Can you think you're awake when actually you're asleep?
Yes you can, and this is a very interesting area of research – Both good and poor sleepers can have nights where they are not sure if they have been sleeping or instead spent a lot of time awake. This can be the case for a variety of reasons such as which stage of sleep you are in, the number of awakenings you have and during which stage of sleep, as well as lifestyle factors, like stress and alcohol
There can be a gray area between wakefulness and sleep, where you have thought content but may well be asleep. Getting sleep into a block and positioned at a time that suits your internal biological clock may help with this.
There are important scientific findings which suggest that polysomnography when scored in the conventional way into sleep stages, may not identify subtle electroencephalography (EEG) characteristics that form part of the underlying pattern of poor sleep.
For example, a tendency towards waking up very, very briefly or the presence of fast EEG waves (like those we have in wakefulness or light sleep) may correspond better to the subjective experience that you are actually lying there awake.