Basics of spectroscopy Andrew Sheinis AAO 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 collimator disperser camera   D Tel Slit (image) plane Spectrograph D cam D coll Anamorphic factor, r = D coll/ D cam

Dispersers: Gratings, Grisms and Prisms Gratings Reflection gratings Ruled vs replicated mosaics Transmission gratings holographic Schroeder ch 13 and 14 Prisms GlassDispersion ratio (9500/3500)notes LiF exotic, hard to get F_silica nice, easy to get FK ““ BK7Y0.0737““ LF50.043poor 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

 d1d1 -- 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 )  b is BIG,  b = 63 degrees to 78 degrees Used at high orders N= (echelle) N= (echellette)

Echelles/echellettes important features High dispersion in compact package High R-value (high tan  b ) High throughput High blaze efficiency over wide wavelength range Nearly free of polarization effects

Echelles/echellettes disadvantages 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 meters b)250 mm c)25 mm d)2.5 mm

Telescope detector collimator disperser camera   D Tel Slit (image) plane Spectrograph D cam D coll Anamorphic factor, r = D coll/ D cam

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 D col 10-meter aperture > 0.61-meter D col 30-meter aperture > 1.84-meter D col Diffraction-limited > 12.8-mm D col !

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 times B)Brightness=(8e3/8)=1,000 times C)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

Spectrograph Speed Schroeder 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 -1 sr -1 ) or (erg cm -2 Hz -1 ) or (m arcsec -2 )

 A0A0 A1A1  A2A2  Surface Brightness Rybicki and Lightman, Radiative Processes in Astrophysics (1979), Ch1 A 0   =A 1    A 2   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 -1 sr -1 ) or (erg cm -2 Hz -1 ) or (m arcsec -2 )

Telescope detector collimator grating camera   A0A0 A1A1  A2A2  Slit (image) plane Spectrograph 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: n pix =# of pixels in the aperture= πr 2 Signal Noise All the noise terms added in quadrature Note: always calculate in e- Noise from sky e- in aperture Noise from the dark current 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=A  I 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=Af dt For an unresolved object, you need the source magnitude, telescope aperture, system losses and resolution.

Ex 1: Thermal Imaging R=5000 Pixel size= 10 microns Final focal ratio at detector = F/3 Source temperature=5000K Operating near 2 microns SB from Planck=1,157,314 watts/(m 2 sr micron)  =2 microns/5000=0.0004

Ex 2: Extended Object in the Visible R=5000 Pixel size= 10 microns Final focal ratio at detector = F/3 Moon (SB=1.81E-16 W/(m2 Sr Hz ) Operating near 1/2 micron  =0.5 microns/5000=1 Angstrom d  =(c/ 2 )d =1.2E11 Hz QE = 1

Ex 2B: Unresolved Object in the Visible R=5000 Pixel size= 10 microns Final focal ratio at detector = F/3 Apparent brightness = Vmagnitude= 10 Operating near 1/2 micron  =0.5 microns/5000=1 Angstrom d  =(c/ 2 )d =1.2E11 Hz QE = 1

Ex 3: Surface brightness of the moon M=-12.6 (V-band apparent magnitude Diameter=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: n pix =# of pixels in the aperture= πr 2 Signal Noise All the noise terms added in quadrature Note: always calculate in e- Noise from sky e- in aperture Noise from the dark current 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 n pix term Read-noise Limited

Thankyou!