Polarization in Interferometry

Transcription

1 Polarzaton n Intrfromtry Stn T. Myrs NRAO-Socorro lnth Synthss Imagng Workshop Socorro, Jun 10-17, 008

2 Polarzaton n ntrfromtry Astrophyscs of Polarzaton Physcs of Polarzaton Antnna Rspons to Polarzaton Intrfromtr Rspons to Polarzaton Polarzaton Calbraton & Obsratonal Stratgs Polarzaton Data & Imag Analyss S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

3 WARNING! Ths s tough stuff. Dffcult concpts, hard to xplan wthout complx mathmatcs. I wll llustrat th concpts wth fgurs and handwang. Many good rfrncs: Synthss Imagng II: Lctur 6, also parts of 1, 3, 5, 3 Born and Wolf: Prncpl of Optcs, Chaptrs 1 and 10 Rolfs and Wlson: Tools of Rado Astronomy, Chaptr Thompson, Moran and Swnson: Intrfromtry and Synthss n Rado Astronomy, Chaptr 4 Tnbrgn: Astronomcal Polarmtry. All Chaptrs. J.P. Hamakr t al., A&A, 117, and srs of paprs Grat car must b takn n studyng ths conntons ary btwn thm. DON T PANIC! S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

4 Polarzaton Astrophyscs S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

5 What s Polarzaton? lctromagntc fld s a ctor phnomnon t has both drcton and magntud. From Maxwll s quatons, w know a propagatng M wa n th far fld has no componnt n th drcton of propagaton t s a transrs wa. k Th charactrstcs of th transrs componnt of th lctrc fld,, ar rfrrd to as th polarzaton proprts. Th -ctor follows a llptcal hlcal path as t propagats: 0 S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

6 Why Masur Polarzaton? lctromagntc was ar ntrnscally polarzd monochromatc was ar fully polarzd Polarzaton stat of radaton can tll us about: th orgn of th radaton ntrnsc polarzaton th mdum through whch t trarss propagaton and scattrng ffcts unfortunatly, also about th purty of our optcs you may b forcd to obsr polarzaton n f you do not want to! S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

7 xampls: Astrophyscal Polarzaton Procsss whch gnrat polarzd radaton: Synchrotron msson: Up to ~80% lnarly polarzd, wth no crcular polarzaton. Masurmnt prods nformaton on strngth and orntaton of magntc flds, ll of turbulnc. Zman ln splttng: Prsnc of B-fld splts RCP and LCP componnts of spctral lns by by.8 Hz/μG. Masurmnt prods drct masur of B-fld. Procsss whch modfy polarzaton stat: Fr lctron scattrng: Inducs a lnar polarzaton whch can ndcat th orgn of th scattrd radaton. Faraday rotaton: Magntoonc rgon rotats plan of lnar polarzaton. Masurmnt of rotaton gs B-fld stmat. Faraday conrson: Partcls n magntc flds can caus th polarzaton llptcty to chang, turnng a fracton of th lnar polarzaton nto crcular possbly sn n cors of AGN S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

8 8.4 GHz -ctors xampl: Rado Galaxy 3C31 along cor of t radal to t at dg Lang kpc S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

9 xampl: Rado Galaxy Cygnus A 8.5 GHz B-ctors Prly & Carll kpc S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

10 xampl: Faraday rotaton of CygA S rw of Clustr Magntc Flds by Carll & Taylor 00 ARAA S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

11 xampl: Zman ffct S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

12 Trac magntc fld structur n galaxs xampl: th ISM of M51 Nnngr 199 S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

13 Scattrng Ansotropc Scattrng nducs Lnar Polarzaton lctron scattrng.g. n Cosmc Mcrowa Background dust scattrng.g. n th mllmtr-wa spctrum Planck prdctons Hu & Dodlson ARAA 00 Anmatons from Wayn Hu S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

14 Polarzaton Fundamntals S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

15 Th Polarzaton llps From Maxwll s quatons B0 and B prpndcular By connton, w consdr th tm bhaor of th -fld n a fxd prpndcular plan, from th pont of w of th rcr. For a monochromatc wa of frquncy ν, w wrt x y A A x y cos πυ t cos πυ t Ths two quatons dscrb an llps n th x-y plan. Th llps s dscrbd fully by thr paramtrs: A X, A Y, and th phas dffrnc, δ Y - X. Th wa s llptcally polarzd. If th -ctor s: Rotatng clockws, th wa s Lft llptcally Polarzd, Rotatng countrclockws, t s Rght llptcally Polarzd. x y S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

16 llptcally Polarzd Monochromatc Wa Th smplst dscrpton of wa polarzaton s n a Cartsan coordnat fram. In gnral, thr paramtrs ar ndd to dscrb th llps. Th angl α atana Y /A X s usd latr S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

17 Polarzaton llps llptcty and P.A. A mor natural dscrpton s n a fram ξ,η, rotatd so th ξ-axs ls along th maor axs of th llps. Th thr paramtrs of th llps ar thn: A η : th maor axs lngth tan χ Α ξ /Α η : th axal rato Ψ : th maor axs p.a. tan Ψ tan sn χ sn α cos δ α sn δ Th llptcty χ s sgnd: χ > 0 RP χ < 0 LP χ 0,90 Lnar δ0,180 χ ±45 Crcular δ±90 S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

18 Crcular Bass W can dcompos th -fld nto a crcular bass, rathr than a lnar Cartsan on: A R ˆ R whr A R and A L ar th ampltuds of two countr-rotatng unt ctors, R rotatng countr-clockws, and L clockws NOT: R,L ar obtand from X,Y by δ±90 phas shft It s straghtforward to show that: A L ˆ L A A R L 1 1 A A X X A A Y Y A A X X A A Y Y sn sn δ δ XY XY S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

19 Th black llps can b dcomposd nto an x- componnt of ampltud, and a y-componnt of ampltud 1 whch lags by ¼ turn. It can altrnatly b dcomposd nto a countrclockws rotatng ctor of lngth 1.5 rd, and a clockws rotatng ctor of lngth 0.5 blu. Crcular Bass xampl S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

20 Th Poncar Sphr Trat ψ and χ as longtud and lattud on sphr of radus A Rohlfs & Wlson S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

21 Stoks paramtrs Sphrcal coordnats: radus I, axs Q, U, V I X Y R L Q I cos χ cos ψ X - Y R L cos δ RL U I cos χ sn ψ X Y cos δ XY R L sn δ RL V I sn χ X Y sn δ XY R - L Only 3 ndpndnt paramtrs: wa polarzaton confnd to surfac of Poncar sphr I Q U V Stoks paramtrs I,Q,U,V dfnd by Gorg Stoks 185 form complt dscrpton of wa polarzaton NOT: abo tru for 100% polarzd monochromatc wa! S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

22 Lnar Polarzaton Lnarly Polarzd Radaton: V 0 Lnarly polarzd flux: Q and U dfn th lnar polarzaton poston angl: Sgns of Q and U: P Q U tan ψ U / Q Q < 0 Q > 0 Q > 0 Q < 0 U > 0 U < 0 U < 0 U > 0 S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

23 Smpl xampls If V 0, th wa s lnarly polarzd. Thn, If U 0, and Q post, thn th wa s rtcally polarzd, Ψ0 If U 0, and Q ngat, th wa s horzontally polarzd, Ψ90 If Q 0, and U post, th wa s polarzd at Ψ 45 If Q 0, and U ngat, th wa s polarzd at Ψ -45. S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

24 Illustrat xampl: Non-thrmal msson from Juptr Apr 1999 VLA 5 GHz data D-confg rsoluton s 14 Juptr mts thrmal radaton from atmosphr, plus polarzd synchrotron radaton from partcls n ts magntc fld Shown s th I mag ntnsty wth polarzaton ctors rotatd by 90 to show B-ctors and polarzd ntnsty blu contours Th polarzaton ctors trac Juptr s dpol Polarzd ntnsty lnkd to th Io plasma torus S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

25 Why Us Stoks Paramtrs? Tradton Thy ar scalar quantts, ndpndnt of bass XY, RL Thy ha unts of powr flux dnsty whn calbratd Thy ar smply rlatd to actual antnna masurmnts. Thy asly accommodat th noton of partal polarzaton of non-monochromatc sgnals. W can as I wll show mak mags of th I, Q, U, and V ntnsts drctly from masurmnts mad from an ntrfromtr. Ths I,Q,U, and V mags can thn b combnd to mak mags of th lnar, crcular, or llptcal charactrstcs of th radaton. S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

26 Non-Monochromatc Radaton, and Partal Polarzaton Monochromatc radaton s a myth. No such ntty can xst although t can b closly approxmatd. In ral lf, radaton has a fnt bandwdth. Ral astronomcal msson procsss ars from randomly placd, ndpndntly oscllatng mttrs lctrons. W obsr th summd lctrc fld, usng nstrumnts of fnt bandwdth. Dspt th chaos, polarzaton stll xsts, but s not complt partal polarzaton s th rul. Stoks paramtrs dfnd n trms of man quantts: S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

27 S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008 Stoks Paramtrs for Partal Polarzaton sn sn cos cos l r xy y x rl l r xy y x rl l r y x l r y x V U Q I δ δ δ δ V U Q I Not that now, unlk monochromatc radaton, th radaton s not ncssarly 100% polarzd.

28 Summary Fundamntals Monochromatc was ar polarzd xprssbl as orthogonal ndpndnt transrs was llptcal cross-scton polarzaton llps 3 ndpndnt paramtrs choc of bass,.g. lnar or crcular Poncar sphr connnt rprsntaton Stoks paramtrs I, Q, U, V I ntnsty; Q,U lnar polarzaton, V crcular polarzaton Quas-monochromatc was n ralty can b partally polarzd stll rprsntd by Stoks paramtrs S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

29 Antnna Polarzaton S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

30 Masurng Polarzaton on th sky Coordnat systm dpndnc: I ndpndnt V dpnds on choc of handdnss V > 0 for RCP Q,U dpnd on choc of North plus handdnss Q ponts North, U 45 toward ast Polarzaton Angl Ψ Ψ ½ tan -1 U/Q North through ast also calld th lctrc ctor poston angl VPA by connton, tracs -fld ctor.g. for synchrotron B-ctor s prpndcular to ths Q U S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

31 Optcs Cassgran rado tlscop Parabolod llumnatd by fdhorn: S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

32 Rflctons Optcs tlscop rspons turn RCP LCP -fld currnts allowd only n plan of surfac Fld dstrbuton on aprtur for and B plans: Cross-polarzaton at 45 No cross-polarzaton on axs S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

33 xampl smulatd VLA pattrns VLA Mmo 58 Usng Grasp8 to Study th VLA Bam W. Brskn Lnar Polarzaton Crcular Polarzaton cuts n R & L S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

34 xampl masurd VLA pattrns AIPS Mmo 86 Wdfld Polarzaton Corrcton of VLA Snapshot Imags at 1.4 GHz W. Cotton 1994 Crcular Polarzaton Lnar Polarzaton S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

35 Polarzaton Rcr Outputs To do polarmtry masur th polarzaton stat of th M wa, th antnna must ha two outputs whch rspond dffrntly to th ncomng llptcally polarzd wa. It would b most connnt f ths two outputs ar proportonal to thr: Th two lnar orthogonal Cartsan componnts, X, Y as n ATCA and ALMA Th two crcular orthogonal componnts, R, L as n VLA Sadly, ths s not th cas n gnral. In gnral, ach port s llptcally polarzd, wth ts own polarzaton llps, wth ts p.a. and llptcty. Howr, as long as ths ar dffrnt, polarmtry can b don. S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

36 Polarzrs: Quadratur Hybrds W dscussd th two bass commonly usd to dscrb polarzaton. It s qut asy to transform sgnals from on to th othr, through a ral dc known as a quadratur hybrd. X Y R L Four Port Dc: port nput ports output mxng matrx To transform corrctly, th phas shfts must b xactly 0 and 90 for all frquncs, and th ampltuds balancd. Ral hybrds ar mprfct gnrat rrors mxng/lakng Othr polarzrs.g. wagud sptum, grds qualnt S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

37 Polarzaton Intrfromtry S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

38 Four Complx Corrlatons pr Par Two antnnas, ach wth two dffrntly polarzd outputs, produc four complx corrlatons. From ths four outputs, w want to mak four Stoks Imags. Antnna 1 Antnna R1 L1 R L X X X X R R1R R R1L R L1R R L1L S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

39 S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008 Outputs: Polarzaton Vctors ach tlscop rcr has two outputs should b orthogonal, clos to X,Y or R,L n f sngl pol output, connnt to consdr both possbl polarzatons.g. for lakag put nto ctor or t t t t t t Y X L R

40 S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008 Corrlaton products: cohrncy ctor Cohrncy ctor: outr product of antnna ctors as aragd by corrlator ths ar ssntally th uncalbratd sblts crcular products RR, RL, LR, LL lnar products XX, XY, YX, YY nd to nclud corruptons bfor and aftr corrlaton qq qp pq pp q q p q q p p p q p q p * * * * * *

41 pq 1 Polarzaton Products: Gnral Cas G pq { I [cos Ψ p Q[cos Ψ U [cos Ψ p p V [cos Ψ Ψ p q Ψ Ψ cos χ q q Ψ q p cos χ sn χ sn χ p p χ sn Ψ p q χ sn Ψ χ sn Ψ q q χ sn Ψ q p p p p Ψ q Ψ Ψ sn χ q Ψ q q p sn χ cos χ cos χ χ ] p p p q χ ] q χ ] q χ ]} q What ar all ths symbols? pq s th complx output from th ntrfromtr, for polarzatons p and q from antnnas 1 and, rspctly. Ψ and χ ar th antnna polarzaton maor axs and llptcty for stats p and q. I,Q, U, and V ar th Stoks Vsblts dscrbng th polarzaton stat of th astronomcal sgnal. G s th gan, whch falls out n calbraton. W WILL ABSORB FACTOR ½ INTO GAIN!!!!!!! S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

42 S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008 Cohrncy ctor and Stoks ctor Maps prfct sblts to th Stoks ctor s xampl: crcular polarzaton.g. VLA xampl: lnar polarzaton.g. ALMA, ATCA V I U Q U Q V I V U Q I s LL LR RL RR crc crc S Q I V U V U Q I V U Q I s YY YX XY XX ln ln S

43 Corruptons: Jons Matrcs Antnna-basd corruptons pr-corrlaton polarzaton-dpndnt ffcts act as a matrx mulplcaton. Ths s th Jons matrx: out J n J J J 11 1 J J 1 1 form of J dpnds on bass RL or XY and ffct off-dagonal trms J 1 and J 1 caus corrupton mxng total J s a strng of Jons matrcs for ach ffct J J F J J D J P Faraday, polarzd bam, lakag, parallactc angl S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

44 Parallactc Angl, P Orntaton of sky n tlscop s fld of w J RL P Constant for quatoral tlscops Vars for alt-az tlscops Rotats th poston angl of lnarly polarzd radaton R-L phas 0 XY cos sn ; J P 0 sn cos dfnd pr antnna oftn sam or array cos l sn h t l cos δ cos l sn δ cos h t t arctan sn l lattud, h t hour angl, δ dclnaton P modulaton can b usd to ad n calbraton S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

45 S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008 Vsblts to Stoks on-sky: RL bass th outr products of th parallactc angl P and th Stoks matrcs gs ths matrx maps a sky Stoks ctor to th cohrnc ctor rprsntng th four prfct crcular polarzaton products: V I U Q U Q V I V U Q I LL LR RL RR P S s J Crcular Fds: lnar polarzaton n cross hands, crcular n paralll-hands

46 S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008 Vsblts to Stoks on-sky: XY bass w ha and for dntcal parallactc angls btwn antnnas: V U Q I YY YX XY XX sn sn cos cos cos cos sn sn cos cos sn sn sn sn cos cos sn cos cos sn cos sn sn cos U Q I V U Q V U Q U Q I YY YX XY XX Lnar Fds: lnar polarzaton n all hands, crcular only n cross-hands

47 S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008 Basc Intrfromtry quatons An ntrfromtr naturally masurs th transform of th sky ntnsty n u-spac conold wth aprtur cross-corrlaton of aprtur oltag pattrns n u-plan ts tranform on sky s th prmary bam A wth FWHM ~ λ/d Th tld quantts ar Fourr transforms, wth connton: n ~ ~ n p p p I A d I A d V x x x u u x x x x u π π ~,, ~ u u x u x x x u x u x u T d T u m l T d T π π

48 S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008 Polarzaton Intrfromtry : Q & U Paralll-hand & Cross-hand corrlatons crcular bass sblty k antnna par, tm, pontng x, channl ν, nos n: whr krnl A s th aprtur cross-corrlaton functon, s th parallactc angl, and QUP s th complx lnar polarzaton th phas of P s ϕ th R-L phas dffrnc LL k k LL k k LL k LR k k LR k k LR k RL k k RL k k RL k RR k k RR k k RR k k k k k k k V I A d V U Q A d V U Q A d V V I A d V n ] ~ ~ [ ~ n ] ~ ~ [ ~ n ] ~ ~ [ ~ n ] ~ ~ [ ~ x x x x u u u u u u u u π ν ν π ν ν π ν ν π ν ν ϕ ~ ~ ~ ~ P U Q P

49 xampl: RL bass magng Parnthtcal Not: can mak a psudo-i mag by grddng RRLL on th Fourr half-plan and nrtng to a ral mag can mak a psudo-v mag by grddng RR-LL on th Fourr half-plan and nrtng to ral mag can mak a psudo-qu mag by grddng RL to th full Fourr plan wth LR as th conugat and nrtng to a complx mag dos not rqur hang full polarzaton RR,RL,LR,LL for ry sblty Mor on magng & dconoluton tomorrow! S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

50 Polarzaton Lakag, D Polarzr s not dal, so orthogonal polarzatons not prfctly solatd Wll-dsgnd systms ha d < 1-5% but som systms >10% A gomtrc proprty of th antnna, fd & polarzr dsgn frquncy dpndnt.g. quartr-wa at cntr ν drcton dpndnt n bam du to antnna For R,L systms paralll hands affctd as d Q d U, so only mportant at hgh dynamc rang bcaus Q,U~d, typcally cross-hands affctd as d I so almost always mportant J pq D 1 d q d 1 p Lakag of q nto p.g. L nto R S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

51 Lakag rstd Prmary on-axs ffct s lakag of on polarzaton nto th masurmnt of th othr.g. R L but, drcton dpndnc du to polarzaton bam! Customary to factor out on-axs lakag nto D and put drcton dpndnc n bam xampl: xpand RL bass wth on-axs lakag Vˆ Vˆ RR RL V V RR RL d d R R V V LR LL d d * R * L V V RL RR d d R R d d * R L V V LL LR smlarly for XY bass S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

52 xampl: RL bass lakag In full dtal: tru sgnal V nd ordr: D I nto I V RR RL 3 rd ordr: D P* nto P sky d d sky d d R R R R RR d RL I V d * R * L l, m[i χ χ χ Q U χ l, m[q U χ Q U V I - V] l, m χ χ χ d d χ * L χ χ * R χ χ π ] l, m χ I V Q U ul m dldm χ π χ 1 st ordr: D I nto P ul m dldm nd ordr: D P nto I S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

53 S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008 xampl: lnarzd lakag RL bass, kpng only trms lnar n I,Q±U,d: Lkws for XY bass, kpng lnar n I,Q,U,V,d,sn - WARNING: Usng lnar ordr wll lmt dynamc rang! I U Q I U Q * * R L LR L R RL d d V d d V ]I sn cos [ V Ucos Qsn ]I sn cos [ V Ucos Qsn * * X Y YX Y X XY d d V d d V

54 Ionosphrc Faraday Rotaton, F Brfrngncy du to magntc fld n onosphrc plasma J J RL F XY F Δ 0 Δ cos Δ sn Δ 0 sn Δ cos Δ s drcton-dpndnt Δ 0.15 λ n cm, o λ cm, B 14 - TC nds ~ 10 cm ; B n ds n 10 B n ds 14 - n G ~1G; o λ 0cm Δ ~ 60 also prsnt n ISM, IGM and ntrnsc to rado sourcs! can com from dffrnt Faraday dpths tomography S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

55 Antnna oltag pattrn, Drcton-dpndnt gan and polarzaton ncluds prmary bam Fourr transform of cross-corrlaton of antnna oltag pattrns ncluds polarzaton asymmtry squnt pq J pp qp l, m l, m pq qq l, m l, m ncluds off-axs cross-polarzaton lakag connnt to rsr D for on-axs lakag mportant n wd-fld magng and mosacng whn sourcs fll th bam.g. low frquncy S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

56 Summary polarzaton ntrfromtry Choc of bass: CP or LP fds usually a tchnology consdraton Follow th sgnal path onosphrc Faraday rotaton F at low frquncy drcton dpndnt and antnna dpndnt for long baslns parallactc angl P for coordnat transformaton to Stoks antnnas can ha dffrng PA.g. VLBI lakag D ars wth ν and or bam mx wth Lakag us full all ordrs D solr whn possbl lnar approxmaton OK for low dynamc rang bwar whn antnnas ha dffrnt parallactc angls S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

57 Polarzaton Calbraton & Obsraton S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

58 So you want to mak a polarzaton mag Makng polarzaton mags follow gnral ruls for magng mag & dconol I, Q, U, V plans Q, U, V wll b post and ngat V mag can oftn b usd as chck Polarzaton ctor plots VPA calbrator to st angl.g. R-L phas dffrnc Φ ½ tan-1 U/Q for ctors B ctors plot ctors lngth gn by P Lakag calbraton s ssntal S Tutorals on Frday.g Juptr 6cm contnuum S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

59 Stratgs for lakag calbraton Nd a brght calbrator! ffcts ar low ll dtrmn antnna gans ndpndntly mostly from paralll hands us cross-hands mostly to dtrmn lakag do matrx soluton to go byond lnar ordr Calbrator s unpolarzd lakag drctly dtrmnd rato to I modl, but only to an orall complx constant addt or array nd way to fx phas δ p -δ q. R-L phas dffrnc,.g. usng anothr calbrator wth known VPA Calbrator of known non-zro lnar polarzaton lakag can b drctly dtrmnd for I,Q,U,V modl unknown p-q phas can b dtrmnd from U/Q tc. S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

60 Othr stratgs Calbrator of unknown polarzaton sol for modl IQUV and D smultanously or tratly nd good parallactc angl corag to modulat sky and nstrumntal sgnals n nstrumnt bass, sky sgnal modulatd by χ Wth a ry brght strongly polarzd calbrator can sol for lakags and polarzaton pr basln can sol for lakags usng paralll hands! Wth no calbrator hop t arags down or parallactc angl transfr D from a smlar obsraton usually possbl for sral days, bttr than nothng! nd obsratons at sam frquncy S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

61 Parallactc Angl Corag at VLA fastst PA swng for sourc passng through znth to gt good PA corag n a fw hours, nd calbrators btwn dclnaton 0 and 60 S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

62 Fndng polarzaton calbrators Standard sourcs plants unpolarzd f unrsold 3C86, 3C48, 3C147 known IQU, stabl sourcs montord.g. by VLA othr brght sourcs bootstrap S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

63 xampl: D-trm calbraton D-trm calbraton ffct on RL sblts should b QU: S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

64 xampl: D-trm calbraton D-trm calbraton ffct n mag plan : Bad D-trm soluton Good D-trm soluton S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008

65 Summary Obsrng & Calbraton Follow normal calbraton procdur prous lctur Nd brght calbrator for lakag D calbraton bst calbrator has strong known polarzaton unpolarzd sourcs also usful Parallactc angl corag usful ncssary for unknown calbrator polarzaton Nd to dtrmn unknown p-q phas CP fds nd VPA calbrator for R-L phas f systm stabl, can transfr from othr obsratons Spcal Issus obsrng CP dffcult wth CP fds wd-fld polarzaton magng ndd for VLA & ALMA S.T. Myrs lnth Synthss Imagng Workshop, Jun 10, 008