A large mask with random apertures may be formed by forming a smaller mask (also called a cell mask) with a random pattern of transmissive apertures which is then repeatedly replicated to create the large mask. The random pattern may be created by perturbing the aperture locations by a small amount or the apertures may be randomly placed within the cell mask provided certain criteria are met. Alternatively, a large mask with a random pattern of transmissive apertures may be formed without using a cell mask. This large mask may be used to fabricate diffusers and other devices that do not suffer from the interference, diffraction and other optical effects common in devices having structures that are non-randomly patterned.