The "direct" measurement of REM is by detecting the electrical patterns in the brain during rapid eye movements. This done in sleep studies and requires hooking up a lot of equipment and being monitored overnight. I vividly remember doing this because of the discomfort I experienced being hooked up in that way. Here is what Medline says about polysomnography. A bit of a hassle.
But suppose you didn't have to do anything? Except wearing your watch to bed. Then waking up the next morning to view a graph of your previous night's sleep states, including REM. The new Basis Peak does this indirectly, using heart rate, skin temperature, and algorithms that they have built into their watch.
REM sleep is the light blue at the top, running about 25% total sleep time. Light sleep is below it, followed by Deep sleep in the darker green. This is a typical night and typical proportions. I am getting enough REM, but I'm making it a point to get at least 8 hours a night, which means going to bed a little earlier than I normally do.
The identification of REM sleep is tricky. Some CPAPers believe they can tease REM sleep out of the CPAP data. I'm inclined to believe they can, but I can't do it myself at this point, but I do have the Basis data, which is based on algorithms which correlate with polysomnography data just as closely as Polar's OwnIndex is correlated with actual VO2 Max studies, or as closely as Benno Fricke's preference data predictions correlated with actual SAT results. Seems like magic, but isn't.