Matthew Colless, MSSSO, 15 June 1995
(This home page is still under construction.)
Types of Spectroscopy
Single-object slit spectroscopy...
point or extended (longslit) spectroscopy
echelle spectroscopy
Multi-object spectroscopy...
slitless, multislits, fibres...
Other types of spectroscopy
images slicing, Fourier transform, time-resolved, etc.
Imaging spectroscopy (monochromators)...
narrow-band imaging
tunable filter (FP) spectrophotometry
Why CCD spectroscopy
pro: wide field, linearity, dynamic range, efficiency
con: size (cf. photography), noise (cf. photon counters)
What these notes cover
Observational design - how to achieve your goal
Instrument setup - how to get the spectra you want
Observing techniques - how to calibrate your data
Data reduction - from raw images to final spectra
Emphasis is on slit spectroscopy (also fibres/multislits)
Spectrophotometry: see Mike Bessell's lecture
Other types of spectroscopy: see references
Reductions described generally, though examples use IRAF
Observational design
Is spatial or spectral resolution more important?
spectrograph versus monochromator
How extended is the source?
short or long slit, FoV for imaging spectroscopy
What is the density of sources on the sky?
high density means gains from multiplex spectroscopy
many single fibres: high multiplex, no spatial info
multislits: moderate multiplex (unless low-R), some spatial info
fibre imager slicer: low multiplex, much spatial info
What spatial resolution is required?
image quality of site and spectrograph/monochromator
What spectral range must be covered?
limited by CCD size / resolution
free spectral range is 1 octave in
unless order sorting
filters, cross-disperser, multi-beam spectrograph
What spectral resolution is required?
spectral resolution
(Å) = FWHM of unresolved line
resolving power R = /
FWHM velocity resolution c/
=
c/R (km/s)
What level of flux calibration is required?
unfluxed, relative, absolute?
How faint is the object and what S/N is required?
target flux limit and S/N required yield exposure time
S/N calculations
The S/N expected from a spectroscopic observation is:
S/N=Ot / sqrt( Ot + St + Dt + R^2 )
The quantities involved are:
t = exposure time (s)
O = object count rate (counts/s/pixel)
S = sky count rate (counts/s/pixel)
D = dark count rate (counts/s/pixel)
R = readout noise (counts/pixel)
The spectrograph manual should provide:
the values of D and R (gain * RON e-) for a given CCD
the conversion from absolute flux to counts/s/pixel
The region extracted (slit width * extracted length) modifies:
the sky flux (area * s.b.; s.b.=flux / sq.arcsec)
the object flux (fraction of total or area * s.b.)
Upper panel: Signal to noise ratio as a function of detected photons. The
solid curve is that expected for pure photon statistics assuming 100% quantum
efficiency. The dotted curve is the same as the solid curve, but with a read
out noise of 10 e-. the dashed curve is the same as the dotted curve, but
with 50% quantum efficiency.
Lower panel: Signal to noise ratio as a function of integration time for
continuum objects with monochromatic magnitudes of 10 and 17 respectively at
H
(solid curves) based on data obtained with a CCD spectrograph. The dotted
lines assumes zero read noise. The dashed curve associated with the 17th
magnitude object is the same as the solid curve except that the sky
background rate is assumed to be five times higher.
Observing setup
Telescope focus and slit jaws:
slit jaws must be co-planar and parallel
image must focus on slit jaws; use knife edge test
Slit width considerations
spectrophotometry demands slit wider than object
otherwise width is signal versus resolution trade-off
Slit angle considerations
slit angle = position angle = P.A. (degrees E from N)
spectrophotometry demands parallactic angle
parallactic angle is normal to horizon
avoids losses due to atmospheric dispersion
otherwise P.A. is signal versus science trade-off
n.b acquisition TV has different _0 to spectrum
Dispersing element
plane reflection grating (most commonly)
grism (high efficiency, low resolution)
echelle grating + cross-dispersing prism (high res.)
Gratings
grating equation is m = d( sin(i) + sin
)
m = order, d = groove spacing, i = angle of inc.,
=
angle of diff.
gratings blazed for maximum efficiency at m_blaze and _blaze
linear dispersion in Å/pixel = (d cos())/(m x F)
x =
pixel size, F = focal length of spectrograph camera
spectrograph manual will usually give....
1 - effective resolution of each available grating
2 - efficiency of each grating as a function
should be aligned so dispersion is precisely perp. to slit.
*******TABLES*************
Comparison of the efficiency curves with respect to aluminum of four
plane reflection gratings. The gratings are identified by their
ruling, blaze angle, and Littrow blaze wavelength. The 158 grooves/mm
grating is more suitable for observations in the red whereas the 150
grooves/mm grating would be the one of choice for spectroscopy in the
ultraviolet and blue. The 600 grooves/mm grating blazed at 12,000
Å in the first order is designed for use in the second order at
H.
It gives twice the spectral resolution as the 600 grooves/mm grating
blazed at 5000Å with nearly the smae peak efficiency, but falls
quickly in efficency away from the peak typical of gratings blazed in
higher orders.
Check if order sorting filters are necessary:
remove light at other 's from other orders
e.g. m=1 at =8000Å will also be m=2 at =4000Å
avoided by cross dispersers, multi-beam spectrographs
Focussing the spectrograph:
achieved by moving the collimator in or out
best focus when FWHM of arc lines min. over all
must do each grating setting; may vary with temp.
Alignment of camera/detector:
desirable to have spectral/spatial axes along CCD axes
check by measuring position of spectrum at each end
Focus of a spectrograph determined from three widely seperated comparison
lines to assess the departures from flatness and its affect on the
optimal focus setting. A compromise focus of 535 can be derived from these
data, but the large deviations in focus across the spectrum can be
found for some CCDs.
Calibration Data
Bias and dark frames - as for imaging/photometry
Then for each grating/setting.....
Dispersed continuum flatfields ("flats"):
for removing pixel to pixel variations in response
requires a smooth spectrum and high S/N
typically use a quartz lamp on dome screen
Slit/fibre illumination images ("twilight skies"):
for correcting variations in throughput along slit
essential for longslit data and multi-slit/fibres
use twilight sky to obtain even illumination
at least moderate S/N required (will sum over )
Wavelength calibration spectra ("arcs"/"comparisons"):
for converting spectral pixel number to wavelength
choose lamp to give many lines over spectrum
line lists available in manuals and in software
take as often as spectrograph stability demands
Spectra of flux standards ("standards"):
only needed if flux-calibrating spectra
lists of standards in literature, data in software
repeats good, various airmasses better
remember: wide slit, parallactic slit angle
Other specialised standards
e.g. radial velocity standards
A stylized version of a ``perfect'' stellar spectrum.
Spectroscopic Reductions
Check and (if nec.) update file headers and keywords:
Identifiers: telescope, object, date/time, etc/
Observational info: exposure time, setup, airmass, etc.
Standard CCD reductions:
remove bias level and dark current
trim the image to remove overscan and edge effects
remove the pixel to pixel variations with flatfield
Further reductions vary for different types of observation:
point source vs extended source (longslit)
multi-slits vs multi-fibres
Point source case
Trace the spectrum of the object
Choose the sky regions to use
Optimally extract (and sky-subtract) a 1D spectrum
******EQUATION*******
optimal weights are W=P^2/V, V=variance in flux:
W=P for object-noise limited case (V proportional to P)
W=P^2 for background-noise limited case (V=constant)
do this for target object and standard stars
******DIAGRAM*********
Wavelength calibrate 1D spectra
extract a 1D wavelength calibration spectra
identify comparison spectrum lines
fit transformation from pixel number to
use nearest comparison(s) to minimise shifts
if desired, rebin to linear or log scale
If flux calibration required
correct for atmospheric extinction
recover response (or sensitivity) function
calibrate object spectra
Measure the desired quantities from spectra
********DIAGRAMS*******
Longslit case
"Longslit" if object (or sky) has large spatial extent
Essential difference is need to remove distortions:
to avoid spectral degradation from errors
to avoid incorrect sky-subtraction from errors
Distortion correction can be derived from a high S/N comparison spectrum:
identify spectral lines at one spatial position
re-identify them at all other spatial positions
do 2D map of CCD (x,y) to (,s) where s=slit position
if desired, rebin to linear or log (velocity) scale
apply transformation to all spectrum images
*********DIAGRAMS***********
Apply slit illumination correction ("slit response"):
sum twilight flat in -direction
can do for whole spectrum or at a series of 's
gives response as function of slit position (and )
normalise, then divide out slit response
Choose sky regions to use:
will interpolate sky along rest of slit (i.e. under objects)
sky regions must span object regions of interest
Sky-subtract object spectra (and standards):
yields object spectrum at each pixel along slit
may optimally combine these if 1D spectrum desired
Flux calibration as in point source case
Measure the desired quantities from spectra
Multislits and fibres
Multislits are usually treated as multiple longslits:
usually need geometric distortion corrections
within each slit spectrum, can be done as for longslit
but may need matrix mask distortion map to find slits
extra bookkeeping to track each slit's position/object
Multi-fibres usually treated as multiple point sources
image-scrambling so spatial information lost
hence treat each fibre as a point source
n.b. means you need separate fibres for sky
again, bookkeeping to track each fibre's position/object
References
Astronomical CCD observing and Reduction Techniques,
ASP conference series, Vol. 23, 1992, ed. S.B. Howell
Point source spectroscopy, R.M. Wagner, p160
Extended object spectroscopy, R.W. Pogge, p195
A User's guide to Reducing Slit Spectra with IRAF
A User's Guide to Reducing Echelle Spectra with IRAF
Guide to the Slit Spectra Reduction Task DOSLIT
Guide to the Multifiber Reduction Task DOFIBERS
CCD School WWW page
Email:
mbrown@physics.unimelb.edu.au
URL: http://www.ph.unimelb.edu.au/~mbrown/home.html