For a system with no light losses, it is straightforward to show that the number of photons per second incident in each resolution element is:
A = Geometric aperture of telescope (m)
= 0.66 (JKT), 4.41 (INT) or 12.47 (WHT)
F = Monochromatic flux density of object (mJy)
For airmass > 1, a correction must be applied for atmospheric extinction.
An AB magnitude of 15 corresponds approximately to 1.9 (U), 4.4 (B),
3.8 (V), 3.0 (R) or 2.4 (I) mJy
f = Fraction of total flux density of object in each spatial resolution element.
Note that for slit spectroscopy, the spatial resolution perpendicular to the
direction of the slit is set by the width of the slit. For many observations, the
slit width will be comparable to the size of the seeing disc, and so even for
sources which are intrinsically unresolved, a significant fraction of the light
will not enter the spectrograph.
= Observing bandpass (Å). For imaging observations, this is the FWHM of the filter
used. For spectroscopy, it is equal to the wavelength resolution of the observations.
= Observing wavelength (Å)
To find the number of photons detected, N must be multiplied by the product of the efficiencies with which the various optical components in the light path reflect and transmit light, and by the efficiency of the detector. For observations at prime focus, Cassegrain and Nasmyth (or WHT auxiliary port), there will be respectively 1, 2 or 3 mirror reflections. Typical reflectivity of a freshly-aluminised mirror surface is 0.85, and this figure probably decreases 10 - 20% before the next aluminising. Efficiencies of diffraction gratings were given in chapter . Filters are listed in Appendix . Glass-air surfaces transmit 0.98 of the incident light, and the many surfaces within cameras result in them having typical throughputs 0.4 - 0.8 e.g. 0.3 for UES (including echelle), 0.4 for IDS, 0.6 for TAURUS, 0.7 (peak) for FOS-2. The throughput of the correctors at WHT and INT prime focus is believed to be 0.9. The WHT Nasmyth optical derotators have a throughput of 0.75. The throughput of the IR derotator has not yet been measured. CCD detector quantum efficiencies are given in Fig. 6.1. The throughput of WYFFOS (including fibres and grating) is expected to be 0.36.
Total throughputs for spectroscopy (telescope + camera + detector) range from 18% for WHT FOS and 11% for ISIS with R300V grating and TEK CCD to 0.5% for WHT UES with IPCS. Throughputs for imaging are higher.