I'm doing some research on equipment used in commercial diving, and I was trying to confirm whether or not the lighting used is generally battery powered, or powered through the umbilical. Or does it vary widely based on preference/job/setting?
Back in the day, an Ikelight Mini-C flashlight taped to the hat was the norm. Now, pretty much everyone has video on every dive, so the camera/light cable is on the umbilical. There is also new equipment available, such as the Sea Sun system. http://www.wildwell.com/index.php?page=subsea-lighting
Keep in mind, not every job requires lighting or visiblity.