Practical applications: CCD spectroscopy

1
Practical applications CCD spectroscopy

• Tracing path of 2-d spectrum across detector
• Measuring position of spectrum on detector
• Fitting a polynomial to measured spectrum
  positions
• Optimal extraction of spectra from CCD images
  with simultaneous sky background subtraction
• Scaling a profile constant background
• Wavelength calibration of 1-d spectra
• Measurement of positions of arc-line images
• Fitting a polynomial to measured positions of
  images of arc lines with known wavelengths

2
Observing hints

• Rotate detector so that arc lines are parallel to
  columns
• To minimise slit losses due to differential
  refraction, rotate slit to parallactic angle
• i.e. keep it vertical
• Spectra are then tilted or curved due to
• camera distortions
• Differential refraction

3
After bias subtraction and flat fielding

• Recall Lecture 3 for subtraction of B(x,?),
  construction of flat field F(x,?) and measurement
  of gain factor G.
• Corrected image values are

4
Tracing the spectrum

• Spectra may be tilted, curved or S-distorted.
• Trace spectrum via a sequence of operations
• divide into ?-blocks
• measure centroid of spectrum in each block (fit
  gaussian)
• fit polynomial in ? to calibrate x0(?).
• Once this is done, use x0(?) to select object/sky
  regions on subsequent steps.

x0
x0
5
Sky subtraction
Slices across spectrum at??const

• Alignment (rotation) of CCD detector relative to
  grating aims to make ?const along columns.
• Imperfect alignment gives slow change in ? along
  columns.
• This causes gradient, curvature of sky background
  when ? is close to a night-sky line.
• Solution fit low-order polynomial in x to sky
  background data.
• Alternative fit linear function to interpolate
  sky from sky regions symmetric on either side
  of object spectrum

Target
Ref
6
Normal extraction

• Subtract sky fit, and sum the counts between
  object limits
• Dilemma How do we pick x1, x2?
• too wide too much noise
• too narrow lose counts

7
Optimal extraction

• 1) Scale profile to fit the data
• 2) Compute ?(x) from the model
• 3) ?-clip to zap cosmic-ray hits.
• Iterate 1 to 3, since ?(x) depends on A

8
Estimating the profile P(x)

• The fraction of the starlight that falls in row x
  varies along the spectrum and is given by
• This is an unbiased but noisy estimator of P(x).
• It varies as a slow function of wavelength.
• Plot against ? and fit polynomials in ? at each x.

Column 20
Column 60
9
Optimal vs. normal extraction

• Pros
• Optimal extraction gives lower statistical noise.
• Equivalent to longer exposure time
• Incorporates cosmic-ray rejection
• Cons
• Requires P(x,?) slowly varying in ? (point
  sources).
• Essential papers
• Horne, K., 1986. PASP 98, 609
• Marsh, T. and Horne, K.

10
Wavelength calibration
threshold level

• Select lines using peak threshold.
• Measure pixel centroid xi by computing x or
  fitting a gaussian
• Identify wavelengths ? i
• Fit polynomial ?(x) to ? i, i1,...,N.
• Reject outliers (usually close blends)
• Adjust order of polynomial to follow structure
  without too much wiggling.

11
Dealing with flexure

• Flexure of spectrograph causes position xi of a
  given wavelength ? to drift with time.
• Measure new arcs at every new telescope position.
• Interpolate arcs taken every 1/2 to 1 hour when
  observing at same position.
• Master arcfit Use a long-exposure arc (or sum of
  many short arcs) to measure faint lines and fit
  high-order polynomial.
• Then during night take short arcs to tweak the
  low-order polynomial coefficients.

12
Statistical issues raised

• Outlier rejection what causes outliers, and how
  do we deal with them?
• Robust statistics.
• Polynomial fitting how many polynomial terms
  should we use?
• Too few will under-fit the data.
• Too many can introduce flailing at ends of
  range.
• Well deal with these issues in the next lecture.