Basics of spectroscopy

Andrew SheinisAAO Head of Instrumentation

Some questions:

• What are the parts of a spectrograph• Why are spectrographs so big?• What sets the sensitivity?• How do I estimate the exposure time?

Some questions:

• What are the parts of a spectrograph• Why are spectrographs so big?• What sets the sensitivity?• How do I estimate the exposure time?

Telescope

detector

collimatordisperser

camera

DTel

Slit (image) plane

Spectrograph

DcamDcoll

Anamorphic factor,

r = Dcoll/ Dcam

Dispersers: Gratings, Grisms and Prisms

•Gratings•Reflection gratings

•Ruled vs replicated•mosaics

•Transmission gratings•holographic

Schroeder ch 13 and 14

•PrismsGlass Dispersion ratio (9500/3500)notesLiF 0.092335 exotic, hard to getF_silica 0.079616 nice, easy to getFK5 0.077572 “ “BK7Y 0.0737 “ “LF5 0.043 poor dispersion ratio•Grisms•High dispersion Grating •Low-dispersion prism•Prism deflection angle chosen to pass some central wavelegth straight throughplus a prism

What causes dispersion

• Optical path difference in the interfering beam,

• Or• Optical time delay in the interfering beam

d1-

n

-

n

W

d

Grating equation:

Differentiate WRT :

How do you get a long time delay

• Long grating (echelle)• High index (immersion grating• Big beam • All of the above

What are Echelles/echellettes?

• Course, precisely-ruled gratings (few grooves/mm)• Used at high-angles= high R; R= tan(b)

• bis BIG, b = 63 degrees to 78 degrees• Used at high orders• N=100-600 (echelle)• N=10-100 (echellette)

Echelles/echellettesimportant features

• High dispersion in compact package• High R-value (high tanb) High throughput• High blaze efficiency over wide wavelength

range• Nearly free of polarization effects

Echelles/echellettesdisadvantages

• Hard to manufacture• Orders overlap• Need order-blocking filters or• Cross-dispersion (becomes an advantage with

a 2-D detector)

Volume Phase Holographic Gratings

Examples of VPH grisms with tilted fringes (above, 1a), and fringes at Littrow (below, 1b). Both gratings are 930 l/mm blazed at 600 nm. For reference, the size of the beam, paraxial camera and focal surface are the same.

* Hill, Wolf, Tufts, Smith, 2003, SPIE, 4842,

Collimators

•Reflective parabola•Off axis, on axis•FOV

•Transmissive•Catadioptric

•Schmidt

ESI on Keck

RSS on SALT

Hermes on AAT

Cameras, second to grating in importance

•Why?•A is effectively larger for the camera than the collimator.•Dispersed slit is effectively a larger field.Anamorphism and dispersion increase “pupil” size•Most challenging part of the optical system. Slits are big, pixels are small so we are often demagnifying, thus cameras are faster and have a larger A .

Cameras

•Reflective •Two Mirror correct for spherical and coma•Un-obscured 3-mirror an-astigmat corrects for spherical, coma and astigmatism, (Paul-Baker, Merseinne Schmidt) (i.e Angel, Woolf and Epps, 1982 SPIE, 332, 134A)

•Transmissive•Epps cameras

•Catadioptric•Schmidt

Slits-MOS plates-IFUS• Slits

– Separates the stuff you want from the stuff you don’t

• Fibers– Allow you to have a

spectrograph far from the telescope (why would you want this?)

• IFUS– Reformat the filed to be along

a slit• Mos

– Separates the lots of stuff you want from lots of the stuff you don’t

Detectors

• Human eye• CCD• CMOS• MCT• InGaAs• PMT• Lots of others

Some questions:

• What are the parts of a spectrograph• Why are spectrographs so big?• What sets the sensitivity?• How do I estimate the exposure time?

Three Spectrographs of similar field and resolution

• Why do they look so different?

SDSS 2.5M Nasmyth Focus at Keck 10M TMT 30M

Thought experiment 1: How Big an aperture do you need to achieve R=100,000 in the diff-limited case on a 10-meter telescope at 1 m?

a) 2.5 metersb) 250 mmc) 25 mmd) 2.5 mm

Telescope

detector

collimatordisperser

camera

DTel

Slit (image) plane

Spectrograph

DcamDcoll

Anamorphic factor,

r = Dcoll/ Dcam

Telescope

detector

collimator

grating

camera

Slit, s

Bingham 1979

Slit-Width resolution product

Diff-limited

seeing-limited

OPD available for interference in the coherent beam !

* Not just for Littrow: n*grooves * n = OPD

•One way to think about this: Spectrograph resolution is NOT a function of the spectrograph or the optics!•R ~ OPD or optical time delay available for interference in the coherent beam (works for prisms and other dispersing elements too)•The job of the telescope/spectrograph/AO system is to create as much OPD as possible then collect that information!

Some numbers:Consider collimator diameter for an R2 (tan=2) spectrograph with R=50,000 at =1 micron

• 2.5-meter aperture > 150mm Dcol

• 10-meter aperture > 0.61-meter Dcol

• 30-meter aperture > 1.84-meter Dcol

• Diffraction-limited > 12.8-mm Dcol!

Some questions:

• What are the parts of a spectrograph• Why are spectrographs so big?• What sets the sensitivity?• How do I estimate the exposure time?

Thought Experiment:You observe the moon using an eyepiece attached to a 8 meter telescope. What is the relative brightness of the image compared to naked-eye viewing? (or will this blind you?) assume your eye has an 8mm diameter pupil.

A) Brightness=(8e3/8)2=1,000,000 timesB) Brightness=(8e3/8)=1,000 timesC) The same, Brightness is conserved!

Spectrograph Speed Speed=# of counts/s/Angstrom

I. Slit-limited

II. Intermediate

III. Image-limited

Bowen, I.S., “Spectrographs,” in Astronomical Techniques, ed. by W.A. Hiltner, (U. of Chicago Press, 1962), pp. 34-62.

Spectrograph SpeedSchroeder 12.2e, Ira Bowen (1962)

I. Slit-limited

II. Intermediate

III. Image-limited

Speed=# of counts/s/Angstrom, W= illuminated grating length

Surface Brightness• Surface brightness is the energy per unit angle per unit area

falling on (or passing through) a surface.• Conserved for Finite size source (subtends a real angle)• Also called

– Specific intensity– Brightness, surface brightness– Specific brightness

• Units: (Jy sr-1) or (W m-2 Hz-1sr -1) or (erg cm-2 Hz -1) or (m arcsec-2)

A0

A1

A2

Surface Brightness Rybicki and Lightman,

Radiative Processes in Astrophysics (1979), Ch1

A0 =A1 A2

• Surface brightness is the energy per unit angle per unit area falling on (or passing through) a surface.

• Conserved for Finite size source (subtends a real angle)• Also called

– Specific intensity– Brightness, surface brightness– Specific brightness

• Units: (Jy sr-1) or (W m-2 Hz-1sr -1) or (erg cm-2 Hz -1) or (m arcsec-2)

Telescope

detector

collimatorgrating

camera

A0

A1

A2

Slit (image) plane

Spectrograph

Energy Collected

Energy Collected

Do not confuse Surface Brightness with Flux

Flux is total energy incident on some area dA from a source (resolved or not). Flux is not conserved and falls of as R-2.

Some questions:

• What are the parts of a spectrograph• Why are spectrographs so big?• What sets the sensitivity?• How do I estimate the exposure time?

S/N for object measured in aperture with radius r: npix=# of pixels in the aperture= πr2

Signal

Noise

All the noise terms added in quadratureNote: always calculate in e-

Noise from sky e- in aperture

Noise from the darkcurrent in aperture

Readnoise in aperture

How do I calculate the number of photo electrons/s on my detector?

• Resolved source – We are measuring surface brightness– E=AI

• For an extended object in the IR that is easy: You just need the temperature of the source, the system losses (absorption, QE etc), resolution and etendu of a pixel. No telescope aperture or F/#, no slit size, no optical train!

• For an extended object in the visible: You just need the surface brightness of the source, the system losses (absorption, QE etc), resolution and etendu of a pixel. No telescope aperture or F/#, no slit size, no optical train!

• Point source – we are measuring flux– E=Afdt

• For an unresolved object, you need the source magnitude, telescope aperture, system losses and resolution.

Ex 1: Thermal ImagingR=5000Pixel size= 10 micronsFinal focal ratio at detector = F/3Source temperature=5000KOperating near 2 microns

SB from Planck=1,157,314 watts/(m2 sr micron)D=2 microns/5000=0.0004

Ex 2: Extended Object in the VisibleR=5000Pixel size= 10 micronsFinal focal ratio at detector = F/3Moon (SB=1.81E-16 W/(m2 Sr Hz )Operating near 1/2 micronD=0.5 microns/5000=1 Angstromdu=(c/2)d=1.2E11 HzQE = 1

Ex 2B: Unresolved Object in the VisibleR=5000Pixel size= 10 micronsFinal focal ratio at detector = F/3Apparent brightness = Vmagnitude= 10Operating near 1/2 micronD=0.5 microns/5000=1 Angstromdu=(c/2)d=1.2E11 HzQE = 1

Ex 3: Surface brightness of the moonM=-12.6 (V-band apparent magnitudeDiameter=30 arcminutes

S=Surface brightness in magnitudes/arcsecond^2

• Noise Sources:

Sources of Background noise•Relic Radiation from Big Bang•Integrated light from unresolved extended sources•Thermal emission from dust•Starlight scattered from dust•Solar light scattered from dust (ZL)•Line emission from galactic Nebulae•Line emission from upper atmosphere (Airglow)•Thermal from atmosphere•Sun/moonlight scattered by atmosphere•Manmade light scattered into the beam•Thermal or scatter from the telescope/dome/instrument

S/N for object measured in aperture with radius r: npix=# of pixels in the aperture= πr2

Signal

Noise

All the noise terms added in quadratureNote: always calculate in e-

Noise from sky e- in aperture

Noise from the darkcurrent in aperture

Readnoise in aperture

S/N - some limiting cases. Let’s assume CCD with Dark=0, well sampled read noise.

Bright Sources:(R*t)1/2 dominates noise term

Sky Limited

Note: seeing comes in with npix term

Read-noise Limited

Thankyou!