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.
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 AB_{lambda} 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
AB_{lambda} magnitudes are not identical to the Johnson magnitudes. Approximate offsets for A0 stars are: AB_{6500 }~ R + 0.2, AB_{5500} ~ V, and AB_{4000 } ~ B - 0.2.
To scale the atmospheric absorption for the expected airmass, extinctions in magnitudes per airmass typical of Siding Spring are: k_{U} = 0.57, k_{B} = 0.30, k_{V} = 0.16, k_{R} = 0.12, and k_{I }= 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.