Although I can't quite find a reference right now, take it from me that it's well documented that we have much more trouble waking up from deep sleep (a.k.a. slow wave sleep) than from light sleep or from REM sleep. You've probably experienced this often enough: sometimes you've had plenty of sleep, but you still feel hopelessly groggy when the alarm wakes you up, and other times you've only had three hours but you feel amazingly alert! And you're like, whuuu?
Well, at least some of the time, the reason is that you woke up between sleep cycles rather than during slow wave sleep. So, in 2002, I had the idea of an alarm clock that would monitor your sleep cycle, and would only wake you between cycles, never during slow wave. Since cycles are regular and last about 90 minutes, if you absolutely needed to be up at a particular time, the alarm would calculate whether there is enough time left for another full cycle, and if there wasn't, it would wake you early.