXAMPLE OF DEM PRESENTED AS CONTOUR LEVELS. _______________________ 65 FIGURE 34: CONTOUR LEVELS OF A DEM. _____________________________________________ 66.

(14) FIGURE 35: GRAY LEVEL VISUALIZATION OF A DEM. ____________________________________ 66 FIGURE 36: PERSPECTIVE VISUALIZATION OF A DEM. ____________________________________ 67 FIGURE 37: COMPOUND VISUALIZATION OF A DEM. _____________________________________ 68 FIGURE 38: 3D SURFACE MODEL GENERATED FROM DEM DATA. ___________________________ 69 FIGURE 39: SURFACE VISUALIZATION USING THE KINETIC VISUALIZATION TECHNIQUE. _________ 70 FIGURE 40: BOUNDARY DEFINITION WITH INTELLIGENT SCISSORS. _________________________ 73 FIGURE 41: SELECTION: A) IMAGE OF A BIRD; B) REGION DEFINITION WITH INTELLIGENT PAINT. __ 73 FIGURE 42: CUT AND PASTE ALGORITHM FOR EDITING OF MULTIRESOLUTION SURFACES. ________ 74 FIGURE 43: EDITING OF A POINT-SAMPLED OBJECT: CARVING. _____________________________ 74 FIGURE 44: OBJECT-BASED IMAGE BENDING. ___________________________________________ 76 FIGURE 45: CONTRAST ENHANCEMENT USING THE LINEAR STRETCH METHOD. ________________ 84 FIGURE 46: THE MEAN FILTER: A) ORIGINAL IMAGE; B) IMAGE SMOOTHED WITH A MEAN FILTER. _ 88 FIGURE 47: ILLUSTRATING THE FUNCTIONING OF A MEDIAN FILTER._________________________ 89 FIGURE 48: MEDIAN FILTER: A) ORIGINAL IMAGE; B) SALT AND PEPPER NOISE; C) SMOOTHED.____ 89 FIGURE 49: A GRAPHICS OBJECT TREE.________________________________________________ 95 FIGURE 50: THE ARCHITECTURE OF THE DEMEDITOR. ___________________________________ 96 FIGURE 51: THE PRESENTATION MODULE. _____________________________________________ 97 FIGURE 52: THE 2D INTERFACE OF THE DEMEDITOR. ____________________________________ 98 FIGURE 53: THE 3D INTERFACE OF THE DEMEDITOR. ____________________________________ 99 FIGURE 54: THE REPRESENTATION MODULE. ___________________________________________ 99 FIGURE 55: THE DEM SURFACE RENDERED AS A WIRE MESH OBJECT. ______________________ 100 FIGURE 56: ZOOMED 3D SURFACE.__________________________________________________ 101 FIGURE 57: COMPOUND VISUALIZATION OF A DEM IN THE VIRTUAL ENVIRONMENT. __________ 102 FIGURE 58: THE DEM WRAPPED WITH ITS AMPLITUDE PICTURE. __________________________ 103 FIGURE 59: ZOOMING THE SURFACE USING A ZOOM BOX ICON. ____________________________ 104 FIGURE 60: INTERACTION MENUS: A) MAIN MENU; B) DISPLAY WINDOW; C) ZOOM WINDOW. ____ 106 FIGURE 61: INTERACTING WITH THE DEM THROUGH THE ZOOM TOOL. _____________________ 106 FIGURE 62: INTERACTING WITH THE 3D ENVIRONMENT: A) OPTIONS MENU; B) EDITING MENU. __ 107 FIGURE 63: SPOTLIGHT: A) UNSELECTED; B) SELECTED/TRANSLATION; C) ROTATION; D) SCALE. _ 108 FIGURE 64: THE NAVIGATION TOOLBAR. _____________________________________________ 109 FIGURE 65: THE ANALYSIS MODULE. ________________________________________________ 110 FIGURE 66: THE ZOOM WINDOW AND ITS CORRESPONDING HISTOGRAM. ____________________ 110 FIGURE 67: SELECTING THE WINDOW WHERE THE PROFILE LINE WILL BE DRAWN. _____________ 112 FIGURE 68: PROFILE: A) DRAWING THE LINE; B) VIEWING GRAPHICALLY THE HEIGHT VARIATIONS. 112 FIGURE 69: OBTAINING STATISTICAL INFORMATION ABOUT A DATASET. ____________________ 113 FIGURE 70: THE POSITION AND HEIGHT VISUALIZATION WINDOW. _________________________ 114 FIGURE 71: THE EDITING MODULE. __________________________________________________ 115 >.

(15) FIGURE 72: SELECTING A ROI IN THE VIRTUAL ENVIRONMENT. ___________________________ 116 FIGURE 73: INTERPOLATING THE DATA CONTAINED IN A ROI. ____________________________ 117 FIGURE 74: CUTTING OUT THE ROI. _________________________________________________ 118 FIGURE 75: THE VIRTUAL DEM SMOOTHED WITH A MEAN FILTER. _________________________ 119 FIGURE 76: MODIFYING THE MINIMUM HEIGHT VALUE OF THE DEM: A) BEFORE; B) AFTER._____ 120 FIGURE 77: VISUALIZING A DEM: A) 2D GRAYSCALE IMAGE; B) 3D SURFACE OBJECT._________ 125 FIGURE 78: ENHANCING REALISM AND COMPREHENSION: A) COLORS; B) COMPOUND VIEW._____ 125 FIGURE 79: INTERACTIVE EDITING: A) ORIGINAL DEM; B) DEM WITH LOWER MAXIMUM VALUE. 126 FIGURE 80: REMOVING DUMMY VALUES: A) ORIGINAL DEM; B) DEM WITHOUT HOLES. _______ 127 FIGURE 81: CUTTING OUT ERROR AREAS: A) A ROI IS DEFINED; B) THE DATA ARE CUT OUT._____ 128 FIGURE 82: INTERPOLATING AND SMOOTHING: A) ORIGINAL DEM; B) EDITED DEM. __________ 128. >.

(16) ! TABLE 1: SYNTHESIS OF ERROR IDENTIFICATION, QUANTIFICATION AND REMOVAL METHODS. ____ 63.

(17) ". # 4 5: :! 5 3 # 5: !5: 8. # $. 2# !!. %. ;3. 7! 6 3 5: 7! 6 3 5:. 8 2!. !# # ! 595#. !43. !# !6. 42. !!. 3. 9 5 44. !5:. !# # ! 595#. !#!# 37! # 8 2!. &. 4 5: # 3. #. '. 9. 39!:. 4 5:. 39!:. #5 !. 3!. !. 3. 33. !5. 5#5 3 < 5# !9 # # 3#. 55. 4 3# 4 5: :! 5 3. !# 5 # ( #. !# # ! 595#. 39!:. 4 5: !# # 5. !34# 5 2. #. 39!:. 3# 75 3. 39!:6. 8 6 !7. ! 5 5 5 4 54!. # 3 7!. 3# 6 5: = 4 754!6. !59. 3. !9. # # 3. 9. # !!. 6 :58 # 5: !5: 8. # 5: !5: 8 39!: 4 5 4 54! "* !. 56!9 754! 9. 3 5. 7"!#. ! !:. !5:. 3"3445 !9 !43 6 3. 4. 7 :5 !9 :5 !5 6.

(18) (. 2! 6 "* ! 3 !9. 2 6 2!6 6 6 ! 25. 45 9 2! 3# # ! 3 3 !# # 3# 6. 2! 9! :38 7! 5. 3 9!6+3. : 5 3 6 25. "! 5 6! 3. 5 9. !. !# 5. 6 :: 2!# ! 5# ! 3 ! 2. # # 3# 9!. 5 3. 6. 7!. !# 5. ! !. 5. "!. 3 6 4339 ! 3 42 3# 3. 4# !73 !. 377!# 5: 63:. !!9 3 599# !66 9 !# !. 3 6. 8 !6 3. ;58 . 65":! "8!> !#. 6!# 6.. 3# 9!# 3. 3. 5# !. # !6! !9. !9 "89!6 #" 4 6 3 #". !6. 56. 65. !# 96. 3::3; 4 3. !6. # 37 2 6. 2!. 3 6 3 2! # !73 ! 6! 6 45 9. : 5# 8;3# +. 5::8 . 2! 6 #. # !3. 26. ! (. 6 5# !. " 6 !66 5. 6!9 3#75. 739!:6. !# # 3# 6L. 3. . /001?. 6 #! 5: !. !:! 5 3 95 5. 5. 2! !>5. 6. . MNNOP. 25 !. # # 3# 6 9!. !6 : 6 3 5 ; 2 !> !#!. 6 9!# !9 # 37. !#5. : 9! ". 95#!6. 5 9 #94! 9! ! :7 5 3 6. 5 9. 5# ! 3. 3 5. !9 56 2! 9! 5# # ! 3 5 7!56 # !7! 4! !# 5:. 6 5 5: 95 56! 6. 6 !. 2! :5 +3 + 3;:!94! 5"3. !9 9 # 4 2 6 2!6 6 9! !:3 7!. 6!# 6 6 44!6. 85 9 # !73 ! !# # 3# 6. 3 63: 95 !9 7! 2393:34!6 25 5# !5. 6. 739!: 4.. 5::8 26. 8 . ;2 2 6 5 7!56 # ! 3 ;25 6 3 + 3;. 3# 75: 6 #!8 3 9 !9. 2!# !. 5 # ! 5 9 :3 5 3 3 !# # 3# 6. 3 "! # ! 6!:89! !# 7 !9. !# # 3# 6 5 5: 95 5 # !6 : 6. 8 . <5. 4 # 39. 3 3 # 6. 6259!9 # !: ! . ;5 !# 62!9 "3. 3 34# 5 28 .. 75 8 8 !6 3 4!34# 5 2. 6 5: = 5 3 . 28 9# 3:34 739!: 4. !# # 5. : 5 3 6 5 9 :5 9 6! :5. 3 : 7 !9 3 !:! 5 3. 9!. # 3 7! 6 25. 6 # !6! !9. 5 5:8 6!6. 3 5. 4. 3#9! !:3. 66!9 3#637!. 6 5# ! 739!:6 3 2! !:! 5 3 6 #5 ! 5 9 5# ! 6!9. # 37. 3. 3 6. 2! # 3":!7 2 6 2!6 6 5 76 3 # !63: ! 5 9 2! 3"* !. 2 6 ;3# + 6 *6. )* ). 6. ,. 6 256 "!! 9 6. 7! 2396. !. # 3 36 4 5 63:. # 5: # !5: 8 377 93. # 5: # !5: 8). 6. 25 ; :: "! 3::3;!9 83. 6. 2! " 4 25::! 4! 6 3 9! !:3 7! 2393:34!6 5 9 33:6. !5 9!. 2! 3::3; 46! # !:! 5. 5: 63:. 5 9 3# # ! 3. 5. ! 2 42 < 5: 8. 5 9. 2!7 5 9K 3# 58 3# 2!7 5 9. !# # 3# . 3#4 5 !9 "89 !# 6! 5 6!6 !. !3. 6, 2# 3 42. ! 2# !! 9 7! 6 3 5: )J , # !6! 5 3 3 95 5. 2! 3# # ! 3 3 !# # 3# 6. 6! 6 4 37 5 !6 3 7 :!7! 5 5 :5":!. 77!# 6 !. # !56 4:8"! 37 45 5 # 5. 6 5" : 8 3 " :9 :3; 36 # !5: 6. 8 !5# 6 3;. ". # 39. 49 4 5: !:! 5 3 739!:6 ). 2!6! 739!:6 6 4 3. 6. !!9 # !5: 6. := !9 5 # 366 ! !# 83. 3 ! 25. ). 25. 2! 7! 2396 6!9 "8 2! 377. 6 5# ! 5663#!9 : !9 3. 2# 3 42 2!. 2!# ! 93. 3 5. 95 5 3 599# !66 # 3":!76 3. 83. !5# 3 "! 3# # !. 4.

(19) !# # 3# 6. ! 6 3 6 5"3. 23; 3 75 54! !# # 3# 6. ! !#2!:!66. 2! 6 #!86 44!6 6 25 9!. 8 . <5. 6 5: = 5 3 7! 2396 5 9. 26 3 5 !# 5. ; 2. 6!# 6. 5#3 6 7! 2396 3. ;3 9 7! 6 3 5: )/ , 33:6. 6!# 6. 5 68 6 !7. # 3 9 4# !5: 6. 33:6. ;!:: + 3; 5 5:8 66. 6 6 !!9!9 "8 2! 377. 2 6 2!6 6 599# !66!6 2!. 9 5:. !5#3 "! # 8 43. 6. "56!9 3. ! !> :3# 5 3. 4 33:6 3 3# # ! !# # 3# 6. 6. 6!# 65. 85 9 # !73 ! !# # 3# 6 # 37. 3# 9 4 3 2! !!9"5 + 3 !9. 2! 95 5 5# ! 759! "8 9. !!9 3 9! !:3. 3 65 9. 8. 7! 2393:34!6 25 9!5: ; 2 !# # 3# 6. 7! 2393:348 5 9 5 33: 3# 3# # !. 4 !# # 3# 6. 6 ; :: "! 9!. !9 5 9. 7 :!7! !9. )* %. (. 2! 3"* ! •. +. #. !6 3 2 6 # !6!5#2 5# !'. 3 9! !:3 5 7! 2393:348 3 3# # ! !#5 !6 3. !:! 5 3 !# # 3# 6. 6 5: = !. !> :3# !. 5 5:8 = ! 5 9 !9. !# # 5. •. 3 9! !:3 5 68 6 !7. 5::!9. •. 3 5: 95 ! 2! 7 :!7! !9 7! 2393:348 . 6 4 2!. 6. "56!9 3. 2! 6! 3 J. 739!:6?. 9 3# . 25 7 :!7! 6 2! # 3 36!9 7! 2393:348 ? 9 3#; 2. 6 "56!9 3. # !5: ;3# :9 95 5. )* $. #. ". # # 3# 6 5# !5 5. 6 5 5: 95 5. !#5. 85663 5 !9 ; 2 2! 95 5 "! 5 3. !#5. 85# ! 9!. !9 5 9 # !73 !9. !# # 3# 6 5 "! 5 6!9 "875 89 !# ! 9!. !: 5":! 5 9 5: 9 6! 3 !:! 5 3 95 5 # !< # !6 25. 5 3. 5 9 3# # ! 3. 26 # !6!5#2. !. # 3 9!6. 3;! !# . 5 # 5: # 3":!7 6 2! 5 # !563 6 3#!5 2 4! !# 5 !9. !# 89. 6 2# 3 42 5 6 7 :! 5 9 !. :. 6!# 6 ; 2 5. !9. 4 2! 7! 2393:3489! !:3 !9 5 9. !9. 4# 3 !9 # !6.. 3 26# !6!5#2 5 "! ! 5. 4; 9! # 5 4 4!# # 3# 6 6!# 6. !56 :85 !66 ":! 7! 239 3 # !9. ! !# # 3# 6. !#5 !6 3# 6 5: = 5 3 . !> :3# 5 3 . 5 5:8 665 9 := !9. 26 # !6!5#2 5. 3 2! 3# # ! 3 3 !# # 3# 6 !#3# 7!9. # 39. 2!6!. !# 63. "! 5. : !9 3 3 2!#. 26# !6!5#2. !6 : 6. 6 56 ;!:: 56 ! 9 6!# 6. ;2 2 ; :: "! 37! 73# !. # 5 ! !:! 5 3 739!:6 2! 5. 5. ! 2396 3# 3# # !. 25. . ;25 75+!6 2! #. # 3 !9 # ! 5# ! 3 # !59 :85 5 :5":! 3. !:! 5 3 739!:6 2# 3 42 2! 6! 3 J 599 3. !9 3#5 9 25 2! !# # 3# 6# !6 3 6 ":! 3# 2 6. : 5 3 # 3":!7 3. : 5" : 83. 3. 77!# 6 !. !#5 !6 3 2! # !73 ! 6! 6 4 !:9 3. 6 5:63 2 42: 42 !9. 3 3 :8 3 !#3# 7 3# # !. 6! 6 4 377. 4!:! 5 3 !# # 3# 6. 6. 6 5: = 5 3 ." 26# !6!5#2. 85 # 3 !66 3 5: 33: 9! !:3 !9 3#!> !#!. 5:63 3 5. # 35 2 2! # !5:. ! 96 3 3 !# 3 2! # !73 ! !9. 6!# 6 3. 6 5: = !5 9 MN.

(20) !> :3# ! :5# 4! !# # 5. 739!:6. 5 5:8 = ! 2! 95 5 6 4;!:: !6 5": 62!9 5 5:8 66. !9 !:! 5 3 739!:6. 3# 9!#3 # !73 ! 2! #!# # 3# 6. 2 6 2!6 6 9 !# 6 # 37 # ! 3 6# !:5 !9 •. 3 # ! 3 6 3. 9!. !. !. 3 6. 5 9. !6 45 3 6. !6 45 3 6 25 ! # 3 9!9 5 68 6 !75. 8 45 9 3# # !. 2! 3::3; 4;58 6'. 7! 239 3#599# !66 4 2! # 3":!7. 4; 9! # 5 4 4!# # 3# 6. # 3 !9 # !. "56!9 3. 6 2# 3 42 5. 2! + 3;:!94! 3 !> !#!. !9. ! 5 9. 6!# 6 5 9 5. :8 4 J. !#5 !6? •. 3 3 2!#6 9 !6 25 ! 7 :!7! !9 5 37 :! ! 33: 3 9! 6 25 6 5 !66 ":! 3 75 8. 6!# 6 #3#3 2 6. 3 6 7 : 5 !3 6:8 6 5: = ! 5 9 !> :3# ! 5 •. # 5 8 . 5 9 !9 !# # 3# 6. 9!6+3. •. 2! !:! 5 3 95 5. "3 2.. 6 5: = 5 3 5 9. !# 5. 5:63 3 6 ! 5: = !9 5 5:8 66. 6! !# 5: 5 5:8 6 6 5 9 !9 2!6 6. "56!9 3. 3. 37 3 ! 6. !. 3 6 5 9 63 2 6. # !< # !7! 6 3. # !< # !7! 6. 3#6 !. 63 2 6. 7 :!7! !9. !> !#. 5 !9. 8 . 37 36!9. : 5# 3 2 6 + 9 3. 5 !9 !9. 25 ! !#5 !.. 47! 2396? 2! 68 6 !7 9! !:3 !9 "8 2 6. 6!# 6. 2!6!. 33:6 25 ! "!!. 377!# 5: 33:6 5 9 595 !9 3. # !. : :: 2!6!. (. # !9 3#5. 5 9 9!6 #" 4 2! # 3 365: !# # 3# 6. 6 ;56. 3 2 6 93. 7!. # 39. # 35 2 4 2! 3. 5 :34 5: 562 3. !9 5 9 2! 3"* !. !73 ! ! 6 4' 3. # !73 ! 6! 6 4. ;2 2 # ! # !6! 6 2! 5. # ! 6! 3 6 6 !9. 3::!. 495 5 5"3. 4# 5 3 5 9 3 # 3: 3. 6! 63# 6!:. 2 6 25 !# . 2! # 3":!7 3. !6 3 2! 2!6 6 ;!# ! 3 : !9. ! 6 5 9 66 !6. 9!6 #"!6 2! 75 : 5 3 5# !5 3. 3: !6 637! 6 ! 6. ;2 2 # !< # ! 2! 6! 3 63 2 6 2! # 3 !66 3. ! 6# !:5 !9 3 # !73 ! 6! 6 45 9 3# # !. 4. 2! # !75 9!#. 6 3# 45 = !9 56 3::3;6. 25 !# ;3.. # 39. 95 5. ". !9 5 9 9! !:3 !9 # 37 6 # 5 2. 2 6 2!6 6 6 6 #. # 39. ;3 5 9 2# !! 9 7! 6 3 6?. : !9 3# 6 5: = 5 3 3 !# # 5. 4 33:6 25 ! "!!. 7 :!7! !9 "56!9 3. )* '. 3# 9!# 3 !# 8 6. 6!9 3 9! !:3 5 37 :! ! 33: 3# 2! # !73 ! 6! 6 4 377. 3 3 :83 ". 9!#5+ 4 2!# ! ;!# ! 3 33:6. 6. 5 5:8 = ! 2! 95 5. !#5 !6 25 ! :5# 4!:8"!! 5. 3 "!!. 85 9 # !73 ! !# # 3# 6. 56 !. !# # 5. 2 6 2!6 6. 5 !9 9! 5# !5.. 3. ! 6 3. 3 4# !73 ! 6! 6 4. !6 5 9 37 :!> 5:43# 276. 3# 9!# 3 "! 6. !66 :. !!96 5. 2! :5 3# 7 25 23:96 2! 754 46! 63# .5 93. 2!. !# 2! 754 4 # 3 !66. 2! 3::! !9 # 5; 95 5 25 ! 3 "! # 3 !66!9 63 25 2 56 3#23# !. !9 68 2!. 2! 5:43# 276 25. )! 4. 9!7 : # 3 !66 6 2!. :!> 4. 73 3. 5 !# # ! # 595#). 37 36! 2! # 3 !66 4 25 37 ! 65 3 ,. , 754!6 5 9 5# ! "56!9 3. 3 2!#7 3#5. !# 5 3 "! ;!! !:! # 3754 !. # 59 5 3. 3. 6 5. "!. 37 :!> 7! 2396 2! # !73 ! 6! 6 4. 5 9 2! 5# 4!. 3 "! 754!9 /0.

(21) 2 6 6 "* ! 256 3 "! ! 4. 9!# 6 339 !# 8;!::. 63 25. 6 5 9 2! # 2!# !. 6 ! 5: 5 !. 3. ; :: "! 4 !. !#3# 7!9 # !45# 9 4 6. # 3 !66 6!9 3 3::! 5 9 5:63 2!. 3 2! !5 # !6 5 9. # !: 5":!. # 39. <5. .. 5 3. # ! 63. 5 9 # !9. 3. 6!9 3 "8 2 6 2!6 6. !> :3# ! :5# 4! 573. !:! 5 3. 7! 2396. !!9 3 "!. 6!9. # !:5 !9 ;3# +6. 5. 6 3 95 5. 2 56 9! 2. 2! 42 5 9. 25 !# 6 5: = 5 3 .. 3. !# 5. !# 5. 3. 5 3 . # 39. 3. !. 3. 5 9. 6 5: = ! 5 9. ! # !6! 5 3 6 3 ! 3 26 5 . J. : !9 "8 2 6 # !6!5#2 3 5 : 5 ! 2! 2! #75. 4 9. 59 5 54!6 3 !## 59 3 5: /. 6 5: = 5 3 . ; :: "! 9!6 #"!9. 2!. 47! 2396 ; :: 5:63 "! 9!6 #"!9. 26. ! 2 6 2!6 6 # 3 36!6 2! 3# # ! 3 3 !:! 5 3 !# # 3# 6 2# 3 42 2! 6! 3 !9 2! : !# 5 # !. # !6!5#2 ;3# +6 3. 6 )6 #!:6,. # !43 6 3. 6 #5 !6. "! # !:!56!9 56 5. 39!:6. 3 "! !# 8!. 5 9 # !5: 6. 3 5 9 9. .. 2!6! 6 "* ! 6. ; :: "!. 37 :!> 625 !6. 77!# 6 !, ; :: "! 6 9 !9 5 9 5. !#5 !6. ;2 2 5# ! 2 42. 33:6. 35. # 3 9! 5. 5::893 ! 5"3. 2!85:63 3 !# !# 8# !5: 6. 3# 75 3 !> :3# 5 3 5 9 5 5:8 66. 25 !# .3. 739!: 5. 3# 9!# 3. 2! 2 # 9 25 !# . 4 5: :! 5 3. 3"* ! 6 ; 2 !5 # !6 6 # 3 !66!6 3. 2! 42 !# # 3# 6 9 ! 3 2!. : !9 3 # 3 !66 2! # 5; 95 5. ! 3# ! 5. 37!. 2! 95 5. 5 9 5 5:8 6!6 5. 739!:6 3 5. !#5 !6 ) 77!# 6 ! 3# 3 , 25 ! # 3 !. !#5 !6 ) 3. 3 2!7. 566!6 2# 3 42 < 5: 8 3 # 3:6. 5 9 2!# ! 3# ! !# # 3# 9!. < 5: 8 37! 3 2! 736 7 3#5 3. :! 5 3. 2! 754!9 # !: !. # 3":!76 # !:5 !9. + 3;:!94! 5"3. 2! # 5; 95 5. 2! 7! 2396 5. 5 # ! 3. !9. !:! 5 3 !# # 3# 6 2! 3"* ! 3 6 983 2 6 # !6!5#2. 5. 25# 5 !#= 5 3 7! 2396 5 "! 6!9 3 3" 5 "!. # ! 6! 95 5 758"! # 39. 9. !# !6 ). 43 !# 5 3 6 3 "! 6!9. 6 3 6,.. !9. 47! 2396 "56!9 3. >!:6. 6 #5 !. 3 3 #:! !:6. 754!6. 754! 3"* ! 6 5 9. 9 !# !. :! !:6 5# ! 5:63 5. # 35 2!9' :3 !. "#62.. . 56 !. 73 !. 6 5:!. # 3 5 !. 6 # ! 2. "! 9. ;5#. 9!:! !. 6733 2. 5 9 :: 23:!6 !9 . 2! 5# !5 3. 4. !# !6 256 3 "! 6!:! !9? 6 9 !6 # !:5 !9 3 2! 6!:!. 3. 3# 9!# 3. 2!. >!:. 3"* !. 5 9 6 #5 ! :! !: ; :: 5:63 "! 9!6 #"!9 2!. 2 25 !# .. # 5:. !5: 8. !#5 !6. : !9 3. 39!:6. 9!6 #"!6 2! 7! 2393:3489! !:3 !9 3# 2 6 2!6 6 !#5 !6. ;2 2 5# ! 6!9 3 !#3# 7 65 6. 5: 5 5:8 6!6. 3# 9!#3 9!. 25 !#6 >. 9. . !# 5. 3. # !6! 6 2!. 25 !#6! ! . 2!. 9 3# 2! ! !. !. # 5:. 9. !5: 8 56!9 8 6 !7 3. 3 6 5 9 !9. :! 5 3. 2! 95 5. 56 ;!:: 56 2! 739!:6 6 5: = !.. 7 :!7! 6 2! 4 7! 2396. 4 5:. # 35 2 6 "56!9 3. 6 5: = 5 3 5 9 !> :3# 5 3 3. 9 3# . 5 68 6 !7 25. ! 2 < !6. 5 5:8 66. 7! 2393:3489!6 #"!9. 2! 5. 8!# # 3# 6. 5 9 3 !9 !# # 3# 6. 3. 9 3# ' 5. 25. 5:8 = ! 5 9. 6 5: = 5 3 25. 5 9. 37 36!. 2!. !9 5. :8 4. 2! # ! 3 6 25 !# 6 4 2!. 9 3# . # !5: ;3# :9 95 56! 6 5# ! ! 25. ! !66 3 2! 68 6 !7 6 !# !9. /M.

(22) 5::8 . 2! # 3 36!6. # !5. 25 !# 3. : 63. 2 42: 42 6 2!. 3 #". 3 6 3. 2 6 2!6 6 5 9. : 5 3 6 3#2! 7! 2396 5 9 9!56 9! !:3 !9 2!# !. //.

(23) (. %* ). (. 26. 25 !#. 6! 6 4 6 75. 3. %. (. ! 96 3 2 42: 42. 2! 5. ! 6 5# ! 9!6 #"!9. "!4. : 5 3. 9375. 3. 4; 2 2! 9!. 2 6 2!6 6' # !73 !. 3 3. 2! !# 7$ # !73 !. 6! 6 4& 3 4# !73 ! 6! 6 4. 3: !6 "56 5::86! ! !:!7! 6' ) , 2! ! !# 4863 #!. ) ,. 2! # !:5 3 "! ;!! # 59 5 3 5 9 5 736 2!# !. ) , 2!. !# 5. 3 3 2! # 59 5 3 ; 2 2!. 5# 4! . ) , 2! 6! 63# 6!9 3 !#3# 7# !73 ! 6! 6 4. ) , 2! # 5 67 66 3 . # ! ! # 3 !66 43 95 5 3::! !9 "8 2! 6! 63# . ) , 2! 95 5. 5 9 ) , 2! 5 5 2 3 !# 5. 3. : 5 3 3 26. !## ! 5 3 5 9 5 5:8 6 6 3 2! # 3 !66!9. 3# 75 3. 2!6! !:!7! 6 6 "#! :89!6 #"!9. # 3 !66 3 !:! # 3754 !. !#!# 37! #. 2 6 25 !# . 4. 4!7 256 6 3 2!. ;5 !6 ; 2 2! 5# 4! "! 46! 6!9. 5 9 2! 6! 3. 7 # 3;5 ! 6! 63# 6. 2 6 !7 256 6. 6 4!. # 6 :8 "! 5 6!. 7! 2393:348 # 3 36!9 "8 2 6 2!6 6. 56 ;!:: 56 2! 63 ;5# ! 9! !:3 !9 3 5 2 6 7! 2393:3485# ! "56!9 3 5:63 7 3#5 !5 # !6. !# 5. 3. 9!# 6 5 9 2! # !6 : 6. 37 # !2! 9 ;28 2!8 # !6!. # 39. !9 "8 9 !# !. 3# 9!# 3 5 : 5 ! 2!. 2!. :85 9 5: 95 !. 6 4! !# 5 !9 # 37 # 5; 95 5 3::! !9 "86. 4 34! 2!# .. 3 5 9. 2 6! 63# 6. 6. ;5 !:! 426 5 9 6 ! !. !## !5 3. 3. 2! 95 5 5 9 3. !# # 3# 6. %* % !73 ! 6! 6 4 6 2! 3. 2 4. # 3 !66 3 45 2!# 4. 3# 75 3. 5"3. 754 ! 2! 3::3; 46 ! 5#3' 5 9585 2! "!5 2. 6!! 4 2! 4: !#3 2! 3 !5. 5 9 2! !3 :!. 2! #"#42 :8 3:3# !9 6; 76. !!: 4 2! ;5# 7 2 3 2! 6. 6. 5 9 2!5# 4 2! # 35#3. 5#2 3"6!#5 3 5 3"* ! ; 23. .# ! 5:: 4 25 # !73 ! 6! 6 4 6 6 7 :83" 5 37 4. 39# !. 3 5. ; 2 .. 9 5 :3 4 7! L. 5 "! 65 9 25. ' ( )! "%&*" + *,( ! "%*" '- .! , +!. 2! ! 2 3:348 3 93 4. +! "%! ". ! (. 3# 75 3 5"3. 65 # 3 !66 25 256. 6 3# 8 . /001?. 2! !# 7$ # !73 ! 6! 6 4& 6 6 5::8 6!9 3 9!6 #"! $ … ! ") / ). 2! ;5 !6 5 9. 2 6 6 93 4# !73 ! 6! 6 4. 2! 2 6 3# 83 # !73 ! 6! 6 4 6 "3 9!9 3 2! 7 : 5# 8 6! 3. "!! 5# 3. 637! 2 4; 23. . MNNOP !". "* .! !. !"*" + *,(+ " #( *! *!" # ! # #(" .*)/"% # (+ ! *" '-. (+* ( ! */&'$. !. #! "! # $! "%& ! ( (# /. $+*$' ! "! # ! *" * % ( ! 0. (.

(24) '. *! */ ! ( ! ',!"& L. '$ / * 1$ &,' *" &*" 7. 2 3 # !73 ! 6! 6 4. 2!. # 59 5 3 5 9 5# 4! 6 3 6! ! !:!7! 6 5# !. !, -.. !# !6. M. 3: !6 5. !# 5. 2 6 6 !>!7 : !9 "8 2! 6! 3. 3. "! ;!!. 9!. 754 468 6 !76 ;2!# !. 3: !9 ) 4 # ! M,. ). &. / &0 0 0 /1 , 0. 3;! !# .# !73 ! 6! 6 45:63 3. # 3 !66. . /001P. / 0. &, &-1. *. 3: !6 2! 6! 6 43 !7 !9 ! !# 485 9 2! 6! 3. 754 46! 63# 6 2! !:!7! 6 5# !L. . /001P'. ! !# 4863 #! 3#:: 7 5 3 ) , Q 2! # 6 # !< # !7!. 3## !73 ! 6! 6 4 6 3 25 ! 5. ! !# 4863 #! ;2 2 :: 7 5 !6 3# # 3 9!6 !:! # 3754 !. ! !# 48 3 2! 5# 4! 3. !# !6 ? /. # 59 5 3 5 9 2! 5 736 2!# ! ) , Q 56 2! ! !# 48 # 5 !:6 # 37 6 63 #! 3 2! 5# 4! . ; :: 37! !# 5. 3. 3 5. ; 2 5 9. !# 5. 758 5+! :5 ! 5 6! 3 9. ; 2 2! 5 736 2!# !. 566!6 2# 3 42. 7! 56 2! ! !# 48 # 5 !:6 # 37 2! 5# 4!. 26 3 2!. 6! 63# ? J. !# 5. 3 ; 2 2! 5# 4! ) , Q 3. 5 736 2!# !.. ! 2! ! !# 4875+!6 6 ;58 3 2! 5# 4! 2# 3 42 2!. !# 5 6 ; 2 2! 5# 4! 9! ! 9 43. 2! # 3 !# !6 3 "3 2 2! 5# 4!. 5 9 2! # 59 5 3 ? 1. # ! 3# 9 43 ! !# 48"8 2! 6! 63#) , Q 5 !#2! ! !# 48256 "!! 6 5 !# !9 "8 . 3#!7 !9 # 37 2! 5# 4! . 5 6! 63# 6 # !< # !9 )# !73 ! Q 3 5 9# ! 3# 9 2! !:! # 3754 !. R. 3 5. ; 2 2! 5# 4! , 3 3::!. # 59 5 3 ?. # 5 67 66 3 . # ! !. 3 .5 9 # 3 !66 4) , Q 2! ! !# 48# ! 3# 9!9 "8 2! 6! 63#256 3 "!. # 5 67 !9. 3 !. !:! # 3. 5# ! # 3 !66!9. 35. 3# 7. 3 5 # ! !. 45 9 # 3 !66 46 5 3 ;2!# ! 2! 95 5. 754! )25# 9 3 85 9K 3#9 4 5:,?. /1.

(25) '. S. !## !5 3. 5 9 5 5:8 6 6 ) , Q 2!. 9 4 5::8 . 3 !> # 5 O. 5. : 5 3. 5. :8 4 2!. 3# 75 3 5"3. ) , Q 2!. !## ! !9.. 3. 2! # !73 ! 6! 6 4 # 3 !66 6 5 2 ! !9 ;2!. 3# 75 3 !> # 5 !9 # 37 2! 754!# 85"3. 2! # 6 # !< # !7!. 3# 75 3 . 3#566 6. 2! 5# 4!. 63:. 45 5#. # 59 5 3. # 59 5 3. 3. :5# # 3":!7. )!:!7!. 4# !M 5. 2 6 ! !# 48 6. 54! /1,. 2! 3# 73. ;5 ! 3#!:! # 3754 !. 6 9!6 #"!9. 573 43 2!# 6. "8 6 :! 42 5 9 # !< !. 7 3#5. 3# 9!# 3 "! !#. 3## !73 ! 6! 6 4 6 3 25 ! 5 ! !# 4863 #! 3 :: 7 5 ! 2!. :!66 2! 6! 6!9 ! !# 48 6 "! 4!7 !9 "8 2! 5# 4! ,. !:! # 3754 !. 6 5::85 9K 3#. 2! 5# 4! ;2 2 ;56 :: 7 5 !9?. 5: !:!7!. 9!# 6 5 9 .# ! !5: 637! !;. 5# 4! ). # 3 !66!9 754! 6. ! 6 3# 9!# 6 5 9 4# !73 ! 6! 6 4L. 8 . ;2 2 5# ! 5#. :5# :8. . /001P. 2! ;5 !:! 42 6 2! :! 42 3 3 ! ;5 ! 8:!. ;2 2 5 "! 7!56 # !9 56 2! 9 6 5 "! ;!!. ;3 # !6 6 )2 ::6, 3#;3 # 3 426 ) 5::!8 6, 3 5 ;5 ! ) 4 # ! /, I5 !:! 42 6 6 5::8. # ! # !6! !9 "8 2! # !!+:! !#:57"95 ) ,. 5 9 6 7!56 # !9 7! !# 6 6 !. 566 4 5 !< 5:!. >!9. 3. 3 3 !. !# 8:!. 2! # !< ! 3. 7!. 8# ! !# 6 3 2!. # !< !. !# 6! 3 9. 5 9. ;5 !:! 42. 2! 2 42!# 2! # !< !. 86. 7"!#3. 8:!6 3 5 ;5 !. 3# 75::87!56 # !9. 5#3 6 7 :. 2!#=) = ,.. :!6 3 2!#= 2! 623#!# 2!. 8 . 5 9 2! :3 4!# 2! ;5 !:! 42. 2! :3;!# 2!. 8. !, -.. 2! !:! # 3754 ! ). 7! !# 6 )7, 3#637! 5 3#3. 5 37! !# 6 ) 7. 10 −9 7! !# 6,. 7 # 37! !# 6 )µ7. 10 −6 7! !# 6, 3#. 2 56. 7! !# 6 ) 7. 10 −2 7! !# 6,. # !< !. !. 3. # 37. 2! 623#!# ;5 !:! 426. 2! :3 4!# ;5 !:! 426 ). : 9 47 # 3;5 !6 5 9. 2!# ! 5# ! 6! !# 5: # !43 6 3. 6! : 3## !73 ! 6! 6 4 3#736 623#!6 ;5 !:! 426 25 5# ! # 5 6 5# 3 2!. &-0 *. 6 ! #7 ) 4 # ! J, # 5 4!6. : 9 4 45775 5 9 > # 58 6,. "# 359 56 # 59 3 ;5 !6,. %. 6 ":! 6 ! #7. 2!. 2! !:! # 3754 !. #36!6. 2! : # 5 3:!. 6 ! #7 25 5# !. 3# 3 3 2! 6 ! #7 256 2!. 5: 3## !73 ! 6! 6 4 2! : 42 25 3 #!8 !6 5 9! ! # 5# !9 # !43. 5 "! 9. 9!9. 3 ;3 5 !43#!6 "56!9 /R.

(26) '. 3. 2! ## 59 5 3. # 3 !# !6' 2! # ! :! !9. 26 # !6!5#2 ;3# + 6 "56!9 3 !:! # 3754 !. 6! 63# 6 25. 6 ! #7. 2! # !43 6 7!. !, -.. $. !, -.. 2! 7 # 3;5 ! # !43. # 5# !9 5 9 2! !7 !9 3#2!# 75: 9! !. # 5# !9. 2! 7 # 3;5 ! # !43. 3 !9 ; :: 3 "! 5 5:8 = !9. 3. ! 2!. 73# ! 9! 5 :. 0 / -& 0 , 1 0./*. '. /,. -,&*. ) 4# ! 1, 3 !# 6 2! # 5 4! # 37 5"3. M µ7 3 M 7. ;25. 3# # !6 3 96 3 2! :3 4!6 ;5 !:! 426 6!9 3## !73 ! 6! 6 4 2! 623#!#;5 !:! 426 25 ! # 3 !# !6 6 7 :5#3 2! 2!# 75:. # 5# !9 # !43 ;2 :! 2! :3 4!#;5 !:! 426 5. # 35 2 /S.

(27) '. 2! ;5 !:! 426 6!9 3## 59 3 "# 359 56 ! 3# !# 59 5 3 2# 3 42 637! 9 6 5 5# :!6 5 9 456!6. 4. 6!9 3## !73 ! 6! 6 4# !5 2!6 2! 5#2D 6 6 #5 ! ! 3. 2!. 5#2D 6 5 736 2!# ! )!:!7!. 2! 5 736 2!# ! 5 5 !. 2!. 256 3 # 5 !:. 4# !M 5. 54! /1,. 37 4: 42 5 9 # 59 5 3. 5 6 4. 6 5 !# 45 9 5"63# 3 5 !# 4) 4 # ! R5, 3 5 736 2!# ! 52. !# 5. 2! < 5. ;5 !:! 42 3 # 59 5 3. # 6 ;2!. 2! 5# :!6 3#:5# 4! 456 73:!. ; 2 2! !:! # 3754 !. 83 6 5 !# 4 25 2! # 59 5 3 . 2! 5". # 59 5 3 5 9 # !9 # ! !9. 5+!6 :5 ! 9! ! 96 3 95. :!6 # !6!. ! 3. 2!. # 37 2! 3#4 5:. 6! !# 5: 5 3# 6. : 9 4 2!. 5# :!6 3#456!6. 5 9 2! 9 6 5. ! 2!. # 5 !:6 2# 3 42 2! 5 736 2!# !. 2 !, -.. 3. & -, &0. 0 , &- , 00. 0 /. "63# 3 ) 4 # ! R", 6 2! 3 2!#75 # 59 5 3 73:!. !# 5 6 ; 2 2! 5 736 2!# !. :!6. 0 0 , &-524 2. 10 ,&*. 3 6 5 !# 4. 2 6 2! 37! 3. 5#3 6 ;5 !:! 426. 5 736 2!# 3 6. 3# 9!# 3 !#3# 7# !73 ! 6! 6 4.. 4. 7! 25 67 5 ;3# +;2! !:! # 3754 !. 3 # 56. 2! 5 736 2!# ! 3 5"63# " ! !# 485. 5 9 ;5 !# 5 3#5# ! 2! 2# !! 75. 1. = 3 !. 5# "3 9 3> 9!.. ! 6 25 5"63# "# 59 5 3. 7 6 "! 236!. 5# ! 3 6! !# !:85 ! !9 "85 736 2!# 5"63# 3. 5 6!6. 2! 5# !56 3 2! 6 ! #7 25. 2!6! 5# !56 5# ! 5::!9 5 736 2!#. ; 93;6. 59 5 3 ; 2 2! !# 5 6 #5 !. 3. 25 6 3 5"63# "!9 3#6 5 !# !9. 5#2D 6 6 #5 ! )!:!7! ) 4# ! S, 25. 5. 4# !M 5. 2! 5 736 2!# ! 5 # !5 2 5 9 54! /1,. 2!# ! 5# ! 2# !! 3# 76 3. 5+! :5 ! ;2! ! !# 486 #+!6. 3# 6. 2!6! 5# !' 5"63# 3 ) ,. # 5 67 66 3 ) ,. 5 9 # ! :!. !# 5. 3 ) ,. 9!. ),. 2! 3 5:. 3. 2! 9!. /O.

(28) '. ! !# 48; ::. !# 5. ; 2 2! 6 #5 !. !5 2 ; :: 9! ! 9 3 !5 # ! ) , 3 "3. 2! ;5 !:! 42 3. "63# 3 ) , 3 # 6 ;2!. !6 3. 3 ! 3#73# ! 3 2!6! 2# !! ;58 6. # 59 5 3. 2! ! !# 485 9 2! 75 !#5: 5 9 3 9 3. # 6 ;2! # 59 5 3. 6 5"63# "!9. 566!6 2# 3 42 5 5# 4!. 3. 2!. 3 2! 5# 4! ;2 :! # 5 67 66 3. ! :!. 3. ) , 3. # 6 ;2!. # 59 5 3. 2! 5# 4! 5 9 6 # !9 # ! !9. !, -.. 6 !. /. 7, &0. 0 ,&2 0. &. # !73 ! 6! 6 4. # !6!5#2!# 6 5# ! 736 # ! :! !9 # 37 5# 4! 6. ;3 8 !6 3 # ! :!. ,0 ,& & 0 - 0 *. !# !6 !9. 6! # ! :!. 7!56 # 4 2! # 59 5 3. 3 5# !# ! !# # !9. ;2 2 # ! # !6!. ! 96 3 2! ;58 ;2 2 ! !# 48 6 # ! :! !9 # 37 5 5# 4! ' 6 ! 9. 2! # 3 3# 3 6 3. :5## ! :!. 2! ;3 !> # !7! 3 ) 4# ! O5, 5 9. 3 ) 4# ! O",. 2 !, -.. 8. .7. 7. 0 ,& 4 1 .. I2! 5 6 #5 ! 6 6733 2. 6 !. 7. 0 ,&524 , 77.. :5#3#7 # # 3#: +! # ! :!. 3. 7. 0 ,&*. 5+!6 :5 !. 2 6 7!5 6. 25 5:: )3#5:736 5::, 3 2! ! !# 48 6 9 # ! !9 5;58 # 37 2! 6! 63#5 9 2 6 3 :85 675:: 573. 3 ! !# 48 6 # ! #!9 3. 26# !6 : 6. 6733 2 6 #5 !6 5. !5# 456 95# +!#3 !9. /T.

(29) '. 5# !56 3. 5. 754!. 6! # ! :!. # ! :! !9 5:736. 3. 3. # 6 ;2!. 2! 6 #5 ! 6 # 3 42 5 9 2! ! !# 48 6. 3# 7:8 5:: 9 # ! 3 6. 63 25 5 6 4. 5. "5 +6 5 !# !9 3 2! 6! 63# 2 6. # 3 42 6 #5 !6 ; :: 5 754! L 6 !. . /001P. :5#3# !#! :89. 637!;2!# !. 6! # ! :! 3# 6. 2!. 937 5 !. 7 3#5. "! ;!!. 6!. 3. 2! 3. 3. 6:3 ! 3 2! !# # 5. 9!. 754!. !. # !:5 3. ;2 2 # !6 : 6. 9 !# !. 2 25. 3. !37! #. 9# ! 3 ;2!. 4# 3. 73. 5. !5# 5 !. 5. 5 :8. # 5 4!6,. 3#5: 4 7! : !. 2 6 5 "!. 3 3 2! 4 # !6 # 3 9! 9 !# !. ! 2! 5. 9!. ! 5 4:! ; 2. 4 3;5# 96 2! 6! 63#. 754! 5 ! 5 9 ! 25. ! 3 34# 5 285 9 # !: !. 4. :58 3 !# . 5 9 62593; 7583. 2!6! ! ! 6 5# ! 9!6 #"!9. #. 9! 5 :. 6 4 5:. 9!. 2! # 5 67 !9 6! 63#. 3 : !5# !5 # !6 3 !5# 5 ! 3 4# !T. !5 # !6 3 # ! )6. 2! 6 #5 ! 5. 5#. 2! :33+9 # ! 3 3#! 25. :5# :8. 2! 54# : # ! 5 9 3# !6 5# !56 5 2!. ! 6 !6 5 3# 9 4 3 2! 3"6!#5 3 9 # ! 3 :5# 3 2! 3#! 5 3. 3. 2! !5 # !. 2!. 5 :5# 4!. ! !# 48; :: "! # ! :! !9 "5 + 3 2! 6! 63#5 9 2! !5 # ! ; :: 5. 6 7 3#5. :5# :8 7 3#5. 754!.. 2! :33+. 2 56 54# : # 5: # 3 6 3#. 6 73# ! 3": < !. # !:5 3. 4 2! 3 # 56 "! ;!!. 3 25 ! 2! # 3 !#:33+9 # ! 3. 73. !5#. 3 2! !5 # ! 3#! 5 3 .. 2! :!66 ! !# 48; :: "! # ! #!9 3 2! 6! 63#5 9 2! !5 # ! ; :: 5 5#. 2! :3 5:. !:86 # 3 4"5 +6 5 !# 4 3 2! 6! 63# .. 5 : !5#6 #. 6 5: = !9. 6 :36! 3 !#! 9. 56 5 "#42 !# 3 ! 33+9 # ! 3. :5# 3 2!. 2! 6! 63# . 5 9 ; 2 !# # 5. 2! 6! 63#9!6 #"!6 2! 3#! 5 3 3. 9 !5 # !6 5# ! 3# 45 = !9. 3# 3 3 2!. 2! #. 6 3# 3 6. 64. 2! :33+9 # ! 3. ; ::. 54! JS.. 35 3. ! !# 5::8 . 6:3 !6 5. 5# 8 49!4# !!6 3 3# !623#!. ! 3 2! 9 # ! 3 5. 4# ! M/ 5. ! 5 4:! 5+!6. 54! JS, 3. ! 5 4:!6. 5 6 4# !:5. 2! :33+9 # ! 3 3 "!57 # !:5. 3. 5# 4! 6 5 9. 3 2! 6! 63#"!57 I 2 :5 !# # 5 . 2! :3 5:. 9! ! 9 43 6 #5 ! 6:3 !. 3#! 5 3 . 5 9 625 ! 6!. ! 5 4:! )6!!. 9!. !; 44!37! # 8; :: 5 !. ;58 6. 6. !# 5 6 ; 2. 2! 6! 63#"!57 5 9 5 : ! !#! 9. 2 6. 2! :3 5:. 5 "#42 3 !9 5. 5#5 3 6. 6! # ! :!. 2!. !5# 5 # :86733 2 3 :3 4;5 !:! 42. 9!. 5 3 2!# 8 ! 3 # !: ! . 2!6! 5 4:!6 5# ! 9 !# ! 9!. 3. 6 ":! ;5 !:! 426. 2! :3 5:. 6 2! 657! 56 2! :33+5 4:! ) 4 # ! M/" 5 ; :: 25 ! 675:: :3 5:. 37 5#63. 2 675::!# 25. 2! 6 #5 !. 9. 2! 6! 63# ! !# 48. 2! 595# , 6 2! 5 4:! "! ;!!. 6:3 ! 5. 6!:8 . 3#. !; 44!37! # 85 9 2! 4!37! # 83 2! 6 #5 ! !5 # !6. 23;. 3# # !6 3 9 4"#42 !66 3 5. 5. !#! :8. :5# :83#9. 2! ;5 !:! 426 5# ! 7. !5#< ! # 3 42 3 2!. # 3:!. 3 ! 3. 2! 6 #5 ! # 3 42 !66 3 2! !5 # !. ! 4# 5 !9 65 9 ;3 :9 5. ;3 :9 5. 2! # !:5 3 62 :58 6 5. :5# 5# 4! # ! :! 6 6 !. 5# :! 6 = !6 25 75+!. 3#!>57 :!.. 7 # 3;5 !6 ". 5#. 37 4# 59 5 3. 5#5 3 6 3# 2!. !5# : 42 !#. 5#2 6 #5 ! !5 # !6 : ! 637!;2!# ! "! ;!!. "! ;!! . 9! ! 9 43. 2! ;5 !:! 42 3 6 #5 !. 36. 3# 3 3 2! ! !# 48; :: "!. !5#95# +!#. !5 # !6. 5. 5 3 6# !43 6. 754!. 3 ! 6. 3# 9!# 3. /N.

(30) '. 7. 7= ! ! ! 6 6. 2 56 :58 3 !#5 9 62593; 4)6!! 6!. 3. 62593; 5 9 :58 3 !#! ! 6 5. !5#56 !# 895# +3# !# 8"#42. 3. 3. 2! 3"6!#5 3. 3"6!#!9 9 !# ! 6:3 !6. 9# ! 3 6 4 5:. 3# !6 6 # # 3. >!:6. 6 3# 3 6,. 2! "3 37 3. 5 3 3 !5 # !6 ; 2 9 !# !. :33+9 # ! 3 6.. 3#! 5 3 6 # !:5. 2!. 2! 754!. 9! ! 9 4 2! 754! 5. ! 6 !6 3 56 3 !9 "862593; 5 9 :58 3 !#! ! 6. 85 < # 4 754!# 8# 37 9 !# !. 9!. 9 46. !37! #. "!. 6 5#!9. 758"! 366 ":! 3 ! 25. !. ! 3 2! 6! 63#. 2 !, -.. 9. : , 0 ,& 7 0. !5 # !6 759! 3#!## ! :!. 3. 3#! 5 3 3. 3 3. 3. 6. 4. 0 ;. 0, 0 ,&524. 0 ;. #. 2!. 3#!# 5 !6 2! 4! !# 5: 9 # ! 3. 2! 3#2343 5: 6 #5 !6 5 6!6 736 3 ! )3#73# !, # ! :!. 3. 3 . 623; 4. 2 56 " :9 46 5 9 6 # !! 6. "#94!6. 5 9 3 2!#75 759! 6 #. 25 4!6. ! )3#5"6!. 56 !# 8"#42 5# 4! 6. ! !# 48 2 6. 2! 73 6 # ! 3 !. : ! ; ::. !5#3 5. # !56!6 ; 2 5 47! !9 73 6 # ! !4! 5 3. 3 !#; :: 5. I2!. 5 5# 4!. # "5 !. 6 73 6. ! 2! 5"63# 3 . # 5 67 66 3 . 5 9 # ! :! : !. 754!. ! 23; 6 #5 !6 # ! :! ! !# 5::8 .# ! :!. 3 !. !5#"#42 !#;2!. 8)5 9 754! "#42 !66,. 3# !>57 :!. 6 #5 !6 6. 2!85# ! ;! 25 ;2!. 2 56 63 : 5 9. 2!85# ! 9# 8. 3# ;! . 6 5 !# 4 # 37 2! 3 736. ! 6 8; :: 9! ! 9 3 23; # 3 42 2! 75 !#5: 5. 5":! 3 3# !6. 2! 5# 4! 6 !# 89# 85 9 6 #5 ! 5. 2! 8 ! 3 # ! :!. 3# 3. 6 !. 6! 63#. 3 3. ! !# 48 # 37 5 6! 63#. # 3 !66 5+ 4 :5 !. 6!, 5 9 2!. # 3 7! 6.. # !6. 6 5 !# 4, 6 2! 937 5 :5# 3 9. 5. !, 3 73 6 # ! 5 ! 6 2! !:! # 5: # 3 !# !6 3 5 !5 # !. 2! !:! # 5: # 3 !# !6. 68 6 !7 5 9 23; 2!8; :: 5. 2! 6! 63# 2!. 2! ! !# 48 3 "! # ! :! !9 "5 + 3 2!. 3#!## ! :! 3# 6 ; 2 37 :!> 5 4 :5#625 !6 5# ! 3773. 2! # !6!. 0, 0 ,&*. ;3 )3#73# !, 3#2343 5: 6 #5 !6 ) 6 5::86733 2, 758 5 6!. 6! 63#9 ! 3 2! 93 ":! "3 754!. &. 3. )6 #5 !. )# 5 44 # 37 !5# 6 3 2!. !5# 6 6733 2 3 2! 6! 63# . 2! ! !# 48758"!. ! !# 5 ! "!:3; 2! 6 #5 !. ;2! 2!# 25 6 #5 ! 6 9 6 3. 3 6 ) 3#!>57 :!.. 5 3 8; 2 :!5 !6 5 9 "# 5 2!6, 3#23734! !3 6 ) 3#!>57 :!. 63 :. 65 9 3# !,. 5 4 ! 6 #5 !. :3 4!#;5 !:! 426 5# ! 5":! 3 ! ! # 5! 4# ! N 623;6 5 !>57 :! 3 2! # !6 : 2! ! !# 485 9 2! 754!9 6 #5 ! L # ! #!9 6 4 5:6 ; 2. 2! "!57 6;!. # 39. #2!#25 623#!#;5 !:! 426. !9 "8 2!. . MNTO 6 # 5# ! :3 !9. 3#. !# 5. . /001P. 3. 2!. # 3 !66 "! ;!! :6!. ! 6 !6 3. 2! :3;!#25: 3 2! 754!. 2! J0.

(31) '. :6!6. 9!# 43. !5 # !L. 5# 84. 9!4# !!6. 3. "5 +6 5 !# 4. <. 01,. &. # 6 :8 . 2! 5"3 ! 9 54# 57 :: 6 # 5 !6 2! : ! 64. 6:3 ! 3. 2! 73. !6 2! 573 5. 5 6 9! 5. 3 ! !# 48 25. 5# 3 2! # 5 67 !9. 2! # 5. 45663 5 !9 ; 2. 9!. 4 2!. 36 473. 5. 3. 2 6 :3;. 9! 9!. ! 5 4:! ! 5 4:!. 5. : !9 56 3 # ! ! ! 637! :: 7 5 3 3#5 73. 5. ; 2 637! 5 !# 54!. # !56!6 ; 2 9! # !56 49! # !66 3 5 4:!. 2!. !# !9 6 !4! 5 3 . ;2 2 8 5::8 3 6 6 6 3 # # !4 :5#3#! !9 6 #5 !6. 4 2! 6! 63#5 9 3 2!# 6. "!25 ! 56 637!;25 # 3 42 5 9 9 5#5":! 6 4 5:6 3. 3. 5. 2!. 6:3 ! )"5 +6 9!, :!59 4 3 3 # ! #. ! 2! # ! #!9 6 4 5: 6 ;!5+)95# +4# 58 ,. ; 2 637! :!5 !6 5. 83. 566 4 5 ## 5. 2! !5 # !# ! :! 6. 6:3 ! 5 9 5 4 ! 2! 42 . 2! 62593; :! 42 !> !5 # !!. 0/*. ! 6 8 !5+. )":5 +, # 37 2 6 62593;!9 5# !5 3# 2! 6:3 ! 6 63. 3. 5. :6!6 6 # ! :! !9 9 # ! :8"5 + 3 2! # ! ! !# 3;! !# .. 2! "!57 5 :6 3 :: 7 5 ! 2! 3 5 2 42. 2!8 # !5 2. . /001P. !, -.. 2! 6 !!. ;2!. !# 7!9 5 !. 9 !# !. 36 3 6. 6! 6 #5 !6. 6 5 !# 4 2! "!57 " ! 6 !6. 9! ! 9 43. 5 3 8 . 573 43 2!# 6. !4! 5 3. 3"* ! 6. 5:63 # ! # 4. :!5 625 ! 5 9 6 = !. # !! 625 !.. 2! 7! 5: "#94!. ; 2 6 6733 2 6 #5 !6. 6 5 6 # 3 4. JM.

(32) '. # ! :! 3#)" :9 46. ; 2 2! #!94!6 5 9 3#!# 6. 5:63 ! 9 3 "!25 ! 25 ;58" 3 2! #!> !#3#75 !#5:6 637!;25 # !9. !6 2! # ! #6,. ;3# +6 56 5 6 !. :5## ! :! 3# 3 9 !# 736 3. # 5 4! 36 3. 733 2 6 #5 !6 5. 2! 6 4 5: 5;58 # 37 2! # ! ! !#. 4# !N 5. !5. 2! 6. 5# !5 3. 2! 4# 3. ! !. # 5# !9 ;5 !:! 426,. D 6. # ! !7 !9 ) 2!# 75:. 566 ! 6! 63# 6 5 3 :8"! 6!9 3 9! !. # # 4! !# 48 6 5 5 :5":!. 7! ;2!. 2! 6. 5 5 :5":! # 37 2! 6. 5 2!. 42. ! !# 48;2!. 3#5:: # ! :! !9 ! !# 48 2 6 5 3 :8 5+! :5 !. :: 7 5 !6 2!. 2!. 42 . 56 :3 456 2! 573 5# !. !66 3 6 3. !73 ! 6! 6 468 6 !76 25 7!56 # ! 5 # 5::85 5 :5":! ! !# 485# !. 5::!9 566 ! 6! 63# 6 ) 4# ! M05,. 6! 63# 6. 2! 6. 63 #! 3 ! !# 48 3## !73 ! 6! 6 4 2! 6. ! !# 48 6 ! 2!## ! :! !9 ) 6 ":! ;5 !:! 426, 3#5"63# "!9 5 9 2!. 9 # 4 2!. 9. 754!. # 3 9!6 5 !# 83. 2! 5 # 5::83. 2 6 5#. 54! JM # ! # !6! 6 5 6 4:! 6 5 : !. ;2 2 6. >!:6. !5 2 3# # !6 3 9 4 3 5 6 !. 6 5 : !6 # 39. 2! :5+!. ; 2 6 6733 2 6 #5 !.. !5## 5 4! :3 5 3 6 ; :: # ! # 73# ! 3 2! 6 4 5:. 2! 6 4 5: # 5 ! 623; 37 36!9 3. 2! 5 # !. 5#2. 3. ! 2!# ! 6. 3 # ! :! !9 ! !# 48. !# 48 25 6 5 # 5::8!7 !9 5 "! 9! ! !9 9583#. 3 ! !# 48 6 :5# 4! ! 3 42 3 "! # ! 3# 9!9. >57 :!6 3. # 59 37! !# .. 6 ! # 3# 59 37! !#. L. 6 ! # 37! !#. 5 9. 566 !. . /001P. 2 !, -.. )=. / 0. &, &- &. ! 6! 63# 6 ) 4# ! M0",. 3 :: 7 5 3. 2! 6! 63#!7 6 # 59 5 3. 41. ,. &. 524 0 ,. &. *. 2! 3 2!#25 9. # 3 9! 2! #3; ! !# 4863 #! 3# 25 6 9 # ! !9 3;5# 9 2! 5# 4! 3 "!. !6 45 !9. 2! # 59 5 3 # ! :! !9 # 37 25 5# 4! 6 9! ! !9 5 9 7!56 # !9 "8 2! 6! 63# 9 5 54!6 3#5. ! 6! 63# 6. 3 958 3#6!563. : 9! 2! 5" : 8 3 3" 5 ! 6! 63# 6 5. "!. 7!56 # !7! 6 5 8 7!. # !45# 9:!66 3 2! 7! 6!9 3 !>57. 4 ;5 !:! 426 25 5# !. 3. J/.

(33) '. 6. ! :8 # 3 9!9 "8 2! 6. 5# 4! 6 :: 7 5 !9. .6. 2 56 7 # 3;5 !6. 3# 3 25 ! "! !# 3 # 3: 3 2! ;585. 3;! !# .5. ! 68 6 !76 # !< # ! 2! 4! !# 5 3 3 5 5# :8:5# 4! 573. 3 ! !# 48 3 59!< 5 !:8 :: 7 5 ! 5# 4! 6 6 5 !# 37! !# .. 2!. !# !. ) 42. !!. 5: 7! !#L. 8 !6 3 5 3. 9. 5 4 4,. 5 9. 2!. :56!#. . /001P. 3# 9!# 3#5 6! 63# 3 3::! )!:!7!. 4# !M 5. 5# 4! "! 43"6!#!9. 54! /1,.. 5 9# ! 3# 9 ! !# 48# ! :! !9 3#!7 !9 # 37 5 5# 4! 7 6 # !6 9! 3 5 6 5":! :5 3# 7# !73 !9 # 37 2!. :5 3# 76 3## !73 ! 6! 63# 6 758"! 6. 5 ## 5 3#"5::33 )3#637! 3 2!# :5 3# 7; 2 3#65 !:: ! 3 6 9! 3 573 4. ! 6! 63# 6 5# ! 2! # 595# . 2!. 2!. :5 3# 76 L. 2!. 5#3 6. 5#2D 6 5 736 2!# ! :5 3# 7. IU. 3. V. 3 6. 5 !9 3. 9. 3 5. 2! 5#2D 6 5 736 2!# !,. 3#3 5 6 5 ! # 5 36. 63 ! 564. 26. # !6!5#2. 5. 5 3#. ;3# + 5. . MNNNP. ;2 2 5# !3 !. 754!6 5 9 5 : 5 ! 2! 3::!. 2! 4# 3. 2336 4. # 35 2!6. 6!9 3 3::!. 5!#5:. !# 89! 5 :!9. 3 3 95 5 3 !#5:736 5 8 3# 3 3 2! 5#2D 6 6 #5 ! 5. 5:736 5 8 7! 2!# ! 5# ! 75 8 8 !6 3 6! 63# 6 25 5# ! 6!9 3## !73 ! 6! 6 4 #36!6. 6 5 9 # 595# . 573 4 3 2!# 6L # !6!5#2 ;3# +5 95 5 L. # 35 2!6 2!. IU. V. 2 56. !63 #!6. /001P. 6! 3 7 # 3;5 ! "56!9 5. 26. ! # 595#6! 63# 6 3. 3::!. . MNNNP. 2223 ! 7 # 3;5 ! 6! 63# 6 5# ! 4! !# 5::89 754 4 5 9 754 4 68 6 !7. 3. 9!9. 3 ;3 9 6. 754 4 7 # 3;5 ! 6! 63# 6. 6 5 !# 37! !# 6. 736. 56!6 2!6! 5# ! # 3 : 49!. !6 25. : !5#9 7! 6 3. 3# 2! # !75 9!#3 2 6 # !6!5#2 ;3# + 2! 3. 5 !43#!6'. 3. : 9! 5: 7! !# 6 5 9. 5+! 7!56 # !7! 6 6 ; :: "! 3 :83. 3 ! 754 4. 6! 63# 6 2! 736 5 # 3 8 7 3#. 3773. 93 !!. 595#6 !66!. 3# 7 3 754 45 3. 9 5 4 4L. 5::85 # 5 4 43#9 6 5. !7 # 3;5 ! 6! 63#6 2! # 595# 595#6 5 . /001P ! 7!56 # 49!. 3 5 # 5 67 !# .5# ! ! !# .5 5 !. 5. 5 9 5 !:! # 3. 95 5. !66 !. 5. 2! # 5 67 !#4! !# 5 !6 6. # 3> 75 !:8M 7 3 M 7 !#5:6. ;2 2 5# ! 3. 2! # 5 67 !9 ! !# 48 # ! :! !9 # 37 7!56 # 4 2!. 7! 9!:58"! ;!!. "5 +6 5 !# !9 $ ! 23& # 37 9 !# ! :3 5 3. 5 "! 9! !# 7 !9. 5. 3 666. 957! 5::8. 6 68 6 !7 3 # 3 !66 5 9 # ! 3# 9 2!. :6!6 3 7 # 3;5 ! ) 3 !# 6 2! # 5 4! # 37. ;5 !:! 42. 56 5 "! 6!!. 6!9 "8 2! 5 !. !. 4# !1 5. 3 5 "!57. 2! 5 !. 5#3 6 3"* ! 6 ; 2. 2! # 5 67 66 3. 3 5. 5# 4! 6. 2! #9 6 5. 54! /S, 5 # !4 :5#. 5# ! ! !6 5 3# 3 3. 2! :: 7 5 !9 "!57 :6! 5 9 2! # ! !. 3. 3. 8 2!. ! # 37 2! # 595#5 9 2 6 2! #. 6 2! 6! 63# :5 3# 7 73 !6 3# ;5# 9. # ! 3# 9 45 9 # 3 !66 4 JJ.

(34) '. 3 2! "5 +6 5 !# !9 6 4 5:6 " :96. 5/. 754! 3 2! 6 #5 !. ! 5 6! # 595# # 3 9!6 6 3; ! !# 4863 #!. 754!6 5 "! 5 < # !9 9583# 42 3# !3 !# . 2! :3 4;5 !:! 426 3 7 # 3;5 ! # 59 5 3 ! 5":! 5 9 736 # 5 . "! 4 366 ":! 3 6! 2! 7 # 3;5 ! # !43 # !< !. 3. 5 8;!5 2!#L. 3 ! !# 5 ! 2# 3 42 :3 96. . /001P. 2! 6 ! #7 6 # ! !# ! !9 5 3# 9 4 3 ;5 !:! 42 5 9. 8 6 :3 4!#5 ;5 ! 6. 9!! !#. 5. ! !# 5!. 26# !43. 6 < ! :5# 4! 5 9 2!# !. 5# ! 6! !# 5: ;5 !:! 42 # 5 4!6 3#"5 96 3773 :8 6!9 ;2 2 4 !. 39! :! !# 6 9 #4. I3# :9 I5# # !75. ;3 3. # # ! :873# ! 3 •. 3 2 6 958 ?. 4# !1 5. 54! /S :: 6 # 5 !6 2!7. 2!6! "5 96.. :5# . 5# ! 9!6 #"!9 "!::3;'. W "5 9 Q 2 6 623# ;5 ! 623;6 8 5::85 2 42 5 !. 5 3 5 9 6 75 :8# ! :! !9 # 37. 2! 6 #5 ! 3# # 37 2! 3 3 2! !4! 5 3 5 9 # 3 9!6. 3# 75 3 5"3. 2! 6 #5 !. 3 3"* ! 6? •. "5 9 Q 2 6 :3 4!6 # 595#;5 !:! 426 3 ! 5:63. 3 2! 4# 3. 3# 75::8 ! ! # 5 ! 9!!. 3 !4! 5 3. 9. 4# ! MM 623;6 ;3 6 ! !6 3 2! 657! :5 96 5 !. 754!9 ; 2 9 !# ! 5. "! 6!!. 5 9. 23; 2! # !< !. 8. : !. !6 2! "5 +6 5 !# 4. # !< !. 2! W "5 9 6 ! !. ) 4# ! MM5, 2! 54# : # ! 5# !56 5 "! !56 :89!75#5 !9. 5 9 2! 6 # !! 6 5 "! 9! 2!. "5 9 6 ! ! ) 4 # ! MM", 2!6! 25# 5 !#6. 6 5# ! 3. "! ;!!. 3# !6 6 5 9 54# : # ! 5# !56 6 73# ! 6 ":!. 2! # !6 9!. !6. 6 ":!. ". !9. 2! 9 !# ! !. 5: 5# !56 5# ! 6 ":!. "3 2. 6 ! !6. 2 !, -.. I2! 7 3#5 9 6 #7 5. )). 96. &. , / -. , 0 , 77. &0. 66 4 7 # 3;5 ! ! !# 48 . 2!. &-0. 3:5#= 5 3. 3:5#7! # 8 . 56 6 57! 7 : !6. 6 5 59 5 4"! ;!!. 4>;2 & 524 ;2 & *. 3. 2! # 59 5 3. 6 5:63. !9 # 595## !6!5#2 5# !5 25. 3: !6. 2! 3:5#= 5 3 6 25 5 # 595#68 6 !7 6 5":! 3 # 5 67 5 9 # ! ! !. 3:5#= 5 3 # ! !# 6 3 2! 3#! 5 3 3 2! !:! #. !:9. 36 # 595#6! 63# 6 5# ! 9!6 4 !9 3 J1.

(35) '. # 5 67 7 # 3;5 ! # 59 5 3 ! 2!#23#= 3 5::8 3:5#= !9 3# !# 5::8 3:5#= !9 2! 5 !. 5# ! ! !6 ! 2!# 2! 23#= 3 5::83# !# 5::8 3:5#= !9 "5 +6 5 !# !9 ! !# 48 .5 9. 637! # 595#6! 63# 6 5 # ! ! ! "3 2 2!6! ;3 3:5#= 5 3. 6 5 !6. 2! :! !# 6. 2 6. 2!# ! 5. # ! ! ! 3:5#= 5 3 6 56 3::3;6'. 3#23#= 3 5:. 5 9. 3# !# 5: 9!6 4 5 !. "! 3 # 37" 5 3 6 3 "3 2 # 5 67. 5 9. Q 3#23#= 3 5: # 5 67 5 9 23#= 3 5: # ! ! !.. Q. 3# !# 5: # 5 67 5 9 !# 5: # ! ! !. 5 9. 7 :5# :8 .. Q 3#23#= 3 5: # 5 67 5 9 !# 5: # ! ! !.. Q 3# !# 5: # 5 67 5 9 23#= 3 5: # ! ! ! 2! # 6 ;3 3:5#= 5 3. # 5 67. 37" 5 3 6 5# !# ! !# # !9 3 56 : +! 3:5#= !9 "! 5 6! 2!. 3:5#= 5 3 5 9 2! # ! ! ! 3:5#= 5 3 5# ! 2! 657!. 2! :56. ;3 37" 5 3 6. 5# !# ! !# # !9 3 56 # 366 3:5#= !9 "! 5 6! 2! # 5 67 5 9 # ! ! ! 3:5#= 5 3 6 5# !3 3 3 ! 5 3 2!# 7 :5# 3 5#5 3 6. ;5 !:! 42. 9! ! 9 43. 5 9 2! # ! ! ! 3:5#= 5 3 . 2! # 59 5 3 ; :: # 37 2! 6 #5 !. 3 2 ;5 !:! 42 5 9. !# 5. 758 # 3 9! 9 !# !. 5 !. 23; # 595#6!!6 2! 6 #5 !. 3:5#= 5 3 5 9 ;5 !:! 42 37" 5 3 6. 5 9 37 :!7! 5# 8 3# 75 3 5"3. 36 # 595#68 6 !76 # 5 67. 3:5#= 5 3. ; 2 5 9 "! "5 +6 5 !# !9 9 !# ! :8. 3:5#= 5 3. 2!# ! 3# !. # 595#754!# 8 3::! !9 6 49 !# !. 2! # 5 67. 36 !. 2! 5# 4! 6. 7 # 3;5 ! # 59 5 3. ! 2!#23#= 3 5: 3# !# 5:. 3:5#= 5 3 . 5 9 6 7 :5# :8 .# ! ! ! 2! "5 +6 5 !# !9 6 4 5: 5 3 :83 ! 3 2!6! 3:5#= 5 3 6 :. 3:5#= 5 3 # 595# 6 5# ! 5":! 3 # 5 67 ! 2!# 3#. : +! 5 9 # 366 3:5#= !9 # ! #6 23#= 3 5: 5 9 !# 5: 37" 5 3 6 3 6! 6. 2!6!. !6 3 9 !# !. 3:5#= 5 3. 3:5#= 5 3 5 9# ! ! ! "3 2 2!. 3:5#7! # # 595# 6 5# ! 5":! 3 # 5 67 5 9 # ! ! ! "3 2. 3:5#= 5 3 6. 2 6. 2!85# ! 5":! 3 # ! ! ! 5 9. 3:5#= 5 3 6. 5 2 3. 6 #5 ! 25# 5 !#6. 95 5 2!: 6 3 7 # 3 ! 2! 9!. !5 # !6 L. 2!6! $3:5#= 5 3. 65 9 # 3 !# !6 5 3. 25. # 3 !66 5:: 3 # !:6& 256. 5# 84. 2 6. 2! 5 5 :5" : 83 7 :. 3 . 5 9 2! 9 6 #7 5 3. "! ;!!. . /000P. 2! 754 44!37! # 83 5 # 595#68 6 !7 ) 4 # ! M/5, 3 6 6 6 3 5 # 5 !:6 3# ;5# 9. 2! : 42 9 # ! 3. ; 2 2!. 7 # 3;5 ! "!57 6 # 5 67 !9 3": < !:8 :: 7 5 5 4! # ! !# 6 3 2! 5 # 366 # 5 + 9 7! 6 3 5=7 2 # ! !# 6 3 2! 5:3 4 # 5 +9 7! 6 3. 59 #9 # ! :8. 9!# 2!. 45 6;5 2 25. !#! 9. :5 3# 7 25 :5 3# 7. 6 3 6!. # 37. 2! 59 #. :5# 3 2! : 42 9 # ! 3 . ;2 :!. 5# 5::!: 3 2! : 42 9 # ! 3. 2! 3# 3 3 2!. 754! 6;5 2 :36!6 3 2! 59 # # 5 +3 2! # 595# :5 3# 7 6 5::!9 2! !5## 5 4! ;2 :! 2! 3# 3 3 6;5 2 5#2!6. # 37 2! 59 # 6 5::!9 2! 5## 5 4!. 2 6 6 9! :33+ 4 !; 4. 4!37! # 86 8 5: 3 754 4# 595#68 6 !76 2! 25. 9!. # !56!6. 73. ! 5 4:! ) , 6 2! 5 4:! "! ;!!. 2! # 595#"!57 5 9 2! 4# 3. 45 # 366 2! 6;5 2 # 37 !5#3 5## 5 4!. 5 ;2 2 2! # 595#$ :33+6& 5 # ! !# # !9 3 56 "! 46 !! . # !:5. 2! 6 #5 !. 2! :33+5 4:! ) , 6 2! 5 4:!. 2! !5## 5 4!. 2!. ! 3 2! 5## 5 4!. ;2!# ! 2!. 9 6 #5 !. !; 44!37! # 8758"!. !; 44!37! # 8 6 625::3; JR.

(36) '. 5:: # 5 4!6 2! # 595#5 ! !5 2 5# 4! 3. 5 7!56 # !6 2! # 59 5: : ! 3 6 42 9 6 5. 2! 6 #5 !. 2 6 6 2! 6:5. 6 2! #! 23#= 3 5: 9 6 5 6:5. # 5 4!. . .. 5 9. # 5 4! 9 6 5. ! 5:3 4 2! 4# 3. 5# ! :: 6 # 5 !9. !) ,. ! "! ;!!. 2! 4# 3. 2! # 595#5 9. 9# 5 4! 9 6 5. 9 3# # !6 3 9 4 3 !5 2 3. !) ,. 7!56 # !9. 4# ! M/". Flight direction. z. y Footprint Swath x 2 !, -.. 5 5: # !63:. 3. M. )%. 65. ! :! 42 3 2!. 2! :: 7 5 3 2! 7. 9!. 2! 754 44!37! # 8 2! # !63:. :6! ) ,. 2! 6:5. ! "! ;!!. ;3 9 6. 6! 5# 5 3. 6 4# !5 !# 25 25:. 4 3. 5# 4! 6 3 2!. 3. 3 4# 3. # 5 4! # !63:. 5 5: # !63:. 2!. 2! ; 9 2 3. 6 5:3 4 2! 5=7 2 9 # ! 3. # 5 4!. :6! :! 42. 3;! !# . ;2!. 3 25. 9# 5 4! # !63:. :5. 3. 2!. 6 2!. 3 4# 3. 3 # ! !# 6 3 2! 6 = ! 3 2! 675::!6. 2! #. ! 5 4:!. 3. 33# 9 5 !6.. 2!. 2 6. 3# >!9 6:5. # !56 4# 5 4! 3# # !6 3 96 3 2! 6 = !3. 366 ":! !5 # ! 25. 754!6 ;2!# ! 3 :8:5# 4! !5 # !6 5# ! 6 ":! 5# ! 65 9 3 25 ! :3; # !63:. 3 # !75 6 3 6 5 .. 9 # 5 4!. 3 ; :: 9! # !56! ; 2 2! # !63:. :6!. 4# ! MJ5 5# 4! 6 M 5 9 /. # 5 4! # !63: 9!. 3 9 !# !. 2! # 5 4! 9 7! 6 3. 3#!>57 :!.. # 3* ! !9. 9# 5 4! ; :: "! 9! ! 9!. 3 . 2! 4# 3. 5 3. 2! 6 #5 ! ; :: "! # !63: !9. 2! 5:3 4 # 5 +3#5=7 2 9 # ! 3. M. 3. 2! # 5 4! 3#5 # 366 # 5 +# !63:. 6 6 93 ! "8 2! 9!. ; :: 3 "! 6! 5# 5":! ;2 :! 5# 4! 6 J 5 9 1 ; :: 3. 6 9! ! 9!. # 5 4! 9 # ! 3 )"5 9; 9 2, 5 9 3. ;3 # ! :!. 3 9 !# !. 9 # 5 3 6. # !63:. 3. 856 6! 5# 5 !. 5 25 # 5 4!. 2! 6! 5# 5 3. 9! ! 9!. 0/*. # 3 !# !6 3 2! 7 # 3;5 ! # 59 5 3. 2! 5=7 2 9 # ! 3 ) 4# ! MJ5,. 7 7 965. # 595# 5. 7. 3 3 2! 6 !. 5 9 2! 4!37! # 5: ! ! 6 3 ! !. / -, &-- / 0. 2!. 5 "! 9! ! !9 "8 2! 6! 63# 3. ! 3#2 42 # !63:. 3. 754!6. 675:: 3"* ! 6 5 "! 9! ! !9 JS.

(37) '. 5 !. 5 33 # 3. 2! 4# 3. 3 2! :: 7 5 3. 5 !#. 9 ) 4# ! MJ",. 6 2! # 595#:: 7 5 3. 2! 6! 63# . 2! 5=7 2 # !63: # 5 4! ;3 :9 "! 6! 5# 5":!. " ;92 6 # 39. 2! "!57 ; 9 2 ) , 6 5 7!56 # ! 3 2! ; 9 2. 3 "! 37!6 35# 6!# 5# 4! 6 J 5 9 1 5. !# 6!:8 # 3 3# 3 5: 3 2! 5 !. ! 5 5# # 3;!#"!57 5 9. # 3 545 !6 3. !## !63:. # !56 49 6 5. ! # 37. 4# ! MJ". 5# 4! 6 M 5 9 / #2!## 5 4! ;3 :9 3. 2! !5#. 2! # 595#"!57. 5 :! 42. ;2 2 7!5 6 25 5 :3 4!#5 !. 5 ; ::. 3. 2 !, -.. )$. !## 5 4! # !63: 93 ! ; 2. !#5. # !56 4 2! 5 !. .0 ,& 4 &-. 3. .0 ,&524 ?, /.0. 5 "! 5 2 ! !9 "8 6 45 623#!# :6! :! 42. ;25. ! 4 !!# 49!6 4 # !6 # 3 6 5 :! 42. .0 ,&*. 3;! !# . 2! 5. !#5=7 2 # !63:. 5: :! 42 3 2! 5 !. 3. 5 "!. 5 "! 5 2 ! !9. 5 6 : 7 !9 "8;25. 5 "! 5# #!9 3 5 5 # "3#! :5 3# 7 595#5 ! 56 3 9 # !. 56 3 5 ## 5 6 5# ! 6 5::873. 2! #"!57 3 2! 6 9! 3 2! 5 #:5 !. 5 ## 5 . 2 6 739! 3 3 !# 5 3. 6 7 : !9. !9 3. 2!. 59# ! 3. 9!# 6 9! 3 2! :5 3# 7 63 3# 75: 3 2! : 42. 2! 5 # 3 8 7. 52. 3#. . 3# 9! 33+ 4 # "3#!. 595# 2!# ! 5# ! ;3 8 !6 3. 68 6 !76' 2!. ) !5:. !# # ! 595# , 5 9 2!. # !5: 5 !# # ! 68 6 !7. 2! # 6 7 # 3;5 ! 754 468 6 !7 6!9. 3 !# 5 !6 ; 2 5 :3 4)5"3 S 7, 5 !. 5 5 9 6!6. 2! 5=7 2 # !63: 5 ! 2 6.. 6 :! 42 3 3" 5. 3. 7 6 "! # !9 366 ":!. 3. 3. 2! 5=7 2 9 # ! 3. 68 6 !76 6 9 # ! :8 # 3 3# 3 5: 3 2! 9 6 5. 5 5 9 2! 5# 4! . 5 9 3# 9!# 3 3" 5. 2! 9!6 # !9 # !63:. R. ! "! ;!!. 2!. !# 6!:8 # 3 3# 3 5: 3 2! ;5 !:! 42 6!9 "8 2! 5 !. 5 "! !#5=7 2 # !63:. !9. 3# 2! :! 42 3. 2! 5 !. ! 3# !5 2 5 5=7 2 # !63:. ;3 :9 "! ! !665# 85 MT0 7 :3 45 !. 5. 3 . 2! 9 6 5 5 7 6 "!. ! "! ;!! # 595#5 9 5# 4!. # !56!9. 26 6. # 5. 3 3 0 R 7 ; 2 5 ;5 !:! 42 3 5"3 2!. 5. 5::8 3 J 7. 6 9!6 #"!9 !>. JO.

(38) '. 2222 2! 5 !# # !3. 5 9. 68 6 !76 7!5 6 2! 3 !. # ! :! !9 # 37 2! 754!9 6 ! !. ;2 2 6 # ! # !6! 6 2!. 3# 75 3. 3## 595# 6 2! 5 !# # ! 6 2! 5 !. :6! "!4. 3 "! # ! 3# 9!9. !6 3 73 ! 3# ;5# 9. 5:: ! 23!6 # 37 2! 5# 4! 3#!5 2 # ! 7! 25 2! 5# 4! 6 ; 2. 2! # 595#"!57 637! 5 !. 5) ,. !#39 3 5 5# 4! # !63:. 2! "!57. 2! 3. 6 ; 2. !5## 5 4!. 2! "!57 56 4# 3. 3 # !75 6 3 6 5. 5 # 366 2! !. 3 5 # 366 2! !. # !56!6. "5:5. # ! 6;5 2. # ! 754 46;5 2 6 5::!9 8 2!. )'. / 0. 5 !# # ! :! 42 Lsamax 5 "! 3"6!#!9 "8 2! !7 66 3. 3 5 7 # 3;5 !. 6 5 !# !9 2!# !. # 5 !:6 "5 + 3 2! 6! 63#5 9 6. 754. 3 # 6!. 3. 2! 3;!#3 2! 6! 63#5 9 3. 9! 6 5 7!56 # ! 3 ;5 ! L. 2! 6 4 5: 6 # ! 42. 5 9 . /001P. 2! 57 :. 4. 2 25. 2!. 3# 7.. !. !# # ! 595# . 3#. *. 68 6 !7. ;2!# ! 2! 75> 75: 68 2!. 6 9!6 #"!9 "! 3# !. 2!. :6! 3 2! 4# 3. # !56!9 7!. ! !5 2 3 2!# . 6. 2 6 7! 239 3 5 2 !. 4# ! MR 623;6 2! 754 44!37! # 83 5. !:! # 3754 !. !; 3. 2! 6 7 :5 !9 3#68 2!6 = !9. 2! !> 5 9 4"!57 ; 9 2 5 9 2!. 9 # 5 4!. !, -.. 7 :. :6! 5# !# ! 3# 9!9 9 # 4 2!. 5 ;2 2 2! 5# 4! :!5 !6 2!. 7! :5 !# . 9! !# 7 !6 2! :! 42 3. 7! 25 3"* ! 65. 9! ! 96. 3. 6 2! :5 3# 7. 5# 4! 6 5 5## 5 4!. ;2!# ! 2! "!57 6 ; 9!6 ; :: "! :: 7 5 !9 3#5 :3 4!#. 5=7 2 # !63:. /. 5. 6 5 5# 4! ) , # 6 ! !# 6 2! # 595#"!57.. 2! "5 +6 5 !# !9 ! 23!6 # 37 !5 2 # 5 67 !9 !. 2! ! !# 48. 6!9 3 4! !# 5 ! 5 3# # !6 3 9 4 754! 25. 4# ! M1 :: 6 # 5 !6 23; 2 6 6 5 2 ! !9 3. 4 6!9 3 3::!. 9. 26. 754 4 # 3 !66 6 93 ! :6! # 5 !:6 3 2! 4# 3. 5::8# ! ! !9 2! 9 6 5. 5#. 2! # ! ! !9 57 :. 9. 6 9!/. ! 3 2! 3"* ! 6. :5# 2! 6 # ! 42 3#$ 2! 42 & 3 5. 9! 758 7 :85 37 :!> 6 4 5:.. : 9 4"3 2. 9! 5 9 256! JT.

(39) '. z. R0. Airborne Θa. Θi. r. y. Point L samax. x !, -.. 2! 736 # ! :!. 8. !# 8 9. )3. !# !6. / -, &-- / 0. 4 5# 57! !# 3# 3. 9 5: 6 5 !# !#. 2! # !63:. 3# # !6 3 96 3 2! 75> 7 7 6 5 5: # !63: # ! ! !9 ;5 ! # 3. 7. 6 5 32!# !. J. 3. 3. 0/*. ! 3. 3 5:. 754 4 6 2! 6 ! !. !:: ) 2! 5# !5 3. 3 !# :583 5:: 2!. ! 3#6 7 3 2! ! 23!6 ci 3. !, -.. J. 2! ;5 !6 5# ! !< 5:. :! 42 5 9. )6. 7. 9. 9 25. 2! 6! 63# , # ! :! 6 2! ;5 !. 5 9 2! 9. 9 5: ;5 !6 L. 4# ! MS :: 6 # 5 !6 2 6 # 3 !66 2# 3 42 2! "5 +6 5 !#! 23 c 3 5 # !63: 5 32!# !. 2! 4# 3. . /00MP 3. !::. ;2 2 6. 9 5: 6 5 !# !#!:!7! 6. 0 ,, 0 7. 256! ) 2! 3#4 3. .0 ,&. *. 2! 256!6 3. 2! ;5 !6 5 0 9!4# !!6 5# !. !#! :85: 4 !9, JN.

(40) '. 2!. 68 6 !7 3 !#37!6 2!. 9!6 4 5 !9 3 5 2 ! ! 2 42 # !63: 5 !# # ! 3 9! ! 9! 965. # 37 2! 6 = ! 3. 2! 68 2!. 2# 3 42 2! 7!56 # !3 43 2!. 2! # !5: 5 !. 2! 6!. 3. 6 7. 3. :6! :! 42? 2 6 # !63:. 3. 5 !# # ! :!596. 9!#5 9 !# !. 657! 7! 5 2! 6! 63# . 5 9 2!8 5 3 !:! 5 3 5 4:! # !63: 68 6 !7 965. 3. !. !. 6!9 3# 2!. # !56!6. 56 7. # 5 4! 9 # ! 3 5 "!. 6 3 :8 2. 6# !5: = !9. # !56!9 2# 3 42 2!. . MNN/P. 6 45 68 2!. 5# ! 6!!. 2! 68 2!. # 37 2! ;5 !:! 42. 2 56 2! 9 6 5. 3 2! # 3":!7. !6 ! 5::86! !# !. 2! 3"6!#!9 5# !5 256 6 # 3 4 3 34# 5 28 . 25 ;3 3 2! 6! 63# .". !6. 5=7 2 9 # ! 3 . 3. 2! # !63:. :6! :! 42 L. 2! # 3 !66 3. 3. 5 !# # !. 3 !9 5"3 ! 5 9 6. 56 3 !#:3 49 6 5. 5. 5 9. 2! 6! 63#5 9 2! 5# 4!. # !56!6 2! :! 42 3. # 3":!76 7!. 3 6 ; 2 675:: 5 !. 5::3;6 5 2 42!#6 5 5: # !63:. ! "! ;!!. 623#!. 68 6 !7. :33+5 4:!. 5. ! 3. 2 6 56! 2! # 595#! 23 5# # !6 5 2!. 3 "! 6! 5# 5 !:8 9!. 3 5# ! 3" 5 !9. ! 25 P 5 9 P '. 6 5 25 ! 2! 657! # 5 4! 9 6 5 !9. 3 2! 42. 3# 75 3 5 9. 4# ! MO :: 6 # 5 !6 2! 754 4 #. 3 "! 6! 5# 5 !:8 9!. :! 3 5. !9. "! 5 6! 2! # 9!. 5:. ! # 37 2! 6! 63#S Height. S Θ r r''. r' P h P''. !, -.. )8. P'. / -, &-1 , &, 1. 7. Range 0/*. 26 # 3":!7 33+ 3 2! 7 :!7! 5 3 3 5 3 2!#5 68 2!. 5 !# # !# 595#). # 35 2' 2!. !#!# 37! #. 3 3 : 42 ;5 !6. 6 6!9 3 7!56 # !965. !6 5 9 5 4:!6. ,. 2224 !#!# ! !. 2! # ! 6!:8. 2! ;3# 9. 7! # 8L. !# 5. !#!# 37! # 8 :: 6 # 5 !6. 2 6'. !#!# ! X 7!56 # !Y. !#!#3. . /001P 2!. 7! 239 # 37 2!. ). !#!# 37! #. 8 2!. !# # !. 68 6 !7 3 # !5: = ! 2! # 5 4! # !63:. 595# , 68 6 !7 5 3. : !6 5 9 !# !. 2 6 7! 239 6 6!9. 3# 9!# 3 10.

(41) '. 63: ! 2! # 3":!7 3 2! 5 2! 657! 9 6 5 # 37 2! 9 !# !. 754 4 #. S1 .. 6 5 9 !# !. 965. 3 9!. 89 !# !. ; 2 9!. 5: 9 6 5. :!. 5 9 623;6 25 9 !# !. 3. 6 25 5# !. S 2 6 6!9 6 5 5::86! 5# 5 !9. 3# 9!# 3 # !63: ! 2! 57" 4 83. 36 3 6 ". 4# ! MT :: 6 # 5 !6 2 6 # 9 !# !. 5. ! # 37 2! 6! 63# 6! 3 9 6! 63# 36 3. # 6 6! 63# 36 3 3. :! 25. 3. # # !9 ;2!. ;3. ! # 37 2! 6! 63#3 6 ; 2 9 !# !. #. 2! 42 6 25 !. !6 3 2! 6! 63# 36 3 6 S1 5 9 S 2 Height. S1. S2. Θ. r2 r1 r1'. r2'. P h P' !, -.. )9. / -, &-1 , &, 1. 7 &&. Range 0/*. !#!# 37! # 8# !: !6 3 "! 45":! 3 7!56 # !5 # 3 !#83 !:! # 3754 ! 5::!9 256! L. . /001P. ;5 !:! 42 5 9 # !< !. 36! 2!# ! 5# ! ;3 ;5 !6 ) 4 # ! MN, ; 2 2! !>5. 8# 5 !: 45:3 4. 6 5 !. ". 2! 6 5# 4 3. 6: 42 :8 # 37 2! 3 2!# 2! 3 6! "! ;!! 75 2 4 3 2! 256! 9 !# ! !. 2! 256!. 6! 63# 6 # 37 2! 657! 6 ! !. 6 6. !, -.. 2! 754! 965. )<. !5 95# 5 937 3"* !. 2! 657! 3"* !. 657!. 3 3 ! 6 3 6!. 2!6! ;3 ;5 !6 ) , 6 5::!9. 3# 75 3 3 2! ;3 754! 95 5 :!6. 5 < # !9 "8 2! ;3 !#7 36!9. , 77. 256! 256 ;3. 63. ;5 !6. &. 70. 5#6. 5 9! !# 7. 0 / -& 0 ,. 6. *. 3 ! 9 ! 3 2! 6! 63#6 5 !# !#. 256!. ;2 2 # !6 : 6 # 37 2! 6 5 !# 4 # 3 !66 3. 6 3"6!#!9 ;3 7!6 # 37 !5# :8 2! 657! 36 3 .. 2! 3"* !. 5 "! 566 7!9 1M.

(42) '. 25. 2! 3"* !. "! ;!!. 256! 6 2! 657! 3#"3 2 3"6!#5 3 6. 2! ;3 754!6 # ! :! 6 2! 9 !# ! ! 87!56 # 4 2! !>5. 9 !# ! ! ) !. 5. "!. 5:. 3. 2! # !63:. :5 !9. 3 5. 3. !::.. 9 !# ! ! "! ;!! 59* 5 !. # !63:. 5. # 5 8 25. 3. 9! 3 6!. 5:. !#!# 37! # "3 2. # ! !5. "8 25 4!6 ; 9. &, &0 7. 5. !. :63.. 6 !# 8 7 3#5. 2!. 256!. !#!# 34# 57 ) 4 # ! /0,. 3. 2! 736. 25. 2! 3"* !. 7 3#5. # !563. :5. 256! 6 3# 256! 25. 32!# ! !. 3 2!# 25 9 56 5 9!6 # 3. 2!. 3 75+! 5 # ! 6! # !46 # 5 3 3 2! ;3. :# !598 . 5. 3 6! 3 3 ! # !63:. 2! 32!# ! ! 9!6 #"!6 2! 573 3 739. ! "8. 2! 6 5:! 3. !#7 36 4 2! ;3 754!6 5 9 # 5 6 3# 7 43 ! 3 2!7 3. # 5 6 3# 7 3 75+! 2!7 75 2. ! 6. 4# 3; 2. 3#9 6 # "5. ! 3 2 6. 56 5:# !598 25 4!6 3. !#!# 34# 57. 6!# 456 7!56 # ! 3# 2! < 5: 83 5 3 6 3. 2!. 3. !#!# 37! #. 3. !:: 5 6!6 5. 256!. 3 6!. 256!. 5 9 3. 2! 6 #5 ! 3# 9 !# !. 9 2! 5 2!. "5 +6 5 !#. 6. 4# ! /M5 623;6 5 32!# ! ! 754! 32!# ! ! 5: !6 754!. "! 9! !# 7 !9. !#!# 37! # 8)!> :5 !9 "!:3;, 6 !7 3# 5: 9! 3# # !:5 3. 754!6. 25 6 3 6586. 25# 5 !#6. 3 2! 5#2D 6 6 #5 !. 2!. 256! 6 3 68 . "! 5 6! 2! 566 7. !#!# 37! # 8 6 !> # !7!:86! 6. 37 :! ! :366 3. 5. 2! ;5 !:! 42. - /*. 2! "5 +6 5 !# . 3#!>57 :! 56 5 # !6 : 3. ;5 !:! 42 5# !6 "!6. %=. 2! 3# 9!# 3. 56 ; 2 # !6 !. 754!6 6 3 5:;58 6 3# # ! 566. 6 3. !::6 6 :: 6 # 5 !9. !. 2! ;3 # ! #6. 2! 5 2 :! 42. : 9 4 6 !:! 5 3 .. !, -.. 2!. 2! 6! 63#6 5 !# !#9 6 5. 256! 9 !# ! ! "! ;!!. 7! !# 6, % 3; 4 2! 36 3 3 2! 5 !. 36 3. 2 6 56!. 2! 256! 9 !# ! !. 25. !# 8"#42 4# 58 6 5:! # ! # !6! 6 2 42. 4# ! /M" 623;6 2! 3# # !6 3 9 457 :. # !56 ; 2 :3;!# 32!# ! ! "! 37! 75 !#5: = !9. 9! 754! 3 2# 3 42. 3# # !:5 3 . 56 3# !6 5# !56 5 9 62593; 3#:58 3 !#5# !56 )6!! 6! 5# !56 ; 2 2 42!# 32!# ! !. 6. 2 56 7!593;6 3# 3:3 !6. 2!. 3. 2! 32!# ! !. 7! 3# 6 4 5: 9!. !37! #. 6 3# 3 6,. !#!# ! ! ! ! 6 "! 37! 1/.

(43) '. 64. 5. 2 !, -.. %). 2!. &. 3# 75 3. 3# 75 3 5 9 # 39. 7 &, / -. 3 5 !9. .7. 4. 5. 754!# 83 !# # 5. !, -.. %% %. 2! 42 .. ,. r2. 2! 9 6 5. 5 9 6 9! ! 9!. 25. 1. 5 9. 2. 754 4 # 3 !66!6 5 "! !#3# 7!9. 5 566. !#!# 37! # 8 2!. 6! 63# :5 3# 7. 6! 9 4 2! 6 4 5: ; 2 3 ! 3 56. 68 6 !7. . 5 9 2! 6:5. r 6 7!56 # !9 2# 3 42 2! 9!. !#!# 37! # 85 9 2! # ! !5. 6 59 5 54! 6 25. 2! !7 3# 5: 9! 3# # !:5 3. 6 ) 4# ! //,. , -0 *. 3 3. 3 2! 754 44!37! # 85 9 75 :83 2! 5# 4!. ;3 9 !# !. ;3 5 !. 6!9 3 9!# ! 3 34# 5 2. :! 6!9 "8 2!. P 2# 3 42 2! 5 4:!6. ! 9 !# ! !. , &. &*. 2! "56!: ! B. 2! ;3 6! 63# 36 3 6 S1 5 9 S 2 . ;2 2 9!. ! "! ;!!. 754 44!37! # 8 3# 3. "!. 3 2!#;3# 96.. 70 0. 4# ! /J :: 6 # 5 !6 2! 7!56 # ! # # ! # !6! 6 2! 9 6 5. & 524>;2 &. !#!# 34# 57 5. !J. & $. &. 2! 5 !. 2! 3"6!#5 3 6 3 6. 5# 4! . 6 46: 42 :89 6 :5 !9 : 42. 3 5 # 5 +6. : 5":!. # 6. 3. 965. !6 r1 5 9. 2! 256! 9 !# ! !. 2! 42 h. :8 4. ' 2! 6 4:! 566. 6!6 5 6! 3 9 5 !. 56 5 9 # ! ! ## 5. ! 2!. 5::85. 53. 2!. 4 2! 6 4 5: ; 2 2! 657!. 7!. 63. 2! 6! 3 9 3 ! :: 7 5 !6 ; ! 2!. 26 # 3 !66 :!596 3 6 # 3 4!#9! 3# # !:5 3 6.. 1J.