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

Abstract

Arbitrary distributions of radiant exposure may be written by transversely scanning a single known spatially-random screen that is normally illuminated by spatially but not necessarily temporally uniform radiation or matter wave fields. The arbitrariness, of the written pattern of radiant exposure, holds up to both (i) a spatial resolution that is dictated by the characteristic transverse length scale of the illuminated spatially random screen, and (ii) a background term that grows linearly with the number of random-illumination patterns. Two classes of the method are developed. The former assumes the distance between the illuminated random mask and the target plane to be sufficiently small that the effects of diffraction may be neglected. The latter accounts for the effects of Fresnel diffraction in the regime of large Fresnel number. Numerical simulations are provided for both variants of the method. Contrast and signal-to-noise ratio are also considered. The method may be parallelized, and is suited to both magnifying and de-magnifying geometries. Possible applications include spatial light modulators and intensity projectors for those matter and radiation wave fields for which such devices do not exist, printing or micro-fabrication in both two and three spatial dimensions, and lithography.

Revised version includes much additional material on contrast, signal-to-noise ratio and an underlying geometric picture