Organic light emitting diode (OLED) displays having an emissive OLED layer and a nanostructured interface configured to reduce variability of color with view angle are described. An optical stack having first and second layers with differing refractive indices includes the nanostructured interface between the first and second layers. The second layer is disposed between the first layer and the emissive OLED layer. The nanostructured interface has a substantially azimuthally symmetric power spectral density (PSD) and a wavenumber-PSD product has a maximum for a wavenumber larger than 6 radians/micrometer times the refractive index of the second layer. For all wavenumbers lower than 6 radians/micrometer times the second refractive index, the wavenumber-PSD product is no more than 0.3 times the maximum.