Systems and methods for laser processing continuously moving sheet material include one or more laser processing heads configured to illuminate the moving sheet material with one or more laser beams. The sheet material may include, for example, an optical film continuously moving from a first roller to a second roller during a laser process. In one embodiment, a vacuum chuck is configured to removably affix a first portion of the moving sheet material thereto. The vacuum chuck controls a velocity of the moving sheet material as the first portion is processed by the one or more laser beams. In one embodiment, a conveyor includes a plurality of vacuum chucks configured to successively affix to different portions of the sheet material during laser processing.