Class Note for ASTR 518 with Professor Rieke at UA
Class Note for ASTR 518 with Professor Rieke at UA
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This 18 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 14 views.
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Date Created: 02/06/15
Appearance of an Etalon FabryPerot spectrometers FabryPerot Adaptation of an etalon for spectroscopic imaging pressure scanning A N 90 kmsec per bar mechanical scanning Entire FSR is scanned for At 7t 2 Encode motion accurately tilt scanning Tilting an etalon away from the normal moves the transmission peaks to the blue as sin2 6 3 AAn17 n Results from a FabryPerot Imager Conceptual drawing of datacube from FP Velocity map of NGC 1365 using Rutgers FP CTIO 15m telescope Advantages amp disadvantages of F P spectrometers d Data cubes provide ima es in series of X s d Central fringe Width A6 N 4A N N Rt often A6 2 measured at etalon d Excellent resolution R 10 105396 possible d LR is higher than for dispersive spectrograph for high resolution on large sources and very high resolution Advantages amp disadvantages of FP spectrometers 9 Requires accurate temperature eontrol Te eliminate unwanted orders use interference pre lter To scan gt1 FSR must team up with a secend scanning etalon to block unwanted nrdeds Scexming is done vs time so valiable sky conditions reduce quality Highest reselutien requires very high quality etalnn and highre ectance coatings gt90 Increases expense and reduces throughput 3000 4000 5000 6000 7000 5000 9000 Wavelength A 10000 lters Mould Filters Colored glass VS i nterference Fouriertransform spectrometers FTS Basically a 2beam scanning etalon telescope focal plane 49L camer l l I I VD detectc Delay length A 11 12 2BM1 BM2 a r Fringe formation in an FTS The combined amplitude of two beams is E hie7quot been2x For h h2 h the observed intensity is I E E rE 2h21 005021 502 IfgpgpI q022nA7t I 21721 cos tp The modulating component is the interesting part Interferograms Scan one mirror at a uniform velocity V so A 2 V I An optical frequency v is then modulated at a much lower frequency f in the measured signal according to The interferogram from a polychromatic source is encoded with a unique frequency f for each optical frequency v 1t 2 21121 CS27rfnt Obviously this must be analyzed by Fourier techniques Fourier transforms I The Fourier transform basically multiplies the interferogram by a cosine wave of a speci ed frequency and integrates over time In so doing it recovers the intensity at the optical frequency vi 2Vc This is carried out for all frequencies 1 lt 139 lt N thereby recovering the incident intensity spectrum Specifically if 039 1 we want to obtain 3a from 1A 35 FT 1IA F IAcos27mAdA Fourier Transforms 11 Unfortunately we can t observe over the full range oo lt A lt 00 but instead 0 lt A lt L Thus we really have B 7 39nL IAos27ro39ArlA HA RotAL os2739r039ArlA RotAL 1 for A g L RotAL 0 for A lt 7L convolutio Using the convolution theorem F T F x G F T F T G B 7 m HA cos 27ro39AdA RoctAL cos eraAdA Fourier Transforms 111 Where we recall that a convolution is fg oga adv Demo here Fourier transforms IV 1 The second term yields the sinc function sinc x sin 75x 75x 33900 functlon Slnlt27TCE27TCE The recovered spectrum is therefore the true intensity 0 spectrum convolved with the observing Window For a rectangular observing Window and a monochromatic source the recovered spectrum is just the sinc function Apodz39zmg is the process of applying a Window function post facto to remove ringing in the FT caused by the Window edges Astr 518 Polar imetry Fall 2007 Fundamentals Light is transverse wave Simplest form 100 polarized stable phase relationship betweenx and y components Agp inZ to 1t2 Unpolarized randomly phase relationship between orthogonal components Partially polarized Fpuz 1 39 r 1 7 p0 11121 1011 00 x FM Em So we now consider 100 polarized light Polarized Light Evector of completely polarized beam is quite generally described hv E E2 Ey Em Coswt w 3 13 coswt W For any E0x and E0 Buyon Easily shown that general case is an ellipse described by y can define angle 8 such that tan 8 E E 213m cos p 2 I V J I J 7 sin Lp E3 0052 7 E sin2 9 E Sin 7 cos 739 Where p gpy 7 gpx Differs from usual form XZa2 yZb2 1 because not necessarily oriented along principal axes The ElectricVector Ellipse 1 angle of major axis to x axis and tall 21 fan 29 cos 7 tan 1 ba where sin 2X sin 245m 97 The ElectricVector Ellipse 1 um 1139 v 39nqmrhnded39 my mum in u e uh General case is called elliptical polarization Limiting cass Linear polarization when tan 1 0 o Requires w 0 y oscillate in phase 0 Then 9 11 tan 9 EvEX Circular polarization when tan 5 1 o Happens when w rr2 and i9 rr4 or w IZ and i9 I l Xy oscill out of phase Then E E 2 E02 Stokes Vector It will Drove to be handV to define I total intensity or ux q E QI 003260052x u E UI sin 219cm 2x StokesVector v E VI 31112x Noteq2u2vzsl
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