Class Note for ASTR 518 at UA
Popular in Course
Popular in Department
This 22 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Arizona taught by a professor in Fall. Since its upload, it has received 19 views.
Reviews for Class Note for ASTR 518 at UA
Report this Material
What is Karma?
Karma is the currency of StudySoup.
You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!
Date Created: 02/06/15
A71 Measuring the Stokes Vector l A perfect linear polarizer transmits one direction of vibration while completely blocking the orthogonal Hence viewed through a linear polarizer an intensity or flux measured over a finite time interval is Im E3 cos2 9 cos wt cos Apr sin wt sin 4px 2 Iy E3 sin2 9 cos wt cos gay sin wt sin 4 2 If no circular polarization 7 45 Then I I Egcos2 93f Egan em cos 29E li 2 I I Egcos2 9H2 Egsmz 9mg lt23 m Af l Measuring t e Sta65 Vector I So ratio 4 IyL 1 ltcos 26gt q 0 in absence of circular polarization Rotating coordinate system 45 switches cos 26 a sin 26 so second set of 2 measurements yields u UI see def n of Stokes parameters when I 0 Then linear polarization P and position angle 6measured N a E are defined P2 2 q2 2 and 6 Af l Linear PolarZa39 on Nature l Blackbody emission in absence of strong B field is mpolarized Scattering of light off small particles electrons or dust grains P can approach 100 and qalmost always J scattering plane Reflection of light off macroscopic objects eg planetary surfaces P typ lt 3 Emission by electrons in magnetic field with transverse component Synchrotron emission relativistic Cyclotron emission non or quasi relativistic Zeeman effect P 100 possible I Lg Linear PolarZaton by Scattering 5 0 5 I 1 Polarization map left and total light image ght of the bipolar Egg nebula both in nearinfrared light The nebula reflects light from an embedded star which is evolving to become a planetary nebula white dwarf Detection of Hidden BroadLhe Regbns in AG of x 39 w MWwMMWWMWWWW quot W man 7200 W WWIMWWWMW c g I Tm 5 7 f 01 d j L M255 an w fn 953375277 w 2 J a ilkam 5 J W WWW Y I 5 7 3000 eeeeeeee th A Af l Circular Polarization in Nature l Measures tendency of E vector to spiral around Poynting vector Astronomical convention V gt 0 when E vector rotates CCW as viewed by observer looking toward source 71 lt Vlt 1 V fractional amount of circular polarization Blackbody emission in absence of strong B field is mpolarized Produced in Nature by Electrons gyrating in magnetic field with component along line of sight Zeeman effect cyclotron emission Vgt 50 possible Scattering of linearly polarized light off particles with dimension a N 7L Typically Vltlt 1 The Zeeman Effect C SDSS spectra of magnetic white dwarfs showing the Zeeman effect on the Balmer series B 0 30 MG MG 106 G 6000 7000 8000 9000 Wavelength A Circulary PolarZed Zeeman Lines from Magnetc WDS 5 03 Tquot gt r 5 5 39u a 39E 1350 090 0 B85kG m 4 n a 2 I 8 5 2 z ollllllllll l 1 I I n 5000 5500 EEOO B500 Wavelength Urcuar y PolarZed Cyclotron Lines from MagnetC Accretors 39 I V D SDSSOB37 13 May 04 g 4 Tll E u m 5 m O E u 7quotl Sheet Linear PolarZers At the heart of every polarimeter is a linear polarizer Natural circular polarizers do not exist Sheet polarizers use aligned long molecules to selectively absorb one direction of vibration Assume a unpolarized transmittance K leak of unwanted orthogonal component Then if input is unpolarized fraction transmitted is Single 12 5 16 2 Crossed 2 6 2 Parallel 12 2 1ZZ Pol efficiency 1 01 5 HN as l 5017 50 T no0 W t 300 mlIEI 3 0 200 20 100 7 mm 00 00 00 500 30 700 BED gt 3 Mn A71 Re ective Indres in Cjstas Wavefront Propagatian in Anisotropic Crystals E u39al aniave quot3 V z e M as V 39 quot39 5 Refractive Index Ellipsoids vz Optical Axis Optical Axs x 3 hi 6 Ordinary Wave Refractive quote lt quoto quote gt a Propagation Exlmordina Index Ne atlve Positive Wave Propag an Eillpse Eire ngence Eiremngence Crystals can be uniaxial common shown above at left or biaxial and have negative or positive birefringence ne lt no or ne gt no 71 39 7 1 Bire 39ingent Linear PolarZers i Crystal polarizers utilize different n for different vibration planes II Mng ne 138 ne no N 0011 L slow ast 2000A 6pm Quartz ne 155 ne no N 0009 2500A 25pm N f D Calcite ne 166 ne no 0176 af 5 W 3500A 18um Best Caco3 still Wolloston Prism i found in minescaves But soft and hygroscopic t approaches 10 Extinction can achieve 6 lt 105 so pol efficiency up to 99999 A71 Fun amp Games with Crystals 2M lowfast H lowslow Beam displacer Af l Wavepates Retardersj Azp 21 rm ne M If no ne 102 l 001mm yields Altp nZ M4 What does this do for us lin pol 6 it4 retarder 6i 45 2 r circ pol icirc pol it4 retarder 6 2 lin pol 6i 45 lin pol it2 retarder 6 2 lin pol 6 So to measure circular polarization convert it to linear and measure the linear A Simple Astronomical Polarmeter for Point Sources l Detector A ll Aperture Wollaston prism Detector B J Problems 0 Rotate entire instrument to measure u Stokes parameter 0 Orthogonal signals for each Stokes measured by different detectors A Modern fmagngSpectropoarmefer TV Guider Camera ve ate pc arized line J CCD image Two exposures with M2 rotation measure a Stokes parameter in m spectrum Additional rotations of M2 measure other Stokes parameter a Polarimetzy AV Refractive indices vary with 7 so must achromatize waveplates to work over wide Ax Timemodulate observations to minimize influences of variations in seeing guiding and detector sensitivity Moonlight is very strongly polarized 77 l A71 F1 F2 qmg K 8 2 8r 2 g 0751 02F10 2 02 Assmne F X N Polarmetric Error Analysis A q 7 uquot diagram W35 n 1 H 1 1011 can S 10W 039 q mM 1 For ltlt 1 3 q MM so 039 1 q MM I With great care can achieve sensitivities of GP 0001 To do this must detect gt2 X 1010 photons 0ft 011 Then i 0q m 0a z oP in dcgl cos A71 Polarmetric Bias First0rdcr correction for bias in P 0P 0P0bs E 0q z o39u P z Pom Pobs 17 Probability distribution for 6 at lowSN is nonGaussian and problematic See Wardle amp Kronberg 1974 ApJ P 17 194 249 Simmons amp Stewart 1985 AampA 142 100 and similar A71 How an LCD Display Works How 3 Liquid Crystals Dilnlay Walk ow 3 Liquid Crystal Display Works llgmwave Folalixed may 9 Polarized V Panela f r Panels i Elec hnde Elec o e 39 r i A 39 Liquid Liquid Crystals Crysms mwsiuuww Tiny NZOA liquid crystals only absorb and emit J to their length Voltage off Crystals twisted and LCD pixel ON left Voltage on Crystals straighten and LCD pixel OFF right quotQS witch f0r UltraShort Light Pulses POWIZATION DIRECT luN 0F PRISM CIRCULAR POLARIZATION x m y L 9 ROTAIIOM w on 2nd Pm of THROUGH OM Pockels cell or Kerr cell operating as onoff M4 plate Cell on No pulse Cell off Pulse GUN AIR SPACED PHBM
Are you sure you want to buy this material for
You're already Subscribed!
Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'