A head-mounted device may have a head-mounted housing and optical components supported by the head-mounted housing. The optical components may include cameras, movable optical modules, and other components. Each optical module may include a display that displays an image and a lens that provides the image to a corresponding eye box. Optical self-mixing sensors may be included in the optical modules and other portions of the head-mounted device to measure changes in optical component position. In response to detecting a change in optical component position, actuators in the device may be adjusted to move the optical components or other action may be taken to compensate for the change.