Rainer,
I do not think the answer is as straight as I mentionned above.
First, you do not want to go faster than F/5 so it is better to be at F/6 rather than F/4 for exemple.
Now, how do you compare F/5 and F/8... F/8 will end up with a lower beam within the LISA so you will shine less grooves on the grating, ending up in loosing some resolution as the resolving power of the spectrograph is actually based on the surface enlighten by your light beam. If I'm not mistaken, if you go faster than F/8, you regain resolution but when you reach F/5, you start loosing signal internally.
Also, at F/8, your star size will appear larger due to seeing. It depends of course on your telescope diamater (larger diameter is and more sensitive to the seeing it will be) and your actual seeing. But in a nutshell you will loose more light at the edge of the slit for the same slit size at F/8 rather than at F/5 for the same telescope diameter.
In summary, for two telescopes with the same number of optical miror/lenses but one at F/5 and the other one at F/8, best is to use F/5.
Now, you are adding up more lenses using a focal reducer to bring your F/8 to F/5. This is what you have to take into account in the light loss equation. Going F/5 this way reduces the signal level but keep the resolution of your F/5. So it is somehow a trade off you have to make and I would recommend to try both configuration on the same night to compare the results.
Cordialement,
Olivier Thizy
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