Display backlight structures may provide backlight illumination that passes through display layers in the display. Computer-controlled equipment such as robotic arms with gripper structures may be used in assembling backlight layers such as a reflector, light guide plate, diffusers, and prism films into a backlight unit. The grippers may include mechanical grippers and vacuum heads. A vacuum gripper head may have a plenum to which a perforated plate and porous layer are attached for distributing the vacuum. Computer-controlled air sources may be used to blow streams of deionized air between backlight layers to separate the backlight layers during assembly. Release liners may be removed using robotic arms and grippers. Translation stages may move a backlight layer storage frame between stations. A cleaning tool with a solvent dispenser and air jets may clean backlight layers. A camera system may be used during alignment and positioning operations.