The cycles for each person is around 90-100 minutes each, with REM at the end of every cycle. You don't spend much time in REM in the first three though, so if you want to set an alarm here's the times I would suggest: "4,5 hours into sleep, 6 hours into sleep, 7 hours into sleep." After 7 hours you'll be spending alot of time in REM, so set the alarm to ring every hour and after 9 hours you can set it to ring anytime you want. This is all ofcourse based on the presumption that you can fall asleep quickly after waking up. I have recalled 10+ dreams in a night by doing this.