Spectroscopy & Spectrographs

Spectroscopy & Spectrographs

Roy van Boekel & Kees Dullemond

Overview

• Spectrum, spectral resolution

• Dispersion (prism, grating)

• Spectrographs– longslit– echelle– fourier transform

• Multiple Object Spectroscopy

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 << ν

• Sampling is continuous but the spectral resolution is limited by the design of the spectrograph

• Spectrum in classical sense holds no direct spatial information. Many spectrographs allow retrieving spatial info in 1 dimension, some even in 2 (“integral field units”)

Spectral resolution• Smallest separation in wavelength that can still be distinguished

by instrument, usually given as fraction of and denoted by R:

R

R

or alternatively

useful, though somewhat arbitrary working definition

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 element• dispersive 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 refraction– prism

• interference– reflection/transmission grating– fourier transform– (Farby-Perot)

Prism• general light path through prism:

one can show that:• dispersion is maximum for a symmetrical light path• dispersion is maximum for grazing incidence. Corresponding top angle

depends on refractive index of material. E.g. ~74° for heavy flint glass• However: most light is reflected instead of refracted for grazing incidence.

In practice, smaller are used (60° and 30° are common choices)

8

Prism dispersion curve

strongly non-linear,dispersion in bluemuch stronger thanin red part of spectrum

9

Prism spectrograph layout

Credit: C.R. Kitchin “Astrophysical techniques”CRC Press, ISBN 13: 978-1-4200-8243-2

Young’s double slit experiment

d

double slit screenlens

θ

incidentwave

θ


d

double slit screenlens

θ

incidentwave

ΔP

P d sinOptical path difference:

Phase difference:

2 P

Add the two waves:

E(t)E1 ei t e i( t ) E1e

i t 1 e i Intensity is amplitude-squared:

I E1

2 1 e i 1 e i E12 2 2cos

4E1

2 cos2( /2)4E1

2 cos2 d sin /


N=2

Now a triple slit experiment...

d

triple slit screenlens

θ

incidentwave

ΔP

P d sinOptical path difference:

Phase difference:

2 P

Add the three waves, and take the norm:

I E1

2 1 e i e2i 1 e i e 2i

Now a triple slit experiment...

N=3

Adding more slits...

N=4


N=5


N=6


N=160th order 1st order 2nd order

Width of the peaks

N=4

For

one has

d sin

n

N

I()0

1n Nwith

Peak width is therefore:

sin Nd

(Later: Relevance for spectral resolution)

Now do 3 different wavelengths

N=4

Green is here the reference wavelength λ.Blue/red is chosen such that its 1st order peak lies in green’s first null on the left/right of the 1st order.

blue green 11

N

red green 11

N

0th order 1st order 2nd order


N=8


Keeping 3 wavelengths fixed, but increasing N


N=16


Keeping 3 wavelengths fixed, but increasing N


N=4


blue green 11

N

red green 11

N



N=8



blue green 11

N

red green 11

N

Spectral resolution:

1

N

Let’s look at the 2nd order

N=8



blue green 11

N

red green 11

N


1

N


N=8


m=0 m=1 m=2

blue green 11

N

red green 11

N

m=3 m=4


N=8


m=2

blue green 11

N

red green 11

N

Zoom-in around2nd order


N=8


m=0 m=1 m=2

blue green 11

N

red green 11

N

m=3 m=4


N=8

Green is here the reference wavelength λ.Blue/red is chosen such that its 2nd order peak lies in green’s first null on the left/right of the 2nd order.

m=0 m=1 m=2

blue green 11

2N

red green 11

2N

m=3 m=4


1

2N

Let’s look at the 3rd order

N=8

Green is here the reference wavelength λ.Blue/red is chosen such that its 3rd order peak lies in green’s first null on the left/right of the 3rd order.

m=0 m=1 m=2

blue green 11

3N

red green 11

3N

m=3 m=4


1

3N

General formula

N=8

Green is here the reference wavelength λ.Blue/red is chosen such that its mth order peak lies in green’s first null on the left/right of the mth order.

m=0 m=1 m=2

blue green 11

mN

red green 11

mN

m=3 m=4


1

mN

Building a spectrograph from this

Place a CCD chip here

Make sure to have small enough pixel size to resolve the individual peaks.

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

Effect of slit width

d

triple slit screenlens

incidentwave

w

Effect of slit widthsingle slit screenlens

incidentwave

wAs we know from the chapter on diffraction: This gives the sinc function squared:

I()I(0)sincw sin

I(0)

sin2 w sin

w sin

2

Effect of slit widthN=16d/w=8

Grating

• many parallel “slits” called “grooves”• Transmission gratings and reflection

gratings

• width 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 concentrated

Ndcos

blazed reflection grating


Grating, spectral resolution

• resolution in wavelength:

dd

dm

cos

Nm

R

Nmblazed transmission grating

Reflection grating with groove width w and groove spacing d

w

d

-i

40

Basic grating spectrograph layout


41

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 for spectroscopy. From here onward,“slit” will have this meaning. Dispersive slit = groove on a grating. Credit: C.R. Kitchin “Astrophysical techniques”

CRC Press, ISBN 13: 978-1-4200-8243-2

Longslit spectrum• Very 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

detector• Spectral resolution set by dispersive element, e.g. Nm for grating.• Spectrum can be regarded as infinite number of monochromatic images of entrance

slit• projected 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 length• slit width often expressed in arcseconds:

where F is the effective focal length ofthe telescope beam entering the slit

sf1

Ndcos

sarcsec 206265f1FNdcos

spatial direction

Example longslit spectrum

• high spectral resolution longslit spectrum of galaxy• Continuum emission from stars, several emission lines from star

forming regions in galaxy

wavelength

spat

ial d

irect

ion

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 orders

• Light 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 equivalently

i is the angle between the grating and the incoming beam. This expression is called the “grating equation”

asinmd sin i

sin sin imd

The “blaze function” describes the transmittance of light transmittedor 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]

I

long go into low m,short go into high m

mm

m

Blaze function vs. wavelength

I mm

m

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:1) For low orders m (low spectral resolution, large free spectral

range) one can use a filter that blocks light from the other orders

2) For 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”

• 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 grating

Echelle grating


Echelle grating: cross dispersion

m=100

m=99

m=98

m=97

m=96

m=101

m=102

m=103

CCD

Without 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.

Echelle grating: cross dispersion

m=100

m=99

m=98

m=97

m=96

m=101

m=102

m=103

Strong blazing angle means that you focus the light on the part of the focal plane where the CCD is. Avoids waste of light.

CCD

51

Echelle spectrograph• Cross dispersion with prism placed

before grating

• high 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 order

• Each order covers small range, but many orders can be recorded simultaneously

optical layout

spectrum on detector

orde

r m

Blaze function• Blazing angle defines in

which order light of given (mostly) ends up

• If 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+1

optical layout

spectrum on detector

orde

r m

order=

Blaze function: “efficiency” of (an order of a) grating as a function of

echelle dispersion

pri

sm d

ispers

ion

Format of cross-dispersedEchelle spetrogr.(Lick Observatory)

Stellar spectrum

Spectroscopy & Spectrographs II

Roy van Boekel & Kees Dullemond

Some applications of spectroscopy• Stellar spectroscopy: temperature, composition, surface gravity,

rotation, micro-turbulence

• Temperatures of interstellar medium, intergalactic medium

• radial velocities, mass and internal structure of stars, exoplanets

• Dynamics & masses of milky way and other galaxies (dark matter)

• Cosmology / redshifts

• spectro-astrometry (direct spatial information on scales << /D, relative between continuum emission and spectral lines)

• composition of dust around young & evolved stars, ISM

Different Resolution for Different Scientific Applications

• Active galaxies, quasars, high-redshift objects: R ≈ 500 - 1,000• Nearby galaxies (velocities 30…300 km/s): R ≈ 3,000 - 10,000• Supernovae (expansion velocity ≈ 3,000 km/s): R > 100• Stellar abundances:

Hot stars: R ≈ 30,000Cool stars: R ≈ 60,000 - 100,000

• Exoplanet 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)

Exoplanet detection by radial velocity measurement

Planet is very difficult to observe directly.

But planet and star rotate aroundcommon center-of-mass

Star wobbles: Measure radial velocity of star (doppler).Small effect: Need Δv=1 m/s effective spectral resolutionThis means: Reff=c/Δv=3x108 !

Exoplanet detection by radial velocity measurement

Flux

λ

Beat the spectral resolution limit!

Shifts 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.

Fourier transform spectrometer• Incoming light is split 50:50 into

two beams, then reflected. Both beams are combined, then focused onto detector

• one mirror is moveable, introduces path difference P

• for monochromatic source the intensity on the detector is:

• interference pattern, modulation with optical path difference (OPD)

I(P)Imax 1 cos2P

P2

I(P)

P

I(k)

k

by wavenumber by OPD position

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:

I(P) I cos2P

0

d

P (mm)

I(P)

Typical FTS interferogram

I(P) I cos 2 Pc

0

d

I(P) 12 I cos 2 P

c

d

Fourier transform spectrometer• Thus, 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

R

2x

example spectrum taken with an FTS

Multiple object spectroscopy• Often you want spectra of many objects in the same region on

the sky

• Doing them one by one with a longslit is very time consuming

• When 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”

Multiple slit(lets) approach• A slitlet is a longslit, but of much shorter length than most “single” longslits

• Normally done using focal plane “masks”: metal plates in which slitlets are cut, nowadays mostly done automatically by cutting devices using high-power lasers

• Advantages:– (can do many objects simultaneously)

– small longslits: sample object and sky background in each slitlet good sky correction in each spectrum

– slits 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/field

– not complete freedom where to put slits (spectra should not overlap on detector)

Multi-object spectroscopy with slitletsCCD slit CCD

Wasted CCD real estate

Wasted CCD real estate

Multi-object spectroscopy with slitletsCCD CCD

• First do pre-imaging to find the stars/objects of interest + reference object• Create mask using computer program (mask is then cut in metal plate with laser)• Go back to telescope, do acquisition to center slits on objects• Do spectroscopic integration

Multi-object spectroscopy with slitletsCCD CCD

• But: Some slit combinations are forbidden: They would result in overlappingspectra

near

infr

ared

mul

tiple

-ob

ject

spe

ctro

scop

y w

ith S

UB

AR

U/M

OIR

CS

Credit: unknown

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 position

– if chip size limits spectral range (end - start) that fits on detector, then start and end depend on position of object (slit) on sky

– if two slits are close together in spatial direction but far apart in dispersion direction, spectra can overlap due to optical distortions

Slit width issues• Spectral resolution is limited by R of the spectrograph...• ...but also by the slit width.• Conversely: Slit width ~ brightness of the spectrum on the CCD

• Optimum 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 same

Signal-to-Noise ratio

Lower RBrighter on CCD,but also morebackground noise

Higher RWeaker signal, but less backgroundnoise

MOS with fibers• 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 instrument

• put the other end of all fibers in a row and feed light into spectrograph

• result: one spectrum for each source, all spectra “nicely” aligned: wavelength scale the same for all spectra, and spectra regularly spaced in spatial direction

• Disadvantage: no spatial info, background subtraction using “sky” fibers.

MMT / Hectochelle

fiber head close-up

Integral Field Units• A multiple object spectrograph is good at getting spectra

of many sources in the same field• Sometimes 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:

1) Using an “image slicer”

2) Using “lenslets” and fibers

• NOTE: It will have low spatial resolution, because 2D space + 1D λ have to fit on a 2D CCD...

Image Slicer

• Many narrow (~spatial resolution element) long slits, each with slightly different tilt

• effectively, do a large number of longslits simultaneously, send each slit into a different direction

• slits imaged next to each other on detector

JWST / MIRI

Credit: unknown

76

“Lenslets” & Fibers

Gemini / CIRPASS

• Focal plane filled with “lenslets”. Each lenslet injects (nearly) all light falling onto it into a fiber

• Fibers are fed into a spectrograph, in the same way as with the fiber Multiple Object Spectrograph

Spectroscopy: procedure• Recording the data

– science observation– calibration observations: flatfield, “arcs” ( calibration), spectro-

photometric standard stars

• Data analysis/calibration– going 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 sources• Thermal structure of objects• Velocity structure of objects• ...

78

Spectroscopic flat field

dispersion direction

spat

ial d

irect

ion

slit

“impe

rfec

tions

”

(Dome flat or twillight flat)

Wavelength calibration• We measure intensity I as a function of pixel

position on a CCD

Part of the CCD

spectrum of target ...but the CCD doesnot “see color”

Wavelength calibration• We measure intensity I as a function of pixel

position on a CCD• How do we know which pixel corresponds to

which wavelength?

Part of the CCD

spectrum of target ...the CCD sees this

Part of the CCD

spectrum of lamp with known linesIlluminate spectrographwith a lamp with knownlines before or after yourobservation.“arc”

81dispersion direction

spat

ial d

irect

ion

Wavelength calibration: “arc”

• Find nearby spectro-photometric standard star, which has known flux-calibrated spectrum

• Extract 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

Fcalibrated, science Fstandard

Fraw, science

Fraw, standard

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) / R

Possibility 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.

Telluric + flux calibration

Choosing standard starsA “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 perfectly• it has as little spectral structure as possible, i.e. a “smooth” spectrum• it is close to your science target on the sky

The “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 discontinuity

• If we study H lines in science target, calibrator should have no H lines– G stars have relatively weak, narrow H lines (but many other lines, careful!)

• For mid-IR applications, we need mid-IR bright calibrators– often limited to K and M type giant stars, + nearest hot stars

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 required

Infrared 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.

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 velocity

• When 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

Quantifying “line strength”The term “line strength” is not uniquely defined.

Various ways of quantifying it exist:

1) Peak intensity– Problem with low spectral resolution, because each “pixel” is

an integral over the pixel width:

Flux

λ



1) Peak intensity– Problem with low spectral resolution, because each “pixel” is

an integral over the pixel width:

Peak strength isunderestimated

Flux

λ



2) Frequency-integrated flux in the line

Advantage: Can also be measured with low-resolution spectrographs (if no continuum is present)

Flux

λ



3) Equivalent width

Only when a continuum is present

Flux

λ

continuumabsorption

line



3) Equivalent width

Only when a continuum is present

Flux

λ

continuumabsorption

line

EW

Spectro-astrometry

• At each velocity channel the emission might be slightly shifted in space.

• Plot spatial shift as a function of velocity

Beat the spatial resolution limit!

Flux

x [“]

Spectro-astrometryBeat the spatial resolution limit!

Diffraction limited resolution of VLT at 4.7 μm is 1.22λ/D=0.15”

Off

set

[AU

at

160

pc] 0.006”

0.003”

0.000”

-0.003”

-0.006”

From: Pontoppidan et al. 2008

SR 21

Spectro-astrometryBeat the spatial resolution limit!

Brown et al. 2009

1000xhigherresolutionthan thisradioimage!

P Cygni line profiles: Stellar winds

star

Star emits emission line.Wind is cooler at large radii.So the wind makes absorption line.But blue-shifted!

Flux

v [km/s]

blue red

wind

P Cygni line profiles: Stellar winds

• McNeal’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!

λ [Å] Aspin et al. 2009

Gemini Observatory/AURA, Travis Rector

Example of low-R Infrared spectroscopy

- Origin of dust species in disk around young stars, solar system comets, and building blocks of planets

- Young star undergoes accretion outburst

- Amorphous dust turns into crystalsCredit: Spitzer Science Center

Abraham et al. 2009

Spectroscopy & Spectrographs

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