Class Note for ASTR 518 at UA
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Date Created: 02/06/15
Considerations Throughputll Matching to detector properties Wavelength coveragemultiorder Wavelength resolutionimage qualitysampling Slit lengthmultiobj ect Sizemass exure Ghosts Versatility Dispersive Spectroscopy Dispersive spectroscopy implies a mapping between wavelength 7 and a spatial coordinate call it x ah In 199 F If E a Where F is the focal length of Whatever optical system is used to image the spectrum onto the detector Obj ectivePrism Grating types 5 l 39 Vk A 3 Place thin glass wedge or transmission grating ahead of telescope objective HS 12464759 N EMISS E 169 172 m 229 W n ZBiD A73959 13quot 1950 r 3 17155 52s i n l 39ln39 n liquotn39 u m quotm latetype star emissionline object eg QSO Here F in slide 2 is the focal length of the entire telescope Advantages of objective dispersion spectroscopy 39 Lowresolution spectra can be taken of many 104105 objects at once using a largeformat imaging detector s No special instrument is required Only expensive item is objective prismgrating Prism needs only thin wedge grating needs only very coarse ruling linesmm Disadvantages of obj ective dispersion spectroscopy Disperser must cover telescope objective expensive Very limited range of available dispersions For prisms nonuniform dispersion For gratings light is dispersed into more than one order cg m 0 2 Source light is spread out over a stripe but sky light is not So relative sky brightness is enhanced by factor roughly equal to the number of resolution elements For AA 4000A and 6A 10013 this is 40x or 4 magnitudes Simple prism spectrograph Telescope focuses incoming light here Detector Imaging in a simple spectrograph camera focal plane Slit heighth 739 239 Z widthw D diameter of an optie 110 subscript telescope objective F focal length of an optic subscript 1 collimator focal ratio of the besz produced by an optic subscrith camera 12 height length of a Slit or image thereof w width of a slit or image thereof Ignoring grating what is projected slit width in the camera s1 1112 S12 Sj 2 f 1 1 Q I Sol and 502 7 X 539i1 00a ane p 512 511 w w w X Su Sal 1 1 1 5111 F1 Sil F1801 53901 F1 5m neigmzh D v F D F widthw Y 2 512F1501 1 w Sal 7 F1X 7 53901 Sol 7 F1 SiZFl Projected slit size 11 Note that when the beam is eolliniated by lens 1 and rein1aged by lens 2 S n1 F1 and S732 F2 Substituting we obtain 39lU2 F2 F1 F2 7 l 7 48 w XF1 F1 Fl2 F1 The image is inverted and modi ed in size usually demagni ed relative to the slit itself Because the beam is collimated we also have D1 D2 But F F F D1 1 1 and Dzi Q f1 1 f2 Substituting these into 48 above we obtain W2 7 f2 71 plane Slit heighlh 3931 F1 D2 2 widthw Camera detector considerations Slit width typically set by seeing for a point source w NF A6 f D A6 in order to maximize throughput from the object and minimize the sky background Thus we write Izszl39f39D39Ag5X1076D39f239A6H For Nyquist sampling of the slit image at the detector we set w2 N 2 pixels 30pm for a typical CCD with lSum pixels lfA 9 N l arcsec thean2 N 6m ForD 4m f2 15 Difficult but possible For D 8mf2 075 Impossible Solutions to the cameradetector problem Close down entrance slit and lose light Inereasej thereby spreading the light over more pixels and consuming valuable detector real estate Mottot BIG TELESCOPES REQUIRE BIG DETECTORS Improve the seeing by nding a better site reducing heat ow around the mirror and illover the dome or ultimately by using adaptive optics How to make those fast cameras Light from telescope objective Entrance slit Spherical mirror Collimator CCD Corrector plate Grating Folding fla r MMT Red Channel camera Dispersion by a simple re ection grating Grating equation for this setup is mkdsm asm I U1 dCl IIUIIIbCl d groove separation at angle of incidence relative to normal to grating surface angle of diffraction or and B have same sign if incident and diffracted rays are on the same side of the grating normal GN 93 blaze angle discussed later Angular dispersion Angular dispersion is found by differentiating with respect to it holding or constant mr A dwtosJ O 337 m 077 loos3 01 7 sin a sin If 0A 7 Acos If Where we have substituted for md Resolution and resolving power Relationship between an increment da slit width as viewed from disperser and corresponding increment d is found by differentiating the grating equation holding 9t constant cos a 10 cos 3 F d8 F1 doc F cos a 16 F1 cos 3 D cos a 19 Objective Collimo tor f1f D 1 cos 3quot Combining we obtain A 115111 a sin 3 D cos 0 d9 the Resolving Power 31E gjrsrememg 113 Qg qzajmmm qm A Wm sz 1w 80 y a a a J azm uq mm JQJEJQCQ awm Resolution and resolving power Note that ultimate resolving power of a spectrographtelescope combination occurs when d6 L D Rayleigh limit which leads to D si If Hill 8 Rm m J l 05 m For the optical D1 has reached 305mm 12 inches so D 1 6XlO5 Resolution of better than 100 msec is possible and precision is nearing 1 ms For comparison Sun s re ex velocity due to Jupiter is 12 ms and due to Earth 01 ms The diffracted intensity pattern Consider diffraction at normal incidence on a single facet of width b Amplitude contribution dE at point P from portion ds is 11 IE 0 sinwt ka A I with A s sin 8 the integral 0 lt s lt b yields I 3111 lkbsinl i 3C lgsh wt 7 km 0 1117 a kbsini y a where y 12 kb sin 8 n b i sin 8