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Arbitrary distributions of radiant exposure may be written by transverselyscanning a single known spatially-random screen that is normally illuminated byspatially but not necessarily temporally uniform radiation or matter wavefields. The arbitrariness, of the written pattern of radiant exposure, holds upto both (i) a spatial resolution that is dictated by the characteristictransverse length scale of the illuminated spatially random screen, and (ii) abackground term that grows linearly with the number of random-illuminationpatterns. Two classes of the method are developed. The former assumes thedistance between the illuminated random mask and the target plane to besufficiently small that the effects of diffraction may be neglected. The latteraccounts for the effects of Fresnel diffraction in the regime of large Fresnelnumber. Numerical simulations are provided for both variants of the method.Contrast and signal-to-noise ratio are also considered. The method may beparallelized, and is suited to both magnifying and de-magnifying geometries.Possible applications include spatial light modulators and intensity projectorsfor those matter and radiation wave fields for which such devices do not exist,printing or micro-fabrication in both two and three spatial dimensions, andlithography.

One mask to rule them all: Writing arbitrary distributions of radiant exposure by scanning a single illuminated spatially-random screen