3 Spectroscopy: what do we measure? Spectrum = the intensity (or flux) of radiation as a function of wavelength“Continuous” sampling in wavelength (as opposed to imaging, where we integrate over some finite wavelength range)Note: In practice, when using CCDs for spectroscopy, one also integrates over finite wavelength ranges – they are just very narrow compared to the wavelength itself: Pixel width Δν << νSampling is continuous but the spectral resolution is limited by the design of the spectrographSpectrum in classical sense holds no direct spatial information. Many spectrographs allow retrieving spatial info in 1 dimension, some even in 2 (“integral field units”)
4 Spectral resolutionSmallest separation in wavelength that can still be distinguished by instrument, usually given as fraction of and denoted by R:or alternativelyuseful, though somewhat arbitrary working definition
5 Basic spectrograph layout a means to isolate light from the source in the focal plane, usually a slit“collimator” to make parallel beams on the dispersive elementdispersive element, e.g. a prism or grating. Reflection gratings much more frequently used than transmission gratings“Camera”: imaging lens to focus beams in the (detector) focal plane + detector to record the signal
6 DispersionSplitting up light in its spectral components achieved by one of two ways:differential refractionprisminterferencereflection/transmission gratingfourier transform(Farby-Perot)
7 Prism Refractive index n of material depends on wavelength Several approximate formulae exist to describe n(). “Sellmeier” equation is accurate over a large wavelength range and used by manufacturers of optical glasses:Bi and Ci are empirically determined coefficients. With 3 terms the Sellmeier approximation is accurate to 1 part in ~510-6 in the whole optical and near-infrared range
8 Prism general light path through prism: one can show that: dispersion is maximum for a symmetrical light pathdispersion is maximum for grazing incidence. Corresponding top angle depends on refractive index of material. E.g. ~74° for heavy flint glassHowever: most light is reflected instead of refracted for grazing incidence. In practice, smaller are used (60° and 30° are common choices)
9 Prism dispersion curve strongly non-linear,dispersion in bluemuch stronger thanin red part of spectrum
23 Width of the peaks N=4 Peak width is therefore: For with one has (Later: Relevance for spectral resolution)
24 Now do 3 different wavelengths 0th order1st order2nd orderN=4Green is here the reference wavelength λ.Blue/red is chosen such that its 1st order peak lies in green’s firstnull on the left/right of the 1st order.
25 Now do 3 different wavelengths 0th order1st order2nd orderN=8Keeping 3 wavelengths fixed, but increasing N
26 Now do 3 different wavelengths 0th order1st order2nd orderN=16Keeping 3 wavelengths fixed, but increasing N
27 Now do 3 different wavelengths 0th order1st order2nd orderN=4Green is here the reference wavelength λ.Blue/red is chosen such that its 1st order peak lies in green’s firstnull on the left/right of the 1st order.
28 Now do 3 different wavelengths 0th order1st order2nd orderN=8Green is here the reference wavelength λ.Blue/red is chosen such that its 1st order peak lies in green’s firstnull on the left/right of the 1st order.Spectral resolution:
29 Let’s look at the 2nd order 0th order1st order2nd orderN=8Green is here the reference wavelength λ.Blue/red is chosen such that its 1st order peak lies in green’s firstnull on the left/right of the 1st order.Spectral resolution:
30 Let’s look at the 2nd order m=0m=1m=2m=3m=4N=8Green is here the reference wavelength λ.Blue/red is chosen such that its 1st order peak lies in green’s firstnull on the left/right of the 1st order.
31 Let’s look at the 2nd order m=2N=8Zoom-in around2nd orderGreen is here the reference wavelength λ.Blue/red is chosen such that its 1st order peak lies in green’s firstnull on the left/right of the 1st order.
32 Let’s look at the 2nd order m=0m=1m=2m=3m=4N=8Green is here the reference wavelength λ.Blue/red is chosen such that its 1st order peak lies in green’s firstnull on the left/right of the 1st order.
33 Let’s look at the 2nd order m=0m=1m=2m=3m=4N=8Green is here the reference wavelength λ.Blue/red is chosen such that its 2nd order peak lies in green’s firstnull on the left/right of the 2nd order.Spectral resolution:
34 Let’s look at the 3rd order m=0m=1m=2m=3m=4N=8Green is here the reference wavelength λ.Blue/red is chosen such that its 3rd order peak lies in green’s firstnull on the left/right of the 3rd order.Spectral resolution:
35 General formula N=8 m=0 m=1 m=2 m=3 m=4 Green is here the reference wavelength λ.Blue/red is chosen such that its mth order peak lies in green’s firstnull on the left/right of the mth order.Spectral resolution:
36 Building a spectrograph from this Place a CCD chip hereMake sure to have small enough pixel size to resolve theindividual peaks.
37 Overlapping orders N=8 m=0 m=1 m=2 m=3 m=4 Going to higher orders means higher spectral resolution.But it also means: a smaller spectral range, because the“red” wavelengths of order m start overlapping with the“blue” wavelengths of order m+1
38 Effect of slit widthtriple slitlensscreenincidentwavedw
39 Effect of slit width single slit lens screen As we know from the incidentwaveAs we know from thechapter on diffraction:This gives the sincfunction squared:w
40 Effect of slit width triple slit lens screen At slit-plane: Convolution of N-slitand finite slit width.At image plane:Fourier transform ofconvolution =multiplicationincidentwavedw
43 Grating blazed reflection grating many parallel “slits” called “grooves”Transmission gratings and reflection gratingswidth of principal maximum (distance between peak and first zeros on either side):“Blazing”: tilt groove surfaces to concentrate light towards certain direction controls in which order m light of given gets concentratedCredit: C.R. Kitchin “Astrophysical techniques”CRC Press, ISBN 13:blazed reflection grating
44 Grating, spectral resolution blazed transmission gratingresolution in wavelength:
45 Reflection grating with groove width w and groove spacing d
47 Basic grating spectrograph layout Note: The word “slit” ishere meant with a differentmeaning: Not a dispersiveelement, but a method to isolate asource on the image plane forspectroscopy. From here onward,“slit” will have this meaning.Dispersive slit = groove on a grating.Credit: C.R. Kitchin “Astrophysical techniques”CRC Press, ISBN 13:
48 Longslit spectrumVery basic setup: entrance slit in focal plane, with dispersive element oriented parallel to slit (e.g. grooves of grating aligned with slit)1 spatial dimension (along slit) and 1 spectral dimension (perpendicular to slit) on the detectorSpectral resolution set by dispersive element, e.g. Nm for grating.Spectrum can be regarded as infinite number of monochromatic images of entrance slitprojected width of entrance slit on detector must be smaller than projected size of resolution element on detector, e.g. for grating:where s is the physical slit width and 1 is the collimator focal lengthslit width often expressed in arcseconds:where F is the effective focal length ofthe telescope beam entering the slitspatial direction
49 Example longslit spectrum spatial direction wavelength high spectral resolution longslit spectrum of galaxyContinuum emission from stars, several emission lines from star forming regions in galaxy
50 Gratings: characteristics Light dispersed. If d ~ w most light goes into 1 or 2 orders at given . Light of (sufficiently) different gets mostly sent to different ordersLight from different orders may overlap (bad, need to deal with that!)Spectral resolution scales with fringe order m and is nearly constant within a fringe order ~linear dispersion (in contrast to prism!)Gratings are often tilted with respect to beam. Slightly different expression for positions of interference maxima:or equivalentlyi is the angle between the grating and the incoming beam. This expression is called the “grating equation”
51 The “blaze function” describes the transmittance of light transmitted or reflected into each order. It is the “envelope” of the interference pattern(i.e. diffraction due to finite width of single groove, D) + i [deg]Ilong go into low m,short go into high mm
53 Free spectral range a b “White” light coming in with wavelength between 1 and 2light of wavelength in first order (m1) is diffracted in same direction as light of /2 in m2, /3 in m3, etc.Free spectral range: largest interval in a given order that doesn’t overlap the same interval in an adjacent order.Credit:shaded area: free spectralrange of order 2 light
54 practical example:We want to measure a spectrum starting from = 400 nm in first order. What spectral range can we cover?Free spectral range is 400 nm in this case nmWe must insert a filter that blocks light of < 400 nm and > 800 nm to get a “clean” spectrumThe optimum blazing angle is such that the direction in which light of ~600 nm (~middle of range) corresponds to the angle of geometrical reflection (with and i definedin same direction w.r.t. normal):
55 practical example (cont’d): If we wish higher spectral resolution, we may use a higher order. Smaller free spectral range, e.g for m = 2, nm for m = 3, etc. Use appropriate filters to block light outside these rangesWe can of course choose a different starting wavelength, e.g nm in order 3.Each combination of central wavelength order has its own optimum blazing angle . But for a given grating, is fixed. Tilting the grating (i.e. change i) allows to control to which order light of given is sent.
56 Order overlap in grating Each order gives its own spectrum. These can overlap in the focal plane: at a given pixel on the detector we can get light from several orders (with different )We must reject light from the unwanted orders. Solution:For low orders m (low spectral resolution, large free spectral range) one can use a filter that blocks light from the other ordersFor high orders m (the free spectral range is very small), use “cross disperser”: a second dispersive element (usually a prism), mounted with the dispersion direction perpendicular to that of the grating. Causes different orders to be spatially offset on the chip. Advantage: multiple orders can be measured simultaneously. High spectral resolution and large coverage can be obtained simultaneously. “Echelle spectrograph”
57 Echelle grating Echelle grating R m. For high spectral resolution, use high order.Relatively large groove spacing (few grooves/mm) but very high blazing angle. Concentrate light in high orders.Strong order overlap (solution: “cross-dispersion”, more later ...)Echelle gratingCredit: C.R. Kitchin “Astrophysical techniques”CRC Press, ISBN 13:
58 Echelle grating: cross dispersion CCDm=103m=102m=101m=100m=99m=98m=97m=96Without cross dispersion: different wavelength ranges overlap.With cross dispersion: You get multiple short spectra.Note of caution: Above cartoon is not exact: colors should be sorted vertically; but it shows the principle of separating orders.
59 Echelle grating: cross dispersion CCDm=103m=102m=101m=100m=99m=98m=97m=96Strong blazing angle means that you focus the light on the partof the focal plane where the CCD is. Avoids waste of light.
60 Echelle spectrograph optical layout Cross dispersion with prism placed before gratinghigh blaze angle, grating used in very high orders (up to m~200)coarse groove spacing (~20 to ~100 mm-1) at optical wavelengths w > few most light concentrated in 1 direction at given most light in 1 orderEach order covers small range, but many orders can be recorded simultaneouslyspectrum on detectororder m
61 Blaze function optical layout spectrum on detector order m Blazing angle defines in which order light of given (mostly) ends upIf sum of angles of “incoming” and “exiting” rays equals m/d (d is groove spacing), all light goes into order m (assuming “perfect”, lossless grating)For slightly smaller , part of the light goes into order m+1order=spectrum on detectororder m Blaze function: “efficiency” of (an order of a) grating as a function of
62 Format of cross-dispersedEchelle spetrogr.(Lick Observatory)echelle dispersionprism dispersion
64 Spectroscopy & Spectrographs II Roy van Boekel & Kees Dullemond
65 Some applications of spectroscopy Stellar spectroscopy: temperature, composition, surface gravity, rotation, micro-turbulenceTemperatures of interstellar medium, intergalactic mediumradial velocities, mass and internal structure of stars, exoplanetsDynamics & masses of milky way and other galaxies (dark matter)Cosmology / redshiftsspectro-astrometry (direct spatial information on scales << /D, relative between continuum emission and spectral lines)composition of dust around young & evolved stars, ISM
66 Different Resolution for Different Scientific Applications Active galaxies, quasars, high-redshift objects: R ≈ ,000Nearby galaxies (velocities 30…300 km/s): R ≈ 3, ,000Supernovae (expansion velocity ≈ 3,000 km/s): R > 100Stellar abundances:Hot stars: R ≈ 30,000Cool stars: R ≈ 60, ,000Exoplanet radial velocity measurements. E.g. R ≈ 115,000 (HARPS). Best accuracy currently reached ~1 m/s, “effective” R ≈ 300,000,000. How: centroid of a single line measured to much higher precision than spectral resolution + use many lines, precision scales like 1/sqrt(Nlines)
67 Exoplanet detection by radial velocity measurement Planet is very difficult toobserve directly.But planet and star rotate aroundcommon center-of-massStar wobbles: Measure radial velocity of star (doppler).Small effect: Need Δv=1 m/s effective spectral resolutionThis means: Reff=c/Δv=3x108 !
68 Exoplanet detection by radial velocity measurement Beat the spectral resolution limit!FluxλShifts of line centroid can be measured even if they are muchsmaller than the line width.Need: High signal-to-noise ratio and/or many lines.
69 Fourier transform spectrometer I(P)PI(k)kby wavenumberby OPD positionIncoming light is split 50:50 into two beams, then reflected. Both beams are combined, then focused onto detectorone mirror is moveable, introduces path difference Pfor monochromatic source the intensity on the detector is:interference pattern, modulation with optical path difference (OPD)
70 Fourier transform spectrometer for a given position P the intensity modulation due to light interfering from all wavelengths is:or, equivalently:Take I(-ν)=I(ν) so that we get:P (mm)I(P)Typical FTS interferogram
71 Fourier transform spectrometer example spectrum taken with an FTSThus, the output signal is the Fourier transform of the spectrum I()Note: Fourier Transform of a symmetric function is real-valued, so the output signal is the complete Fourier transform (no imaginary part exists).Inverse Fourier transform of the interferogram I(P) yields source spectrum I()Spectral resolution scales directly with total length of OPD scan (say, x):x can be up to ~2m R can be several million in the optical
72 Multiple object spectroscopy Often you want spectra of many objects in the same region on the skyDoing them one by one with a longslit is very time consumingWhen putting a slit on a source in the focal plane, the photons from all other sources are blocked and thus “wasted”Wish to take spectra of many sources simultaneously!Solution: “multiple object spectrograph”. Constructed to guide the light of >>1 objects through the dispersive optics and onto the detector(s), using:a small slit over each source (“slitlets”)a glass fiber positioned on each source“integral field unit”
73 Multiple slit(lets) approach A slitlet is a longslit, but of much shorter length than most “single” longslitsNormally done using focal plane “masks”: metal plates in which slitlets are cut, nowadays mostly done automatically by cutting devices using high-power lasersAdvantages:(can do many objects simultaneously)small longslits: sample object and sky background in each slitlet good sky correction in each spectrumslits can be cut in almost any shape (useful for extended sources)Disadvantages:a new mask must be made for each field, often more than 1 mask/fieldnot complete freedom where to put slits (spectra should not overlap on detector)
74 Multi-object spectroscopy with slitlets CCDslitCCDWasted CCD real estateWasted CCD real estate
75 Multi-object spectroscopy with slitlets CCDCCDFirst do pre-imaging to find the stars/objects of interest + reference objectCreate mask using computer program (mask is then cut in metal plate with laser)Go back to telescope, do acquisition to center slits on objectsDo spectroscopic integration
76 Multi-object spectroscopy with slitlets CCDCCDBut: Some slit combinations are forbidden: They would result in overlappingspectra
77 near infrared multiple- object spectroscopy with SUBARU/MOIRCS Credit: unknown
78 Slitlets approach, “peculiarities” Optical layout essentially the same as with normal (single) longslit, but instead of single slit ~centered in focal plane, multiple slits distributed over focal plane. Consequences:all slitlets have same dispersion direction all slitlets must have similar orientation ~perpendicular to dispersion direction (simple straight slits exactly perpendicular to dispersion direction in most cases)wavelength scale is different for each slitlet, depending on its positionif chip size limits spectral range (end - start) that fits on detector, then start and end depend on position of object (slit) on skyif two slits are close together in spatial direction but far apart in dispersion direction, spectra can overlap due to optical distortions
79 Slit width issuesSpectral resolution is limited by R of the spectrograph......but also by the slit width.Conversely: Slit width ~ brightness of the spectrum on the CCDOptimum slit width is balance between low slit losses (wide slit) versus low background and high spec. res. (narrow slit)In general: Higher R requires longer exposure for sameSignal-to-Noise ratioLower RBrighter on CCD,but also morebackground noiseHigher RWeaker signal,but less backgroundnoise
80 Seeing vs. spectral resolution If the slit is wide, then it is the seeing that determines the spectral resolution:Good seeingconditions:high spectralresolutionBad seeingconditions:low spectralresolution
81 Slit width issuesIf flux calibration is important: Slight pointing errors could cause problems:Star is perfectlyon the slitSlight offsetyields muchlower fluxDefocusing thetelescope canhelp! All flux islower, but this canbe calibrated.
82 MOS with fibers MMT / Hectochelle fiber head close-up instead of putting a slitlet on each source in the focal plane, position the head of a glass fiber on each source (movable)fibers pass light of each object into the instrumentput the other end of all fibers in a row and feed light into spectrographresult: one spectrum for each source, all spectra “nicely” aligned: wavelength scale the same for all spectra, and spectra regularly spaced in spatial directionDisadvantage: no spatial info, background subtraction using “sky” fibers.fiber head close-up
83 Integral Field UnitsA multiple object spectrograph is good at getting spectra of many sources in the same fieldSometimes we would like to take a spectrum at every position of a spatially extended object (e.g. a galaxy). This can be done with an Integral field unit (IFU)We need to “catch” the light at each position, guide it through dispersive optics and project the spectrum of each position onto (a different part of) the detector. This can be done in two basic ways:Using an “image slicer”Using “lenslets” and fibersNOTE: It will have low spatial resolution, because 2D space + 1D λ have to fit on a 2D CCD...
84 JWST / MIRIImage SlicerMany narrow (~spatial resolution element) long slits, each with slightly different tilteffectively, do a large number of longslits simultaneously, send each slit into a different directionslits imaged next to each other on detectorCredit: unknown
85 Gemini / CIRPASS“Lenslets” & FibersFocal plane filled with “lenslets”. Each lenslet injects (nearly) all light falling onto it into a fiberFibers are fed into a spectrograph, in the same way as with the fiber Multiple Object Spectrograph
86 Spectroscopy: procedure Recording the datascience observationcalibration observations: flatfield, “arcs” ( calibration), spectro-photometric standard starsData analysis/calibrationgoing from raw data to a calibrated spectrum in e.g. [erg/s/cm2/Hz]Interpretation of spectra, i.e. what do we learn about the object?Use laws from your physics textbook or more elaborate numerical models of your science target to derive:Chemical composition of sourcesThermal structure of objectsVelocity structure of objects...
87 Spectroscopic flat field (Dome flat or twillight flat)spatial direction slit “imperfections”dispersion direction
88 Wavelength calibration We measure intensity I as a function of pixel position on a CCDPart of the CCD...but the CCD doesnot “see color”spectrum of target
89 Wavelength calibration We measure intensity I as a function of pixel position on a CCDHow do we know which pixel corresponds to which wavelength?Part of the CCDspectrum of target...the CCD sees thisPart of the CCDspectrum of lamp with known linesIlluminate spectrographwith a lamp with knownlines before or after yourobservation.“arc”
90 Wavelength calibration: “arc” spatial direction dispersion direction
91 Telluric + flux calibration Find nearby spectro-photometric standard star, which has known flux-calibrated spectrumExtract the spectrum of the standard star(s). If the standard was taken immediately before and/or after the science exposure you can get a science spectrum that is corrected for telluric absorption and is flux calibrated as follows:where Fstandard is the (known)spectrum of the standard star
92 Telluric + flux calibration More general approach if science target and standard star were not taken at (nearly) the same airmass:Possibility 1: observe standards at various airmasses and fit the instrument response R and the atmospheric extinction coefficient A (i.e. the same procedure as for photometry, but now at each wavelength instead of integrating over a filter). Calculate the calibrated science spectrum F from the raw science spectrum S observed at airmass am using F = S exp(A am) / RPossibility 2: Use a theoretical model for the Earth atmosphere and fit this to the calibrator observation and then extrapolate to the airmass of the science observation, or fit it to the science observation directly. Divide by synthetic spectrum to correct for Atmosphere. Use the standard star observation(s) for flux calibration.
93 Choosing standard stars A “good” standard star has the following properties:it is comparatively bright (so we don’t need much time for calibration)its intrinsic spectrum is known perfectlyit has as little spectral structure as possible, i.e. a “smooth” spectrumit is close to your science target on the skyThe “best choice” depends on the application and regime:Hot stars (spectral type B, the hotter the better) are much used because:they have relatively little spectral structure: H lines, weak lines of He and ionized metals, weak Balmer discontinuityIf we study H lines in science target, calibrator should have no H linesG stars have relatively weak, narrow H lines (but many other lines, careful!)For mid-IR applications, we need mid-IR bright calibratorsoften limited to K and M type giant stars, + nearest hot stars
94 A note on telluric calibration Optical regime:in most of the optical regime (~350 to ~1000 nm) the Earth atmosphere has no “structure” in its absorption spectrum, i.e. no atomic/molecular absorption lines. In the “red” part there are some lines (mainly O2 and H2O). There is, of course, scattering off molecules and aerosols causing substantial but smooth extinction.For work requiring no absolute calibration, e.g. measuring equivalent widths of lines in astronomical sources, no telluric calibration is requiredInfrared regime:Strong spectral structure in the atmospheric absorption spectrum (and in its emission spectrum!)Very careful telluric calibration needed, even if no absolute flux calibration is required.
95 Very high R work: peculiarities For accurate calibration, need to take Earth motion into account (orbital motion up to 30 km/s corresponding to R = 104, daily rotation up to 460 m/s corresponding to R = 6.5105)In the infrared, at high resolution the atmospheric opacity breaks up into very many narrow absorption lines. A specific spectral line you wish to measure may coincide with a telluric line and not be measurable at some instant, but due to the Earth’s orbital motion it may have red- or blue shifted out of the telluric absorption line later in the year. “Best time of year” depends on position of source w.r.t. ecliptic and the source radial velocityWhen calibration must be extremely good (e.g. for Exoplanet radial velocity measurements) we cannot use separate calibration frames, calibration must be done simultaneously with science observation. Use gas absorption cell or telluric lines
96 Quantifying “line strength” The term “line strength” is not uniquely defined.Various ways of quantifying it exist:1) Peak intensityProblem with low spectral resolution, because each “pixel” is an integral over the pixel width:Fluxλ
97 Quantifying “line strength” The term “line strength” is not uniquely defined.Various ways of quantifying it exist:1) Peak intensityProblem with low spectral resolution, because each “pixel” is an integral over the pixel width:FluxPeak strength isunderestimatedλ
98 Quantifying “line strength” The term “line strength” is not uniquely defined. Various ways of quantifying it exist: 2) Frequency-integrated flux in the line Advantage: Can also be measured with low-resolution spectrographs (if no continuum is present)Fluxλ
99 Quantifying “line strength” The term “line strength” is not uniquely defined. Various ways of quantifying it exist: 3) Equivalent width Only when a continuum is presentFluxcontinuumabsorptionlineλ
100 Quantifying “line strength” The term “line strength” is not uniquely defined. Various ways of quantifying it exist: 3) Equivalent width Only when a continuum is presentEWFluxcontinuumabsorptionlineλ
101 Beat the spatial resolution limit! Spectro-astrometryBeat the spatial resolution limit!Fluxx [“]At each velocity channel the emission might be slightly shifted in space.Plot spatial shift as a function of velocity
102 Beat the spatial resolution limit! Spectro-astrometryBeat the spatial resolution limit!Offset [AU at 160 pc]0.006”0.003”0.000”-0.003”-0.006”From: Pontoppidan et al. 2008SR 21Diffraction limited resolution of VLT at 4.7 μm is 1.22λ/D=0.15”
103 Beat the spatial resolution limit! Spectro-astrometryBeat the spatial resolution limit!1000xhigherresolutionthan thisradioimage!Brown et al. 2009
104 P Cygni line profiles: Stellar winds starFluxv [km/s]blueredStar emits emission line.Wind is cooler at large radii.So the wind makes absorption line.But blue-shifted!
105 P Cygni line profiles: Stellar winds λ [Å]Aspin et al. 2009McNeal’s nebula is a reflection of light from a just-born star.This reflection appears only now-and-then: when the star has a “hickup” (outburst).The P Cyg Hα profile shows: mass is ejected during this outburst!Gemini Observatory/AURA, Travis Rector
106 Example of low-R Infrared spectroscopy Origin of dust species in disk around young stars, solar system comets, and building blocks of planetsYoung star undergoes accretion outburstAmorphous dust turns into crystalsCredit: Spitzer Science CenterAbraham et al. 2009