Chemical Shift Imaging (CSI) by precise object displacement

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(1)Chemical Shift Imaging (CSI) by precise object displacement Sebastien Leclerc, Gregory Trausch, Benoit Cordier, Denis Grandclaude, Alain Retournard, Jacques Fraissard, Daniel Canet. To cite this version: Sebastien Leclerc, Gregory Trausch, Benoit Cordier, Denis Grandclaude, Alain Retournard, et al.. Chemical Shift Imaging (CSI) by precise object displacement. Magnetic Resonance in Chemistry, Wiley, 2006, 44 (3), pp.311-317. �10.1002/mrc.1757�. �hal-00124995�. HAL Id: hal-00124995 https://hal.archives-ouvertes.fr/hal-00124995 Submitted on 17 Jan 2007. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

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(12) ÿHp L ["p T[ OWL ø{T O RV T KMKþK jUi L [T KKPL X+RV²XsR"["R;VV T}\wk O j O p*R ["j*X O \ j K j NO p*R VwT1ç æ+K R æ jV LÒL j*X ì æ n K V3R;V N j*\ O p*RV O R æ*æ R]\çj O jU\ f>j æOWL [ÂT K R"X+["j+v*R]\ æ n K V RÒ["j;n+X O R}\3f K@L ç LdO Vÿ LdO []pV L i+X*T K V3f R]\wjûVwR OPOWL X;i j N%O psRþj æ;OWL ["T K R1Xs["j+v*R]\ï é O []j*ççÒn>X L ["T O RV5ÿ LdO p O p*RÃçT L X[Âjç æ n O R]\ O j O \ L i*i+R]\ O p*Rv L V æ+K T"["R"çR"X O T æ*æ T]\wT O n VT]Xsv O j æ \j;ø L v*R O p*RZV O T O n Vj NO p L Vv*Roø L [R | KPK R æ R}\ L çR"X O V æ \3RVwR"X O R"v²p*R]\3R.["j*X*["R}\X æ \3j O j*X FHGJI ìT O ô+õ*õ G ÂïÒT]XsvûÿHR]\3R æ R]\ N j*\çR"vJT O T"çÒS L R"X O O R"ç æ R}\3T O n+\3R ÿ LÒ p T¹p*j+çR"òçT"v*R [ÂjUX+V3j K Rìlp*T]\wvÿT]\wR T]Xsv Vwj NPO ÿT}\3R]ï j æ R]\3T O R"v L X ["j*Xoüln{X*[ O L j*XHÿ LdO pTÿ L v*R"òlSUjU\3R N jU\3v mçHT]iXsR O ì3V3R"R NlL i;n+\3Rô*ï m¼p*R æ \ jsSUR L V5RÂn Lxæ*æ RÂvHÿ LdO p TZV3TÂv*v K R[Âj LMK j N ççv L T"çR O R]\T]Xsv Ãçç psR L i+p O |V O psRþV æ T OWL T K \wRV3j K n OL j*X L Vi+jsøUR]\X+R"vþS*k O p*RV æ T O L T K V3R K R"[ O L ø LÒ k j N O p*R\ NNWL R K v*f LdOL V L ç æ j*\ O T]X O O j ë*X*j;ÿ O p*RÒr æ \3j NlLDK R T K j+X;i O psRþø+R]\ O L ["T K v L \3R"[ O L j*X é OL Vtv*R O R]\3ç L X+R"vúS*k\ln{X*X L X*i O p*R R æ R]\ L çR"X O v*RVw[]\ L S{RÂvT]S+j;ø+RÃì TúV L X*i K R æ n K V RÃR æ R]\ L çÃR"X ON j*\RÂT"[]pVwT1ç æ+K R æ j>V LdOL jUXqï)ÿ LdO p TQUp L i{R"ç LO n*S{R ["j*X O T L X L X*i Tþv;\wj æ j N ÿHT O R]\Vwj O p*T O¼O psR KML n L v O p L []ë+X*R;VV L V¨TÂSUjsn O ñoçç m¼p L VR æ R]\ L çR"X O k L R K v>V á.

(13) ÿ *p T O ÿR²["T KDK)O p*RV L i+X+T K)æ \wj NlLDK Rÿp L [1p L V X*j O R T"[ O K k O psR]r æ \3j NlLDK RJTsVR æK T L X+R"v X*j;ÿ å æ \3j;ø L v*R"v O p*T O¼O psR æ n K V3Rvn+\3T OWL jUX τ L VV3çÃT KDK R}\j*\¨R"n+T K>O j O p*T O []j;\ \3RV æ j*X*v L X;i O j O p*R π æ n K V3R N j*\ O p*RÃ\3R]i L jUX²j N çT L çÒn{ç \ NNL R K v T"ç æ+KPLÒ n{v*R"fÿHR ["T]X.ÿÒ\ LdO R O psRúV L iXsT K T"ç æKMLdO n{v*R T O TÃi L øURX K j+["T O L j*X TV

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(15) f O p*R N T[ O jU\ ³ T]\ L V3R;V N \3j+ç O p*R V L iXsT K \3R"[R æ;OWL ø LdO kÿ p L ["psf/S*kø L \ O n{Rj NO psRþ\3RÂ[ LMæ \3j+[ LdO k æ \ L X*[ LMæK R"f L V æ \3j æ j;\ OWL jUXsT K+O j T"[]pv*T O T æ j L X O k L R K vVTø+T K n R N j*\ ³ T]Xsv O psR æ+K j O j N>³ ø+R]\VWn V æ \3j;ø L v*RV O psRÃ\3R"n L \3R"v æ \3j NWL@K R éX æ \wT"[ O L ["RþÿHR ["T"Xún V3R O psR"X*T O n+\wT K æ \3j NWLMK R j N5O p*RÃ\ N ["j LMK j*\T æ \3j NlLMK Rj;S O T L X*R"vZS*k V KDL [ÂRZV R K R"[ OL j*X æ \3j+["R"vn+\wRVTVv*R"V3[}\ L SUR"v L XT æ \3R]ø L j;n VÿHjU\ ë! |VT NL \oV O çj+v*R K Vk{V O R"çf ÿþR [ÂjUX+V L v+R]\3RÂv T FÒGùI O n*S+R²["j*X O T L X L Xqi O ÿHj X*j*X*òlç L V [ L S K R KDL n L vV ìîÿHT O R]\T]X*v O j K n{R"X*R}ï L i;n+\3R |V O p*RVwR O ÿj KML n L vVp*T]øUR øUR]\kJv LMNN R]\3R"X O VWn+\ N T["R O R]X+V L jUX>VwfT çR"X L V [=n V N jU\3çÃVzT OO p*R L X O R]\ N T"[R S+R O ÿR"R"X O p*R O ÿ j KML n L v>V X O p*RçT æ j N¼NlL i;n+\3R +fUÿ p L ["p L VTÒV L ç æ+K R["j*X O j;n*\ æ*K j O j N O p*RÒV æ R"[ O \3T ["j*\l\wRV æ j*X*v L X;i O j O p*RÒVln{["[ÂRsV V L ø{RþV3T"ç æK Rv L V æ+K T"["R"ç R]X O V3f>j*X*R["T"X V R"R O p*T O4O j K n{R"X*RÒT"X*vÒÿT O R]\5T}\3R æ \3RVwR]X O V L çÒn KdO T"X*R"j;n V K k L X.T j*X+RtÿHp L ["p L V çç p L i+p*f*ÿp*R]\wR"T;V O psRÒçÃR"X L V3[onV L V T]S+j;n O ñ " çÃç p L ip m¼p L V L V¨[ K R"T]\ K k vn{R O j O psRZÿ L v O p.j N%O psRþR [ LÒ T OWL jUX æ \3j NWLPK R"fT}X*v.["jsn K vÃS{R L ç æ \3j;ø+R"vÃS*k O p*R \3R"[ÂjUX+V O \ln{[ OWL j*XT K i+j*\ LdO p*ç÷ìîÿp L ["pZÿT;VX*j O ksR O¼L ç æK R"çR"X O R"vT O O p*R OWL çRj N>O p L V NWL \V O R æ R]\ L çR"X O ï Q+R=ø+R}\3T K5L X O R]\3R;V OWL Xqi æ p*R"X*j+çR"X*T.["T"X X+R]øUR]\ O p*R K RV VZS+R.j;S>V3R}\wøUR"v åNL \V O K ksf LÒ [ÂT1X²S+RV3R"R"X O p+T O)O psR \3RVwjUXsT]X+["R N \wR"n{R"X*[ L RsVzj N5O p*R O j K n{R"XsR æ R"T}ë>VÒì T1Xsv O jT K R;VV3R}\ÒR O R}X O f O p*j>V3R j N ÿHT O R]\ ï L X*[}\3R"TV R ìÍV p LPNPO¼O j O p*R K R NPO ïÿ p*R"X.j*X*RÒçjUøURV O j;ÿHT]\3vV O psR K jsÿHR]\ æ T}\ O j NO p*RþVwT"ç æ+K R mp L V æ p*R"X*j+çR"X*j*X L V vn{R O jT}X L X O R}\ÍXsT K V O T OWL [çT]iX+R OWL [ NlL R K v.T]\ L V L X*i N \wjUç O p*RÃv LMNN R]\3R"X*["R L XçT]i+X*R OL [ Vln V ["R æ;OL S LMKPLdO k S+R O ÿR"R"X O p*R²i K T;V V j NZO p*R SUj ODO j*ç j NZO p*R O n*S+RJT1X+v O p*R O j K nR1XsR m¼p L V L X O R]\XsT KNL R K v L V L X O p*R j æ*æ j>V LdO R.v L \3R"[ O L j*X O j O psR NWL R K vr

(16) j N)O p*R.çT]i+X*R O L qT OWL j*XJT1Xsv L X*[]\3RÂTsVwRV T;VÒj*X*R.T æ*æ \3j+T"[]psRV O p*R S+j OPO jUçj N>O p*R O n*S{R X*R["T"XT K VwjÃj;S>VwR]\ø+Rj*X O p L Vç T æÒO p*R)ø{T]\ L T OL j*Xj N>O psR\3RV3j*X*T"X+["R N \3R"n{R"X+["k.

(17) T OO p*R L X O R}\ N TÂ[RþSUR O ÿHR"R]X O psR O ÿHj KML n L vV åO p L V\wRVln KdO V L X²T KPL X+RþS*\wjT"v*R}X L X*i N jU\ O p*RÒÿT O R}\ æ R"T]ë T]XsvþR O \3T æ R"T]ë>V N j*\ O j K n{R1XsRì O p L V L V æ T]\ OWL [=n K T]\ K kþø L V L S K R N j*\ O p*RçR O p;k K \wRsVwjUXsT"X*["R]ï L i;n+\3R " m¼p*R X+R O Vk+V O R"ç ÿp L ["pûÿHT;V L X;ø+R;V OL i+T O R"v L V T æ+L R["Rúj N p L i+pJv*R1X>V LÒ k æ j K kUR O p;k K R"X+R ÿ p L [1pJp*T;V S+RÂR1X L X.["j*X O TÂ[ O ÿ LdO p TÒç L O n+\3R j N Vwj K ø+R"X O V jUX jUXsRZj NLÒ VV L v+R m%psRÒj;S}ü3R"[ O L ø+RÒj NO p*RÒR æ R]\ L çR"X O L V O júV O n{vk O psR æ R"X+R O \3T OWL j*Xj N R"T["p["jç æ j*X*R"X O j N/O p*Rç L O n+\3R L X O j O p*R æ j K k+çR]\ \3jç NWL i;n+\3R " f LdOtL VVwR"R"X O p*T O f N j*\ O p L V["j*X O T"[ O5OWL çÃR ì3V L ÿRÂR]ë>V T O +õ u ï3f5V3j K øUR"X O V O R]Xsv O jTÂ["[=n{çZn K T O R T O5O p*R ["R]X O R]\j N O p*RÒV3T"ç æ+K R Q+jUçRj O p*R]\¼ø+T K n{T]S K R L X N j*\3çT OWL jUX["T"XþSURzi+T L X+R"v N \3j+ç O psRZR T"ç L X+T O L jUXj N KPL X+R L X O R1X>V LÒL RV L XV æ R[ O \3TjsS O T L X*R"vT O v LMNN R}\3R"X O psR L i*p O V åULdOL V [ K R"T}\ O psT OL V3j+j[ O T]X*Rv*j+RVX*j O R]X O R]\ O p L V æ j K k+çR]\ L [þçT O R]\ L T K ÿp LPK RR O p*T"Xsj K æ R1XsR O \3T O RV5çj*\3RÃV K j;ÿ K k ì LdOL V æ \3RV3R"X O jUX K k T OO p*R["R"X O R]\ j N%O psRýV3T"ç æ+K R}ïT"Xsv æ \3RVWn>çT]S K kûR]ø+T æ j*\3T O RVçHjU\3R;n L []ë K k O p*T"X O j K n{R"XsR N \3jç O p*R V L v*RZÿp L ["p L V X*j O L X["j*X O TÂ[ O ÿ LdO p O p*RZV3j K ø+R"X O ç L O n+\3R

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(20) . | dK O psjsn+i*p O psRv*RÂø L ["RT KPK jsÿVZVwT"ç æ+K Rv L V æ+K T"["R"çR"X O VtTV K jsÿ TV¨jUXsRþç L []\3jçR O R]\3f%V O R æ Vj N " õ µç j*\Ãñ}õ*õ µç T]\3Ri+R"X*R]\3T KMK k.n4V3R"v m¼p*R;V3R K T ObO R}\)ø+T K n{RVT]\3RT]X;k;ÿT]kû["j*XV L v*R]\3T]S K kJV3çT KPK R]\ O psT"X O p+R ÿ L v O pj N O p*RìR æ R]\ L çR"X O T KMK k v*R O R]\3ç L X+R"v;ï)V L i+X*T K>æ \ j NlLMK R"fUÿp L ["p L Vi+R1XsR]\3T KPK kÃSUR O ÿRÂR]Xõ " T"X*v çÃç mp*RV æ R"[ O \ln+ç jsS O T L XsR"vù["j*\\3RV æ jUXsvV O p*R}\3R N jU\3R O j O p*R æ T]\ OWL T K jsøUR]\ K T æ j N V3R]ø{R]\wT KO R]X>Vj N R K R"çR1X O T]\k V KDL ["R;V.ìîS*k R K R"çÃR"X O T]\lk V KPL [R ÿRùçR"T"X T V KML [ÂRùj NÒO p L []ë+X+RVoV.RÂn{T KO j O p*R V O R æ j N v L V æ+K T[ÂR1çR"X O ï m%psRT L ç j NÃO p*R T K i+jU\ LdO p*ç v*R;Vw[]\ L SUR"v S+R K j;ÿ L V O j \wR"["j*XV O \Wn{[ OO p*RV æ R"[ O \Wn>ç ["j*\l\wRV æ j*X*v L X;i O j RÂT"[]pj N O p*RVwRZR K R"çR1X O T]\k V KPL ["R;V N \3j*ç O p*RÒV æ R"[ O \wTZçR"TVWn+\3R"v N j*\5T KMKO psRHVwT1ç æ+K R æ j>V LdO L j*X>Vì O p*RXn{çÒS{R]\j N V3T"ç æK R æ j>V LdOL jUX>V L V3fUS*k v+R NlL X LdOL jUXsfR"nT KUO j O psRzXn>çÒS{R]\j N R K R"çÃR"X O T]\k V KML [RVï m¼p L V L V5\wR K T O RÂv O j T æ \ j["RÂvn+\3Rtÿ p L ["pÒÿTV æ \3j æ jVwR"výVwjUçHR O L çÃRT]i+j O j []j*\\3R"[ O v L V O j*\ OWL j*X R NlN R"[ O V L X L çÃT}i+RsV æ \3jvn{[ÂR"vZS*kTZVWn+\ N TÂ["R["j LMK j N T æ T]\ OWL [=n K T]\¼i+RÂjUçR O \wk L i;n+\3Ró à.

(21) YR O XþSUR O p*RZXn>çÒS{R]\j N v L V æK T"[ÂR1çR"X O V%j N>O p*RÒV3T"ç æK RT1Xsvþç O psRzXn>çÒS{R]\j N R K R1çR"X O T}\wk V K@L [RV L X T]X÷R [ LdO T O L j*X æ \3j NWLPK R ì N j*\ùR T1ç æ+K R"f LMNúO psR v L V æ+K T"["R"çR"X O²L V ñ}õ*õ µç T"X*v O p*R ÿ L v O p j NúO p*R R [ LÒ T OL jUX æ \3j NWLPK R L VñÒçç f O psR1X.çñ}õ;ï O j · T]\ R O psRÒXV æ R"[ O \wTÒjsS O T L X*R"v N \3jç Vln{[["RVoV L ø{R. 3V T"ç æ+K Rv L V æK T"[ÂR1çR"X O V O j 7 T]\3R O psR V æ R"[ O \3T ÿR ÿ L V3p O j j;S O T L X T OJO p*RR]X*v j N O p+R \3R"[ÂjUX+V O \ln{[ OWL j*X æ \3j[ÂRVVwfùR"T"["p j NùO p+R1ç ["j*\\3RV æ j;X*v L X*i O j T i L øUR"X R K R"çÃR"X O T]\k V KPL ["R mp*R R [ LÒ T OL jUX æ \3j NWLPK R L V NlL \V O v*R"[ÂjUç æ j>V3RÂv L X O jùç R K R"çR1X O T]\kV KDL [ÂRV3f ì ñ O j çÒïÒSUR L X*i O p*R p*R L i+p O j N/O psRÒR [ LdO T O L j*X æ \3j NWLPK R L X O psRZç L v*v K Rj N O p+R

(22) V KDL [Rì NlL i;n+\3R *ï |ÒVÿHRþV3psT KDK S+RvR"T KDL X*i ÿ LdO p T"X LÒ R]\3T OWL ø+R æ \3j+["RVVwf ÿHRV3p+T KMK v*R"X*j O RúS*k O p*R\3RÂ["jUX>V O \ln{[ O R"vV æ RÂ[ O \ln+ç N j*\ O p*R ?

(23). R ["p*j+jVwR O j²v*R NWL X+R O psR L X LdO L T K V æ R"[ O \3T T"çj;n+X O V O j L v*R1X OLMN ksf+TVT NlL \V O T æ*æ \j L çT OL jUXsf O j · ï R K R"çR1X O T]\kV KDL [R T O5O p*R

(24) LdO R]\wT OWL j*X % " (' ) = $ # " ! & !. TVìîÿ p L [p. ì]ñoï. =. ÿ p LPK R O p*RçR"T;Vln+\wR"vÃV æ R"[ O \Wn+ç ) ( ["T]XZSURR æ \3RVoVwR"v*f L XTi+R]X*R}\3T K ÿT]k+f+TV 0 - =* + 1 / , - 1 ×. , , 4j*\R "T ç æ+K R"f N j*\¼ç4ö*fsÿHRp*T]øUR å 9 9 9 ; 8 =: 8 × 9 8 +: 7 × 9 7 +: 5 × 9 5 ; 7 =: 7 × 8 +: 5 × 7 +: 6 × 5 23242 =. + −. ìlô*ï. ìö;ï. \3j*ç "R n{T OL j*Xìlô*ïT1Xsv N \3jç O psRZR æ R]\ L çR"X O T K V æ RÂ[ O \Wn+ç=<?>©fUÿHR["T"X v*R]\ L ø{R"f>T O4O p*R NWL \oV OLÒ R]\3T OWL j*X TX*Roÿ V æ RÂ[ O \ln{çA@B>1ìîÿÒp L [1pV3p*j;n K vÒ\3R æ \3RV3R"X O T}X L ç æ \3jsøUR"çR"X O ÿ LÒ pÒ\3RV æ R"[ O O j O psR æ \3R=ø L j;n Vj*X*R]ï E N (U ) = U GHF O − I K P N Q T S ×M D C R J MQ L L J J L =. + −. ì *ï. 4j*\ O psRR T"ç æ K R j N R"n{T O L jUX+Vìö;ï3f;ÿHRj;S O T L X ä.

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(27). −. − . ( ) × . ( ) × . − . . −. ( ) × ]. . ì"ï. ( ) × ]. . . m¼p*RVwRR"n{T O L jUX+V["T"XÒS+Ri+R"X*R}\3T K@L qR"v N jU\ O p*R. LdO R]\3T ObL jX å. . $. ( )= . . . ". . −. . " % + − . = . ìó;ï. ! . −. . $ #. ×. . m¼p*R LÒ R]\3T OWL ø+R æ \3j+["RV Vÿ PL KDK S+R¹V O j æ*æ R"vÿ p*R}X O ÿj VwR]\ L R;VJj N V æ RÂ[ O \3T["j*\l\3RV æ j*X*v L Xqi O j O ÿ j Vln{[Â["RVoV L ø{R LÒ R]\3T OWL j*X>V ]T X*v T]\3R)ø+R}\wkH[ K j>V3R å + 1 0 2. =. 4 2. 5. 7. + 3. 8 6. *. ')(. −. 4. /. 2. &. 7 3. - .. , +. ì ï. 6. <ε. ÿ *p R]\3R ε L VT O pq\3RVpsj K vÒø+T K n{RZV3R O T"["[ÂjU\3v L Xqi O j O p*R æ \wR"[ L V L jXÒ\wR"n L \3R"v éX æ \3T"[ OWL ["RÂf¼T KMK [T K [=n K T O L j*XVtT]\3R æ R]\ N jU\3çR"v N j*\T KMK%O psR v*T O T æ j L X O Vÿp L ["pv*R NWL X+R T V æ "R [ O \ln>ç m¼p*RÒT"ç æKMLdO n{v+RÒT O4O p*R æ j L X OL X O p*R N \3RÂn{R1X+[]k v*j*çÃT L XÃÿ LDKPK>O pn V5SURÒv*R"X*j O R"v TV T]Xsv O p*R O RV O ì ï L V%T"[ O n{T KMK kÿÒ\ LdObO R]XHTV :9. B. <;>= ?. E G CDC F. =. KD H K. =. J. F H. (I. +. F. ) − H (I ) < ε L J. A. @. ìï. m¼p*RT]S+j;ø+RT K i+jU\ LdO p*çfþT KdO p*j;n+i*p S+T;V L ["f æ \3j;ø+R"v O j S+Rùn V3R N n K TVùV3p*j;ÿÒX L X O p*R N jU\ O p*["j*ç L X*i R T1ç æ+K R éX jU\3v*R}\ O j.[]p*R"[}ë O p L VT K i+jU\ LdO p*ç ÿ LdO p T æ R]\ N R"[ O K k NWK T OL X O R]\ N T"[ÂRÒT"X*vÃS+R"["TonVwRzÿRÿR]\wRzn+X*T]S K R O j NL X+vùT O ÿHjò æ p*TVwR Vk>V O R1ç ÿ LÒ psjsn O TúçR"X L V3[=n4V3fÿHR²v*R"[ L v*RÂv O j L ç æ \3R]i+X*T O R T æL R"[ÂRj N X*T O n+\3T K \ln*S*SUR]\ÿ LdO p O j K n{R"X*RÂf O j æ*K T["R LdO T O5O psRþS+j OPO j*ç j N T " çç v L T1çR O R}\ O n*S+R T]Xsv O j æ n O5O p L V O n*S+R L X>V L v*RþT"Xsj O psR]\ NlK T O òîSUj OPO jUçRÂv O n*SURÒ["j*X O T L X L X*i ÿHT O R]\ \3j*ç NL i;n+\3R f LdO ["T"X NWL \V O S+RÒXsj OWL [ÂR"v O psT O.

(28) O p*RÃ\wRV3j*X*T"X*[ÂR N \ R"n{R"X*[]kùV3p LDNPO Vì L Xj O p*R}\ÿj*\3vV3f L X O R]\ X*T K i*\wT"v L R"X O V ïT]\3R K R;VV æ \wjUXsjsn+Xs["R"v psR]\3R ì NWK T OL X O R]\ N T"["R]ï O psT"X ÿ LdO p¹T"X L X O R}\ N T["R ["jUX>V OWLdO n O R}v¹j N TçR"X L V [on V F j æ \ j["RÂvn+\3R N j*\V KML [R V3R K R"[ O L j*X.j N¼O p+RÃV3R"[ OL j*XÃÿTV¨T æ*æKDL RÂv*fT"X*vÃÿR V L ç æ+K k.\3R æ RÂT O R"v*f N j*\¨v LMNWN R}\3R"X O v L V æ+K T"["R"çR"X O V3f4T]X R æ R]\ L çR"X O [ÂjUX+V L V OL Xqi¹j N T π ô æ n K V R N j K@K jsÿRÂv S*k V L iXsT K T"["n L V LdO L j*X I R"["j*XV O \ln{[ OWL j*XÿT;V ["T]\ \ L R"v j;n O j*X O p*RS+T;V L V j NO p*R R æ R]\ L çR"X O T KMK kv*R O R]\ ç L X+R"v¹V L iXsT K æ \3j NWLPK R T"X*v \wR"n L \3R"v ô LdO R]\wT OL jUX+V m%psR\3RVln KdO VT}\3R æ \3RVwR]X O R"v L X NWL i;n+\3R L i;n+\3R m¼p*RR NlN R"[ O j N \3R"[ÂjUX+V O \ln{[ OWL j*X L V æ T]\ O L [=n K T]\ K k ø L V L S K R å R=ø+R"X L@NO p*R]\3R L VV O L@KDK T j*X*RZÿpsR]\3R O p*R O ÿ j V3j K ø{R"X O Vj;ø+R]\ K T æ ìîÿÒp L ["p v*jRVX*j O \3R"T KMK k R L V O ï3f O p*R L X O R1X+V LdO k j NzO p+R æ R"T}ë/V L X O p L V j*X*R²p*T;V v*R"[]\wR"TV3RÂvþ[ÂjUX>V L v*R]\3T]S K kìîS*k T N T"[ O j;\j N ô O jÃö;ïÿ LdO p+j;n O>O psR L X O R]X>V LdO kj N>O psR æ R"T}ë>V%S{R L X*iT NlN R[ O R"v T O4O p*R æ j L X O Vÿ p*R}\3R O p*R}\3RþV3p*j;n K vÃS+RÒX*j.j;ø+R]\ K T æ ì N j*\R T1ç æ+K R"f L XV L v*R O psRZ\ln+S*S+R]\ ï m%psRV3RZ\wRVln KdO V ["j*X NlL \Íç O p*R"X O p*T O fT KdO p*j;n+i*p L ç æ R]\ N R"[ O ìîÿ LdO p \wRV æ R[ O¼O j O psR O p L []ëXsRVoV¨j N¼O p*RZr æ \3j NWLMK RÃT"X*v O p*R v L V æ+K T[ÂR1çR"X O V O R æ ï f O p*R \3R"[}jUX+V O \ln{[ OWL j*X æ \wj["RÂvn+\3R XsR]ø+R]\ O psR K RVoV K R"TÂvV O j T V L iX LDNL ["T"X O L ç æ \3j;ø+R"çR"X OL X O psRZn{T KPLÒ k j N O p*R æK j O VjsS O T L X*R"v m%psRz\3RV L vn{T K n{XÿHT"X O R"v O \3T"["RV5T}\ L V3R æ \3jsSUT]S K k N \3jç O psR L XsT[Â[=n+\3T"[]kHj N>O p*RZV L i+X*T K+æ \3j NWLPK R)n VwR"v L X O p+R\3RÂ["jUX+V O \ln{[ OWL j*XT K i+j*\ LÒ p*ç m¼p L V¨\3R"[ÂjUX>V O \ln{[ OWL jUX æ \3j+["R"vn+\3Rp+TVS+RR"X T æ*æKDL R"v O j²T æ \ jsS K R1ç j N çHjU\3R["p+R1ç L [T K ["jUXs[R]\X²T"X*v v*R"T K Vþÿ LdO p i+T;VwR"jsn VS+R"X R"X+R æ R]X+R O \wT OWL j*X L X O jT "R"j KMLdO R m¼p*RùV L ç æK R FHGJI O n*S+Rûn VwR"v L X O p*R æ \3R=ø L jsn VHR æ R]\ L çR"X O V L V \3R æ+K T["R"v S*k'TûçHjU\3R R K TÂS{j*\3T O R"vv*Roø L [ÂR"fV OWLMKPK j N T L T K Vk+çÃçR O \lksf5S;n O L X+[ K n{v L X*iV3R]ø{R]\3T K ["j*ç æ T]\ O çR"X O V¨Vln{["p O psT O¼O p*R æ R]X+R O \3T OWL j*X j N SUR1X 1R1XsR L X æ j;ÿHv*R]\3R"v RÂj KMLdO RÒ[ÂTX S+R O \ L i*i+R]\wR"vúT O TçjçR"X O []psjVwR1X S*k O p*RR æ R]\ L çR1X O R]\ u Q*é¨R æ R]\ L çR"X O V¨p*T]øURHS+RÂR1X.\ln+X.R]ø{R]\3k ö*õç L X;n O RV T"["pJR æ R]\ L çR"X OL X;øUj K ø+R;V T O j O T K v L V æK TÂ["R"çÃR"X O j N ñ çÃç ì[ÂjU\\wRV æ j*X*v L X;i O j O psR p*R L i+p O j NÒO psRù["jUç æ T]\ O çR"X O ["j*X O T L X L X*i O p*R R"j K@LÒ R æ j;ÿv*R}\ïþÿ LdO p " õ µç L X+[]\3R"çR"X O V Q*j*çR O k æL ["T K v LMNN n V L jXH[=n+\lø{RVv*RÂvn{["R"v N \wjç O p*RVwRR æ R]\ L çR1X O T K v*T O TT]\3Rv L V æK T]k+RÂv L X NL i;n+\3R L i;n+\3R .

(29) |VR æ R[ O R"v*f jUXsR ["T"X Xsj O RÂv T çHjU\3R\3T æ+L v v LDNlN n4V L jX L X O p*R n æ*æ R]\ æ T}\ O j NO psRR"j KMLdO R ["j*ç æ T]\ O çR"X O T K jUXqiþÿ LÒ p*f>T OK j*X;i OWL çR;V3f>Ti+TVT"["[on>çÒn K T OL j*XT O O p*RS+j OPO jUç÷j N O p*R["jç æ T}\ O çR"X O y LMNWN n4V L jX \3T O RVûv*R"vn{["R"v N \3jç O psR;V3RR æ R]\ L çR1X O V²p*T]ø{R S+R"R"X[1p+RÂ[]ë+R"v ÿ LdO p¹T"XT æ*æ \wj æ \ L T O R O p*RÂjU\lkHT]Xsv ÿ LPKPK S+R O psRZVln+S}ü R"[ O j N T)ÿ j*\ë æ n*S KML V3p+R"vR K VwR=ÿpsR]\3R

(30) . m¼p L VÿHjU\ ëp*TVþV3psjsÿHX O psT O T \3R K T OL øUR K kV L ç æK RúçRq[]p*T"X L [T K v+RÂø L ["R.["jçÒS L X+R"vÿ LdO pTV æ T OL T KDK k V3R K R"[ O L ø+R\3TÂv L j+ò N \3R"n{R"X*[]k NWL R K vìj;S O T L X+R"vZS*kT æ \3j æ R]\¼i+R"j*çR O \Wkj N>O psR FHGJI \ N ["j LMK ï[T"X K RT"v O j V L i+X LPNL ["T"X Ou Q*é5\3RVWn KÒ V /jU\5çHjV O5æ \3TÂ[ OWL [ÂT K T æ*æ+KPL ["T OWL j+XV3fçHTwüwjU\ O \3R]XsvV5ÿ LMKPK S{RþTÂ["["RVoVwR"v S*k.\wT=ÿ v*T O T"f L R R=ø+j K n OL j*X j NO p*R FHGùI V æ RÂ[ O \ln{ç TVT N n{X+[ OWL j*X j NO p*R K j+["T O L j*X L X>V L v*R O psRÒj;S}ü3R[ O Q;n{[]p T"["[ÂR æ;O T=S K R\3RVWn KdO V ["T"XS+Rùj;S O T L X*RÂv vn{R O j T]XR [ LdO T OWL j*X æ \3j NWLPK RùT K \wR"T"v;k VwR K RÂ[ OL øUR S*k LdO V R KMN O p*T}X;ë V O j²T æ*æ \j æ \ L T O R V3T"v*v K RÃ["j L@K v*R;V L i+X é N5æ \3R"[ L V RÃv*R O T LMK VzT]\3RÃX*RÂR"vRÂv*f LdO¨L V æ jV V L S K R O jû\Wn+XT \3R"[ÂjUX+V O \ln{[ OWL j*X T K i+j*\ LdO p*ç O T]ë L X;i L X O j TÂ["["j;n+X O O p*R jsøUR]\ K T æ j N V æ R[ O \3T N jU\ Vln{[Â["RVV L ø{R v L V æ+K T[ÂR1çR"X O V j NO psRþV3T"ç æ+K R m%psRZ\3RVWn KÒ Vj;S O T L X*R"v L X O p+R æ \3RV3R"X Oæ T æ R]\To\3RZ\3T O p*R}\R]X*[Âjsn+\3T}i L X*i LPN ["j+ç æ T]\3R"v O j[}jUXø{R1X OWL j*X+T Ku Q*é3fRV æ RÂ[ L T KPK kT;V N T]\.TV V æ R"[ O \wT K \wRV3j K n O L jUX L V.["j*X*[ÂR]\3X*R"v | KPL ç LdO T OWL jUXJj N5O p+RýçR O psjv²["j*çR;Vp*j;ÿR=øUR]\ N \3jç V æ R"[ O \3T K S*\wjT"v*R}X L X*iJvn{R O j L X O R}\X*T K i*\3T"v L R"X O V ÿ p L ["pJT æ*æ R"T}\ÒT OtL X O R]\ N T["RV3fT KÒ psjsn+i*p O p*RV3R N R"T O n+\ RV["T"X²k L R K v L X O R]\3R;V OWL X;i L X N j*\3çÃT OL j*X\3R K T O R"v æ \3R"[ L V R K k.V3T"ç æK R L X*p*jçj*i+R]X+R LdO k |ZX;kqÿT]ksf;ÿR["T"XT]X OL [ LMæ T O R L ç æ \wjsøUR"v[]p+R"ç L [T K V3p LMNPOL çT]i L X*i ÿ LdO pçj*\3RR K T]S+j*\3T O R\3R"[}jUX+V O \ln{[ OWL j*XT K i+jU\ LÒ p*çýV !"#$. R T]\3R i*\wT O R N n KûO j í\j N R;VV3j*\ G L ["psT"R K íR O \Wk;ë+f N \3jç mR]\Xsj æ k K ì Òë*\wT L X+R]ï N j*\ O psR"j*\3R OWL ["T K v L@NWN nV L j+XÒ\3T O R¨["T K [=n K T OL j*XV4ÿp L [1pHT]\3R L XHT]i*\3R"R"çR"X O ÿ LÒ p O p*R[=n+\Wø+RVj NNWL i;n+\wR &%. . .

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(41) 9P - ô+õ*õ;ô ð u p LMæ VwR O Q u ñoô+ò I m QsfsrtR"[]ë Q ñ}õ | KdO R]\3T R G T R í G ñoô Q;Y u +fU|Ym I | u j*\ æ j;\ T OWL j*X ñ*ñ QUksçÃçR O \ L [T K ç L []\3j O n*SURzçHT O []p*RÂv ÿ LdO pTy S f Q é3h G é u j Y O v;f*m¼j*ë;ksj ñoô rtT]\ LMK*F f{mp L T=n{v 0L U \wR 5f Vn{RVoV3j*XþrtfUyHR K T K T"X*v*R u f u T]X L jX L í¼f \wT1Xs["j*X L ~ G I7(+*5- #8

(42) 9 - ô+õ*õ*õÃ5ð C+KA*f*ô*ô+ö;òWô*ô .

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(45) N ìÍV L iX+T KÒæ \wj NWLPK R]ï²T"Xsv : ìR K R"çR"X O T]\kV KPL ["RV ï L X;øUj K ø{R"v L X O p*R \wR"["j*XV O \Wn{[ OWL j*X T K i+j*\ LÒ p*çìwç 4ö;ï L i;n+\3R yR"çj*XV O \3T OWL j*XJj NO p*R L X O R}\3RV O j N)O psRý\3RÂ["jUX+V O \ln{[ OWL j*X æ \3j[ÂR"vn+\3R N jU\ TûVwT"ç æK R.j NO p*R V3T"çRX*T O n+\3RTV L X NlL i;n+\3R þSqn O¼L X;ø+j K ø L X*i T NlK T OL X O R]\ N T["R I T=ÿ÷v*T O T"fv L V æK T]k+R"vjUX O psR K R NPO f/Vpsjsÿ T XsjUXsòX*R]i KPL i L S K R ìT"Xsv n>XÿT"X O R"v;ï¹j;ø+R]\ K T æ j N O j K n{R"X* R ÿ LdO p ÿT O R]\ m¼p L V¹j;ø+R}\ K T æ T K çj>V O v L V T æ*æ R"T]\ VT NPO R]\ O psR\3R"["j*XV O \ln{[ OWL jUX æ \wj["RÂvn+\3Rìî\ L ip O ï L i;n+\3R y LMNN n V L jX¹[=n+\Wø{RV j N i{TV3RÂjsn V.S+R" X qR"X*R L X O j æ jsÿHv*R]\3R"vê¨Q G " 1R"j KMLdO RT O v LMNWN R}\3R"X O K j+["T O L j*XV õþçç["j*\\3RV æ j*X*vV O j O p*R æ T]\ O4L XH["jUX O T"[ O ÿ LdO pZS{R"X R"X*R . .

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(75) 1 0.9 0.8. 0 mm 5mm. 0.7. 10mm. Signal. 0.6 0.5 0.4 0.3 0.2 0.1 0 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. Time (hours). L i;n+\3R . .

(76)