An electronic device such as a wearable device may have an optical sensor. The optical sensor may have a light source such as one or more visible-light light-emitting diodes or other light-emitting devices and may have a light detector formed from one or more photodetectors. The wearable device may have a wearable housing in which the optical sensor is mounted. During operation, light from the light source may pass through a transparent portion of the housing, may reflect from an external object such as a wrist or other body part of a user, and may be received by the photodetectors after passing through light control members. The light control members may be arranged in a ring with a center and may have curved shapes with concave surfaces that face the center. Each light control member may be formed from a stack of laminated bent light control films.