The Coude Echelle Spectrographs

2.1 System Efficiencies of UCLES

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Signal-to-Noise Calculator


A Signal to Noise Calculator is provided on line. Please use this where possible when preparing observing proposals, as this calculator will also be used by the technical assessors. This tool allows you to specify various parameters for an observation (seeing, slit width, CCD, source magnitude at the wavelength of observations, etc), and then outputs the total number of counts from the object, together with a signal-to-noise ratio taking into account the sky and read-noise contributions.

Calculation of Efficiencies

Table 2.1.1 gives the latest (22 January 2000) efficiency measurements for UCLES, scaled for the EEV2 CCD (unbinned pixels). These figures were consistent with the previous figures obtained in April 1996. The efficiencies are expressed in three different units, explained below. Note that the values in Table 2.1.1 refer to blaze peak; at the edges of the free spectral range (that is half a FSR off peak) the efficiency drops to ~70% of that at blaze peak.

Table 2.1.1: Efficiencies for UCLES + EEV2.
Lambda
(Å)
AB(1hz/Å)
(magnitudes)
Countrate(J=12)
(e/s/pixel)
J(S/N=100/pixel)
(magnitudes)
3886 17.27    
4024 17.33 0.95 10.83
5500 17.54 1.71 11.45
6627 17.09 1.22 11.10

Definitions

AB(1hz/Å) is defined as the ABlambda magnitude of a star which, observed at an airmass X=0 and with a wide slit, yields a count rate of 1 Hz/Å (i.e. atmospheric absorption and slit losses not included).

Countrate(J=12) is defined as the electrons per second per pixel expected for a J=12 star, where J is the Johnson magnitude closest to lambda, with a 1 arcsec slit in 1.5" seeing at X=1.3 airmasses, and using the 31.6 lines/mm grating.

J(S/N=100) is defined as the Johnson magnitudes yielding S/N=100 at blaze peak in 1 hour with a 1 arcsec slit in 1.5" seeing at X=1.3 airmasses. It is assumed that S/N = sqrt(N), where N is the number of photons per pixel (31.6 lines/mm grating).

Scaling factors

ABlambda magnitudes are not identical to the Johnson magnitudes. Approximate offsets for A0 stars are: AB6500 ~ R + 0.2, AB5500 ~ V, and AB4000  ~ B - 0.2.

To scale the atmospheric absorption for the expected airmass,  extinctions in magnitudes per airmass typical of Siding Spring are:  kU = 0.57, kB = 0.30, kV = 0.16, kR = 0.12, and kI = 0.08.

Table 2.1.2 can be used to estimate slit losses (assuming perfect guiding and a 0.7" slit length). The numbers are derived from Diego (1985 PASP 97, 1209).

Table 2.1.2  Slit loss corrections
Slit 
(arcsec)
Seeing FWHM  (arcsec)            
 0.5 1.0  2.0  4.0
0.5 0.76 0.38 0.19 0.09
0.7 0.89 0.51 0.26 0.12
1.0 0.94 0.66 0.37 0.18
1.5   0.81 0.52 0.26
2.0   0.88 0.64 0.34
3.0   0.94 0.79 0.47

While for observations of bright objects the S/N approaches sqrt(N), where N is the number of photons, for fainter targets, the sky contribution is significant. Around 5000A, sky becomes an issue in bright time for ~V>15.5, depending on slit size and location relative to the moon. Broad-band measurements of night sky brightness at Siding Spring are given in Table 2.1.3. Note that for wavelength regions between OH lines the sky is substantially darker in the R and I bands.

Table 2.1.3 Sky brightness in magnitudes/sq arcsec
  B V R I
Dark Sky 22.5 21.5 20.8 19.3
6-Day Moon 21.3 20.8 20.4 19.2
Full Moon 18.8 18.5 18.9 18.2

See the detectors page for parameters needed to convert to different detectors, and to calculate the contribution of dark count and readout noise which can be significant for faint targets.

Throughput History of UCLES

For expert users, the throughput history of UCLES is summarised in the cookbook.



Ray Stathakis (ras@aaoepp.aao.gov.au)
Last Update: 21 March 2000