An electronic device display may have an active area with an array of pixels and an inactive area. A light-transmitting window may be formed in the inactive area. A light-sensing component such as an ambient light sensor may be mounted within the housing in alignment with the window. Opaque masking material may be provided on one or more layers of the display in the inactive area and may have an opening for the window. Backlight structures in the display may generate backlight illumination for pixels in the active area. Stray portions of the backlight illumination may be blocked using a stray light absorption layer on one of the layers of the display such as a layer other than the layer on which the opaque masking material is formed. The stray light absorption layer may have an opening aligned with the window.