ULTRASPEC spectroscopic ETC

This form allows you to calculate ULTRASPEC object counts, sky counts and signal-to-noise ratios when performing spectroscopy with EFOSC2 on the NTT. The calculation is based on measured zero points in u', g', r', i' and z'. The form also tells you when you are in danger of saturating the avalanche register of the EMCCD, which can significantly shorten the lifetime of the detector.

The following assumptions are made:
  • No order-sorting filters are used.
  • Avalanche gain = 9 (i.e. the highest possible value) is used whenever the avalanche output is selected.
  • The stellar magnitude given is appropriate for the central wavelength of the grism being used.
  • Proportional mode, rather than photon-counting mode, is used when calculating the signal-to-noise ratio. In theory, a factor of 1.4 improvement in the signal-to-noise ratio is achievable when photon counting, but in reality the improvement is more marginal than this.
  • A single electron entering the avalanche register results in a distribution of electrons at the output with mean value ~1750. The distribution is an exponential, hence the probability of obtaining an amplification n times higher than the mean is given by e-n. A value of 5 for n is adopted for safety, which will occur once in every ~100 amplifications.
  • The amount of light entering the slit is calculated assuming a two-dimensional Gaussian profile and takes into account the wavelength-dependent change in profile as a function of airmass and angle from parallactic. Uses Chris Benn's light_in_slit.f routine.
  • The peak signal per pixel in the spatial direction is calculated assuming a one-dimensional Gaussian profile.
  • The number of pixels covered by the seeing profile is calculated by assuming it has a FWZI of 3 times the seeing.
  • Extinction and sky bightness values have been taken from the ING ETC: signal

Details of the available grisms are given here.

A note on gain in avalanche mode. I use the following definition:

system gain (e-/ADU) = electronic gain (e-/ADU) / avalanche gain

  • electronic gain (e-/ADU). Measured from avalanche-output flats taken with no avalanche gain. The number of ADU that each electron measured at the output is converted into. This is the same as gain measured in a conventional CCD.
  • avalanche gain (no units). The factor by which an electron entering the avalanche register is multiplied by when it gets to the output.
  • system gain (e-/ADU). Measured from bias frames with avalanche gain. The number of ADU that each photo-electron is converted into after passing through the avalanche register.

object magnitude
exposure time  secs
sky brightness   dark         grey         bright      
angle from parallactic  degrees
seeing  arcsecs
slit width
x,y binning factors  
readout mode   normal         avalanche      
readout speed   slow         medium         fast