A blind deconvolution approach For resolution enhancement oF near

depends mainly on the dimensions of the waveguide, the operating frequency, the ... Unlike the plane-wave far-field approach, the PSF associated with these.
203KB taille 2 téléchargements 314 vues
  $%,-  . !"$/#01 !    $% &'  )(*+  24365 798;:=?>@¶~k|–{ ·

¦ ~ v €sŽ*“ ‘¦ “.~ § ‘D“.~k|o’© ¸

µÏ kÓ œÏ ˜Ó µÏ kÓ œÏ kÓ

„L

¡‘ ¦ “ xwy(z –{°‘ “

¦ ~ v €sŽ* ‘D¦ ”~ § ‘.~k’© |‹

¹¯"°²¿É¯Í"°½­š®o¯"¶tÒ"ºRÂ"·o°”¶L· ¾˜ºŒÃœ´µ°½­͘»;¶L¿¸ºŒÃa¶Œö …Ï kÓ Ï ˜Ó Ï ˜Ó Ï ˜Ó Ï ˜Ó …Ï ˜Ó

J

•Ž “

± ¦ ~k|¨€sŽ* ‘D¦ ”~e‘6¶"~k«{ |‹ ² ³µ´ ´

|a’ /ˆ8

Š w^y Š z

Ï kÓ xN

Ï kÓ Ï ˜Ó Ï kÓ Ï ˜Ó

±  ¹ ² ³¡´

„º^y(» /   €Ž    ¼  xº+y$»    ¶ ½

xº+y$» ¾{

¹À¿ „º^y(» oÁ

xº+y$» €sŽ    ¼

 „º^y(» /   ½’ xº+y$»

 ½

xº+y$»    €Ž “   ¼ “ xº+y$»    ¶ ¹

xº+y$» ¾{

½ ¿ „º^y(» ÂÁ

„º^y(» ^€sŽ “   ¼

“ „º^y(» /   ¹ ’ xº+y$»

´

Ï RÓ O

´µ­I¾4±‘ºa¹)¶yºR»˜®o´Œ°”­ö

Ï kÓ ŒÏ ˜Ó …œÏ Ï k˜Ó Ó Ï ]Ó IÏ Ï ˜˜Ó Ó Ï kÓ Ï ˜Ó œÏ Ï ˜˜Ó Ó IÏ Ï ˜˜Ó Ó RÏ kÓ ?Ï ˜Ó Ï ŒÓ Ô¯"¶G±J¶®–¹º‹¼²´Œ±J®¶LÊ]´µ®‘°½ºŒ­±´Œ·‘¶1ÁŒ¶L·‘Æa洌Ãa°”¼½° ´Œ·Äꌷ®o¯"¶t¿¸´R±J¶1¹¯"¶L·‘¶ Ï "Ó a´µ­I¾ Ï ˜Ó "Ë ºŒ»""®oËT´µï𬰽­"­%¯"°”®‘¶L´‹°²­Ì´µ±‘¼½ºŒ°®‘Ú¸¼½¯"˜¶ ¶/®oD°”³ºRÏ ­%´Œ·o¿¸´Œ"ºŒÃ‹Ó)·o·‘¶¸®‘¶G®‘º ±J¶L³;·o± ºŒ­IÏ ¾˜°”­"´µÅtÓ­´µ®‘¾ ºX­I¾š´‹·o¼½¶¸º˜´µ³;¿¸­I¶L´µ¾ª´µ¼p®ºR®‘³˜¯"®‘¶4­R°½®oÃFÄΰ”Â"¼+­¿ÀÃ&ºR¿À®‘­]°½ºµÁRºŒÄ¶¸­·oÏ ± ŌR¶LÓ­»]¿ÀÏÆ4¶Rö ´µ"­%ÓÀÍ°¤®o¶¸·É´*Ï ®o°”ÁR"¶ÓÀ´ŒÍ ¼”ÅRºŒ·oÏ °¤®o¯""Ã&Óu´µ±‘­¿É¾ ¯/´R±1Ï ö "ÓF´Œ·‘¶œÈÛk¶G¾pͺR­"¶š¿¸´Œ­ ˜ºŒ· ŒËË ))ºRºRË˳³˜˜®‘®‘¶¶ …Ï Ï kkÓ)Ó)ÄÎÄηo·oºŒºŒÃ Ã Ï Ï RµÓÓ´Œ´Œ­­¾X¾š®o®‘¯"¯"¶¸¶L­ ­ TDÏ Ï ""ÓÓ»k»kƚƚ¬ ¬ ÒTÒTÔ Ô "ŒËTË ¬)­"ºR°”®‘Ë°²´µ³¼½Â˜° Ú¸®‘¶ ¶ T…Ï Ï "kÓ)Ó)®‘º ÄηoºŒÃ Ï Ï µ"ÓÓ´Œ´µ­­¾š¾/®‘·o¯"¶¸¶L³;­ ¶L´µD®Ï ­R"®oÓ°”¼D»k¿ÀƚºŒ­k¬ ÁR¶¸ÒT·oÅŒÔ ¶¸­I¿À¶Œö ç˜Â˜Ë ®LÍ)Â"ºR­˜Ã‹Äꌳ·‘˜®‘®‘¶ ­´*®o¶¸Ï ¼½ÆŒÍ"k°½Ó)­4Äηo³ºŒ·oôR¿ˆ®‘Ï °²R¿¸Ó´Œ¼´Œ´µ­³"¾X³®o¼”¯"°²¿¸¶¸´µ­ ®‘°½TºŒ­Ï ±LÍk"®–¹)Óºœ»kƚ¾˜°”¬ ØX¿ÀÒTÂ"Ô'¼”®‘°½Ë¶L± ´µ·o°½±‘¶Œö °”Ô­mÁŒ¯]¶L»IÂI­-ºŒ±¸ÍI®‘¹¯ ®‘ºX¯"…¶¸ºR­ »˜´Œ®o­´Œ¾ °”­†Í ª´š"±J¶LÂ"Í ³­"´µ°²Ê]·ÉÏ ´*Â"®o¶u¶¸˜¼½±oƌÓÀ´*ÍÍ ®o°”°½®t±JI洌°²Ï ±1¿À®‘­"ºŒ"ºµ·oӈ®tÆ4Í ´-±‘ºŒR¿À¼½Ï ˜ºR­k®o°”ÁŒ"ºR¶ÀÓ­Û-Í´µ¹Äέ¾ ¶F­¿ˆ­"®o¶L]°”¶LºRÏ ¾-­m´4"ºŒÄ)Ó ±–®o»;´Œ·‘·‘ºµºR¶F®o­"¯mÈ"Ō¶LۘºŒ· ¶LÄ)¾†¿À®oºR¯"´Œ­¶¸­±–Ãô¾-®o·o´Œ¶¸´µÁR°”­­]¶¸¾|® ­|ºR°”®F°¤­%Ä¿¸®o®‘´µ¯"¯"­m¶a¶‹¯¿À±J·oºR´d°¤ÁR¼”®o˜¶¸¶u®o·o°”Ãœ°”ºRºR­­…´µË­kÏƆŒÓ ¼½­"º˜°²¶F¿¸±´Œ¹Ê]¼=´dºŒÆ4´R³˜¾˜®‘®o·oºš°”Ãœ´µ®‘¾"´"°²º¿ Ë ®‘°½±¯"°²°½±­X°½Ä‡±´Œ®o¿Àº‹® ´F¿¸ºŒ¹­°²±J±J®‘¯#·É´µöD°½ÄέXºR·)®o¯"¶¸¶1Û"´µ°”­Ãa³"³"˜¼½® ¶ŒÍ˜%¹®o¯"ºa¶L»I­š¶y¹´u¶³"´Œ°”·‘¶G¶¿À¶L±J¹¶G´µ°½·É±‘¶y¿É¯"¿À°”ºŒ­­IÅt±–ÄήɺŒ´µ·­]®)´uÄξ˜Â¶À­ć¿ˆ´Œ®oÂ"°”¼¤ºR®­·oË=¶¸¬ÅR­°”ºR¾˜­X¶G´Œ°”¾p­%͘´F°½­4±o´*ºRÄÎÂ"¶· ¯"´µºR³˳"ºR¼”°²ÅŒ¿¸¶L´µ­"®‘¶¸°½ºŒºR­ÂÍ]±®o·o¯"¶¸°½ÅR±°”ºR¿¸ºŒ­­Í]±J¹)®‘¶1·É´µ´µ°½­]·o¶® ¼”ò]ºk°½ºŒ­òk¾4°½­"ºµÅtÄ=¿ÀÄκRºR·­±–´Œ®o­š·o´Œ°½°”Ãœ­]®É´µ±Ō®o¶ ºœTºŒÏ »˜®É´µ"°½Ó)­/¹±o¯"´*®o°½¿É°½±J¯4洌°½±¿À®‘´uºR·‘»"Ɯ°½­·o´µ¶L·o±‘ÆaÂ"¼”®oÁd±L´ŒË ¼”¶L¾pËT¬­4®‘¯"¶­"¶ÀÛk®±J¶G¿ˆ®o°”ºR­š¹¶¹°½¼”p±‘¶¸¶¯"º*¹ø¹¶¿L´µ­š°½Ãa³Iº]±J¶®‘¯¶L±‘¶ ¼”ù ±Jº˜ºR­"¿¸¼”˜´ŒºŒ®o¼®‘°”¯"ºŒºR¶L³"­·t®‘Ë °½ÃœÃFïm´µÂ"¶‹°½Ã ­m³"°²·‘ºµ±oºRÄT±J³IÂ"®‘º]¶œ¯±J¶F¶t°½­ª¿À®‘·oºš®‘°¤®o¯ÂI¶¸°½·o±u±J°”¶FºR´µ­Ì®‘¼½ÅŒ¯"ºŒÏ¶‹Œ·oÓÀ°”³"®‘˯k¯"ÔƘà ±J¯k°²¿¸Â°²±1´Œ± ¼D®o®‘¯"òk¯"¶X­"¶Fº*°½°”¹­"­"°¤¼½°”®o®‘¶L°½°²¾˜´Œ´µÅR¼”¼½°½°¶tÚLÚL´µ´*ºµ®‘®oÄ=°½°”ºŒºR®o­­-¯"Ë%¶‹ºµÃ‹Ä+ù ®‘±t¶G¯"´Œ¹)¶‹±‘Â"¶œ´µ·o¼½Ãa¶¸ÅŒÃaºR¶¸·‘­]¶¸°”­]®‘®o¯"°”®ºRÃ&­"±‘Ƙ­"Ãa±–¶L®o¾´d¶¸Í#ÃÆ4®o¯¯"®‘´d°½º4±uÁŒ¶tºŒ´µ»˜¼½´aŌ®É´µºRÅR°½·‘·‘­z°”¶G®‘´*¯"´µ® í|°½­ °”¿À­"ºŒ°”Â"®‘­k°²¶LÁR´µ­¶¸¼+¿À·o¶L¶FŌ±J¶L®‘ºŒ±°½­%Ü®oº†®‘´*¯®o´¶¶ ÄÎŌºŒºk·º˜®o¾š¯"´µ¶t³°½³"Ë·‘³ºdۘÂ"°½¼½Ãœ±‘¶F´*·o®‘¶L°½ºŒ±‘³;­šºŒÄέºŒ±‘·¶Œ®o˯"Ò"¶yºR°”· Ãa¶À³"Û"´µ¼½Ãa±‘¶y³"·‘¼½¶Œ¶G±JÍI³;°¤ÄºŒ­I¹±J¶F¶1´R°²±±‘±‘ÅŒÂ"°½ÃaÁŒ¶¸¶1­/®‘»k¯Æ ´µ® ®‘¯¶u±J®o´µ­I¾˜ºµÖmºµÄ+®‘¯"¶‹±J¶L­±JºR· ¹´dÁŒ¶¸ÅRÂ"°²¾˜¶1°½± Ú¸¶¸·oºÍ"®‘¯"¶L­†´ Ï ˜Ó ¿Àº]±¸Ï kÓ Ï ]Ó ®‘ÒD¯"I°½­¶ Ï ´Œ¼”½"ƌÓÍV°½´µ­z­¾p³"·É±‘ºŒ´Œ¼½¿À˜®‘Ï ®‘°²¿¸°½ºŒ´µ˜­I¼+Ó± ±J´Œ°”®‘·‘ÂIR¶1Ï´*·o®‘¶L°½ºŒ±‘"³I­IÓ¶G±¸´Œ¿ˆÍV­®o¹°”¾ ÁR¶u¶¸¼½¯ÆX]´dÏ ÁR¿É¯"¶yºR"®‘±‘Óˆºš¶¸Ë=­%È"ïðÛ-´Œ±¯®‘´µ¯±‘® ¶¸¶u³¹)³´Œ¶1´Œ·o´Œ·o³"´Œ»"·oÃa¼½ºŒ¶ ³;¶ÀÈ®‘ºR·É¶L±‘±J·o¶1®± ¯"´Œ¶¸­/·o¾%¶1´Œ±J°½­±¶G¾ ¿À®oºR¯"­¶1"¾šÍ;ÄκŒºR®o¼½¯"·o”º*¾"¶F¹¶¸Äη°½Â­"¾˜­Å%¶¸¿ˆ·o®oö °½°”ÁdºR´µ­®‘± °½ÁŒ¶1;ºŒÏ ³;¶¸"·É´*ӈ®oÍ ºŒ·ÉI± Ï "Ó ´Œ­¾ ®‘¯"Œ¶1Ï ®–¹"ºuÓ ·o¶¸ÅRÂ"Ï ¼²´µ·o˜°”ÚGÓ´*´Œ®‘­°½ºŒ¾ ­4³]´µÏ ·É´µÃa"Ó¶¸®‘¶¸·É±´µÏ ·o¶È"ÓÛk¶G´R¾/±¶À°”­Ìۘ³IÏ ¶LR·‘Ó °½"Ãa´Œ¶¸­­]¾ ®o´Œ¼”½Æœ®oº ´µ­¾ Ë Té =é ¬­-±JºRÃa¶¶¸Û˜³I¶L·‘°½Ãa¶¸­]®o±L͘¹)¶1Ü´dÆX¯´dÁR¶1˺R·‘¶®‘¯I´µ­%ºŒ­"¶y±‘¶À® ºŒÄ+¾"´µ®o´"ͶL´Œ¿É¯4ºŒ»˜®É´µ°½­"¶L¾/¹°”®‘¯-´a¾˜°”Ö;¶L·‘¶L­R® ±‘¶¸­I±JºR·Lö Ï "Ó Ï "Ó TÏ "Ó Ï "Ó Ï ]Ó ¹¾˜¶¸¯"ȶL­"·‘¶1¶®‘®‘¯¯¶t¶³±JºR·‘¼”ºR˜»"®o¼”°”¶LºRà ­/´R¯"±¶L·‘®‘¶1¯"¶y°²±ºR®‘³˜ºa®‘°½¶LÃa±J®‘°”°½ÚLܶ¸·´*®‘ºŒ¶yÄD±‘®o°”¯"Ãu¶1Â"Äμ”ºŒ®o¼½´µ”º*­¹¶¸ºŒ°½­"ÂIÅa±J¼½Æ¿À·oT°¤®o϶¸·o°”ºR"­ Ó´µ­¾/´µ¼½V®‘¯¶1ÐÑ˜Ò ± Ï "Ó .Ë+ïm¶y´µÅ]´µ°½­4¿¸´Œ­ Ï 4Ó Ï dÓ Ï Ó Ï ]Ó ¹À¿ xº+y$» ÂÁ

½ „º^y(» Ã{

¹

 ¹

½ ¿ xº+y$» ÂÁ

xº+y$» ¾{

 ½

xº+y$» €Ž    ¼

 xº+y$»    ½^’ „º^y(»

xº+y$» €Ž1“   ¼˜“ xº+y$»    ¹¸’ „º^y(»

Æ

Ž “

¸‘  „wy$z J

‚ É J É

¨| xwy(z ½ „º^y(» ¹ „º^y(»

È| ’ xw^y$z Ä Å

• „wy$z K| x^ w y$z

t t

‰Ê ‰Ê

‚ É J É

¨ xw^y$z ¹ „º^y(» ½ „º^(y »

È ’ xw^y$z Å Ä

K| xw^y$z • „w$y z

t t

‰Ê

Æ

ËsÌ

U

­Ž1 Ž*“