plane with a standoff distance D along the zYaxis2the direction of the traveling wave. This SAr system requires a horn or lens antenna having a focused beam ...
'HVLJQDQG3HUIRUPDQFHRID0LFURZDYH 1RQGHVWUXFWLYH7HVWLQJ6\VWHPIRU'DPDJH $QDO\VLVRI)53&RPSRVLWHV
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
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²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±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²DSRUWLRQRIWKH(0ZDYHLVUHIOHFWHGEDFNLQWRPHGLXP ZKLOHDQRWKHUSRUWLRQLVWUDQVPLWWHGLQWRPHGLXP6LQFHHYHU\PHGLXPKDVXQLTXH PDWHULDO SURSHUWLHV WUDQVPLVVLRQ DQG UHIOHFWLRQ RQ HDFK LQWHUIDFH ZLOO SURYLGH LQIRUPDWLRQEDVHGRQWKHERXQGDU\FRQGLWLRQV 7KH(0ZDYHRI)LJXUHFDQEHGHILQHGDVDZDYHWUDYHOLQJLQWKHzGLUHFWLRQ 7KHFRRUGLQDWHVRIDOOILJXUHVDQGHTXDWLRQVZLOOEHEDVHGRQWKHVDPHxyDQGz GLUHFWLRQFRRUGLQDWHV\VWHPIRUFRQVLVWHQF\DQGVLPSOLFLW\RIGLVFXVVLRQ7KHHOHFWULF ILHOGV LQ D WUDQVPLVVLRQUHIOHFWLRQ W\SH (0 PRGHO DUH JLYHQ E\ WKH IROORZLQJ H[SUHVVLRQV
2379
ሬሬԦ ൌ ݕොܧ ݁ ିభ ௭ ,QFLGHQWZDYH ࡱ ሬࡱ ሬԦ௧ ൌ ݕොܧ௧ ݁ ିమ ௭ 7UDQVPLWWHGZDYH ା ௭ ሬԦ ൌ ݕොܧ ݁ భ 5HIOHFWHGZDYH ࡱ
ZKHUH E i t r LV WKH FRUUHVSRQGLQJ DPSOLWXGH RI HDFK ZDYH DQG k LV WKH FRUUHVSRQGLQJZDYHQXPEHUZKLFKLVEDVHGRQWKHPDWHULDOSURSHUWLHVRIWKHPHGLD 7KH ZDYH QXPEHU LV UHODWHG WR WKH DQJXODU IUHTXHQF\ Z SHUPLWWLYLW\ H DQG SHUPHDELOLW\PE\WKHIROORZLQJHTXDWLRQ>@ ݇ ൌ ߱ඥߝ ߤ ሺͶሻ
)LJXUH8QLIRUPSODQHZDYHVFKHPDWLFDWWKHLQWHUIDFHEHWZHHQPDWHULDOV>@
6LQFH WKH XQLIRUP SODQH ZDYHV WUDYHO EHWZHHQ LQWHUIDFHV RI HDFK PHGLD WUDQVPLVVLRQDQGUHIOHFWLRQVKRXOGEHH[SUHVVHGEDVHGRQWKHORFDWLRQRIREVHUYDWLRQ $VFDQEHVHHQLQ)LJXUHWKHVHQVRULVSODFHGRQWKHOHIWVLGHRIWKHVDPSOHVRWKDW WKHV\VWHPZLOOFROOHFWWKHWRWDOUHIOHFWHGZDYHIURPWKHVSHFLPHQ,WLVWREHQRWHG WKDWWKHUHDUHWZRERXQGDULHV DLUWRPDWHULDODQG PDWHULDOWRDLUZKLFKZLOOOHDG WRWKHWRWDOUHIOHFWLRQ*WRWDO,ZKLFKPD\EHREWDLQHGIURPWKHIROORZLQJHTXDWLRQ ߁୲୭୲ୟ୪ ൌ
ாభష ாభశ
ൌ
ோభ ାோమ షమೕೖభ ଵାோభ ோమ షమೕೖభ
ൌ
ோభ ାோమ షమೕഇభ ଵାோభ ோమ షమೕഇభ
ZKHUHR1DQGR2DUHWKHUHIOHFWLRQFRHIILFLHQWVRIHDFKLQWHUIDFHZKLFKDUHEDVHGRQ WKHUHODWLRQVKLSRIWKHLQWULQVLFLPSHGDQFHRIPDWHULDOVZLWKUHVSHFWWRWKHPDWHULDO SURSHUWLHV 7KH HOHFWULFDO OHQJWK T LV SURSRUWLRQDO WR WKH SURGXFW RI ZDYHQXPEHU k DQG SK\VLFDOWKLFNQHVVdRIWKHGLHOHFWULFOD\HUDVFDQEHVHHQIURPHTXDWLRQ ,QJHQHUDO WKH UHIOHFWLRQ FRHIILFLHQW R DQG WKH LQWULQVLF LPSHGDQFH Z LQ WKH iWK OD\HU FDQ EH GHVFULEHGDV
2380
ܴ ൌ
శభ ି శభ ା
ఓ
ǡ ܼ ൌ ට ǡ ߠ ൌ ݇ ݀ ఌ
DQGk1LVDJDLQWKHZDYHQXPEHURIWKHPDWHULDOOD\HUKDYLQJWKLFNQHVVd> @
)LJXUH:DYHSURSDJDWLRQRQLQWHUIDFHVIRUUHIOHFWLRQGDWDFROOHFWLRQVFKHPH
([SDQGLQJWRWKHFDVHRIPXOWLOD\HUHGRUPXOWLLQWHUIDFHPDWHULDOVLWFDQEHHDVLO\ REWDLQHG XVLQJ WKH JHQHUDOL]HG SURSDJDWLRQ PDWUL[ RQ WKH iWK OD\HU ZKLFK FDQ EH GHULYHGDVIROORZV ܧ ܴ ݁ ఏ ܴାଵ ܧԢሺାଵሻା ଵ ͳ Ͳ ൨ ଵ ͳ ൨ ൨ ൨ ା ൨ ൌ ିఏ ் ܴ ܧି ͳ ͳ Ͳ ݁ ்శభ ܴାଵ Ͳ ZKLFKUHVXOWVLQDQH[SUHVVLRQVLPLODUWRHTXDWLRQ DVIROORZV
߁ ൌ
ாష ாశ
ൌ
ோ ାோశభ షమೕഇ ଵାோ ோశభ షమೕഇ
5$',2)5(48(1&@ZKLFKLQQRLV\HQYLURQPHQWVUHGXFHVWKHOLNHOLKRRGRIVLJQDO LQWHUIHUHQFH$UDGLRIUHTXHQF\ 5) QRLVHOHWLVDSXOVHGVLJQDOFRQWDLQLQJDUDQGRP RUDSVHXGRUDQGRPVLJQDODQGFDQEHWKRXJKWRIDVD³QRLV\ZDYHOHW´$QH[DPSOH RI DQ LQWHUPHGLDWH IUHTXHQF\ ,) 8:% UDQGRP DPSOLWXGHIUHTXHQF\ QRLVHOHW LV VKRZQLQ)LJXUH%DVHGRQWKHDWWUDFWLYHEHQHILWVRIQRLVHOHWVLJQDOVWKLVW\SHRI ZDYHIRUP ZLOO EH H[SORUHG IRU V\QWKHWLF DSHUWXUH UDGDU 6$5 LPDJLQJ RI OD\HUHG VWUXFWXUHV
2381
)LJXUH ([DPSOHRIDQRLVHOHWSXOVHXVHGIRU1'7LPDJLQJWHVWVRI)53SDQHOV7KHDPSOLWXGH LVUDQGRPZKLOHWKHIUHTXHQF\UHVSRQVHLVUHODWLYHO\IODWRYHUWKHEDQGZLGWK
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
)LJXUH1RLVHWROHUDQFHRI0RUOHWZDYHOHW OHIW DQGQRLVHOHW ULJKW EDVHGRQSHDNFRUUHODWLRQ YDOXH
2382
6@ZKLFKLVWKHFDOLEUDWLRQSURFHVVXVHGWRFRQYHUWWKHUHFHLYHGGDWDLQWRDSODQH ZDYH6WROWLQWHUSRODWLRQZDVRULJLQDOO\LQWURGXFHGLQJHRORJ\IRUSURFHVVLQJVHLVPLF GDWD 6LQFH WKH ZDYHIURQW IRU VHLVPLF GDWD FROOHFWLRQ LV VLPLODU WR QHDUILHOG 6$5 WHFKQLTXHV 6WROW LQWHUSRODWLRQ LV DSSOLFDEOH IRU RSWLPL]DWLRQ DQG FDOLEUDWLRQ RI UHFHLYHGUDZGDWD
)LJXUH7UDQVPLWWHGDQGUHFHLYHGVLJQDOLQQHDUILHOGDQGIDUILHOGUDQJHV
6LQFHWKH6WROWLQWHUSRODWLRQLVH[HFXWHGRQWKHIUHTXHQF\GRPDLQGDWDD)RXULHU WUDQVIRUP RI UHFHLYHG WLPH GRPDLQ GDWD VKRXOG EH SHUIRUPHG EHIRUH DSSO\LQJ WKLV FDOLEUDWLRQSURFHVV%DFNWR50$²WKHFRRUGLQDWHUHIHUHQFHVIURP)LJXUHZLOOEH XVHG IRU WKHRUHWLFDO H[SDQVLRQ 7KLV H[SDQVLRQ ZLOO EH EDVHG RQ D VLQJOH SRLQW RI VSHFLPHQZKLFKZLOOIRUPDQLPDJHGDWDPDWUL[RQFHWKHGDWDKDVEHHQJDWKHUHGDW HDFKVDPSOHSRLQW+HUHWKHUHIOHFWLRQFRHIILFLHQWFDQEHZULWWHQDVR xyz DQGWKH UHIOHFWHG UDZ GDWD ZLOO EH sr x0 y0 kr ZKHUH kr LV WKH ZDYHQXPEHU EDVHG RQ WKH RSHUDWLQJIUHTXHQF\7KHUHIOHFWHGUDZVLJQDOFDQEHUHSUHVHQWHGDVIROORZV ݏ ሺݔ ǡ ݕ ǡ ݇ ሻ ൎ ܴሺݔǡ ݕǡ ݖሻ ή ݁ ೝ ή ݁ ିೝ౪౨ౝ౪ ZKHUH D LV WKH VWDQGRII GLVWDQFH EHWZHHQ DQWHQQD DQG VSHFLPHQ DQG DWDUJHW LV WKH GLVWDQFHIURPDQWHQQDWRDUELWUDU\WDUJHWSRLQWDWDUJHWFDQEHH[SUHVVHGDV ୲ܦୟ୰ୣ୲ ൌ ඥሺݔ െ ݔሻଶ ሺݕ െ ݕሻଶ ሺെ ܦെ ݖሻଶ ,QHTXDWLRQ WKHUHDUHWZRH[SRQHQWLDOWHUPV WKHILUVWWHUPLVWKHUHIHUHQFH SKDVH EHWZHHQ WKH DQWHQQD DQG QRUPDO LQFLGHQW LQWHUIDFH RI VSHFLPHQ ZKLOH WKH VHFRQGWHUPUHSUHVHQWVWKHSKDVHLQIRUPDWLRQIURPWKHDUELWUDU\SRLQWRIVSHFLPHQ 6LQFH LW LV DOUHDG\ PHQWLRQHG WKDW GRPDLQ WUDQVIRUPDWLRQ LV QHFHVVDU\ WKH UHIOHFWHGUDZVLJQDOsrFDQEHWUDQVIHUUHGIURPWLPHWRZDYHQXPEHUGRPDLQXVLQJ WKH)RXULHUWUDQVIRUPVRWKDWSrFDQEHREWDLQHGDQGZULWWHQDV ܵ ൫݇௫ ǡ ݇௬ ǡ ݇ ൯ ൌ ܴሺݔǡ ݕǡ ݖሻ ݁ ೝ ή ݁ ିೝ౪౨ౝ౪ ή ݁ ିೣ௫బ ή ݁ ି ௬బ ݀ݔ ݀ݕ 8VLQJWKHVWDWLRQDU\SKDVHDSSUR[LPDWLRQWKHUHVXOWLV
2384
మ ήሺ௭ାሻ ିටೝమ ିೣమ ି
ή ݁ ିೣ௫ ή ݁ ି ௬ (TXDWLRQ FDQEHUHDUUDQJHGIRUPDWFKHGILOWHULQJDVIROORZV ܵ ൫݇௫ ǡ ݇௬ ǡ ݇ ൯ ൌ ܴሺݔǡ ݕǡ ݖሻ ή ݁ ೝ ή ݁
మ ൰ ൬ೝ ିටೝమ ିೣమ ି
మ ή௭൰ ି൬ೣ ௫ା ௬ାටೝమ ିೣమ ି
ή݁ ܵ ൫݇௫ ǡ ݇௬ ǡ ݇ ൯ ൌ ܴሺݔǡ ݕǡ ݖሻ ή ݁ 6LPLODUO\ WKH WUDQVPLWWHG VLJQDO FDQ EH )RXULHU WUDQVIRUPHG DQG WKH PDWFKHG ILOWHULQJFDQEHH[SUHVVHGDV ܵ ൫݇௫ ǡ ݇௬ ǡ ݇ ൯ ൌ ܵ௧ ή ܵ ൎ ൫݇ െ ඥ݇ଶ െ ݇௫ଶ െ ݇௬ଶ ൯ ή ܦ IROORZLQJ ZKLFK WKH 6WROW LQWHUSRODWLRQ FDQ EH DSSOLHG IRU RSWLPL]DWLRQ DQG FDOLEUDWLRQ GXH WR WKH ZDYH IRUPDWLRQ UHVXOWLQJ LQ ܵ௦௧ ൫݇௫ ǡ ݇௬ ǡ ݇௭ ൯ $IWHU 6WROW LQWHUSRODWLRQ WKH UHODWLRQVKLS EHWZHHQ WLPHGRPDLQ FRRUGLQDWHV x y z DQG ZDYHQXPEHUV kxkykz LVOLQHDUL]HGVRWKDWLWFDQEHDSSOLHGWRLPDJHUHFRQVWUXFWLRQ ZKLFKLVWKHILQDOJRDORIRXU6$51'7LPDJLQJV\VWHP 6LPXODWLRQ5HVXOW,PDJHV )LJXUH VKRZV WKH VLPXODWLRQ UHVXOWV RI WKH 6$5 1'7 PHWKRG WR YHULI\ WKH H[SHULPHQWDOWHVWVZKHUHDQDOXPLQXPLQFOXVLRQLVKLGGHQEHKLQGD*)53FRPSRVLWH 7KHGLPHQVLRQRILQFOXVLRQLVPPîPPDQGWKHVWDQGRIIGLVWDQFHLVPP $VGLVFXVVHGLQWKHSUHYLRXVVHFWLRQPXOWLSOHVLPXODWLRQVDUHSHUIRUPHGE\YDU\LQJ WKHDGGLWLYHZKLWH*DXVVLDQQRLVHWRFRPSDUHWKHSHUIRUPDQFHDW615YDOXHVRI DQGG%%DVHGRQH[DPLQDWLRQRIWKHLPDJHVWKHLQFOXVLRQFDQEHLGHQWLILHGHYHQ LIWKHWHVWHQYLURQPHQWLQFOXGHVODUJHDPRXQWRIXQZDQWHGLQWHUIHUHQFHQRLVH7KXV QRLVHOHWZDYHIRUPVDSSHDUWRKDYHDGYDQWDJHVWRFRPEDWXQGHVLUHGQRLVHDVZHKDYH GLVFXVVHGHDUOLHU
)LJXUH6LPXODWLRQUHVXOWVRI687 îPP LQFOXVLRQ XVLQJ6$5VFDQQLQJDOJRULWKPE\ YDU\LQJVLJQDOWRQRLVHUDWLR 615 DWDVWDQGRIIGLVWDQFHRIPP
2385
1'70,&52:$9(,0$*,1*6@ ZKLFKQHHGVWREHILOWHUHGRXWWRLVRODWHWKHRULJLQDOVLJQDO$ZD\RIRYHUFRPLQJRXW RIEDQG VLJQDO RU LPSHGDQFH PLVPDWFK LVVXHV ZLWKRXW LQYHVWPHQWV LQ FRVWO\ 5) KDUGZDUHLVWRZLVHO\SODFHDWWHQXDWRUVWKURXJKRXWWKHV\VWHP)RUH[DPSOHSODFLQJ DWWHQXDWRUVRQWKHLQSXWDQGRXWSXWSRUWVRIDPL[LQJGHYLFHZLOOLQFUHDVHWKHUHWXUQ
2386
ORVVRIRXWRIEDQGVLJQDOVUHVXOWLQJLQLQFUHDVHGSHUIRUPDQFHRIWKHPL[HU7RDOVR DFFRXQW IRU DQ\ LPSHGDQFH PLVPDWFKHV EHWZHHQ WKH DQWHQQDV D ZHOOSODFHG DWWHQXDWRUSULRUWRQH[WGHYLFHLQWKH5)VLJQDOSDWKZLOOKHOSDGGUHVVWKHLPSHGDQFH PLVPDWFKRIORZFRVWDQWHQQDV )RUGLPHQVLRQDOVFDQQLQJWHVWVSDUDPHWHUVVXFKDVVWDQGRIIGLVWDQFHDQWHQQD VSDFLQJDQGIUHTXHQF\VKRXOGEHRSWLPL]HG7KHVWDQGRIIGLVWDQFHPD\EHRSWLPL]HG XVLQJWHFKQLTXHVGLVFXVVHGLQ>@ZKHUHWKHYROWDJHRIDQRSHQHQGHGZDYHJXLGH SUREHZDVPHDVXUHGRYHUWKHUDQJHVRIVWDQGRIIGLVWDQFHIRUFDVHVRIwith DGHIHFW SUHVHQWDQGwithout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
)LJXUH )ORZFKDUWRI8:%QHDUILHOGLPDJLQJWHVWV\VWHPIRU1'7RYHU;EDQG ± *+] IUHTXHQF\UDQJH7HVWVDUHUXQLQDUDVWHUIDVKLRQDFURVVWKHIURQWRIWKH)53SDQHOV
2QFHWKHLQFLGHQWVLJQDOLQWHUDFWVZLWKWKH)53SDQHOVWKH5[DQWHQQDFDSWXUHV DQGSDVVHVWKHUHIOHFWHGVLJQDOWRWKHUHFHLYHU¶VIURQWHQGZKLFKGRZQFRQYHUWVWKH 5)VLJQDOEDFNWR,)7KH'62 $RVFLOORVFRSHWKHQVDPSOHVWKHUHFHLYHG,) 2387
VLJQDODW*6DVDQGDFRS\RIWKHWUDQVPLWWHGZDYHIRUPLVDOVRVDYHGIRUDGGLWLRQDO VLJQDOSURFHVVLQJIXQFWLRQV 7KHVHWRIWUDQVPLWWHGDQGUHFHLYHGZDYHIRUPVLVVDYHGDWHDFKVDPSOLQJORFDWLRQ RIWKHUDVWHUVFDQURXWLQH2QFHWKHZDYHIRUPVDUHVDYHGDWDVLQJOHORFDWLRQWKH; @)RUDUHDOYDOXHG VLJQDOWKHGLVFUHWHFURVVFRUUHODWLRQLVJLYHQE\WKHIROORZLQJH[SUHVVLRQ ݎ௦௦ೝ ሾ݈ሿ ൌ σஶ ୀିஶ ݏ௧ ሾ݊ሿݏ ሾ݊ െ ݈ሿǡ݈ ൌ Ͳǡ േͳǡ േʹǡ ǥ ǡ ZKHUH ݏ௧ LV WKH WUDQVPLWWHG QRLVHOHW ZDYHIRUP DQG ݏ LV WKH UHFHLYHG QRLVHOHW ZDYHIRUP>@7KLVWHFKQLTXHRIFURVVFRUUHODWLRQDOORZVIRUWKHPHDVXUHPHQWRI WKHVLPLODULW\RIWZRVLJQDOVHYHQLIWKH\DUHQRWWLPHDOLJQHGDFFXUDWHO\>@ 7KHWHVWVFRQGXFWHGDUHGRQHE\VFDQQLQJRIDUHIHUHQFH*)53VDPSOHZLWKRXW WKHSUHVHQFHRIDQ\GHIHFWRULQFOXVLRQIROORZHGE\VFDQQLQJD*)53SDQHOZLWKDQ
2388
LQFOXVLRQSUHVHQW7RHVWDEOLVKDQRWDWLRQIRUHDFKVLJQDOIRUWKHIROORZLQJWHVWVOHW XVGHQRWHHDFKPHDVXUHPHQWDVIROORZV ݏ௧୰ୣ
ؠ ݏ୰ୣ
ؠ ݏ௧ୗ
ؠ ݏୗ
ܴ ؠ 7KHFURVVFRUUHODWLRQVDUHH[HFXWHGIRUHDFKGDWDVHWDWHDFKVDPSOLQJORFDWLRQRI WKH'VFDQQLQJPDWUL[²DUHSUHVHQWDWLRQRIWKLVLVVKRZQLQ)LJXUHD7RIRUP ILQDO VXUIDFH LPDJHV DQG FRPSHQVDWH IRU VWDQGRII GLVWDQFH HUURUV WKH IROORZLQJ GLIIHUHQFHVTXDUHGIRUPXODZDVDSSOLHGWRWKHPHDVXUHGGDWDXVLQJHTXDWLRQ ሺሾݎ௦౨௦ೝ౨ ሿ െ ሾݎ௦௦ೝ ሿሻଶ ሺͳሻ ߞଵ ൌ ܰήܯ ZKHUHܰLVWKHQXPEHURIURZVDQGܯLVWKHQXPEHURIFROXPQVLQWKHGDWDPDWUL[ ,IHTXDWLRQ LVDSSOLHGWRWKHFRUUHODWLRQGDWDPDWUL[ )LJXUHD WKHQWKHGDWD PD\EHWUDQVIRUPHGLQWRWKHVLQJOHYDOXHGGLIIHUHQFHVTXDUHGPDWUL[VKRZQLQ)LJXUH E7KLVLVWKHGDWDVHWWKDWZLOOWKHQEHXVHGIRULPDJHJHQHUDWLRQ
)LJXUH D 'UDVWHUVFDQFURVVFRUUHODWLRQPDWUL[ E 'LIIHUHQFHVTXDUHGPDWUL[FUHDWHG XVLQJHTXDWLRQ RU
$QRWKHUDSSURDFKLVWHVWHGXVLQJWKHDXWRFRUUHODWLRQIXQFWLRQZKLFKLVJLYHQE\ WKHJHQHUDOH[SUHVVLRQ ୱ౨ୱ౨ ሾ݈ሿ ൌ σஶ ୀିஶ ݏ ሾ݊ሿݏ ሾ݊ െ ݈ሿǡ݈ ൌ േͲǡ േͳǡ േʹ ǥ ǡ %\ GLYLGLQJ WKH PD[LPXP YDOXH RI WKH FURVVFRUUHODWLRQ IXQFWLRQ RI WKH UHFHLYHG UHIHUHQFHDQGVDPSOHXQGHUWHVW 687 ZDYHIRUPVE\WKHDXWRFRUUHODWLRQIXQFWLRQ RIWKHUHFHLYHGUHIHUHQFHZDYHIRUPVLWZDVIRXQGSRVVLEOHWRVXFFHVVIXOO\GHWHFWWKH SUHVHQFHRIGHIHFWV>@7KLVLVVXPPDUL]HGE\WKHIROORZLQJH[SUHVVLRQ
2389
Ƀଶ ൌ
ሼݎ௦ೝ౨௦ೝ ሾ݈ሿሽ ሼݎ௦ೝ౨௦ೝ౨ ሾ݈ሿሽ
ൌ
୰ୣ ୗ ሾ݊ ሼσஶ െ ݈ሿሽ ୀିஶ ݏ ሾ݊ሿݏ ሺͳͺሻ ୰ୣ ୰ୣ ሼσஶ ୀିஶ ݏ ሾ݊ሿݏ ሾ݊ െ ݈ሿሽ
7KLVGDWDIRUߞଶ PD\DOVREHUHSUHVHQWHGLQWKHVDPHPDQQHUDVWKHGDWDIRUߞଵ VKRZQ LQ)LJXUHE $SSOLFDWLRQ7HVWVDQG5HVXOWV *ODVVILEHUUHLQIRUFHGSRO\PHUV *)53 SDQHOVZHUHLQYHVWLJDWHGIRUWKHSXUSRVHRI GHWHFWLQJWKHSUHVHQFHRIDQDOXPLQXPLQFOXVLRQ7KH*)53VDPSOHVZHUHPP îPPDQGWKHDOXPLQXPLQFOXVLRQKLGGHQEHKLQGWKHSDQHOVZDVPPî PP7KHVFDQZDVFRQGXFWHGRYHUDVTXDUHDUHDRIPPîPP7KHVWDQGRII GLVWDQFHV WHVWHG ZHUH D PP DQG D PP 6OLJKW YDULDWLRQV LQ VWDQGRII GLVWDQFHV RYHU WKH VFDQQLQJ DUHD ZHUH LQWURGXFHG WR WHVW WKH HIIHFWLYHQHVV RI WKH VWDQGRIIGLVWDQFHFRPSHQVDWLRQDSSURDFK HTXDWLRQ WRHOLPLQDWHWKHHIIHFWVRI VWDQGRIIHUURUHGJHGLIIUDFWLRQVDQGPXOWLSDWKVLJQDOV )LJXUHVKRZVWKHVFDQUHVXOWVWDNHQZLWKWKHVWDQGRIIGLVWDQFHVHWWRD PP7KHWRSWZRLPDJHVUHSUHVHQWWKHUHIHUHQFHLPDJH XSSHUOHIW DQGUDZLPDJHRI WKH 687 ZLWK DOXPLQXP LQFOXVLRQ XSSHU ULJKW ²ERWK LPDJHV UHSUHVHQW WKH PD[LPXP FURVVFRUUHODWLRQ YDOXH EHWZHHQ 7[ DQG 5[ VLJQDOV DW HDFK VDPSOLQJ ORFDWLRQ 7KH ERWWRP WZR LPDJHV UHSUHVHQW WKH FRPSHQVDWHG LPDJH JHQHUDWHG E\ DSSO\LQJHTXDWLRQ ERWWRPOHIW DQGDSSO\LQJHTXDWLRQ ERWWRPULJKW )LJXUHVKRZVVLPLODUUHVXOWVIRUWKHFDVHRIWKHVWDQGRIIGLVWDQFHRID PP
2390
)LJXUH5HIHUHQFHLPDJH WRSOHIW UDZVFDQRILQFOXVLRQ WRSULJKW FRPSHQVDWHGXVLQJ HTXDWLRQ ERWWRPOHIW FRPSHQVDWHGXVLQJHTXDWLRQ ERWWRPULJKW DWDVWDQGRIIGLVWDQFH RID PP
2391
)LJXUH5HIHUHQFHLPDJH WRSOHIW UDZVFDQRILQFOXVLRQ WRSULJKW FRPSHQVDWHGXVLQJ HTXDWLRQ ERWWRPOHIW FRPSHQVDWHGXVLQJHTXDWLRQ ERWWRPULJKW DWDVWDQGRIIGLVWDQFH RID PP
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
2392
5()(5(1&(6
6PLWK 5 $ ³&RPSRVLWH GHIHFWV DQG WKHLU GHWHFWLRQ´LQ Materials Science and EngineeringVol. III5'5DZOLQJVHG2[IRUG8. (ROVV3XEOLVKHUVSS± -RQHV 7 6 ³1RQGHVWUXFWLYH HYDOXDWLRQ PHWKRGV IRU FRPSRVLWHV´ LQ Handbook of Composites673HWHUVHG/RQGRQ8. &KDSPDQ +DOOSS± *DR/0(77KRVWHQVRQ==KDQJDQG7:&KRX ³6HQVLQJRIGDPDJHPHFKDQLVPV LQ ILEHUUHLQIRUFHG FRPSRVLWHV XQGHU F\FOLF ORDGLQJ XVLQJ FDUERQ QDQRWXEHV´ Advanced Functional Materials ± 2VSDOG ) : =RXDJKL 5 %HLJDQJ & 0DWKHLV - -RQXVFKHLW % 5HFXU - ±3 *XLOOHW 3 0RXQDL[ : 9OHXJHOV 3 9 %RVRP / 9 *RQ]iOH] , /ySH] DQG 5 0 (GR ³$HURQDXWLFVFRPSRVLWHPDWHULDOLQVSHFWLRQZLWKDWHUDKHUW]WLPHGRPDLQVSHFWURVFRS\V\VWHP´ Optical Engineering ± &ULVWRIDQL ( 0 %HFTXDHUW 0 9DQGHZDO DQG - -RQXVFKHLW ³8OWUDZLGHEDQG QRQ GHVWUXFWLYH WHVWLQJ 6$5 V\VWHPV WRZDUGV FRPSUHVVLYH VHQVLQJ´ LQ Proc. 1st International Workshop on Compressed Sensing Applied to Radar%RQQ*HUPDQ\0D\ =KDQJ+%*DR*
