SPECTROSCOPY and. spectrometers

Transcription

1 Observatioal Astroomy SPECTROSCOPY ad spectrometers Kitchi, pp Chromey, pp March

2 Spectroscopic methods Differet purposes require differet istrumets Mai spectroscopic methods: Low resolutio Log slit, high resolutio High resolutio Spectroscopic observatios are characterized by spectral resolutio ad wavelegth coverage 28 March

3 Defiitio of resolutio Resolutio R is defied as λ/δλ Δλ is the smallest distiguishable separatio betwee two wavelegths aroud λ High resolutio is above Low resolutio is below March

4 Low-resolutio Typical goal: search for objects with specific spectral features Method 1: objective prism, telescope "sees" the source through a prism, therefore each poit source looks like a small spectrum Method 2: spectrophotometry - arrow bad filters for give spectral features. Ofte, such filters have the possibility to chage cetral wavelegth these are called tuable filters. There is o slit! 28 March

5 Objective prism spectra Sky viewed through a prism. White box marks a sigle spectrum Spectrum of Vega take with objective prism. Theoretical model is show i color. 28 March

6 Spectrophotometry Spectral eergy distributio as a fuctio of stellar temperature Spectral eergy distributio as a fuctio of stellar surface gravity 28 March

7 Fabry-Perot iterferometer Moochromatic poit source Cotiuum produces rigs. Exteded source i white light produces a image. Exteded source i emissio lie maps velocities. H alpha Velocity field H alpha profiles 28 March

8 Gratig spectroscopy ESO HARPS spectrometer uses two echelle gratigs aliged to a few aometers 28 March

9 Covetioal gratig Gratigs δ Iterferece betwee grooves Echelle gratig W Gratig formula: OPD = δsiα + δsi β = mλ 28 March

10 Gratig spectrometers Collimator Slit Simplified view of a gratig spectrometer: 1. Slit 2. Collimator 3. Gratig 4. Camera 5. Detector 28 March

11 A bit of math: Expressio for agular dispersio is foud by differetiatig the gratig equatio, assumig costat icidece agle: mdλ = δ cos βdβ dλ = δ cos β dβ Liear dispersio is readily obtaied for a give focal legth of the camera: dλ cos β = δ dx m f cam m Agular dispersio Liear dispersio 28 March

12 ad some more Agular resolutio. Thik of a gratig as a mirror, its diffractio agle is give by: Δ β = λ W cos β ( ) Projected size of the gratig Agular dispersio equatio gives the correspodig wavelegth iterval: λ W R= m Δλ δ? = m N Resolvig power depeds i the umber of illumiated grooves! 12

13 Free spectral rage The free spectral rage (FSR) of a diffractio gratig is defied as the largest badwidth i a give order which does ot overlap the adjacet orders. FSR δ si β δ si β = λm λm+ 1 = = m m+ 1 δ si β = m m+ 1 ( ) Order m+1 For a prism FSR is the whole spectral rage! 28 March

14 Real world: the slit size ad seeig A spectrometer also works as a optical system that creates ad image of the slit o the detector. Slit image ca be magified or de-magified depedig if the focal legth of the camera is larger or smaller tha the focal legth of the collimator Slit Detector Collimator Camera If, give the two focal legths, we try to match the size of the slit image to the diffractio image of the gratig, the slit will have to be too arrow compared to the images of stars produced by a telescope. We will loose light! 28 March

15 Real world: the seeig ad the pixel size The slit is located i the focal plae of the telescope. If the seeig (image quality) is such that poit sources (stars) are 1 o the sky, the image o the slit will be 1/ rad x focal legth of the telescope. For BWT, the diameter is 0.9m ad the focal ratio is f/4 so the focal legth f tel =3.6m. Typical seeig is 2, so image of a star is 35 micro across. A 20cm echelle gratig with 72 groves/mm ad 60 degrees blaze agle will have a oe-to-oe relatio betwee order umber m ad the cetral wavelegth of the order λ i micros: m m =2si blaze = /72 24 Thus 500m wavelegth is best observed i order 48 (24/0.5=48) ad 600m falls ito order 40 (24/0.6=40). 28 March

16 Real world: the seeig ad the pixel size I order to achieve the theoretical resolvig power of the gratig we have to match the diffractio agle of the echelle to the slit size. I other words we eed to match the agular size of the slit to the agular resolutio elemet of the gratig: = /(W cos blaze ) The right-had side is radia at 600m. For the gratig to see the 35 micro slit width at this agle to collimator focal legth must be 35/ = 5.83m! This value scales with the diameter of the telescope. I practice we select shorter focal legth (1m) sacrificig resolvig power. 28 March

17 Real world: matchig the seeig ad the pixel size The agular slit size as see by the gratig is: f coll Δ α = s f coll where is the focal legth of the collimator ad s is the liear width of the slit. Gratig equatio coects this to the agular resolutio elemet. For a fixed wavelegth: Δ αcosα = s f cosα = Δβcos β Δ β = coll coll s cosα f cos β I practice, we select the slit matchig the seeig ad select the camera focal legth to match the pixel scale. The resolutio is the defied by the slit image size! 28 March

18 Puttig some umbers Home work The spectrograph for the BWT is based o a 20 cm gratig with a blaze agle of 66.5º ad 72 grooves per mm Fid agular resolutio of the gratig at 4000 Å, 6000 Å ad 8000 Å Fid the optimal slit size with collimator focal legth of 80cm Take a realistic seeig (2 ) ad the matchig etrace slit size. Compute the resolvig power R ad the camera focal legth to have 3 pixel samplig of resolutio elemet (for 15 micro pixel size) Why is it hard to make high-resolutio spectrometers for large telescopes? How the size of the primary mirror affects parameters of a spectrometer? 18

19 Equatio summary m = si + si m m =2 si blaze = cos /m di = /(W cos ) 28 March

20 Moder cocepts Echelle gives high resolvig power (high orders) ad high efficiecy (o dark stripes) Spectral orders overlap (maximum reflectio at blaze agle) order selectio or crossdisperser is eeded (e.g. gratig or prism) Cetral wavelegth of order m is give by: λ = 2δsiθ m blaze With a cross-disperser the whole spectrum is packed i a rectagular 2D format, perfect for a electroic detector m 20

21 Spectrograph desigs Echelle, white pupil scheme (e.g. FEROS) This spectrometer cosists of two well separated parts helpig reducig scattered light ad matchig resolutio with pixel size 28 March

22 HARPS 28 March

23 Echelle focal plae layout Thorium Argo emissio lie spectrum 28 March

24 PSF example for UVES 28 March

25 Side effects Orders are curved Order spacig chages Short FSR Camera aberratios directly affect resolutio Strog frigig 28 March

26 Other spectroscopic istrumets IFU istrumets 2D image slices are re-arraged i 1D slit. E.g. SINFONI Multi-object istrumets. E.g. FORS, FLAMES 28 March