An electronic device may have a display with an array of pixels configured to display images for a user. The electronic device may have an ambient light sensor for gathering ambient light information. The ambient light sensor may be at least partially covered by the display. The ambient light sensor may be switched into use during blanking periods when a portion of the display overlapping with the display is temporarily turned off. The ambient light sensor may include a photodetector, a first stage with an amplifier, first and second capacitors selectively coupled across the amplifier, and a second accumulation stage. During blanking time, the first capacitor may integrate photodetector current. During non-blanking, the charge stored in the first capacitor may be transferred to the second accumulation stage while the second capacitor applies an offset voltage to the photodetector to prevent undesired charge injection into the photodetector.